jbutcher5 / lambda-calculus

A minimal lambda calculus reducer.

Lambda Calculus Interpreter

A basic lambda calculus interpreter.

Syntax

Rather than the standard lambda calculus syntax λx.y x the equivelant for lci is \x y -> x. This is for three main reasons: it's easier to parse, it's easier type and it's easier to read.

Constants

All assignment operations are ran during in the parsing process. For example TRUE = \x y -> x will lexed and then parsed and this will be stored in a hash map. These tokens will then be removed. This "feature" was more of an oversight than anything and maybe fixed in the future.

Examples

1. Logic (if true and true a else b)

TRUE = \x y -> x
FALSE = \x y -> y
AND = \x y -> x y (\x y -> y)
RESULT = AND TRUE TRUE

RESULT a b

TRUE = \x y -> x
FALSE = \x y -> y
AND = \x y -> x y (\x y -> y)
RESULT = AND TRUE TRUE

RESULT a b

((\x y -> x y (\x y -> y))) ((\x y -> x)) ((\x y -> x)) a b
(\x y -> x y (\x y -> y)) ((\x y -> x)) ((\x y -> x)) a b
(\x y -> x y (\x y -> y)) (\x y -> x) ((\x y -> x)) a b
(\x y -> x y (\x y -> y)) (\x y -> x) (\x y -> x) a b
(\y -> (\x y -> x) y (\x y -> y)) (\x y -> x) a b
(\x y -> x) (\x y -> x) (\x y -> y) a b
(\y -> (\x y -> x)) (\x y -> y) a b
(\x y -> x) a b
(\y -> a) b
a