https://github.com/elliottt/auto

Decision procedure for intuitionistic logic
https://github.com/elliottt/auto

logic rust

Last synced: 23 days ago
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Decision procedure for intuitionistic logic

• Host: GitHub
• URL: https://github.com/elliottt/auto
• Owner: elliottt
• Created: 2021-06-12T17:30:09.000Z (over 3 years ago)
• Default Branch: main
• Last Pushed: 2024-01-15T22:40:39.000Z (10 months ago)
• Last Synced: 2024-05-22T21:33:11.511Z (6 months ago)
• Topics: logic, rust
• Language: Rust
• Homepage:
• Size: 104 KB
• Stars: 0
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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• awesome-rust-formalized-reasoning - auto - decision procedure for intuitionistic logic. (Projects / Libraries)

README

        
# auto

An implementation of [CONTRACTION-FREE SEQUENT CALCULI FOR INTUITIONISTIC

LOGIC](https://www.jstor.org/stable/2275431) by Roy Dyckhoff.

## Commands

* `help` will give a short summary of each command.

* The `?` command (which unfortunately requires its full argument to be quoted)

  will derive a term in the lambda calculus for the given logical formula, if

  it's possible to do so.

* `?!` will derive a term and apply simplification rules to turn it into

  something a bit more readable.

* `prove` will somewhat clunkily display the proof tree constructed that's used

  to derive the terms of the lambda calculus.

```

auto> ? (A \/ B) -> (A -> C) -> (B -> C) -> C

λ a: A ∨ B. λ b: A → C. λ c: B → C.

  match a {

    Left d ->

      let e = b d in e

    Right f ->

      let g = c f in g

  }

auto> ?! (A \/ B) -> (A -> C) -> (B -> C) -> C

λ a: A ∨ B. λ b: A → C. λ c: B → C.

  match a {

    Left d -> b d

    Right f -> c f

  }

auto> prove (A \/ B) -> (A -> C) -> (B -> C) -> C

          ------------- Axiom

          C, A, B → C ⇒ C

        ------------- IMP-VAR-L

        A, B → C, A → C ⇒ C

          ------------- Axiom

          C, B, A → C ⇒ C

        ------------- IMP-VAR-L

        B, B → C, A → C ⇒ C

      ------------- OR-L

      B → C, A → C, A ∨ B ⇒ C

    ------------- IMP-R

    A → C, A ∨ B ⇒ (B → C) → C

  ------------- IMP-R

  A ∨ B ⇒ (A → C) → (B → C) → C

------------- IMP-R

A ∨ B → (A → C) → (B → C) → C

auto>

```

## References

I came across a [stack

overflow](https://stackoverflow.com/questions/10217931/how-does-djinn-work)

question a long time back when wondering how the haskell program `djinn` worked.

Lennart Augustsson gave a helpful answer, and through a series of jumps that I

don't remember now, I came across the paper [CONTRACTION-FREE SEQUENT CALCULI

FOR INTUITIONISTIC LOGIC](https://www.jstor.org/stable/2275431). That paper

gives a pretty clear outline of the decision procedure that Lennart mentions in

his reply. After reading the paper I decided to implement `auto` to put it into

practice and learn some more rust in the process.

## TODO

It would be really nice if the input language knew about ADT declarations and

type aliases, as that would push it up to feature parity with `djinn`. There's a

start on this in the form of the `data` and `env` commands, but it's fun to play

around with in its current state, so I'm happy to call it done.

The REPL doesn't currently support history or editing commands, which makes

interacting with it a chore. Fixing these problems would be great.