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feat: formalize regular expression -> εNFA #20648

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feat: formalize regular expression -> εNFA #20648

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@anthonyde anthonyde commented Jan 10, 2025 •
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The file Computability/RegularExpressionsToEpsilonNFA.lean contains a formal definition of Thompson's method for constructing an εNFA from a RegularExpression and a proof of its correctness.

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@anthonyde
feat(Data/List/ReduceOption): add replicate theorems
c159aff 
These theorems make it easier to prove statements about
`List.reduceOption`, building up to a more general theorem,
`reduceOption_eq_concat_iff`, which is useful for inductive proofs.
@anthonyde
feat(Computability/EpsilonNFA): define path relation
63bc4b3 
`Path` enables path-based reasoning in proofs involving `εNFA`.
@anthonyde
feat: formalize regular expression -> εNFA
03b40d4 
The file `Computability/RegularExpressionsToEpsilonNFA.lean` contains a
formal definition of Thompson's method for constructing an `εNFA` from a
`RegularExpression` and a proof of its correctness.
@anthonyde
Fix lint errors
ed1c597 
Definitions are either marked private (details of the automaton
definition) or have documentation strings.

Unneeded `[DecidableEq α]` declarations are removed.
@anthonyde anthonyde added the t-computability Computability theory (TMs, DFAs, languages, grammars, etc) label Jan 10, 2025
@github-actions github-actions bot added the new-contributor This PR was made by a contributor with at most 5 merged PRs. Welcome to the community! label Jan 10, 2025
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github-actions bot commented Jan 10, 2025 •
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PR summary dbc35ee318

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.Computability.EpsilonNFA 1
Mathlib.Computability.RegularExpressionsToEpsilonNFA (new file) 682

Declarations diff

+ BinSt
+ Path
+ Path_append_iff
+ Path_nil_eq
+ Path_singleton_iff
+ St
+ accept_final
+ accepts_Path_iff
+ char_accepts
+ comp_accepts
+ comp_embed_left
+ comp_embed_right
+ comp_one_way
+ comp_split
+ epsilon_accepts
+ evalFrom_Path_iff
+ mem_evalFrom_choice_iff
+ mem_εClosure_choice_iff
+ plus_accepts
+ plus_embed_left
+ plus_embed_right
+ plus_no_cross_left
+ plus_no_cross_right
+ star_accepts
+ star_concat
+ star_cons
+ star_embed
+ star_end
+ star_no_restart
+ star_parts
+ star_split
+ step_accept_empty
+ toεNFA
+ toεNFA_correct
+ zero_accepts
+ εClosure_Path_iff

You can run this locally as follows 
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@mathlib4-dependent-issues-bot mathlib4-dependent-issues-bot added the blocked-by-other-PR This PR depends on another PR to Mathlib (this label is automatically managed by a bot) label Jan 10, 2025
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mathlib4-dependent-issues-bot commented Jan 10, 2025 •
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This PR/issue depends on:

@anthonyde
Use suggested theorem names
2c55724 
`reduceOption_replicate_of_none` -> `reduceOption_replicate_none`
`reduceOption_eq_nil_replicate_iff` -> `reduceOption_eq_nil_iff`
`reduceOption_eq_singleton_replicate_iff` ->
  `reduceOption_eq_singleton_iff`
@anthonyde
Merge branch 'anthonyde/list-replicate' into anthonyde/enfa-path
aa239fe
@anthonyde
Fix for changes in #20644
e73681c 
Theorems were renamed.
@anthonyde
Merge branch 'anthonyde/enfa-path' into anthonyde/re-to-enfa
e6cc76f
@anthonyde
Fix for changes in #20644
dbc35ee 
Theorems were renamed.
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