https://github.com/konn/lk-proof-assistant
Simple Proof assistant for LK Calculus (First-Order logic)
https://github.com/konn/lk-proof-assistant
Last synced: about 1 month ago
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Simple Proof assistant for LK Calculus (First-Order logic)
- Host: GitHub
- URL: https://github.com/konn/lk-proof-assistant
- Owner: konn
- License: other
- Created: 2012-09-30T14:09:13.000Z (over 12 years ago)
- Default Branch: master
- Last Pushed: 2013-03-04T14:09:53.000Z (about 12 years ago)
- Last Synced: 2025-03-24T21:38:54.696Z (about 2 months ago)
- Language: Haskell
- Size: 188 KB
- Stars: 6
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Installation
> $ cabal install
If compilation fails by GHC's bug, try `cabal clean` and run `cabal install` again.
# Usage
```
$ prover
|- ((P -> Q) -> P) -> P
----------------------
Goal: |- ((P → Q) → P) → P
> right
----------------------
Goal: (P → Q) → P |- P
> left 0 0
----------------------
Goal: |- P, P → Q
> right
----------------------
Goal: P |- P, Q
> weakenR
complete: P |- P
----------------------
Goal: P |-
> :r
----------------------
Goal: (P → Q) → P |- P
> contractR
----------------------
Goal: (P → Q) → P |- P, P
> left 0
***invalid command: left 0
----------------------
Goal: (P → Q) → P |- P, P
> left 0 1
----------------------
Goal: |- P, P → Q
> right
----------------------
Goal: P |- P, Q
> weakenR
complete: P |- P
complete: P |- P
\AxiomC{}\UnaryInfC{$P\vdash{}P$}\RightLabel{\scriptsize{\sc{WeakenR}}}\UnaryInfC{$P\vdash{}P, Q$}\RightLabel{\scriptsize{\sc{$\to$-Right}}}\UnaryInfC{$\vdash{}P, P\to{}Q$}\AxiomC{}\UnaryInfC{$P\vdash{}P$}\RightLabel{\scriptsize{\sc{$\to$-Left}}}\BinaryInfC{$\left({}P\to{}Q\right){}\to{}P\vdash{}P, P$}\RightLabel{\scriptsize{\sc{ContractR}}}\UnaryInfC{$\left({}P\to{}Q\right){}\to{}P\vdash{}P$}\RightLabel{\scriptsize{\sc{$\to$-Right}}}\UnaryInfC{$\vdash{}\left({}\left({}P\to{}Q\right){}\to{}P\right){}\to{}P$}
```
Output tex code can be compiled with [bussproofs.sty](http://www.math.ucsd.edu/~sbuss/ResearchWeb/bussproofs/index.html).
Above example generates following proof tree.
