ivo/README.md

James Martin's Lambda Calculus

This is a simple implementation of the untyped lambda calculus with an emphasis on clear, readable Haskell code.

Usage

Type in your expression at the prompt: >> . The expression will be evaluated to normal form and then printed. Exit the prompt with Ctrl-c (or equivalent).

Example session

>> let D = (\x. x x) in let F = (\f. f (f y)) in D (F (\x. x))
(y y)
>> let T = (\f x. f (f x)) in (\f x. T (T (T (T T))) f x) (\x. x) y
y
>> (\x y z. x y) y
(\y'. (\z. (y y')))
>> ^C

Notation

Conventional Lambda Calculus notation applies, with the exception that variable names are multiple characters long, \ is used in lieu of λ to make it easier to type, and spaces are used to separate variables rather than commas.

• Variable names are alphanumeric, beginning with a letter.
• Outermost parentheses may be dropped: M N is equivalent to (M N).
• Applications are left-associative: M N P may be written instead of ((M N) P).
• The body of an abstraction or let expression extends as far right as possible: \x. M N means \x.(M N) and not (\x. M) N.
• A sequence of abstractions may be contracted: \foo. \bar. \baz. N may be abbreviated as \foo bar baz. N.
• Variables may be bound using let expressions: let x = N in M is syntactic sugar for (\x. N) M.