Maxixe

Version 0.2 | Entry @ catseye.tc | See also: See also: Philomath ∘ LCF-style-ND ∘ Madison

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, and runs under (at least) Python 2.7.18 and Python 3.8.10. To use maxixe, 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 the definitions that it is using, even if those definitions are flawed.

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.