# Maxixe

*Work-in-progress. Subject to change in backwards-incompatible ways.*

Maxixe is a simple proof-checking language. Given a proof written out fully and explicitly (including all rules of inference), a computer can check if it is valid or not.

Here is an example of a valid proof in propositional logic written in Maxixe:

```
given
Modus_Ponens = impl(P, Q) ; P |- Q
Simplification = and(P, Q) |- Q
Commutativity_of_Conjunction = and(P, Q) |- and(Q, P)
Premise = |- and(p, impl(p, q))
show
q
proof
Step_1 = and(p, impl(p, q)) by Premise
Step_2 = and(impl(p, q), p) by Commutativity_of_Conjunction with Step_1
Step_3 = impl(p, q) by Simplification with Step_1
Step_4 = p by Simplification with Step_2
Step_5 = q by Modus_Ponens with Step_3, Step_4
qed
```

For Maxixe's design goals, related work, and discussion, see doc/Design.md.

For a description of the language, see doc/Maxixe.md.

For examples of proofs witten in Maxixe, see doc/Examples.md.

The reference implementation of Maxixe, called `maxixe`

, is written in Python 2.7.
Simply add the `bin`

directory of this repository to your executable search path
and run it on a text file containing your proof, like

```
maxixe my_proof.maxixe
```

It will output `ok`

if the proof is valid. Otherwise it will display a (currently
rather poor) error message.

### Disclaimer

I am not prepared to claim that, given an invalid proof, Maxixe will never mistakenly tell you that it is valid.

However, if you find such a proof, please do open a bug report about it.

Note that since Maxixe requires that you supply all the axioms and rules of inference used in a proof, it is entirely possible to give it an inconsistent system of logic in which anything can be proved — but that's not quite the same thing as what I'm talking about. Such a proof is still valid relative to its axioms and rules of inference.

But on that note, I am also not prepared to claim that all of the rules of inference I've used in the example proofs Maxixe are consistent (or otherwise fit for writing proofs in), either.

So, if you find a flaw in one of the example proofs, please do open a bug report about that as well.

##
Commit History
@logic-syntax-sugar
`git clone https://git.catseye.tc/Maxixe/`

- Experimentally support some syntactic sugar for logic notation. Chris Pressey 6 years ago
- Fix the definition of UG in the number theory proofs. Chris Pressey 7 years ago
- Add definition of nonlocal to spec and refactor example proofs. Chris Pressey 7 years ago
- Allow hole in Universal Generalization to be plugged. Chris Pressey 7 years ago
- Simplify further, now that we can. Chris Pressey 7 years ago
- Internally, the steps of a proof are their own "neutral" block. Chris Pressey 7 years ago
- Improve error subsystem. Chris Pressey 7 years ago
- Make internals more Pythonic. Document the operations on Terms. Chris Pressey 7 years ago
- Fix formatting in Socrates example and illustrate a problem. Chris Pressey 7 years ago
- Sugar also in the rule: `case`...`end` can be omitted if only 1. Chris Pressey 7 years ago