https://github.com/co-dan/bi-cutelim

Cut elimination for the logic of Bunched Implications (BI), and some extensions.
https://github.com/co-dan/bi-cutelim

coq formalization logic metatheory

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Cut elimination for the logic of Bunched Implications (BI), and some extensions.

• Host: GitHub
• URL: https://github.com/co-dan/bi-cutelim
• Owner: co-dan
• License: bsd-3-clause
• Created: 2021-06-18T15:32:45.000Z (over 3 years ago)
• Default Branch: main
• Last Pushed: 2023-07-27T09:27:48.000Z (over 1 year ago)
• Last Synced: 2024-11-06T08:44:13.432Z (3 months ago)
• Topics: coq, formalization, logic, metatheory
• Language: Coq
• Homepage:
• Size: 769 KB
• Stars: 2
• Watchers: 3
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
A semantic cut admissibility proof for the logic of Bunched Implications and extensions.

See the [preprint](https://groupoid.moe/pdf/cutelim-ext.pdf) for more details and information.

## Intro

We formalize the sequent calculus of BI and give an algebraic proof of

cut admissibility. We parametrize the calculus by an arbitrary

collection of "simple structural rules" (see `theories/seqcalc.v` for

the definition).

Structure (in the `theories` directory):

- `syntax.v`, `terms.v` -- formulas of BI and "bunched terms".

  A bunched term is essential a formula built up only from `∗/,` and

  `∧/;` and variables.

- `interp.v` -- interpretation of formulas and bunched terms in a BI algebra

- `seqcalc.v` -- sequent calculus + soundness

- `bunch_decomp.v` -- helpful lemmas about decompositions of bunches

- `seqcalc_height.v` -- the same sequent calculus, but with the notion of proof height.

  Includes proofs of invertibility of some of the rules.

- `algebra/bi.v`, `algebra/interface.v` -- BI algebras

- `algebra/from_closure.v` -- BI algebra from a closure operator

- `cutelim.v` -- the universal model for cut elimination

- `analytic_completion.v` -- the analytic completion for arbitary structural rules

There is also a formalization of the same method but for BI with an S4-like box modality.

See `seqcalc_s4.v`, `seqcalc_height_s4.v`, `interp_s4.v`, and `cutelim_s4.v` in the `theories` folder.

## Compilation

You will need a copy of std++ installed.

This version is tested with Coq 8.17 and std++ 1.8.0.

You can install the dependency with opam using `opam install --deps-only .` or the whole developement with `opam install .`

If you have std++ installed then you can compile the project with `make -jN` where `N` is the number of threads you want to use.

Compile the HTML docs with `make html`.

Note: this Coq developement is automatically tested for Coq versions 8.16 and 8.17, and we will try to support the two latest versions of Coq.

![CI workflow status](https://github.com/co-dan/BI-cutelim/actions/workflows/build.yml/badge.svg)

## Copyright

The Coq formalization is distributed under the BSD-3 licence.

Some code was adapted from the Iris project .