Lambda Calculus

A formal logic developed by Alonzo Church and Stephen Kleene to address the computable number problem. In the lambda calculus,  is defined as the abstraction operator. Three theorems of lambda calculus are -conversion, -conversion, and -conversion. Lambda-reduction (also called lambda conversion) refers to all three.

REFERENCES

Barendregt, H. P. The Lambda Calculus. Amsterdam, Netherlands: North-Holland, 1981.

Hankin, C. Lambda Calculi: A Guide for Computer Scientists. Oxford, England: Oxford University Press, 1995.

Hindley, J. R. and Seldin, J. P.Introduction to Combinators and lambda-Calculus.Cambridge, England: Cambridge University Press, 1986.

Penrose, R. The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford, England: Oxford University Press, pp. 66-70, 1989.

Révész, G. E. Lambda-Calculus, Combinators, and Functional Programming. Cambridge, England: Cambridge University Press, 1988.

Seldin, J. P. and Hindley, J. R. (Eds.). To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism. New York: Academic Press, 1980.