DavidLeoni / makemath

A Python representation of MetaMath theorems and proofs

MakeMath

A Python representation of MetaMath theorems and proofs

DISCLAIMER: I'm no logician, just a programmer trying to figure out things. What follows may well be quite wrong.

The idea is to build proofs like you compose Python objects, and test/debug them like regular programs

Status: proof of concept (incomplete)

Expected benefits:

• syntax familiar to developers with no formal training of Python popular programming language
• you can debug proofs like they were code in regular IDEs
• if used in Jupyter, you should be able to interactively display proofs exploiting the many Python visualization libraries

Cons:

• we bring in all Python baggage, which could cause confusion
• if users' Python proofs are not checked carefully, they could write code which cannot be translated back to MetaMath

Current limitions (MANY):

• does not parse .mm databases
• proofs code is manually written, and only supports t=t first example from the book
• Metamath classes are not supported
• there is no way to go from Python proofs to Metamath ones
• does not exploit any Python feature which could help simplifying syntax (sets, comprehensions, functions, typing with mypy, ...)

Example

As found in test_example1.py:

from makemath import Var, expr, check_type, check_eq, provable, wff, wffv
from example1 import t,r,s,P,Q,tze,tpl,a1,a2,weq,wim, mp

# if test passes, you proved it !

def test_theorem():
    assert mp(a2(t), mp(a2(t), a1(tpl(t,tze()),t,t))) == provable(weq(t,t))

Testing:

Install dependencies:

python3 -m pip install --user requirements.txt 

Execute tests:

pytest