https://github.com/ekdohibs/foundations-of-proof-systems-project

Project for the "Foundation of proof systems" course of the MPRI.
https://github.com/ekdohibs/foundations-of-proof-systems-project

coq

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Project for the "Foundation of proof systems" course of the MPRI.

• Host: GitHub
• URL: https://github.com/ekdohibs/foundations-of-proof-systems-project
• Owner: Ekdohibs
• License: mit
• Created: 2017-12-06T18:06:24.000Z (about 7 years ago)
• Default Branch: master
• Last Pushed: 2017-12-06T18:21:23.000Z (about 7 years ago)
• Last Synced: 2024-11-01T10:42:25.661Z (3 months ago)
• Topics: coq
• Language: Coq
• Homepage:
• Size: 17.6 KB
• Stars: 1
• Watchers: 4
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
This project is the one requested for the MPRI course "Foundation of proof

systems" (MPRI 2.7.1).

--

It contains two independant Coq proofs:

- arith.v contains a formalization of Peano and Heyting arithmetic, a proof that

Heyting arithmetic is consistent in Coq (with reflection of Heyting arithmetic),

and the proof through Friedman-translation that Peano arithmetic is

Pi_0^2-conservative over Heyting arithmetic.

See the [task description (in French)](http://www.enseignement.polytechnique.fr/informatique/MPRI/2-7-1/arith.pdf) ([mirror](http://web.archive.org/web/20171206181709/http://www.enseignement.polytechnique.fr/informatique/MPRI/2-7-1/arith.pdf)).

- while.v contains verified computation of the weakest preconditions for the

language While. See the [task description (in French)](http://www.enseignement.polytechnique.fr/informatique/MPRI/2-7-1/wp.pdf) ([mirror](http://web.archive.org/web/20171206181734/http://www.enseignement.polytechnique.fr/informatique/MPRI/2-7-1/wp.pdf)).