samarthkulshrestha / nox

a simple mathematical expression transformer.

nox

A simple expression transformer, not inspired by coq.

quickstart

$ cargo run examples/add.nox

usage

expression

expression syntax:

<expression> ::= <symbol> | <functor>
<symbol> ::= [a-zA-Z0-9]+
<functor> ::= <symbol> ( [<expression>],* )

rules and shapes

the two main entities of the languare are rules and shapes. a rule defines pattern (head) and it's corresponding substitution (body). the rule definition has the following syntax:

rule <name:symbol> <head:expression> = <body:expression>

here is an example of a rule that swaps elements of a pair:

rule swap swap(pair(a, b)) = pair(b, a)

shaping is a process of sequential applying of rules to an expression transforming it into a different expression. shaping has the following syntax:

shape <expression>
  ... sequence of rule applications ...
done

for example here is how you shape expression swap(pair(f(a), g(b))) with the swap rule defined above:

shape swap(pair(f(a), g(b)))
  apply swap
done

the result of this shaping is pair(g(b), f(a)).

anonymous rules

you don't have to define a rule to use it in shaping. you can directly describe it after the apply keyword:

shape swap(pair(f(a), g(b)))
  apply rule swap(pair(a, b)) = pair(b, a)
done