Lambda calculus

In computer science, the lambda calculus is a formal system designed to investigate function definition, function application, and recursion. It was introduced by Alonzo Church and Stephen Cole Kleene in the 1930s; Church used the lambda calculus in 1936 to give a negative answer to the Entscheidungsproblem. The calculus can be used to cleanly define what is a computable function. The question of whether two lambda calculus expressions are equivalent cannot be solved by a general algorithm, and this was the first question, even before the halting problem, for which undecidability could be proved. Lambda calculus has greatly influenced functional programming languages, especially Lisp.

References

• Abelson, Harold & Gerald Jay Sussman. Structure and Interpretation of Computer Programs. The MIT Press. ISBN 0262510871.
• Barendregt, Henk, The lambda calculus, its syntax and semantics, North-Holland (1984), is the comprehensive reference on the (untyped) lambda calculus; see also the paper Introduction to Lambda Calculus.
• Church, Alonzo, An unsolvable problem of elementary number theory, American Journal of Mathematics, 58 (1936), pp. 345–363. This paper contains the proof that the equivalence of lambda expressions is in general not decidable.
• Punit,Gupta, Amit & Ashutosh Agte, Untyped lambda-calculus, alpha-, beta- and eta- reductions and recursion
• Henz, Martin, The Lambda Calculus. Formally correct development of the Lambda calculus.
• Kleene, Stephen, A theory of positive integers in formal logic, American Journal of Mathematics, 57 (1935), pp. 153–173 and 219–244. Contains the lambda calculus definitions of several familiar functions.
• Larson, Jim, An Introduction to Lambda Calculus and Scheme. A gentle introduction for programmers.

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