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There is a considerable body of programming idioms for lambda calculus. Many of these were originally developed in the context of using lambda calculus as a foundation for programming language semantics, effectively using lambda calculus as a low-level programming language. Because several programming languages include the lambda calculus (or ...
The Y combinator is an implementation of a fixed-point combinator in lambda calculus. Fixed-point combinators may also be easily defined in other functional and imperative languages. The implementation in lambda calculus is more difficult due to limitations in lambda calculus. The fixed-point combinator may be used in a number of different areas:
A Calculus of Mobile Processes, Part I (PostScript) (by Milner, Parrow, and Walker) shows a scheme for combinator graph reduction for the SKI calculus in pages 25–28. the Nock programming language may be seen as an assembly language based on SK combinator calculus in the same way that traditional assembly language is based on Turing machines ...
System F (also polymorphic lambda calculus or second-order lambda calculus) is a typed lambda calculus that introduces, to simply typed lambda calculus, a mechanism of universal quantification over types. System F formalizes parametric polymorphism in programming languages, thus forming a theoretical basis for languages such as Haskell and ML.
A redex [1] (one says also β-redex) is a term of the lambda calculus of the form (λ x. t) u. If a term has the shape (λ x. t) u 1... u n it is said to be a head redex. A head normal form is a term of the lambda calculus which is not a head redex. [a] A head reduction is a (non empty) sequence of contractions of a term which contracts head ...
Anonymous functions originate in the work of Alonzo Church in his invention of the lambda calculus, in which all functions are anonymous, in 1936, before electronic computers. [2] In several programming languages, anonymous functions are introduced using the keyword lambda , and anonymous functions are often referred to as lambdas or lambda ...
Going further, for every proof in the logic, there was a matching function (term) in the programming language. One of Curry's examples was the correspondence between simply typed lambda calculus and intuitionistic logic. [2] Predicate logic is an extension of propositional logic, adding quantifiers.
2 Lambda calculus. 3 Combinatory logic. 4 Intuitionistic logic. ... Lambda programming; Static scoping; Higher-order function; Referential transparency; Lambda calculus