untyped-lambda-calculus

A simple implementation of the untyped lambda calculus as an exercise.

This implementation lacks many features necessary to be useful, for example let bindings, built-in functions, binding free variables, or a good REPL. This project purely exists as an exercise and is not intended for general use. I will make useful programming languages in the future, but this is not one of them.

Usage

Type in your expression at the prompt: >> . The result of the evaluation of that expression will then be printed out. Exit the prompt with Ctrl-C (or however else you kill a program in your terminal).

Bound variables will be printed followed by a number representing the number of binders between it and its definition for disambiguation. This is not guaranteed not to capture free variables.

Examples

>> (\D F I. D (F I)) (\x. x x) (\f. f (f y)) (\x. x)
y y
>> \x. \y. y x
\x. \y. y:0 x:1
>>

Syntax

• Variables are alphanumeric, beginning with a letter.
• Applications are left-associative, and parentheses are not necessary.
• Lambdas are represented by \\, bind as far right as possible, and parentheses are not necessary.

Examples

• Variables: x, abc, D, fooBar, f10
• Applications: (\x. x x) y, a b, ((g f) y)
• Lambdas: \x. N, \x y. y, (\x. f x)