nonproc

Homework assignments for Nonprocedural Programming at Matfyz, Charles University in Prague.

Why? The reason I decided to publish my solutions to these "simple" educational tasks is my belief that one of the most efficient learning method is learning by examples, and I hope that students consulting Google and Stack Overflow for solutions for help with their own homework might come across this repository and get inspiration :)

List of tasks

1. (HW 1-1 Prolog) Implement division of two numbers in Prolog in succesor notation hw1-1_arithmetics.pl (includes all basic arithmetical operations)

   add(+X, +Y, ?Z)
   sub(+X, +Y, ?Z)
   mod(+X, +Y, ?Z)
   div(+X, +Y, ?D, ?R)    % x div y = d, x mod y = r
   log2(+X, ?N)           % n is a base integer of log_2(x)

2. (HW 1-2 Prolog) Implement predicate for n-th Fibonacci's number hw1-2_generalisedFibbonacci.pl (includes "generalised version" enabling to define first two elements of the sequence)

   fib(+N, ?F)    % f is the n-th Fibbonaci's number
   gFib(+N, +F0, +F1, ?R)    % r is the n-th "Fibonacci's number" in a sequence starting with _f0_ and _f1_

3. (HW 2-1 Prolog) Implement list flattening.

   flat(+List, ?Result)
   ====================
   % Examples
   ?- flat([], R).
   R = [].
   
   ?- flat([[]], R).
   R = [].
   
   ?- flat([a,b,c], R).
   R = [a,b,c].
   
   ?- flat([a,[[],b,[]],[c,[d]]], R).
   R = [a,b,c,d].

4. (HW 2-2 Prolog) Implement (rectangular) matrix transposition.

   transp(+Matrix, ?Result)
   ========================
   % Examples
   ?-  transp([[a,b],[c,d],[e,f]], R).
   R = [[a,c,e],[b,d,f]]

5. (HW 4-1 Haskell) Implement functions on, while and pairwise:

   1. on f gapplies g on both arguments and then applies f

      on :: (b -> b -> c) -> (a -> b) -> a -> a -> c
      > (max `on` abs) (-5) 4
      5

   2. while c f a applies a given function f on its argument a as long as the argument satisfies condition c

      while :: (a -> Bool) -> (a -> a) -> a -> a
      > while (<100) (*2) 1
      128

   3. pairwise f applies function f on pairs in a given list and results puts in a new list; if the list length is odd, the last element is not changed

      pairwise :: (a -> a -> a) -> [a] -> [a]
      > pairwise (+) [1..9]
      [3,7,11,15,9]

6. sortWith op xs sorts a list according to a given operator, ciSort sorts an array of strings case insensitively

   sortWith  :: (a -> a -> Bool) -> [a] -> [a]
   > sortWith (<) [10,9..1]
   [1,2,3,4,5,6,7,8,9,10]
   
   ciSort :: [String] -> [String]
   > ciSort ["Sort", "me"]
   ["me","Sort"]