xaviershay / axiomator

axiomator

An experiment in creating a proof-assistant DSL for applying mathematical axioms to expressions. The following program:

import Axiomator

main = runSolution $ do
  initial "a(b + c)"

  apply axiomDistribute
  apply axiomCommuteSum

Generates the following report, listing the result of applying each axiom and a summary of all axioms used:

1. Identity:                     a = a
2. Distributive law:             a*(b+c) = ab+ac
3. Commutative law for addition: a+b = b+a

a(b + c) ; Identity
ab + ac  ; Distributive law
ac + ab  ; Commutative law for addition

Sub-expressions can be "focused" on, with _ able to be used as a placeholder to avoid repeating complex formulae:

import Axiomator

main = runSolution $ do
  initial "a(b + sin(c))"

  focus "b + _" $ apply axiomCommuteSum

Resulting in:

1. Identity:                     a = a
2. Commutative law for addition: a+b = b+a

a(b + sin(c)) ; Identity
a(sin(c) + b) ; Commutative law for addition