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https://github.com/joom/wangsalgorithm
A classical propositional theorem prover in Haskell, using Wang's Algorithm.
https://github.com/joom/wangsalgorithm
haskell sequent-calculus theorem-prover wang-algorithm
Last synced: 3 months ago
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A classical propositional theorem prover in Haskell, using Wang's Algorithm.
- Host: GitHub
- URL: https://github.com/joom/wangsalgorithm
- Owner: joom
- License: mit
- Created: 2015-01-01T00:02:48.000Z (about 10 years ago)
- Default Branch: master
- Last Pushed: 2019-06-12T18:29:19.000Z (over 5 years ago)
- Last Synced: 2023-08-13T04:02:26.276Z (over 1 year ago)
- Topics: haskell, sequent-calculus, theorem-prover, wang-algorithm
- Language: Haskell
- Homepage:
- Size: 17.6 KB
- Stars: 35
- Watchers: 4
- Forks: 4
- Open Issues: 2
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
WangsAlgorithm [](http://travis-ci.org/joom/WangsAlgorithm)
==============
A propositional theorem prover in Haskell, using [Wang's Algorithm](http://www.cs.bham.ac.uk/research/projects/poplog/doc/popteach/wang), based on the sequent calculus (LK). Reading [a Prolog implementation](https://github.com/benhuds/Prolog) helped me understand it better.
## Usage
In order to use or compile the program you need to have [Stack](http://haskellstack.org) installed.
After you cloning the repository, go to the repository folder and do
```bash
stack install
```
Now you installed the program. You can run it like this:
```bash
wang --sequent "[(p->q)&(p->r)] |- [p->(q&r)]" --backend Text
```
Or shortly:
```bash
wang -s "[(p->q)&(p->r)] |- [p->(q&r)]" -b Text
```
You can also use `LaTeX` for an output.
Here's an example text proof for that:
```
Before: [((p) ⊃ (q)) ∧ ((p) ⊃ (r))] ⊢ [(p) ⊃ ((q) ∧ (r))]
Rule: AndLeft
-------------------
Before: [(p) ⊃ (q),(p) ⊃ (r)] ⊢ [(p) ⊃ ((q) ∧ (r))]
Rule: ImpliesRight
-------------------
Before: [(p) ⊃ (q),(p) ⊃ (r),p] ⊢ [(q) ∧ (r)]
Rule: AndRight
-------------------
First branch:
Before: [(p) ⊃ (q),(p) ⊃ (r),p] ⊢ [q]
Rule: ImpliesLeft
-------------------
First branch:
Before: [(p) ⊃ (r),p] ⊢ [p,q]
Rule: WeakeningLeft
-------------------
Before: [p] ⊢ [p,q]
Rule: WeakeningRight
-------------------
Before: [p] ⊢ [p]
Rule: Id
-------------------
End.
-------------------
Second branch:
Before: [q,(p) ⊃ (r),p] ⊢ [q]
Rule: WeakeningLeft
-------------------
Before: [q,p] ⊢ [q]
Rule: WeakeningLeft
-------------------
Before: [q] ⊢ [q]
Rule: Id
-------------------
End.
-------------------
-------------------
Second branch:
Before: [(p) ⊃ (q),(p) ⊃ (r),p] ⊢ [r]
Rule: ImpliesLeft
-------------------
First branch:
Before: [(p) ⊃ (r),p] ⊢ [p,r]
Rule: WeakeningLeft
-------------------
Before: [p] ⊢ [p,r]
Rule: WeakeningRight
-------------------
Before: [p] ⊢ [p]
Rule: Id
-------------------
End.
-------------------
Second branch:
Before: [q,(p) ⊃ (r),p] ⊢ [r]
Rule: ImpliesLeft
-------------------
First branch:
Before: [q,p] ⊢ [p,r]
Rule: WeakeningLeft
-------------------
Before: [p] ⊢ [p,r]
Rule: WeakeningRight
-------------------
Before: [p] ⊢ [p]
Rule: Id
-------------------
End.
-------------------
Second branch:
Before: [r,q,p] ⊢ [r]
Rule: WeakeningLeft
-------------------
Before: [r,p] ⊢ [r]
Rule: WeakeningLeft
-------------------
Before: [r] ⊢ [r]
Rule: Id
-------------------
End.
-------------------
-------------------
-------------------
Proof completed.
```
Here's the LaTeX output for the same sequent.
```
\begin{prooftree}
\AxiomC{} \RightLabel{\scriptsize $I$}
\UnaryInfC{$p\vdash p$} \RightLabel{\scriptsize $WR$}
\UnaryInfC{$p\vdash p,q$} \RightLabel{\scriptsize $WL$}
\UnaryInfC{$\left( p\supset r\right) ,p\vdash p,q$}
\AxiomC{} \RightLabel{\scriptsize $I$}
\UnaryInfC{$q\vdash q$} \RightLabel{\scriptsize $WL$}
\UnaryInfC{$q,p\vdash q$} \RightLabel{\scriptsize $WL$}
\UnaryInfC{$q,\left( p\supset r\right) ,p\vdash q$}
\RightLabel{\scriptsize $\supset L$}
\BinaryInfC{$\left( p\supset q\right) ,\left( p\supset
r\right) ,p\vdash q$} \AxiomC{}
\RightLabel{\scriptsize $I$} \UnaryInfC{$p\vdash p$}
\RightLabel{\scriptsize $WR$} \UnaryInfC{$p\vdash p,r$}
\RightLabel{\scriptsize $WL$}
\UnaryInfC{$\left( p\supset r\right) ,p\vdash p,r$}
\AxiomC{} \RightLabel{\scriptsize $I$}
\UnaryInfC{$p\vdash p$} \RightLabel{\scriptsize $WR$}
\UnaryInfC{$p\vdash p,r$} \RightLabel{\scriptsize $WL$}
\UnaryInfC{$q,p\vdash p,r$} \AxiomC{}
\RightLabel{\scriptsize $I$} \UnaryInfC{$r\vdash r$}
\RightLabel{\scriptsize $WL$} \UnaryInfC{$r,p\vdash r$}
\RightLabel{\scriptsize $WL$}
\UnaryInfC{$r,q,p\vdash r$}
\RightLabel{\scriptsize $\supset L$}
\BinaryInfC{$q,\left( p\supset r\right) ,p\vdash r$}
\RightLabel{\scriptsize $\supset L$}
\BinaryInfC{$\left( p\supset q\right) ,\left( p\supset
r\right) ,p\vdash r$}
\RightLabel{\scriptsize $\wedge R$}
\BinaryInfC{$\left( p\supset q\right) ,\left( p\supset
r\right) ,p\vdash \left( q\wedge r\right) $}
\RightLabel{\scriptsize $\supset R$}
\UnaryInfC{$\left( p\supset q\right) ,\left( p\supset
r\right) \vdash \left( p\supset \left( q\wedge
r\right) \right) $}
\RightLabel{\scriptsize $\wedge L$}
\UnaryInfC{$\left( \left( p\supset q\right) \wedge
\left( p\supset r\right) \right) \vdash \left(
p\supset \left( q\wedge r\right) \right) $}
\end{prooftree}
```
If you want to run the tests, use this command:
```bash
stack test
```
# Further Reading
* Hao Wang, 1960, "Toward Mechanical Mathematics"
* John McCarthy, 1961, "LISP 1.5 Programmer's Manual"
## License
The MIT License (MIT)
Copyright (c) 2014 Joomy Korkut