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Introduced by Alonzo Church and his student Stephen Cole Kleene in the 1930s to

study computable functions.

A (very simple) formal system for defining functions and their operational meanings,

yet is shown to be as powerful as other systems.

This project aims to be a journey of discovery from the foundations of computing to the first commercial functional language on an industrial strength platform.

Blog: http://fsharpcode.blogspot.com/

Recommended Reading

Programming F#

Lambda-Calculus, Combinators, and Functional Programming

Lambda Calculus Interpreter:

Identity

Lambda Calculus interpreter 0.0.0.0 > (λx.x) (λy.y) (λy.y)

Church Numerals

Lambda Calculus interpreter 0.0.0.0 > (λf.λx.x) (λf.(λx.x)) > (λn.λf.λx.(f (n f x))) (λf.λx.x) (λf.(λx.(f x))) > (λn.λf.λx.(f (n f x))) (λf.λx.(f x)) (λf.(λx.(f (f x)))) > (λn.λf.λx.(f (n f x))) (λf.λx.(f (f x))) (λf.(λx.(f (f (f x))))) > (λn.λf.λx.(f (n f x))) (λf.λx.(f (f (f x)))) (λf.(λx.(f (f (f (f x))))))

Addition

Lambda Calculus interpreter 0.0.0.0 > (λm.λn.λf.λx.((m f) (n f x))) (λh.λx.(h (h x))) (λg.λx.(g (g (g x)))) (λf.(λx.(f (f (f (f (f x))))))) > (λm.λn.λf.λx.((m f) (n f x))) (λh.λx.(h (h (h (h x))))) (λg.λx.(g (g (g (g (g (g x))))))) (λf.(λx.(f (f (f (f (f (f (f (f (f (f x))))))))))))

Last edited Sep 9, 2009 at 11:23 PM by holoed, version 16