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.

See also

• SKI combinator calculus
• H.P. Barendregt's Lambda cube
• Jean-Yves Girard's System F
• Thierry Coquand's calculus of constructions
• Typed lambda calculus
• Curry-Howard isomorphism