https://github.com/guidanoli/peg-coq

Formalizing PEGs and a well-formedness algorithm in Coq
https://github.com/guidanoli/peg-coq

coq lpeg parsing-expression-grammars well-formed

Last synced: 14 days ago
JSON representation

Formalizing PEGs and a well-formedness algorithm in Coq

• Host: GitHub
• URL: https://github.com/guidanoli/peg-coq
• Owner: guidanoli
• License: gpl-3.0
• Created: 2023-04-04T20:05:05.000Z (over 1 year ago)
• Default Branch: main
• Last Pushed: 2024-10-30T12:03:48.000Z (15 days ago)
• Last Synced: 2024-10-30T12:32:17.837Z (15 days ago)
• Topics: coq, lpeg, parsing-expression-grammars, well-formed
• Language: Coq
• Homepage:
• Size: 376 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • Changelog: CHANGELOG
  • License: LICENSE

Awesome Lists containing this project

README

        
## Formalization of PEGs using the Coq proof assistant

This repository formalizes the syntax and the semantics of [PEGs]

using the [Coq] proof assistant.

It also formalizes the algorithm implemented in [LPeg]

for detecting well-formed PEGs,

and proves that it terminates and is correct.

Correctness here implies in termination of the parsing procedure.

## Syntax

We define use the desugared syntax of PEGs

first established by (Ford, 2024).

It contains the empty pattern, terminals,

non-terminals, repetitions, not-predicates,

sequences, and choices.

From these, we can construct more complex patterns

such as character classes from choices,

and and-predicates from not-predicates.

This simplification helps us formalize PEGs

without losing expressiveness.

## Semantics

We define the match procedure both

as a fixed point function which takes

a gas counter and returns an optional result,

and an inductive predicate.

The fixed point definition is interesting

for proving termination,

and the inductive predicate is useful

for proving correctness,

and other complex results

which may benefit from proofs by induction.

## Well-formedness

We define the algorithm implemented in [LPeg]

that detects well-formed PEGs,

a subset of complete PEGs whose

detection is decidable.

Ford proved that, in the general case,

the problem of identifying complete PEGs

is undecidable, so this is a conservative

approach that ensures termination.

## Files

This repository contains some `.v` files:

- `PEG.v`: defines the syntax and the semantics of PEGs, and the well-formedness algorithm

- `Pigeonhole.v`: states and proves the pigeonhole principle

- `Strong.v`: states and proves the strong induction primitive

- `Suffix.v`: defines the suffix and proper suffix relations, and proves some results about them

[PEGs]: https://doi.org/10.1145/964001.964011

[Coq]: https://coq.inria.fr/

[LPeg]: https://www.inf.puc-rio.br/~roberto/lpeg/