Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application...
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A typed lambda calculus is a typed formalism that uses the lambda-symbol ( λ {\displaystyle \lambda } ) to denote anonymous function abstraction. In this...
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simply typed lambda calculus ( λ → {\displaystyle \lambda ^{\to }} ), a form of type theory, is a typed interpretation of the lambda calculus with only one...
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Lambda calculus is a formal mathematical system based on lambda abstraction and function application. Two definitions of the language are given here:...
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Knights of the Lambda Calculus is a semi-fictional organization of expert Lisp and Scheme hackers. The name refers to the lambda calculus, a mathematical...
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Combinatory logic (redirect from Combinator calculus)
computation. Combinatory logic can be viewed as a variant of the lambda calculus, in which lambda expressions (representing functional abstraction) are replaced...
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intuitionistic version as a typed variant of the model of computation known as lambda calculus. The Curry–Howard correspondence is the observation that there is an...
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System F (redirect from Second order lambda calculus)
polymorphic lambda calculus or second-order lambda calculus) is a typed lambda calculus that introduces, to simply typed lambda calculus, a mechanism...
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Dependent type (redirect from ΛΠ-calculus)
extensional. In 1934, Haskell Curry noticed that the types used in typed lambda calculus, and in its combinatory logic counterpart, followed the same pattern...
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systems of typed lambda calculus including the simply typed lambda calculus, Jean-Yves Girard's System F, and Thierry Coquand's calculus of constructions...
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Verse (programming language) (section Lambda calculus)
shares several similarities with lambda calculus, particularly in how it handles functions and data. In lambda calculus, functions are first-class citizens...
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interpretation Curry–Howard correspondence Linear logic Game semantics Typed lambda calculus Typed and untyped languages Type signature Type inference Datatype...
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the predicative calculus of inductive constructions (which removes some impredicativity). The CoC is a higher-order typed lambda calculus, initially developed...
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(also written lambda cube) is a framework introduced by Henk Barendregt to investigate the different dimensions in which the calculus of constructions...
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Church encoding (category Lambda calculus)
representing data and operators in the lambda calculus. The Church numerals are a representation of the natural numbers using lambda notation. The method is named...
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Fixed-point combinator (category Lambda calculus)
{\displaystyle Y=\lambda f.\ (\lambda x.f\ (x\ x))\ (\lambda x.f\ (x\ x))} (Here we use the standard notations and conventions of lambda calculus: Y is a function...
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to computational theory Kappa calculus, a reformulation of the first-order fragment of typed lambda calculus Rho calculus, introduced as a general means...
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Church–Rosser theorem (category Lambda calculus)
In lambda calculus, the Church–Rosser theorem states that, when applying reduction rules to terms, the ordering in which the reductions are chosen does...
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logic and computer science, lambda is used to introduce anonymous functions expressed with the concepts of lambda calculus. Lambda indicates an eigenvalue...
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Expression (mathematics) (section Lambda calculus)
basis for lambda calculus, a formal system used in mathematical logic and the theory of programming languages. The equivalence of two lambda expressions...
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Scheme (programming language) (section Lambda calculus)
evaluation of "closed" Lambda expressions in LISP and ISWIM's Lambda Closures. van Tonder, André (1 January 2004). "A Lambda Calculus for Quantum Computation"...
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mathematical logic and computer science, the lambda-mu calculus is an extension of the lambda calculus introduced by Michel Parigot. It introduces two...
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version of the untyped lambda calculus. It was introduced by Moses Schönfinkel and Haskell Curry. All operations in lambda calculus can be encoded via abstraction...
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and algebraic laws, that is, to the algebraic study of data types. Lambda calculus-based languages (such as Lisp, ISWIM, and Scheme) are in actual practice...
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foundations of theoretical computer science. He is best known for the lambda calculus, the Church–Turing thesis, proving the unsolvability of the Entscheidungsproblem...
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the lambda calculus and Turing machines are equivalent models of computation, showing that the lambda calculus is Turing complete. Lambda calculus forms...
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Church, the λ-calculus is strong enough to describe all mechanically computable functions (see Church–Turing thesis). Lambda-calculus is thus effectively...
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Canonical form (section Lambda calculus)
system. In the untyped lambda calculus, for example, the term ( λ x . ( x x ) λ x . ( x x ) ) {\displaystyle (\lambda x.(xx)\;\lambda x.(xx))} does not have...
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Reduction strategy (redirect from Reduction strategy (lambda calculus))
z)((\lambda w.www)(\lambda w.www)(\lambda w.www)(\lambda w.www))\\\rightarrow &(\lambda x.z)((\lambda w.www)(\lambda w.www)(\lambda w.www)(\lambda w.www)(\lambda...
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predates even the development of programming languages themselves. The lambda calculus, developed by Alonzo Church and Stephen Cole Kleene in the 1930s, is...
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