bench_dafny_repeat_run_hints.txt

========
Experiment configuration: python experiments.py --experiment_name run.py --n_trials 10 --mins_timeout 10 --language Dafny --problem_name problem_repeat --seed 42 


[2024-01-15 06:18:17,086] [INFO] [real_accelerator.py:158:get_accelerator] Setting ds_accelerator to cuda (auto detect)
Trial  1
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>

SCORE
1.0
['function repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0

SCORE
1.0
['    requires n > 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n

SCORE
1.0
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x

SCORE
1.0
['    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{

  |
5 | {
  |  ^

ex.dfy(5,1): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var s := new int[n];

  |
6 |     var s := new int[n];
  |              ^^^

ex.dfy(6,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var s := new int[n];
  |                  ^

ex.dfy(6,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    var s := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var s := new int[n];
    for i in 0..n-1

  |
6 |     var s := new int[n];
  |              ^^^

ex.dfy(6,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var s := new int[n];
  |                  ^

ex.dfy(6,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i in 0..n-1\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var s := new int[n];
    for i in 0..n-1
        s[i] := x;

  |
6 |     var s := new int[n];
  |              ^^^

ex.dfy(6,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var s := new int[n];
  |                  ^

ex.dfy(6,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['        s[i] := x;\n']
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var r := new int[n];

  |
6 |     var r := new int[n];
  |              ^^^

ex.dfy(6,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var r := new int[n];
  |                  ^

ex.dfy(6,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    var r := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var r := new int[n];
    for i := 0 to n - 1

  |
6 |     var r := new int[n];
  |              ^^^

ex.dfy(6,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var r := new int[n];
  |                  ^

ex.dfy(6,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i := 0 to n - 1\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var r := new int[n];
    for i := 0 to n - 1
        r[i] := x;

  |
6 |     var r := new int[n];
  |              ^^^

ex.dfy(6,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var r := new int[n];
  |                  ^

ex.dfy(6,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['        r[i] := x;\n']
['    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x\n']
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var result := new int[n];

  |
6 |     var result := new int[n];
  |                   ^^^

ex.dfy(6,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var result := new int[n];
  |                       ^

ex.dfy(6,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var result := new int[n];
    for i in 0..n-1

  |
6 |     var result := new int[n];
  |                   ^^^

ex.dfy(6,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var result := new int[n];
  |                       ^

ex.dfy(6,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i in 0..n-1\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var result := new int[n];
    for i in 0..n-1
        result[i] := x;

  |
6 |     var result := new int[n];
  |                   ^^^

ex.dfy(6,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var result := new int[n];
  |                       ^

ex.dfy(6,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['        result[i] := x;\n']
['{\n']
['    var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var result := new int[n];
    for i in 0..n {

  |
6 |     var result := new int[n];
  |                   ^^^

ex.dfy(6,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var result := new int[n];
  |                       ^

ex.dfy(6,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i in 0..n {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var result := new int[n];
    for i in 0..n {
        result[i] := x;

  |
6 |     var result := new int[n];
  |                   ^^^

ex.dfy(6,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var result := new int[n];
  |                       ^

ex.dfy(6,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['        result[i] := x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{

  |
3 | {
  |  ^

ex.dfy(3,1): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)

  |
4 |     if n == 1 then [x] else [x] + repeat(x, n - 1)
  |                                                   ^

ex.dfy(4,50): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 1 then [x] else [x] + repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}


SCORE
1.0
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)

SCORE
1.0
['lemma repeat_correct(x: int, n: nat)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0

SCORE
1.0
['    requires n > 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n

SCORE
1.0
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x

SCORE
1.0
['    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{

   |
11 | {
   |  ^

ex.dfy(11,1): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case

   |
12 |     // Base case
   |                 ^

ex.dfy(12,16): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    // Base case\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {

   |
13 |     if n == 1 {
   |                ^

ex.dfy(13,15): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 1 {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert |[x]| == 1;

   |
14 |         assert |[x]| == 1;
   |                           ^

ex.dfy(14,26): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |[x]| == 1;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert |[x]| == 1;
        assert forall i :: 0 <= i < 1 ==> [x][i] == x;

   |
15 |         assert forall i :: 0 <= i < 1 ==> [x][i] == x;
   |                                                       ^

ex.dfy(15,54): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < 1 ==> [x][i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert |[x]| == 1;
        assert forall i :: 0 <= i < 1 ==> [x][i] == x;
    } else {

   |
16 |     } else {
   |             ^

ex.dfy(16,12): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    } else {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert |[x]| == 1;
        assert forall i :: 0 <= i < 1 ==> [x][i] == x;
    } else {
        repeat_correct(x, n - 1);

   |
17 |         repeat_correct(x, n - 1);
   |                                  ^

ex.dfy(17,33): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        repeat_correct(x, n - 1);\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert |[x]| == 1;
        assert forall i :: 0 <= i < 1 ==> [x][i] == x;
    } else {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;

   |
18 |         assert |repeat(x, n - 1)| == n - 1;
   |                                            ^

ex.dfy(18,43): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n - 1)| == n - 1;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert |[x]| == 1;
        assert forall i :: 0 <= i < 1 ==> [x][i] == x;
    } else {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

   |
19 |         assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
   |                                                                        ^

ex.dfy(19,71): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert |[x]| == 1;
        assert forall i :: 0 <= i < 1 ==> [x][i] == x;
    } else {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;


   |
19 |         assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
   |                                                                        ^

ex.dfy(19,71): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert |[x]| == 1;
        assert forall i :: 0 <= i < 1 ==> [x][i] == x;
    } else {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |[x] + repeat(x, n - 1)| == n;

   |
21 |         assert |[x] + repeat(x, n - 1)| == n;
   |                                              ^

ex.dfy(21,45): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |[x] + repeat(x, n - 1)| == n;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert |[x]| == 1;
        assert forall i :: 0 <= i < 1 ==> [x][i] == x;
    } else {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |[x] + repeat(x, n - 1)| == n;
        assert forall i :: 0 <= i < n ==> ([x] + repeat(x, n - 1))[i] == x;

   |
22 |         assert forall i :: 0 <= i < n ==> ([x] + repeat(x, n - 1))[i] == x;
   |                                                                            ^

ex.dfy(22,75): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < n ==> ([x] + repeat(x, n - 1))[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert |[x]| == 1;
        assert forall i :: 0 <= i < 1 ==> [x][i] == x;
    } else {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |[x] + repeat(x, n - 1)| == n;
        assert forall i :: 0 <= i < n ==> ([x] + repeat(x, n - 1))[i] == x;
    }

   |
23 |     }
   |      ^

ex.dfy(23,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert |[x]| == 1;
        assert forall i :: 0 <= i < 1 ==> [x][i] == x;
    } else {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |[x] + repeat(x, n - 1)| == n;
        assert forall i :: 0 <= i < n ==> ([x] + repeat(x, n - 1))[i] == x;
    }
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert |[x]| == 1;
        assert forall i :: 0 <= i < 1 ==> [x][i] == x;
    } else {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |[x] + repeat(x, n - 1)| == n;
        assert forall i :: 0 <= i < n ==> ([x] + repeat(x, n - 1))[i] == x;
    }
}
``` package io.github.dunwu.javacore.jdk8.lambda;

SCORE
1.0
['``` package io.github.dunwu.javacore.jdk8.lambda;\n']
CHOSEN SOLUTION
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert |[x]| == 1;
        assert forall i :: 0 <= i < 1 ==> [x][i] == x;
    } else {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |[x] + repeat(x, n - 1)| == n;
        assert forall i :: 0 <= i < n ==> ([x] + repeat(x, n - 1))[i] == x;
    }
}
``` package io.github.dunwu.javacore.jdk8.lambda;


STATS

number of nodes: 27
number of gen nodes: 14 (including leaves: 3)
number of back nodes: 13 (including leaves: 11)

expansion count: 17 (including failed: 4)

cache stats {'hit': 5, 'miss': 39}
=====SUMMARY STATISTICS FOR ALL TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101]

Trial calls: [44]


Time Statistics:

  Min: 101.00 sec, Max: 101.00 sec, Average: 101.00 sec, Standard Deviation: 0.00 sec

Call Statistics:

  Min: 44 calls, Max: 44 calls, Average: 44.00 calls, Standard Deviation: 0.00 calls

=====SUMMARY STATISTICS FOR NON_TIMED OUT TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101]

Trial calls: [44]


Time Statistics:

  Min: 101.00 sec, Max: 101.00 sec, Average: 101.00 sec, Standard Deviation: 0.00 sec

Call Statistics:

  Min: 44 calls, Max: 44 calls, Average: 44.00 calls, Standard Deviation: 0.00 calls

Trial  2
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['function method repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];
    for i in 0 .. n

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    for i in 0 .. n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];
    for i in 0 .. n
    {

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
-1.0
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>

SCORE
1.0
['function repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];
    for i in 0 .. n

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i in 0 .. n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];
    for i in 0 .. n
        result[i] := x;

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['        result[i] := x;\n']
['{\n']
['    var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];
    for i in 0 .. |result| - 1

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i in 0 .. |result| - 1\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];
    for i in 0 .. |result| - 1
        result[i] := x;

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['        result[i] := x;\n']
['function method repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['    requires n > 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
    reads x, n

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['    reads x, n\n']
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)

  |
3 |     if n == 0 then [] else [x] + repeat(x, n - 1)
  |                                                  ^

ex.dfy(3,49): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0 then [] else [x] + repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}


SCORE
1.0
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)

SCORE
1.0
['lemma repeat_correct(x: int, n: nat)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true

SCORE
1.0
['    requires true\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true
    ensures |repeat(x, n)| == n

SCORE
1.0
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x

SCORE
1.0
['    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{

   |
10 | {
   |  ^

ex.dfy(10,1): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0

   |
11 |     if n == 0
   |              ^

ex.dfy(11,13): Error: lbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {

   |
12 |     {
   |      ^

ex.dfy(12,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;

   |
13 |         assert |repeat(x, n)| == 0;
   |                                    ^

ex.dfy(13,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n)| == 0;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x;

   |
14 |         assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x;
   |                                                                ^

ex.dfy(14,63): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x;
    }

   |
15 |     }
   |      ^

ex.dfy(15,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x;
    }
    else

   |
16 |     else
   |         ^

ex.dfy(16,8): Error: invalid IfStmt
1 parse errors detected in ex.dfy

SCORE
None
['    else\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x;
    }
    else
    {

   |
17 |     {
   |      ^

ex.dfy(17,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x;
    }
    else
    {
        assert |repeat(x, n)| == n;

   |
18 |         assert |repeat(x, n)| == n;
   |                                    ^

ex.dfy(18,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n)| == n;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x;
    }
    else
    {
        assert |repeat(x, n)| == n;
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;

   |
19 |         assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |                                                                ^

ex.dfy(19,63): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x;
    }
    else
    {
        assert |repeat(x, n)| == n;
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
    }

   |
20 |     }
   |      ^

ex.dfy(20,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x;
    }
    else
    {
        assert |repeat(x, n)| == n;
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
    }
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x;
    }
    else
    {
        assert |repeat(x, n)| == n;
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
    }
}
```

SCORE
1.0
['```\n']
CHOSEN SOLUTION
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires true
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x;
    }
    else
    {
        assert |repeat(x, n)| == n;
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
    }
}
```


STATS

number of nodes: 19
number of gen nodes: 10 (including leaves: 1)
number of back nodes: 9 (including leaves: 9)

expansion count: 13 (including failed: 4)

cache stats {'hit': 4, 'miss': 34}
=====SUMMARY STATISTICS FOR ALL TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76]

Trial calls: [44, 38]


Time Statistics:

  Min: 76.00 sec, Max: 101.00 sec, Average: 88.50 sec, Standard Deviation: 12.50 sec

Call Statistics:

  Min: 38 calls, Max: 44 calls, Average: 41.00 calls, Standard Deviation: 3.00 calls

=====SUMMARY STATISTICS FOR NON_TIMED OUT TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76]

Trial calls: [44, 38]


Time Statistics:

  Min: 76.00 sec, Max: 101.00 sec, Average: 88.50 sec, Standard Deviation: 12.50 sec

Call Statistics:

  Min: 38 calls, Max: 44 calls, Average: 41.00 calls, Standard Deviation: 3.00 calls

Trial  3
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['function method repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    var s := new int[n];

  |
3 |     var s := new int[n];
  |              ^^^

ex.dfy(3,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var s := new int[n];
  |                  ^

ex.dfy(3,17): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    var s := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    var s := new int[n];
    for i in 0..n-1

  |
3 |     var s := new int[n];
  |              ^^^

ex.dfy(3,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var s := new int[n];
  |                  ^

ex.dfy(3,17): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    for i in 0..n-1\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    var s := new int[n];
    for i in 0..n-1
        s[i] := x;

  |
3 |     var s := new int[n];
  |              ^^^

ex.dfy(3,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var s := new int[n];
  |                  ^

ex.dfy(3,17): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
-1.0
['        s[i] := x;\n']
['function method repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['    requires n > 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['function method repeat(x: int, n: nat): seq<int> \n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
    requires n > 0

  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['    requires n > 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
    requires n > 0
    ensures |repeat(x, n)| == n

  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>

SCORE
1.0
['function repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0

  |
3 |     if n == 0
  |              ^

ex.dfy(3,13): Error: then expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []

  |
4 |     then []
  |            ^

ex.dfy(4,11): Error: else expected
1 parse errors detected in ex.dfy

SCORE
None
['    then []\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)

  |
5 |     else [x] + repeat(x, n - 1)
  |                                ^

ex.dfy(5,31): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    else [x] + repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}


SCORE
1.0
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)

SCORE
1.0
['lemma repeat_correct(x: int, n: nat)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{

  |
9 | {
  |  ^

ex.dfy(9,1): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert |repeat(x, n)| == n;

   |
10 |     assert |repeat(x, n)| == n;
   |                                ^

ex.dfy(10,31): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    assert |repeat(x, n)| == n;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert |repeat(x, n)| == n;
    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;

   |
11 |     forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |              ^

ex.dfy(11,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert |repeat(x, n)| == n;
    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
}

   |
11 |     forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |              ^

ex.dfy(11,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert |repeat(x, n)| == n;
    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
}
```

   |
11 |     forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |              ^

ex.dfy(11,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
-1.0
['```\n']
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert repeat(x, n).Length == n;

   |
10 |     assert repeat(x, n).Length == n;
   |                                     ^

ex.dfy(10,36): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    assert repeat(x, n).Length == n;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert repeat(x, n).Length == n;
    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;

   |
11 |     forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |              ^

ex.dfy(11,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert repeat(x, n).Length == n;
    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
}

   |
11 |     forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |              ^

ex.dfy(11,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert repeat(x, n).Length == n;
    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
}
``` package com.example.spring.cloud.eureka.consumer.config;

   |
11 |     forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |              ^

ex.dfy(11,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
-1.0
['``` package com.example.spring.cloud.eureka.consumer.config;\n']
['lemma repeat_correct(x: int, n: nat)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n

SCORE
1.0
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x

SCORE
1.0
['    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{

   |
11 | {
   |  ^

ex.dfy(11,1): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0

   |
12 |     if n == 0
   |              ^

ex.dfy(12,13): Error: lbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {

   |
13 |     {
   |      ^

ex.dfy(13,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.

   |
14 |         // Base case: If n is 0, repeat should return an empty list.
   |                                                                     ^

ex.dfy(14,68): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        // Base case: If n is 0, repeat should return an empty list.\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;

   |
15 |         assert |repeat(x, 0)| == 0;
   |                                    ^

ex.dfy(15,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, 0)| == 0;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }

   |
16 |     }
   |      ^

ex.dfy(16,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }
    else

   |
17 |     else
   |         ^

ex.dfy(17,8): Error: invalid IfStmt
1 parse errors detected in ex.dfy

SCORE
None
['    else\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }
    else
    {

   |
18 |     {
   |      ^

ex.dfy(18,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        // Inductive case: If n is not 0, then repeat is defined as [x] + repeat(x, n - 1).

   |
19 |         // Inductive case: If n is not 0, then repeat is defined as [x] + repeat(x, n - 1).
   |                                                                                            ^

ex.dfy(19,91): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        // Inductive case: If n is not 0, then repeat is defined as [x] + repeat(x, n - 1).\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        // Inductive case: If n is not 0, then repeat is defined as [x] + repeat(x, n - 1).
        // Let's assume the lemma is true for n - 1.

   |
20 |         // Let's assume the lemma is true for n - 1.
   |                                                     ^

ex.dfy(20,52): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
["        // Let's assume the lemma is true for n - 1.\n"]
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        // Inductive case: If n is not 0, then repeat is defined as [x] + repeat(x, n - 1).
        // Let's assume the lemma is true for n - 1.
        repeat_correct(x, n - 1);

   |
21 |         repeat_correct(x, n - 1);
   |                                  ^

ex.dfy(21,33): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        repeat_correct(x, n - 1);\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        // Inductive case: If n is not 0, then repeat is defined as [x] + repeat(x, n - 1).
        // Let's assume the lemma is true for n - 1.
        repeat_correct(x, n - 1);


   |
21 |         repeat_correct(x, n - 1);
   |                                  ^

ex.dfy(21,33): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        // Inductive case: If n is not 0, then repeat is defined as [x] + repeat(x, n - 1).
        // Let's assume the lemma is true for n - 1.
        repeat_correct(x, n - 1);

        // Then the length of repeat(x, n) is 1 + the length of repeat(x, n - 1), which is n.

   |
23 |         // Then the length of repeat(x, n) is 1 + the length of repeat(x, n - 1), which is n.
   |                                                                                              ^

ex.dfy(23,93): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        // Then the length of repeat(x, n) is 1 + the length of repeat(x, n - 1), which is n.\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        // Inductive case: If n is not 0, then repeat is defined as [x] + repeat(x, n - 1).
        // Let's assume the lemma is true for n - 1.
        repeat_correct(x, n - 1);

        // Then the length of repeat(x, n) is 1 + the length of repeat(x, n - 1), which is n.
        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|;

   |
24 |         assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|;
   |                                                           ^

ex.dfy(24,58): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        // Inductive case: If n is not 0, then repeat is defined as [x] + repeat(x, n - 1).
        // Let's assume the lemma is true for n - 1.
        repeat_correct(x, n - 1);

        // Then the length of repeat(x, n) is 1 + the length of repeat(x, n - 1), which is n.
        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|;
        assert |repeat(x, n)| == n;

   |
25 |         assert |repeat(x, n)| == n;
   |                                    ^

ex.dfy(25,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n)| == n;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        // Inductive case: If n is not 0, then repeat is defined as [x] + repeat(x, n - 1).
        // Let's assume the lemma is true for n - 1.
        repeat_correct(x, n - 1);

        // Then the length of repeat(x, n) is 1 + the length of repeat(x, n - 1), which is n.
        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|;
        assert |repeat(x, n)| == n;


   |
25 |         assert |repeat(x, n)| == n;
   |                                    ^

ex.dfy(25,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        // Inductive case: If n is not 0, then repeat is defined as [x] + repeat(x, n - 1).
        // Let's assume the lemma is true for n - 1.
        repeat_correct(x, n - 1);

        // Then the length of repeat(x, n) is 1 + the length of repeat(x, n - 1), which is n.
        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|;
        assert |repeat(x, n)| == n;

        // For all i, repeat(x, n)[i] is x.

   |
27 |         // For all i, repeat(x, n)[i] is x.
   |                                            ^

ex.dfy(27,43): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        // For all i, repeat(x, n)[i] is x.\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        // Inductive case: If n is not 0, then repeat is defined as [x] + repeat(x, n - 1).
        // Let's assume the lemma is true for n - 1.
        repeat_correct(x, n - 1);

        // Then the length of repeat(x, n) is 1 + the length of repeat(x, n - 1), which is n.
        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|;
        assert |repeat(x, n)| == n;

        // For all i, repeat(x, n)[i] is x.
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;

   |
28 |         assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |                                                                ^

ex.dfy(28,63): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        // Inductive case: If n is not 0, then repeat is defined as [x] + repeat(x, n - 1).
        // Let's assume the lemma is true for n - 1.
        repeat_correct(x, n - 1);

        // Then the length of repeat(x, n) is 1 + the length of repeat(x, n - 1), which is n.
        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|;
        assert |repeat(x, n)| == n;

        // For all i, repeat(x, n)[i] is x.
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
    }

   |
29 |     }
   |      ^

ex.dfy(29,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        // Inductive case: If n is not 0, then repeat is defined as [x] + repeat(x, n - 1).
        // Let's assume the lemma is true for n - 1.
        repeat_correct(x, n - 1);

        // Then the length of repeat(x, n) is 1 + the length of repeat(x, n - 1), which is n.
        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|;
        assert |repeat(x, n)| == n;

        // For all i, repeat(x, n)[i] is x.
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
    }
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        // Inductive case: If n is not 0, then repeat is defined as [x] + repeat(x, n - 1).
        // Let's assume the lemma is true for n - 1.
        repeat_correct(x, n - 1);

        // Then the length of repeat(x, n) is 1 + the length of repeat(x, n - 1), which is n.
        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|;
        assert |repeat(x, n)| == n;

        // For all i, repeat(x, n)[i] is x.
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
    }
}
``` import { Component, OnInit } from '@angular/core';

SCORE
1.0
["``` import { Component, OnInit } from '@angular/core';\n"]
CHOSEN SOLUTION
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        // Base case: If n is 0, repeat should return an empty list.
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        // Inductive case: If n is not 0, then repeat is defined as [x] + repeat(x, n - 1).
        // Let's assume the lemma is true for n - 1.
        repeat_correct(x, n - 1);

        // Then the length of repeat(x, n) is 1 + the length of repeat(x, n - 1), which is n.
        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|;
        assert |repeat(x, n)| == n;

        // For all i, repeat(x, n)[i] is x.
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
    }
}
``` import { Component, OnInit } from '@angular/core';


STATS

number of nodes: 19
number of gen nodes: 10 (including leaves: 2)
number of back nodes: 9 (including leaves: 8)

expansion count: 14 (including failed: 5)

cache stats {'hit': 3, 'miss': 50}
=====SUMMARY STATISTICS FOR ALL TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76, 110]

Trial calls: [44, 38, 53]


Time Statistics:

  Min: 76.00 sec, Max: 110.00 sec, Average: 95.67 sec, Standard Deviation: 14.38 sec

Call Statistics:

  Min: 38 calls, Max: 53 calls, Average: 45.00 calls, Standard Deviation: 6.16 calls

=====SUMMARY STATISTICS FOR NON_TIMED OUT TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76, 110]

Trial calls: [44, 38, 53]


Time Statistics:

  Min: 76.00 sec, Max: 110.00 sec, Average: 95.67 sec, Standard Deviation: 14.38 sec

Call Statistics:

  Min: 38 calls, Max: 53 calls, Average: 45.00 calls, Standard Deviation: 6.16 calls

Trial  4
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['function method repeat(x: int, n: nat): seq<int> \n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{
    if n == 0 then []

  |
3 |     if n == 0 then []
  |                      ^

ex.dfy(3,21): Error: else expected
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    if n == 0 then []\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)

  |
4 |     else [x] + repeat(x, n - 1)
  |                                ^

ex.dfy(4,31): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    else [x] + repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['function method repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []

  |
3 |     if n == 0 then []
  |                      ^

ex.dfy(3,21): Error: else expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    if n == 0 then []\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else

  |
4 |     else
  |         ^

ex.dfy(4,8): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    else\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else
    {

  |
5 |     {
  |      ^

ex.dfy(5,5): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else
    {
        var r := repeat(x, n-1);

  |
6 |         var r := repeat(x, n-1);
  |                                 ^

ex.dfy(6,32): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['        var r := repeat(x, n-1);\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else
    {
        var r := repeat(x, n-1);
        r.Append(x)

  |
7 |         r.Append(x)
  |                    ^

ex.dfy(7,19): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['        r.Append(x)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else
    {
        var r := repeat(x, n-1);
        r.Append(x)
    }

  |
8 |     }
  |      ^

ex.dfy(8,5): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else
    {
        var r := repeat(x, n-1);
        r.Append(x)
    }
}

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['}\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];
    for i in 0 .. |result|

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    for i in 0 .. |result|\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];
    for i in 0 .. |result|
    {

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
-1.0
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>

SCORE
1.0
['function repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];
    for i in 0 .. n

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i in 0 .. n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];
    for i in 0 .. n
    {

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['    {\n']
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []

  |
3 |     if n == 0 then []
  |                      ^

ex.dfy(3,21): Error: else expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0 then []\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)

  |
4 |     else [x] + repeat(x, n - 1)
  |                                ^

ex.dfy(4,31): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    else [x] + repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}


SCORE
1.0
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)

SCORE
1.0
['lemma repeat_correct(x: int, n: nat)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n

SCORE
1.0
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x

SCORE
1.0
['    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{

   |
10 | {
   |  ^

ex.dfy(10,1): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0

   |
11 |     if n == 0
   |              ^

ex.dfy(11,13): Error: lbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {

   |
12 |     {
   |      ^

ex.dfy(12,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;

   |
13 |         assert |repeat(x, 0)| == 0;
   |                                    ^

ex.dfy(13,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, 0)| == 0;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;

   |
14 |         assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
   |                                                                ^

ex.dfy(14,63): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }

   |
15 |     }
   |      ^

ex.dfy(15,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else

   |
16 |     else
   |         ^

ex.dfy(16,8): Error: invalid IfStmt
1 parse errors detected in ex.dfy

SCORE
None
['    else\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {

   |
17 |     {
   |      ^

ex.dfy(17,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        var r := repeat(x, n - 1);

   |
18 |         var r := repeat(x, n - 1);
   |                                   ^

ex.dfy(18,34): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        var r := repeat(x, n - 1);\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        var r := repeat(x, n - 1);
        assert |r| == n - 1;

   |
19 |         assert |r| == n - 1;
   |                             ^

ex.dfy(19,28): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |r| == n - 1;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        var r := repeat(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;

   |
20 |         assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
   |                                                         ^

ex.dfy(20,56): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        var r := repeat(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
        repeat_correct(x, n - 1);

   |
21 |         repeat_correct(x, n - 1);
   |                                  ^

ex.dfy(21,33): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        repeat_correct(x, n - 1);\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        var r := repeat(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
        repeat_correct(x, n - 1);
        assert |r| == n - 1;

   |
22 |         assert |r| == n - 1;
   |                             ^

ex.dfy(22,28): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |r| == n - 1;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        var r := repeat(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
        repeat_correct(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;

   |
23 |         assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
   |                                                         ^

ex.dfy(23,56): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        var r := repeat(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
        repeat_correct(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
        assert repeat(x, n)[0] == x;

   |
24 |         assert repeat(x, n)[0] == x;
   |                                     ^

ex.dfy(24,36): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert repeat(x, n)[0] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        var r := repeat(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
        repeat_correct(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
        assert repeat(x, n)[0] == x;
        assert |repeat(x, n)| == n;

   |
25 |         assert |repeat(x, n)| == n;
   |                                    ^

ex.dfy(25,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n)| == n;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        var r := repeat(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
        repeat_correct(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
        assert repeat(x, n)[0] == x;
        assert |repeat(x, n)| == n;
    }

   |
26 |     }
   |      ^

ex.dfy(26,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        var r := repeat(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
        repeat_correct(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
        assert repeat(x, n)[0] == x;
        assert |repeat(x, n)| == n;
    }
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        var r := repeat(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
        repeat_correct(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
        assert repeat(x, n)[0] == x;
        assert |repeat(x, n)| == n;
    }
}
```

SCORE
1.0
['```\n']
CHOSEN SOLUTION
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        var r := repeat(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
        repeat_correct(x, n - 1);
        assert |r| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> r[i] == x;
        assert repeat(x, n)[0] == x;
        assert |repeat(x, n)| == n;
    }
}
```


STATS

number of nodes: 17
number of gen nodes: 9 (including leaves: 1)
number of back nodes: 8 (including leaves: 8)

expansion count: 12 (including failed: 4)

cache stats {'hit': 3, 'miss': 48}
=====SUMMARY STATISTICS FOR ALL TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76, 110, 95]

Trial calls: [44, 38, 53, 51]


Time Statistics:

  Min: 76.00 sec, Max: 110.00 sec, Average: 95.50 sec, Standard Deviation: 12.46 sec

Call Statistics:

  Min: 38 calls, Max: 53 calls, Average: 46.50 calls, Standard Deviation: 5.94 calls

=====SUMMARY STATISTICS FOR NON_TIMED OUT TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76, 110, 95]

Trial calls: [44, 38, 53, 51]


Time Statistics:

  Min: 76.00 sec, Max: 110.00 sec, Average: 95.50 sec, Standard Deviation: 12.46 sec

Call Statistics:

  Min: 38 calls, Max: 53 calls, Average: 46.50 calls, Standard Deviation: 5.94 calls

Trial  5
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['function method repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['    requires n > 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['function method repeat(x: int, n: nat): seq<int> \n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
    requires n > 0

  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['    requires n > 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
    requires n > 0
{

  |
3 | {
  |  ^

ex.dfy(3,1): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
    requires n > 0
{
    var result := new int[n];

  |
4 |     var result := new int[n];
  |                   ^^^

ex.dfy(4,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |     var result := new int[n];
  |                       ^

ex.dfy(4,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
    requires n > 0
{
    var result := new int[n];
    for i in 0 .. n - 1

  |
4 |     var result := new int[n];
  |                   ^^^

ex.dfy(4,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |     var result := new int[n];
  |                       ^

ex.dfy(4,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    for i in 0 .. n - 1\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
    requires n > 0
{
    var result := new int[n];
    for i in 0 .. n - 1
        invariant 0 <= i <= n - 1

  |
4 |     var result := new int[n];
  |                   ^^^

ex.dfy(4,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |     var result := new int[n];
  |                       ^

ex.dfy(4,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
-1.0
['        invariant 0 <= i <= n - 1\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['    requires n > 0\n']
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>

SCORE
1.0
['function repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    var s := new int[n];

  |
3 |     var s := new int[n];
  |              ^^^

ex.dfy(3,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var s := new int[n];
  |                  ^

ex.dfy(3,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    var s := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    var s := new int[n];
    for i in 0..n-1

  |
3 |     var s := new int[n];
  |              ^^^

ex.dfy(3,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var s := new int[n];
  |                  ^

ex.dfy(3,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i in 0..n-1\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    var s := new int[n];
    for i in 0..n-1
    {

  |
3 |     var s := new int[n];
  |              ^^^

ex.dfy(3,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var s := new int[n];
  |                  ^

ex.dfy(3,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['    {\n']
['{\n']
['    var s := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    var s := new int[n];
    for i in 0 .. n

  |
3 |     var s := new int[n];
  |              ^^^

ex.dfy(3,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var s := new int[n];
  |                  ^

ex.dfy(3,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i in 0 .. n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    var s := new int[n];
    for i in 0 .. n
        s[i] := x;

  |
3 |     var s := new int[n];
  |              ^^^

ex.dfy(3,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var s := new int[n];
  |                  ^

ex.dfy(3,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['        s[i] := x;\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['    requires n > 0\n']
['    ensures |repeat(x, n)| == n\n']
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []

  |
3 |     if n == 0 then []
  |                      ^

ex.dfy(3,21): Error: else expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0 then []\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)

  |
4 |     else [x] + repeat(x, n - 1)
  |                                ^

ex.dfy(4,31): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    else [x] + repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}


SCORE
1.0
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)

SCORE
1.0
['lemma repeat_correct(x: int, n: nat)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{

  |
8 | {
  |  ^

ex.dfy(8,1): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert |repeat(x, n)| == n;

  |
9 |     assert |repeat(x, n)| == n;
  |                                ^

ex.dfy(9,31): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    assert |repeat(x, n)| == n;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert |repeat(x, n)| == n;
    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;

   |
10 |     forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |              ^

ex.dfy(10,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert |repeat(x, n)| == n;
    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
}

   |
10 |     forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |              ^

ex.dfy(10,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert |repeat(x, n)| == n;
    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
}
```

   |
10 |     forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |              ^

ex.dfy(10,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
-1.0
['```\n']
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert repeat(x, n).Length == n;

  |
9 |     assert repeat(x, n).Length == n;
  |                                     ^

ex.dfy(9,36): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    assert repeat(x, n).Length == n;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert repeat(x, n).Length == n;
    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;

   |
10 |     forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |              ^

ex.dfy(10,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert repeat(x, n).Length == n;
    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
}

   |
10 |     forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |              ^

ex.dfy(10,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert repeat(x, n).Length == n;
    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
}
```

   |
10 |     forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |              ^

ex.dfy(10,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
-1.0
['```\n']
['lemma repeat_correct(x: int, n: nat)\n']
['{\n']
['    assert |repeat(x, n)| == n;\n']
['    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;\n']
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert |repeat(x, n)| == n;
    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
}
``` package com.example.android.pets.data;

   |
10 |     forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |              ^

ex.dfy(10,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
-1.0
['``` package com.example.android.pets.data;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n

SCORE
1.0
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x

SCORE
1.0
['    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{

   |
10 | {
   |  ^

ex.dfy(10,1): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0

   |
11 |     if n == 0
   |              ^

ex.dfy(11,13): Error: lbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {

   |
12 |     {
   |      ^

ex.dfy(12,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;

   |
13 |         assert |repeat(x, 0)| == 0;
   |                                    ^

ex.dfy(13,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, 0)| == 0;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }

   |
14 |     }
   |      ^

ex.dfy(14,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }
    else

   |
15 |     else
   |         ^

ex.dfy(15,8): Error: invalid IfStmt
1 parse errors detected in ex.dfy

SCORE
None
['    else\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }
    else
    {

   |
16 |     {
   |      ^

ex.dfy(16,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;

   |
17 |         assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
   |                                                         ^

ex.dfy(17,56): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < 1 + |repeat(x, n - 1)| ==> repeat(x, n)[i] == x;

   |
18 |         assert forall i :: 0 <= i < 1 + |repeat(x, n - 1)| ==> repeat(x, n)[i] == x;
   |                                                                                     ^

ex.dfy(18,84): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < 1 + |repeat(x, n - 1)| ==> repeat(x, n)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < 1 + |repeat(x, n - 1)| ==> repeat(x, n)[i] == x;


   |
18 |         assert forall i :: 0 <= i < 1 + |repeat(x, n - 1)| ==> repeat(x, n)[i] == x;
   |                                                                                     ^

ex.dfy(18,84): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < 1 + |repeat(x, n - 1)| ==> repeat(x, n)[i] == x;

        repeat_correct(x, n - 1);

   |
20 |         repeat_correct(x, n - 1);
   |                                  ^

ex.dfy(20,33): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        repeat_correct(x, n - 1);\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < 1 + |repeat(x, n - 1)| ==> repeat(x, n)[i] == x;

        repeat_correct(x, n - 1);


   |
20 |         repeat_correct(x, n - 1);
   |                                  ^

ex.dfy(20,33): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < 1 + |repeat(x, n - 1)| ==> repeat(x, n)[i] == x;

        repeat_correct(x, n - 1);

        assert |repeat(x, n - 1)| == n - 1;

   |
22 |         assert |repeat(x, n - 1)| == n - 1;
   |                                            ^

ex.dfy(22,43): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n - 1)| == n - 1;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < 1 + |repeat(x, n - 1)| ==> repeat(x, n)[i] == x;

        repeat_correct(x, n - 1);

        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

   |
23 |         assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
   |                                                                        ^

ex.dfy(23,71): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < 1 + |repeat(x, n - 1)| ==> repeat(x, n)[i] == x;

        repeat_correct(x, n - 1);

        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;


   |
23 |         assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
   |                                                                        ^

ex.dfy(23,71): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < 1 + |repeat(x, n - 1)| ==> repeat(x, n)[i] == x;

        repeat_correct(x, n - 1);

        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert repeat(x, n)[0] == x;

   |
25 |         assert repeat(x, n)[0] == x;
   |                                     ^

ex.dfy(25,36): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert repeat(x, n)[0] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < 1 + |repeat(x, n - 1)| ==> repeat(x, n)[i] == x;

        repeat_correct(x, n - 1);

        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert repeat(x, n)[0] == x;
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == repeat(x, n - 1)[i - 1];

   |
26 |         assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == repeat(x, n - 1)[i - 1];
   |                                                                                      ^

ex.dfy(26,85): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == repeat(x, n - 1)[i - 1];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < 1 + |repeat(x, n - 1)| ==> repeat(x, n)[i] == x;

        repeat_correct(x, n - 1);

        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert repeat(x, n)[0] == x;
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == repeat(x, n - 1)[i - 1];
    }

   |
27 |     }
   |      ^

ex.dfy(27,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < 1 + |repeat(x, n - 1)| ==> repeat(x, n)[i] == x;

        repeat_correct(x, n - 1);

        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert repeat(x, n)[0] == x;
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == repeat(x, n - 1)[i - 1];
    }
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < 1 + |repeat(x, n - 1)| ==> repeat(x, n)[i] == x;

        repeat_correct(x, n - 1);

        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert repeat(x, n)[0] == x;
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == repeat(x, n - 1)[i - 1];
    }
}
```

SCORE
1.0
['```\n']
CHOSEN SOLUTION
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < 1 + |repeat(x, n - 1)| ==> repeat(x, n)[i] == x;

        repeat_correct(x, n - 1);

        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert repeat(x, n)[0] == x;
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == repeat(x, n - 1)[i - 1];
    }
}
```


STATS

number of nodes: 19
number of gen nodes: 10 (including leaves: 2)
number of back nodes: 9 (including leaves: 8)

expansion count: 18 (including failed: 9)

cache stats {'hit': 15, 'miss': 53}
=====SUMMARY STATISTICS FOR ALL TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76, 110, 95, 122]

Trial calls: [44, 38, 53, 51, 68]


Time Statistics:

  Min: 76.00 sec, Max: 122.00 sec, Average: 100.80 sec, Standard Deviation: 15.38 sec

Call Statistics:

  Min: 38 calls, Max: 68 calls, Average: 50.80 calls, Standard Deviation: 10.11 calls

=====SUMMARY STATISTICS FOR NON_TIMED OUT TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76, 110, 95, 122]

Trial calls: [44, 38, 53, 51, 68]


Time Statistics:

  Min: 76.00 sec, Max: 122.00 sec, Average: 100.80 sec, Standard Deviation: 15.38 sec

Call Statistics:

  Min: 38 calls, Max: 68 calls, Average: 50.80 calls, Standard Deviation: 10.11 calls

Trial  6
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>

SCORE
1.0
['function repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []

  |
3 |     if n == 0 then []
  |                      ^

ex.dfy(3,21): Error: else expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0 then []\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)

  |
4 |     else [x] + repeat(x, n - 1)
  |                                ^

ex.dfy(4,31): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    else [x] + repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}


SCORE
1.0
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)

SCORE
1.0
['lemma repeat_correct(x: int, n: nat)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n

SCORE
1.0
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x

SCORE
1.0
['    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{

   |
10 | {
   |  ^

ex.dfy(10,1): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0

   |
11 |     if n == 0
   |              ^

ex.dfy(11,13): Error: lbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {

   |
12 |     {
   |      ^

ex.dfy(12,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;

   |
13 |         assert |repeat(x, 0)| == 0;
   |                                    ^

ex.dfy(13,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, 0)| == 0;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true since there is no such i.

   |
14 |         assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true since there is no such i.
   |                                                                                                                    ^

ex.dfy(14,115): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true since there is no such i.\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true since there is no such i.
    }

   |
15 |     }
   |      ^

ex.dfy(15,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true since there is no such i.
    }
    else

   |
16 |     else
   |         ^

ex.dfy(16,8): Error: invalid IfStmt
1 parse errors detected in ex.dfy

SCORE
None
['    else\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true since there is no such i.
    }
    else
    {

   |
17 |     {
   |      ^

ex.dfy(17,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true since there is no such i.
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;

   |
18 |         assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
   |                                                         ^

ex.dfy(18,56): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true since there is no such i.
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n)[i] == x;

   |
19 |         assert forall i :: 0 <= i < n - 1 ==> repeat(x, n)[i] == x;
   |                                                                    ^

ex.dfy(19,67): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true since there is no such i.
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n)[i] == x;
        assert |repeat(x, n - 1)| == n - 1;

   |
20 |         assert |repeat(x, n - 1)| == n - 1;
   |                                            ^

ex.dfy(20,43): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n - 1)| == n - 1;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true since there is no such i.
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n)[i] == x;
        assert |repeat(x, n - 1)| == n - 1;
        assert repeat(x, n)[n - 1] == x;

   |
21 |         assert repeat(x, n)[n - 1] == x;
   |                                         ^

ex.dfy(21,40): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert repeat(x, n)[n - 1] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true since there is no such i.
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n)[i] == x;
        assert |repeat(x, n - 1)| == n - 1;
        assert repeat(x, n)[n - 1] == x;


   |
21 |         assert repeat(x, n)[n - 1] == x;
   |                                         ^

ex.dfy(21,40): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true since there is no such i.
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n)[i] == x;
        assert |repeat(x, n - 1)| == n - 1;
        assert repeat(x, n)[n - 1] == x;

        repeat_correct(x, n - 1);

   |
23 |         repeat_correct(x, n - 1);
   |                                  ^

ex.dfy(23,33): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        repeat_correct(x, n - 1);\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true since there is no such i.
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n)[i] == x;
        assert |repeat(x, n - 1)| == n - 1;
        assert repeat(x, n)[n - 1] == x;

        repeat_correct(x, n - 1);
    }

   |
24 |     }
   |      ^

ex.dfy(24,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true since there is no such i.
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n)[i] == x;
        assert |repeat(x, n - 1)| == n - 1;
        assert repeat(x, n)[n - 1] == x;

        repeat_correct(x, n - 1);
    }
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true since there is no such i.
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n)[i] == x;
        assert |repeat(x, n - 1)| == n - 1;
        assert repeat(x, n)[n - 1] == x;

        repeat_correct(x, n - 1);
    }
}
```

SCORE
1.0
['```\n']
CHOSEN SOLUTION
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true since there is no such i.
    }
    else
    {
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n)[i] == x;
        assert |repeat(x, n - 1)| == n - 1;
        assert repeat(x, n)[n - 1] == x;

        repeat_correct(x, n - 1);
    }
}
```


STATS

number of nodes: 17
number of gen nodes: 9 (including leaves: 1)
number of back nodes: 8 (including leaves: 8)

expansion count: 8 (including failed: 0)

cache stats {'hit': 0, 'miss': 26}
=====SUMMARY STATISTICS FOR ALL TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76, 110, 95, 122, 63]

Trial calls: [44, 38, 53, 51, 68, 26]


Time Statistics:

  Min: 63.00 sec, Max: 122.00 sec, Average: 94.50 sec, Standard Deviation: 19.89 sec

Call Statistics:

  Min: 26 calls, Max: 68 calls, Average: 46.67 calls, Standard Deviation: 13.06 calls

=====SUMMARY STATISTICS FOR NON_TIMED OUT TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76, 110, 95, 122, 63]

Trial calls: [44, 38, 53, 51, 68, 26]


Time Statistics:

  Min: 63.00 sec, Max: 122.00 sec, Average: 94.50 sec, Standard Deviation: 19.89 sec

Call Statistics:

  Min: 26 calls, Max: 68 calls, Average: 46.67 calls, Standard Deviation: 13.06 calls

Trial  7
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['function method repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];
    for i in 0 .. |result|

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    for i in 0 .. |result|\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];
    for i in 0 .. |result|
    {

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
-1.0
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['function method repeat(x: int, n: nat): seq<int> \n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
  requires n > 0

  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['  requires n > 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
  requires n > 0
{

  |
3 | {
  |  ^

ex.dfy(3,1): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
  requires n > 0
{
  var result := new int[n];

  |
4 |   var result := new int[n];
  |                 ^^^

ex.dfy(4,16): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |   var result := new int[n];
  |                     ^

ex.dfy(4,20): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['  var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
  requires n > 0
{
  var result := new int[n];
  for i in 0 .. n

  |
4 |   var result := new int[n];
  |                 ^^^

ex.dfy(4,16): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |   var result := new int[n];
  |                     ^

ex.dfy(4,20): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['  for i in 0 .. n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
  requires n > 0
{
  var result := new int[n];
  for i in 0 .. n
  {

  |
4 |   var result := new int[n];
  |                 ^^^

ex.dfy(4,16): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |   var result := new int[n];
  |                     ^

ex.dfy(4,20): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
-1.0
['  {\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []

  |
3 |     if n == 0 then []
  |                      ^

ex.dfy(3,21): Error: else expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    if n == 0 then []\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else

  |
4 |     else
  |         ^

ex.dfy(4,8): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    else\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else
    {

  |
5 |     {
  |      ^

ex.dfy(5,5): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else
    {
        var r := repeat(x, n-1);

  |
6 |         var r := repeat(x, n-1);
  |                                 ^

ex.dfy(6,32): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['        var r := repeat(x, n-1);\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else
    {
        var r := repeat(x, n-1);
        r + [x]

  |
7 |         r + [x]
  |                ^

ex.dfy(7,15): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['        r + [x]\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else
    {
        var r := repeat(x, n-1);
        r + [x]
    }

  |
8 |     }
  |      ^

ex.dfy(8,5): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else
    {
        var r := repeat(x, n-1);
        r + [x]
    }
}

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['}\n']
['function method repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n >= 0

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['    requires n >= 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n >= 0
    ensures |repeat(x, n)| == n

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['    ensures |repeat(x, n)| == n\n']
['function method repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['    requires n > 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat| >= n

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['    ensures |repeat| >= n\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['{\n']
['    var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];
    for i in 0 .. n - 1

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    for i in 0 .. n - 1\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];
    for i in 0 .. n - 1
        result[i] := x;

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
-1.0
['        result[i] := x;\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['{\n']
['    var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];
    for i in 0 .. n

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    for i in 0 .. n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    var result := new int[n];
    for i in 0 .. n
    {

  |
3 |     var result := new int[n];
  |                   ^^^

ex.dfy(3,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var result := new int[n];
  |                       ^

ex.dfy(3,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
-1.0
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>

SCORE
1.0
['function repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []

  |
3 |     if n == 0 then []
  |                      ^

ex.dfy(3,21): Error: else expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0 then []\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)

  |
4 |     else [x] + repeat(x, n - 1)
  |                                ^

ex.dfy(4,31): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    else [x] + repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}


SCORE
1.0
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)

SCORE
1.0
['lemma repeat_correct(x: int, n: nat)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{

  |
8 | {
  |  ^

ex.dfy(8,1): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert repeat(x, n).Length == n;

  |
9 |     assert repeat(x, n).Length == n;
  |                                     ^

ex.dfy(9,36): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    assert repeat(x, n).Length == n;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert repeat(x, n).Length == n;
    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;

   |
10 |     forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |              ^

ex.dfy(10,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert repeat(x, n).Length == n;
    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
}

   |
10 |     forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |              ^

ex.dfy(10,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
{
    assert repeat(x, n).Length == n;
    forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
}
``` import React from 'react';

   |
10 |     forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |              ^

ex.dfy(10,13): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
-1.0
["``` import React from 'react';\n"]
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n

SCORE
1.0
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x

SCORE
1.0
['    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{

   |
10 | {
   |  ^

ex.dfy(10,1): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0

   |
11 |     if n == 0
   |              ^

ex.dfy(11,13): Error: lbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {

   |
12 |     {
   |      ^

ex.dfy(12,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;

   |
13 |         assert |repeat(x, n)| == 0;
   |                                    ^

ex.dfy(13,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n)| == 0;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x; // Vacuously true

   |
14 |         assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x; // Vacuously true
   |                                                                                  ^

ex.dfy(14,81): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x; // Vacuously true\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x; // Vacuously true
    }

   |
15 |     }
   |      ^

ex.dfy(15,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x; // Vacuously true
    }
    else

   |
16 |     else
   |         ^

ex.dfy(16,8): Error: invalid IfStmt
1 parse errors detected in ex.dfy

SCORE
None
['    else\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x; // Vacuously true
    }
    else
    {

   |
17 |     {
   |      ^

ex.dfy(17,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x; // Vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);

   |
18 |         repeat_correct(x, n - 1);
   |                                  ^

ex.dfy(18,33): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        repeat_correct(x, n - 1);\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x; // Vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;

   |
19 |         assert |repeat(x, n - 1)| == n - 1;
   |                                            ^

ex.dfy(19,43): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n - 1)| == n - 1;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x; // Vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

   |
20 |         assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
   |                                                                        ^

ex.dfy(20,71): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x; // Vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By list concatenation

   |
21 |         assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By list concatenation
   |                                                                                    ^

ex.dfy(21,83): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By list concatenation\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x; // Vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By list concatenation
        assert |repeat(x, n)| == n;

   |
22 |         assert |repeat(x, n)| == n;
   |                                    ^

ex.dfy(22,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n)| == n;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x; // Vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By list concatenation
        assert |repeat(x, n)| == n;
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x; // By list concatenation

   |
23 |         assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x; // By list concatenation
   |                                                                                         ^

ex.dfy(23,88): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x; // By list concatenation\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x; // Vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By list concatenation
        assert |repeat(x, n)| == n;
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x; // By list concatenation
    }

   |
24 |     }
   |      ^

ex.dfy(24,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x; // Vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By list concatenation
        assert |repeat(x, n)| == n;
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x; // By list concatenation
    }
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x; // Vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By list concatenation
        assert |repeat(x, n)| == n;
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x; // By list concatenation
    }
}
``` package com.example.android.pets;

SCORE
1.0
['``` package com.example.android.pets;\n']
CHOSEN SOLUTION
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, n)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, n)[i] == x; // Vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By list concatenation
        assert |repeat(x, n)| == n;
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x; // By list concatenation
    }
}
``` package com.example.android.pets;


STATS

number of nodes: 17
number of gen nodes: 9 (including leaves: 1)
number of back nodes: 8 (including leaves: 8)

expansion count: 16 (including failed: 8)

cache stats {'hit': 10, 'miss': 57}
=====SUMMARY STATISTICS FOR ALL TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76, 110, 95, 122, 63, 123]

Trial calls: [44, 38, 53, 51, 68, 26, 67]


Time Statistics:

  Min: 63.00 sec, Max: 123.00 sec, Average: 98.57 sec, Standard Deviation: 20.94 sec

Call Statistics:

  Min: 26 calls, Max: 68 calls, Average: 49.57 calls, Standard Deviation: 14.03 calls

=====SUMMARY STATISTICS FOR NON_TIMED OUT TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76, 110, 95, 122, 63, 123]

Trial calls: [44, 38, 53, 51, 68, 26, 67]


Time Statistics:

  Min: 63.00 sec, Max: 123.00 sec, Average: 98.57 sec, Standard Deviation: 20.94 sec

Call Statistics:

  Min: 26 calls, Max: 68 calls, Average: 49.57 calls, Standard Deviation: 14.03 calls

Trial  8
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['function method repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['    requires n > 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
{

  |
3 | {
  |  ^

ex.dfy(3,1): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)

  |
4 |     if n == 1 then [x] else [x] + repeat(x, n - 1)
  |                                                   ^

ex.dfy(4,50): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    if n == 1 then [x] else [x] + repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    if n == 1 then [x] else [x] + repeat(x, n - 1)
}

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['}\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['    requires n > 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['    ensures |repeat(x, n)| == n\n']
['function method repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
  if n == 0 then []

  |
3 |   if n == 0 then []
  |                    ^

ex.dfy(3,19): Error: else expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['  if n == 0 then []\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
  if n == 0 then []
  else [x] + repeat(x, n - 1)

  |
4 |   else [x] + repeat(x, n - 1)
  |                              ^

ex.dfy(4,29): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['  else [x] + repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
  if n == 0 then []
  else [x] + repeat(x, n - 1)
}

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>

SCORE
1.0
['function repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []

  |
3 |     if n == 0 then []
  |                      ^

ex.dfy(3,21): Error: else expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0 then []\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else

  |
4 |     else
  |         ^

ex.dfy(4,8): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
['    else\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else
    {

  |
5 |     {
  |      ^

ex.dfy(5,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else
    {
        var r := repeat(x, n - 1);

  |
6 |         var r := repeat(x, n - 1);
  |                                   ^

ex.dfy(6,34): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
['        var r := repeat(x, n - 1);\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else
    {
        var r := repeat(x, n - 1);
        r + [x]

  |
7 |         r + [x]
  |                ^

ex.dfy(7,15): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        r + [x]\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else
    {
        var r := repeat(x, n - 1);
        r + [x]
    }

  |
8 |     }
  |      ^

ex.dfy(8,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else
    {
        var r := repeat(x, n - 1);
        r + [x]
    }
}

  |
3 |     if n == 0 then []
  |     ^^

ex.dfy(3,4): Error: the two branches of an if-then-else expression must have the same type (got seq<int> and set<seq<int>>)
1 resolution/type errors detected in ex.dfy

SCORE
-1.0
['}\n']
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)

  |
3 |     if n == 0 then [] else [x] + repeat(x, n - 1)
  |                                                  ^

ex.dfy(3,49): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0 then [] else [x] + repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}


SCORE
1.0
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)

SCORE
1.0
['lemma repeat_correct(x: int, n: nat)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n

SCORE
1.0
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x

SCORE
1.0
['    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{

  |
9 | {
  |  ^

ex.dfy(9,1): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0

   |
10 |     if n == 0
   |              ^

ex.dfy(10,13): Error: lbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {

   |
11 |     {
   |      ^

ex.dfy(11,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;

   |
12 |         assert |repeat(x, 0)| == 0;
   |                                    ^

ex.dfy(12,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, 0)| == 0;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;

   |
13 |         assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
   |                                                                ^

ex.dfy(13,63): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }

   |
14 |     }
   |      ^

ex.dfy(14,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else

   |
15 |     else
   |         ^

ex.dfy(15,8): Error: invalid IfStmt
1 parse errors detected in ex.dfy

SCORE
None
['    else\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {

   |
16 |     {
   |      ^

ex.dfy(16,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        repeat_correct(x, n - 1);

   |
17 |         repeat_correct(x, n - 1);
   |                                  ^

ex.dfy(17,33): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        repeat_correct(x, n - 1);\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;

   |
18 |         assert |repeat(x, n - 1)| == n - 1;
   |                                            ^

ex.dfy(18,43): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n - 1)| == n - 1;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

   |
19 |         assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
   |                                                                        ^

ex.dfy(19,71): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
        assert |repeat(x, n)| == n;

   |
20 |         assert |repeat(x, n)| == n;
   |                                    ^

ex.dfy(20,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n)| == n;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
        assert |repeat(x, n)| == n;
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;

   |
21 |         assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |                                                                ^

ex.dfy(21,63): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
        assert |repeat(x, n)| == n;
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
    }

   |
22 |     }
   |      ^

ex.dfy(22,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
        assert |repeat(x, n)| == n;
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
    }
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
        assert |repeat(x, n)| == n;
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
    }
}
```

SCORE
1.0
['```\n']
CHOSEN SOLUTION
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x;
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
        assert |repeat(x, n)| == n;
        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
    }
}
```


STATS

number of nodes: 17
number of gen nodes: 9 (including leaves: 1)
number of back nodes: 8 (including leaves: 8)

expansion count: 12 (including failed: 4)

cache stats {'hit': 4, 'miss': 41}
=====SUMMARY STATISTICS FOR ALL TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76, 110, 95, 122, 63, 123, 89]

Trial calls: [44, 38, 53, 51, 68, 26, 67, 45]


Time Statistics:

  Min: 63.00 sec, Max: 123.00 sec, Average: 97.38 sec, Standard Deviation: 19.84 sec

Call Statistics:

  Min: 26 calls, Max: 68 calls, Average: 49.00 calls, Standard Deviation: 13.21 calls

=====SUMMARY STATISTICS FOR NON_TIMED OUT TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76, 110, 95, 122, 63, 123, 89]

Trial calls: [44, 38, 53, 51, 68, 26, 67, 45]


Time Statistics:

  Min: 63.00 sec, Max: 123.00 sec, Average: 97.38 sec, Standard Deviation: 19.84 sec

Call Statistics:

  Min: 26 calls, Max: 68 calls, Average: 49.00 calls, Standard Deviation: 13.21 calls

Trial  9
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>

SCORE
1.0
['function repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []

  |
3 |     if n == 0 then []
  |                      ^

ex.dfy(3,21): Error: else expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0 then []\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)

  |
4 |     else [x] + repeat(x, n - 1)
  |                                ^

ex.dfy(4,31): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    else [x] + repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}


SCORE
1.0
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)

SCORE
1.0
['lemma repeat_correct(x: int, n: nat)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n

SCORE
1.0
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x

SCORE
1.0
['    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{

   |
10 | {
   |  ^

ex.dfy(10,1): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0

   |
11 |     if n == 0
   |              ^

ex.dfy(11,13): Error: lbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {

   |
12 |     {
   |      ^

ex.dfy(12,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;

   |
13 |         assert |repeat(x, 0)| == 0;
   |                                    ^

ex.dfy(13,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, 0)| == 0;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true

   |
14 |         assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
   |                                                                                          ^

ex.dfy(14,89): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }

   |
15 |     }
   |      ^

ex.dfy(15,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else

   |
16 |     else
   |         ^

ex.dfy(16,8): Error: invalid IfStmt
1 parse errors detected in ex.dfy

SCORE
None
['    else\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {

   |
17 |     {
   |      ^

ex.dfy(17,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);

   |
18 |         repeat_correct(x, n - 1);
   |                                  ^

ex.dfy(18,33): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        repeat_correct(x, n - 1);\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;

   |
19 |         assert |repeat(x, n - 1)| == n - 1;
   |                                            ^

ex.dfy(19,43): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n - 1)| == n - 1;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

   |
20 |         assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
   |                                                                        ^

ex.dfy(20,71): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;


   |
20 |         assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
   |                                                                        ^

ex.dfy(20,71): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By the definition of `repeat`

   |
22 |         assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By the definition of `repeat`
   |                                                                                            ^

ex.dfy(22,91): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By the definition of `repeat`\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By the definition of `repeat`
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|; // By the length of a list concatenation

   |
23 |         assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|; // By the length of a list concatenation
   |                                                                                                  ^

ex.dfy(23,97): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|; // By the length of a list concatenation\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By the definition of `repeat`
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|; // By the length of a list concatenation
        assert |repeat(x, n)| == n; // By the induction hypothesis

   |
24 |         assert |repeat(x, n)| == n; // By the induction hypothesis
   |                                                                   ^

ex.dfy(24,66): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n)| == n; // By the induction hypothesis\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By the definition of `repeat`
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|; // By the length of a list concatenation
        assert |repeat(x, n)| == n; // By the induction hypothesis


   |
24 |         assert |repeat(x, n)| == n; // By the induction hypothesis
   |                                                                   ^

ex.dfy(24,66): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By the definition of `repeat`
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|; // By the length of a list concatenation
        assert |repeat(x, n)| == n; // By the induction hypothesis

        assert repeat(x, n)[0] == x; // The first element is `x` by the definition of `repeat`

   |
26 |         assert repeat(x, n)[0] == x; // The first element is `x` by the definition of `repeat`
   |                                                                                               ^

ex.dfy(26,94): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert repeat(x, n)[0] == x; // The first element is `x` by the definition of `repeat`\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By the definition of `repeat`
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|; // By the length of a list concatenation
        assert |repeat(x, n)| == n; // By the induction hypothesis

        assert repeat(x, n)[0] == x; // The first element is `x` by the definition of `repeat`
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == repeat(x, n - 1)[i - 1]; // The rest of the elements are from `repeat(x, n - 1)`

   |
27 |         assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == repeat(x, n - 1)[i - 1]; // The rest of the elements are from `repeat(x, n - 1)`
   |                                                                                                                                              ^

ex.dfy(27,141): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == repeat(x, n - 1)[i - 1]; // The rest of the elements are from `repeat(x, n - 1)`\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By the definition of `repeat`
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|; // By the length of a list concatenation
        assert |repeat(x, n)| == n; // By the induction hypothesis

        assert repeat(x, n)[0] == x; // The first element is `x` by the definition of `repeat`
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == repeat(x, n - 1)[i - 1]; // The rest of the elements are from `repeat(x, n - 1)`
        assert forall i :: 1 <= i < n ==> repeat(x, n - 1)[i - 1] == x; // By the induction hypothesis

   |
28 |         assert forall i :: 1 <= i < n ==> repeat(x, n - 1)[i - 1] == x; // By the induction hypothesis
   |                                                                                                       ^

ex.dfy(28,102): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 1 <= i < n ==> repeat(x, n - 1)[i - 1] == x; // By the induction hypothesis\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By the definition of `repeat`
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|; // By the length of a list concatenation
        assert |repeat(x, n)| == n; // By the induction hypothesis

        assert repeat(x, n)[0] == x; // The first element is `x` by the definition of `repeat`
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == repeat(x, n - 1)[i - 1]; // The rest of the elements are from `repeat(x, n - 1)`
        assert forall i :: 1 <= i < n ==> repeat(x, n - 1)[i - 1] == x; // By the induction hypothesis
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == x; // By transitivity of equality

   |
29 |         assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == x; // By transitivity of equality
   |                                                                                               ^

ex.dfy(29,94): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == x; // By transitivity of equality\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By the definition of `repeat`
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|; // By the length of a list concatenation
        assert |repeat(x, n)| == n; // By the induction hypothesis

        assert repeat(x, n)[0] == x; // The first element is `x` by the definition of `repeat`
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == repeat(x, n - 1)[i - 1]; // The rest of the elements are from `repeat(x, n - 1)`
        assert forall i :: 1 <= i < n ==> repeat(x, n - 1)[i - 1] == x; // By the induction hypothesis
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == x; // By transitivity of equality
    }

   |
30 |     }
   |      ^

ex.dfy(30,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By the definition of `repeat`
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|; // By the length of a list concatenation
        assert |repeat(x, n)| == n; // By the induction hypothesis

        assert repeat(x, n)[0] == x; // The first element is `x` by the definition of `repeat`
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == repeat(x, n - 1)[i - 1]; // The rest of the elements are from `repeat(x, n - 1)`
        assert forall i :: 1 <= i < n ==> repeat(x, n - 1)[i - 1] == x; // By the induction hypothesis
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == x; // By transitivity of equality
    }
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By the definition of `repeat`
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|; // By the length of a list concatenation
        assert |repeat(x, n)| == n; // By the induction hypothesis

        assert repeat(x, n)[0] == x; // The first element is `x` by the definition of `repeat`
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == repeat(x, n - 1)[i - 1]; // The rest of the elements are from `repeat(x, n - 1)`
        assert forall i :: 1 <= i < n ==> repeat(x, n - 1)[i - 1] == x; // By the induction hypothesis
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == x; // By transitivity of equality
    }
}
``` import { Component, OnInit, Input, ViewChild, ElementRef, Output, EventEmitter } from '@angular/core';

SCORE
1.0
["``` import { Component, OnInit, Input, ViewChild, ElementRef, Output, EventEmitter } from '@angular/core';\n"]
CHOSEN SOLUTION
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 0
    {
        assert |repeat(x, 0)| == 0;
        assert forall i :: 0 <= i < 0 ==> repeat(x, 0)[i] == x; // This is vacuously true
    }
    else
    {
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert |repeat(x, n)| == |[x] + repeat(x, n - 1)|; // By the definition of `repeat`
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|; // By the length of a list concatenation
        assert |repeat(x, n)| == n; // By the induction hypothesis

        assert repeat(x, n)[0] == x; // The first element is `x` by the definition of `repeat`
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == repeat(x, n - 1)[i - 1]; // The rest of the elements are from `repeat(x, n - 1)`
        assert forall i :: 1 <= i < n ==> repeat(x, n - 1)[i - 1] == x; // By the induction hypothesis
        assert forall i :: 1 <= i < n ==> repeat(x, n)[i] == x; // By transitivity of equality
    }
}
``` import { Component, OnInit, Input, ViewChild, ElementRef, Output, EventEmitter } from '@angular/core';


STATS

number of nodes: 17
number of gen nodes: 9 (including leaves: 1)
number of back nodes: 8 (including leaves: 8)

expansion count: 8 (including failed: 0)

cache stats {'hit': 0, 'miss': 32}
=====SUMMARY STATISTICS FOR ALL TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76, 110, 95, 122, 63, 123, 89, 89]

Trial calls: [44, 38, 53, 51, 68, 26, 67, 45, 32]


Time Statistics:

  Min: 63.00 sec, Max: 123.00 sec, Average: 96.44 sec, Standard Deviation: 18.89 sec

Call Statistics:

  Min: 26 calls, Max: 68 calls, Average: 47.11 calls, Standard Deviation: 13.55 calls

=====SUMMARY STATISTICS FOR NON_TIMED OUT TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76, 110, 95, 122, 63, 123, 89, 89]

Trial calls: [44, 38, 53, 51, 68, 26, 67, 45, 32]


Time Statistics:

  Min: 63.00 sec, Max: 123.00 sec, Average: 96.44 sec, Standard Deviation: 18.89 sec

Call Statistics:

  Min: 26 calls, Max: 68 calls, Average: 47.11 calls, Standard Deviation: 13.55 calls

Trial  10
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['function method repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
  var result := new int[n];

  |
3 |   var result := new int[n];
  |                 ^^^

ex.dfy(3,16): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |   var result := new int[n];
  |                     ^

ex.dfy(3,20): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['  var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
  var result := new int[n];
  for i in 0..n-1

  |
3 |   var result := new int[n];
  |                 ^^^

ex.dfy(3,16): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |   var result := new int[n];
  |                     ^

ex.dfy(3,20): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['  for i in 0..n-1\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
  var result := new int[n];
  for i in 0..n-1
  {

  |
3 |   var result := new int[n];
  |                 ^^^

ex.dfy(3,16): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |   var result := new int[n];
  |                     ^

ex.dfy(3,20): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
-1.0
['  {\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []

  |
3 |     if n == 0 then []
  |                      ^

ex.dfy(3,21): Error: else expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    if n == 0 then []\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)

  |
4 |     else [x] + repeat(x, n - 1)
  |                                ^

ex.dfy(4,31): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    else [x] + repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then []
    else [x] + repeat(x, n - 1)
}

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['function method repeat(x: int, n: nat): seq<int> \n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{
    if n == 0 then []

  |
3 |     if n == 0 then []
  |                      ^

ex.dfy(3,21): Error: else expected
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    if n == 0 then []\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{
    if n == 0 then []
    else 

  |
4 |     else
  |         ^

ex.dfy(4,8): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    else \n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{
    if n == 0 then []
    else 
    {

  |
5 |     {
  |      ^

ex.dfy(5,5): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{
    if n == 0 then []
    else 
    {
        var s := repeat(x, n-1);

  |
6 |         var s := repeat(x, n-1);
  |                                 ^

ex.dfy(6,32): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['        var s := repeat(x, n-1);\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{
    if n == 0 then []
    else 
    {
        var s := repeat(x, n-1);
        s.Append(x)

  |
7 |         s.Append(x)
  |                    ^

ex.dfy(7,19): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['        s.Append(x)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{
    if n == 0 then []
    else 
    {
        var s := repeat(x, n-1);
        s.Append(x)
    }

  |
8 |     }
  |      ^

ex.dfy(8,5): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{
    if n == 0 then []
    else 
    {
        var s := repeat(x, n-1);
        s.Append(x)
    }
}

  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['}\n']
['function method repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
None
['    requires n > 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
{

  |
3 | {
  |  ^

ex.dfy(3,1): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    var result := new int[n];

  |
4 |     var result := new int[n];
  |                   ^^^

ex.dfy(4,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |     var result := new int[n];
  |                       ^

ex.dfy(4,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    var result := new int[n];
    for i in 0..n {

  |
4 |     var result := new int[n];
  |                   ^^^

ex.dfy(4,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |     var result := new int[n];
  |                       ^

ex.dfy(4,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    for i in 0..n {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    var result := new int[n];
    for i in 0..n {
        result[i] := x;

  |
4 |     var result := new int[n];
  |                   ^^^

ex.dfy(4,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |     var result := new int[n];
  |                       ^

ex.dfy(4,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
-1.0
['        result[i] := x;\n']
['function method repeat(x: int, n: nat): seq<int> \n']
['{\n']
['    if n == 0 then []\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{
    if n == 0 then []
    else

  |
4 |     else
  |         ^

ex.dfy(4,8): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    else\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{
    if n == 0 then []
    else
    {

  |
5 |     {
  |      ^

ex.dfy(5,5): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{
    if n == 0 then []
    else
    {
        var result := repeat(x, n-1);

  |
6 |         var result := repeat(x, n-1);
  |                                      ^

ex.dfy(6,37): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['        var result := repeat(x, n-1);\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{
    if n == 0 then []
    else
    {
        var result := repeat(x, n-1);
        result := result + [x];

  |
7 |         result := result + [x];
  |                ^

ex.dfy(7,15): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['        result := result + [x];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{
    if n == 0 then []
    else
    {
        var result := repeat(x, n-1);
        result := result + [x];
        result

  |
7 |         result := result + [x];
  |                ^

ex.dfy(7,15): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['        result\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int> 
{
    if n == 0 then []
    else
    {
        var result := repeat(x, n-1);
        result := result + [x];
        result
    }

  |
7 |         result := result + [x];
  |                ^

ex.dfy(7,15): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int> 
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
-1.0
['    }\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['    requires n > 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['    ensures |repeat(x, n)| == n\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['{\n']
['    if n == 0 then []\n']
['    else [x] + repeat(x, n - 1)\n']
['}\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0

  |
3 |     if n == 0
  |              ^

ex.dfy(3,13): Error: then expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    if n == 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []

  |
4 |     then []
  |            ^

ex.dfy(4,11): Error: else expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    then []\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)

  |
5 |     else [x] + repeat(x, n - 1)
  |                                ^

ex.dfy(5,31): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    else [x] + repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n - 1)
}

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['}\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['{\n']
['    if n == 0 then []\n']
['    else [x] + repeat(x, n - 1)\n']
['}\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else

  |
3 |     if n == 0 then [] else
  |                           ^

ex.dfy(3,26): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    if n == 0 then [] else\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else
    [x] + repeat(x, n - 1)

  |
4 |     [x] + repeat(x, n - 1)
  |                           ^

ex.dfy(4,26): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    [x] + repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0 then [] else
    [x] + repeat(x, n - 1)
}

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['}\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['    requires n > 0\n']
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    var r := new int[n];

  |
4 |     var r := new int[n];
  |              ^^^

ex.dfy(4,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |     var r := new int[n];
  |                  ^

ex.dfy(4,17): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    var r := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    var r := new int[n];
    for i in 0 .. n

  |
4 |     var r := new int[n];
  |              ^^^

ex.dfy(4,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |     var r := new int[n];
  |                  ^

ex.dfy(4,17): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    for i in 0 .. n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    var r := new int[n];
    for i in 0 .. n
        r[i] := x;

  |
4 |     var r := new int[n];
  |              ^^^

ex.dfy(4,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |     var r := new int[n];
  |                  ^

ex.dfy(4,17): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
-1.0
['        r[i] := x;\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['    requires n > 0\n']
['{\n']
['    var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    var result := new int[n];
    for i in 0 .. n

  |
4 |     var result := new int[n];
  |                   ^^^

ex.dfy(4,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |     var result := new int[n];
  |                       ^

ex.dfy(4,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
None
['    for i in 0 .. n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    var result := new int[n];
    for i in 0 .. n
        invariant 0 <= i <= n

  |
4 |     var result := new int[n];
  |                   ^^^

ex.dfy(4,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |     var result := new int[n];
  |                       ^

ex.dfy(4,22): Error: invalid UnaryExpression
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
3 parse errors detected in ex.dfy

SCORE
-1.0
['        invariant 0 <= i <= n\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['{\n']
['    if n == 0 then []\n']
['    else [x] + repeat(x, n - 1)\n']
['}\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['    requires n > 0\n']
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>

SCORE
1.0
['function repeat(x: int, n: nat): seq<int>\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0

SCORE
1.0
['    requires n > 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n

SCORE
1.0
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x

SCORE
1.0
['    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{

  |
5 | {
  |  ^

ex.dfy(5,1): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var s := new int[n];

  |
6 |     var s := new int[n];
  |              ^^^

ex.dfy(6,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var s := new int[n];
  |                  ^

ex.dfy(6,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    var s := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var s := new int[n];
    for i in 0..n-1 {

  |
6 |     var s := new int[n];
  |              ^^^

ex.dfy(6,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var s := new int[n];
  |                  ^

ex.dfy(6,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i in 0..n-1 {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var s := new int[n];
    for i in 0..n-1 {
        s[i] := x;

  |
6 |     var s := new int[n];
  |              ^^^

ex.dfy(6,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var s := new int[n];
  |                  ^

ex.dfy(6,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['        s[i] := x;\n']
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var result := new int[n];

  |
6 |     var result := new int[n];
  |                   ^^^

ex.dfy(6,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var result := new int[n];
  |                       ^

ex.dfy(6,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var result := new int[n];
    for i in 0 .. n

  |
6 |     var result := new int[n];
  |                   ^^^

ex.dfy(6,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var result := new int[n];
  |                       ^

ex.dfy(6,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i in 0 .. n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var result := new int[n];
    for i in 0 .. n
        invariant 0 <= i <= n

  |
6 |     var result := new int[n];
  |                   ^^^

ex.dfy(6,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var result := new int[n];
  |                       ^

ex.dfy(6,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['        invariant 0 <= i <= n\n']
['    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x\n']
['{\n']
['    var s := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var s := new int[n];
    for i in 0 .. n

  |
6 |     var s := new int[n];
  |              ^^^

ex.dfy(6,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var s := new int[n];
  |                  ^

ex.dfy(6,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i in 0 .. n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var s := new int[n];
    for i in 0 .. n
        invariant 0 <= i <= n

  |
6 |     var s := new int[n];
  |              ^^^

ex.dfy(6,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var s := new int[n];
  |                  ^

ex.dfy(6,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['        invariant 0 <= i <= n\n']
['{\n']
['    var result := new int[n];\n']
['    for i in 0 .. n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var result := new int[n];
    for i in 0 .. n
    {

  |
6 |     var result := new int[n];
  |                   ^^^

ex.dfy(6,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var result := new int[n];
  |                       ^

ex.dfy(6,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['    {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{

  |
3 | {
  |  ^

ex.dfy(3,1): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    var s := new int[n];

  |
4 |     var s := new int[n];
  |              ^^^

ex.dfy(4,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |     var s := new int[n];
  |                  ^

ex.dfy(4,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    var s := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    var s := new int[n];
    for i in 0 .. n

  |
4 |     var s := new int[n];
  |              ^^^

ex.dfy(4,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |     var s := new int[n];
  |                  ^

ex.dfy(4,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i in 0 .. n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
{
    var s := new int[n];
    for i in 0 .. n
        s[i] := x;

  |
4 |     var s := new int[n];
  |              ^^^

ex.dfy(4,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
4 |     var s := new int[n];
  |                  ^

ex.dfy(4,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['        s[i] := x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{

  |
2 | {
  |  ^

ex.dfy(2,1): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    var s := new int[n];

  |
3 |     var s := new int[n];
  |              ^^^

ex.dfy(3,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var s := new int[n];
  |                  ^

ex.dfy(3,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    var s := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    var s := new int[n];
    for i in 0..|s|-1

  |
3 |     var s := new int[n];
  |              ^^^

ex.dfy(3,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var s := new int[n];
  |                  ^

ex.dfy(3,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i in 0..|s|-1\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
{
    var s := new int[n];
    for i in 0..|s|-1
        s[i] := x;

  |
3 |     var s := new int[n];
  |              ^^^

ex.dfy(3,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
3 |     var s := new int[n];
  |                  ^

ex.dfy(3,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['        s[i] := x;\n']
['function method repeat(x: int, n: nat): seq<int>\n']
['{\n']
['    if n == 0\n']
['    then []\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n-1)

  |
5 |     else [x] + repeat(x, n-1)
  |                              ^

ex.dfy(5,29): Error: rbrace expected
  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
2 parse errors detected in ex.dfy

SCORE
None
['    else [x] + repeat(x, n-1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function method repeat(x: int, n: nat): seq<int>
{
    if n == 0
    then []
    else [x] + repeat(x, n-1)
}

  |
1 | function method repeat(x: int, n: nat): seq<int>
  | ^^^^^^^^

ex.dfy(1,0): Error: the phrase 'function method' is not allowed when using --function-syntax:4; to declare a compiled function, use just 'function'
1 parse errors detected in ex.dfy

SCORE
-1.0
['}\n']
['{\n']
['    var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var result := new int[n];
    for i in 0 .. n - 1

  |
6 |     var result := new int[n];
  |                   ^^^

ex.dfy(6,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var result := new int[n];
  |                       ^

ex.dfy(6,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i in 0 .. n - 1\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var result := new int[n];
    for i in 0 .. n - 1
        invariant 0 <= i <= n - 1

  |
6 |     var result := new int[n];
  |                   ^^^

ex.dfy(6,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var result := new int[n];
  |                       ^

ex.dfy(6,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['        invariant 0 <= i <= n - 1\n']
['{\n']
['    var s := new int[n];\n']
['    for i in 0 .. n\n']
['        invariant 0 <= i <= n\n']
['    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x\n']
['{\n']
['    var s := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var s := new int[n];
    for i in 0..n {

  |
6 |     var s := new int[n];
  |              ^^^

ex.dfy(6,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var s := new int[n];
  |                  ^

ex.dfy(6,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i in 0..n {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var s := new int[n];
    for i in 0..n {
        s[i] := x;

  |
6 |     var s := new int[n];
  |              ^^^

ex.dfy(6,13): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var s := new int[n];
  |                  ^

ex.dfy(6,17): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['        s[i] := x;\n']
['{\n']
['    var result := new int[n];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var result := new int[n];
    for i in 0..n {

  |
6 |     var result := new int[n];
  |                   ^^^

ex.dfy(6,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var result := new int[n];
  |                       ^

ex.dfy(6,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
None
['    for i in 0..n {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    var result := new int[n];
    for i in 0..n {
        result[i] := x;

  |
6 |     var result := new int[n];
  |                   ^^^

ex.dfy(6,18): Error: Calls with side-effects such as constructors are not allowed in expressions.
  |
6 |     var result := new int[n];
  |                       ^

ex.dfy(6,22): Error: invalid UnaryExpression
2 parse errors detected in ex.dfy

SCORE
-1.0
['        result[i] := x;\n']
['{\n']
['    var result := new int[n];\n']
['    for i in 0 .. n\n']
['        invariant 0 <= i <= n\n']
['{\n']
['    var result := new int[n];\n']
['    for i in 0 .. n\n']
['        invariant 0 <= i <= n\n']
['{\n']
['    var result := new int[n];\n']
['    for i in 0 .. n\n']
['        invariant 0 <= i <= n\n']
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 1 then [x] else x :: repeat(x, n - 1)

  |
6 |     if n == 1 then [x] else x :: repeat(x, n - 1)
  |                               ^

ex.dfy(6,30): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 1 then [x] else x :: repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 1 then [x] else x :: repeat(x, n - 1)
}

  |
6 |     if n == 1 then [x] else x :: repeat(x, n - 1)
  |                               ^

ex.dfy(6,30): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 1 then [x] else x :: repeat(x, n - 1)
}


  |
6 |     if n == 1 then [x] else x :: repeat(x, n - 1)
  |                               ^

ex.dfy(6,30): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    if n == 1 then [x] else x :: repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)

  |
6 |     if n == 1 then [x] else x :: repeat(x, n - 1)
  |                               ^

ex.dfy(6,30): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
-1.0
['lemma repeat_correct(x: int, n: nat)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{

  |
4 | {
  |  ^

ex.dfy(4,1): Error: invalid UnaryExpression
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]

  |
5 |     if n == 1 then [x]
  |                       ^

ex.dfy(5,22): Error: else expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 1 then [x]\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)

  |
6 |     else [x] + repeat(x, n - 1)
  |                                ^

ex.dfy(6,31): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    else [x] + repeat(x, n - 1)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}


SCORE
1.0
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)

SCORE
1.0
['lemma repeat_correct(x: int, n: nat)\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0

SCORE
1.0
['    requires n > 0\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n

SCORE
1.0
['    ensures |repeat(x, n)| == n\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x

SCORE
1.0
['    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{

   |
13 | {
   |  ^

ex.dfy(13,1): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['{\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case

   |
14 |     // Base case
   |                 ^

ex.dfy(14,16): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    // Base case\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {

   |
15 |     if n == 1 {
   |                ^

ex.dfy(15,15): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    if n == 1 {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];

   |
16 |         assert repeat(x, 1) == [x];
   |                                    ^

ex.dfy(16,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert repeat(x, 1) == [x];\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];
        assert |repeat(x, 1)| == 1;

   |
17 |         assert |repeat(x, 1)| == 1;
   |                                    ^

ex.dfy(17,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, 1)| == 1;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];
        assert |repeat(x, 1)| == 1;
    } else {

   |
18 |     } else {
   |             ^

ex.dfy(18,12): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    } else {\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];
        assert |repeat(x, 1)| == 1;
    } else {
        // Inductive step

   |
19 |         // Inductive step
   |                          ^

ex.dfy(19,25): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        // Inductive step\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];
        assert |repeat(x, 1)| == 1;
    } else {
        // Inductive step
        repeat_correct(x, n - 1);

   |
20 |         repeat_correct(x, n - 1);
   |                                  ^

ex.dfy(20,33): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        repeat_correct(x, n - 1);\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];
        assert |repeat(x, 1)| == 1;
    } else {
        // Inductive step
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;

   |
21 |         assert |repeat(x, n - 1)| == n - 1;
   |                                            ^

ex.dfy(21,43): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n - 1)| == n - 1;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];
        assert |repeat(x, 1)| == 1;
    } else {
        // Inductive step
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

   |
22 |         assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
   |                                                                        ^

ex.dfy(22,71): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];
        assert |repeat(x, 1)| == 1;
    } else {
        // Inductive step
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;


   |
22 |         assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;
   |                                                                        ^

ex.dfy(22,71): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];
        assert |repeat(x, 1)| == 1;
    } else {
        // Inductive step
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert repeat(x, n) == [x] + repeat(x, n - 1);

   |
24 |         assert repeat(x, n) == [x] + repeat(x, n - 1);
   |                                                       ^

ex.dfy(24,54): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert repeat(x, n) == [x] + repeat(x, n - 1);\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];
        assert |repeat(x, 1)| == 1;
    } else {
        // Inductive step
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert repeat(x, n) == [x] + repeat(x, n - 1);
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;

   |
25 |         assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
   |                                                         ^

ex.dfy(25,56): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];
        assert |repeat(x, 1)| == 1;
    } else {
        // Inductive step
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert repeat(x, n) == [x] + repeat(x, n - 1);
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert |repeat(x, n)| == n;

   |
26 |         assert |repeat(x, n)| == n;
   |                                    ^

ex.dfy(26,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert |repeat(x, n)| == n;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];
        assert |repeat(x, 1)| == 1;
    } else {
        // Inductive step
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert repeat(x, n) == [x] + repeat(x, n - 1);
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert |repeat(x, n)| == n;


   |
26 |         assert |repeat(x, n)| == n;
   |                                    ^

ex.dfy(26,35): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];
        assert |repeat(x, 1)| == 1;
    } else {
        // Inductive step
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert repeat(x, n) == [x] + repeat(x, n - 1);
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert |repeat(x, n)| == n;

        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;

   |
28 |         assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
   |                                                                ^

ex.dfy(28,63): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];
        assert |repeat(x, 1)| == 1;
    } else {
        // Inductive step
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert repeat(x, n) == [x] + repeat(x, n - 1);
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert |repeat(x, n)| == n;

        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
    }

   |
29 |     }
   |      ^

ex.dfy(29,5): Error: rbrace expected
1 parse errors detected in ex.dfy

SCORE
None
['    }\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];
        assert |repeat(x, 1)| == 1;
    } else {
        // Inductive step
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert repeat(x, n) == [x] + repeat(x, n - 1);
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert |repeat(x, n)| == n;

        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
    }
}

SCORE
1.0
['}\n']
TEXT
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];
        assert |repeat(x, 1)| == 1;
    } else {
        // Inductive step
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert repeat(x, n) == [x] + repeat(x, n - 1);
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert |repeat(x, n)| == n;

        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
    }
}
```

SCORE
1.0
['```\n']
CHOSEN SOLUTION
### Spec: In Dafny:
(1) Write a function `repeat` that takes an integer `x` and a natural number `n` as inputs, and returns a list of length `n` in which every element is `x`.
(2) Then write a lemma `repeat_correct` that checks that for any `x` and `n`, `repeat` returns a list of length `n` and that every element of the list is `x`.
### Hint: The length of a list or sequence `s` is `|s|`.
### Hint: In a specication, you can write `forall i :: 0 <= i < n ==> CONDITION`.

```dafny
function repeat(x: int, n: nat): seq<int>
    requires n > 0
    ensures |repeat(x, n)| == n
{
    if n == 1 then [x]
    else [x] + repeat(x, n - 1)
}

lemma repeat_correct(x: int, n: nat)
    requires n > 0
    ensures |repeat(x, n)| == n
    ensures forall i :: 0 <= i < n ==> repeat(x, n)[i] == x
{
    // Base case
    if n == 1 {
        assert repeat(x, 1) == [x];
        assert |repeat(x, 1)| == 1;
    } else {
        // Inductive step
        repeat_correct(x, n - 1);
        assert |repeat(x, n - 1)| == n - 1;
        assert forall i :: 0 <= i < n - 1 ==> repeat(x, n - 1)[i] == x;

        assert repeat(x, n) == [x] + repeat(x, n - 1);
        assert |repeat(x, n)| == 1 + |repeat(x, n - 1)|;
        assert |repeat(x, n)| == n;

        assert forall i :: 0 <= i < n ==> repeat(x, n)[i] == x;
    }
}
```


STATS

number of nodes: 29
number of gen nodes: 15 (including leaves: 4)
number of back nodes: 14 (including leaves: 11)

expansion count: 43 (including failed: 29)

cache stats {'hit': 72, 'miss': 103}
=====SUMMARY STATISTICS FOR ALL TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76, 110, 95, 122, 63, 123, 89, 89, 258]

Trial calls: [44, 38, 53, 51, 68, 26, 67, 45, 32, 175]


Time Statistics:

  Min: 63.00 sec, Max: 258.00 sec, Average: 112.60 sec, Standard Deviation: 51.67 sec

Call Statistics:

  Min: 26 calls, Max: 175 calls, Average: 59.90 calls, Standard Deviation: 40.46 calls

=====SUMMARY STATISTICS FOR NON_TIMED OUT TRIALS=====

Experiment: run.py for 10 trials

Trial times: [101, 76, 110, 95, 122, 63, 123, 89, 89, 258]

Trial calls: [44, 38, 53, 51, 68, 26, 67, 45, 32, 175]


Time Statistics:

  Min: 63.00 sec, Max: 258.00 sec, Average: 112.60 sec, Standard Deviation: 51.67 sec

Call Statistics:

  Min: 26 calls, Max: 175 calls, Average: 59.90 calls, Standard Deviation: 40.46 calls

To complete all experiments, 19 minutes and 25 seconds elapsed.