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  2. Lambda calculus - Wikipedia

    en.wikipedia.org/wiki/Lambda_calculus

    Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. [3] Its namesake, the Greek letter lambda (λ), is used in lambda expressions and lambda terms to denote binding a variable in a function.

  3. Lambda calculus definition - Wikipedia

    en.wikipedia.org/wiki/Lambda_calculus_definition

    Lambda calculus is a formal mathematical system based on lambda abstraction and function application. Two definitions of the language are given here: a standard definition, and a definition using mathematical formulas.

  4. Simply typed lambda calculus - Wikipedia

    en.wikipedia.org/wiki/Simply_typed_lambda_calculus

    In the 1930s Alonzo Church sought to use the logistic method: [a] his lambda calculus, as a formal language based on symbolic expressions, consisted of a denumerably infinite series of axioms and variables, [b] but also a finite set of primitive symbols, [c] denoting abstraction and scope, as well as four constants: negation, disjunction, universal quantification, and selection respectively ...

  5. Fixed-point combinator - Wikipedia

    en.wikipedia.org/wiki/Fixed-point_combinator

    In this case particular lambda terms (which define functions) are considered as values. "Running" (beta reducing) the fixed-point combinator on the encoding gives a lambda term for the result which may then be interpreted as fixed-point value. Alternately, a function may be considered as a lambda term defined purely in lambda calculus.

  6. de Bruijn index - Wikipedia

    en.wikipedia.org/wiki/De_Bruijn_index

    In mathematical logic, the de Bruijn index is a tool invented by the Dutch mathematician Nicolaas Govert de Bruijn for representing terms of lambda calculus without naming the bound variables. [1] Terms written using these indices are invariant with respect to α-conversion, so the check for α-equivalence is the same as that for syntactic ...

  7. Church encoding - Wikipedia

    en.wikipedia.org/wiki/Church_encoding

    Lambda calculus is usually interpreted as using ... Using a lambda calculus calculator, the above expression reduces to 3, using normal order. ... Wikipedia® is a ...

  8. SKI combinator calculus - Wikipedia

    en.wikipedia.org/wiki/SKI_combinator_calculus

    It can be likened to a reduced version of the untyped lambda calculus. It was introduced by Moses Schönfinkel [1] and Haskell Curry. [2] All operations in lambda calculus can be encoded via abstraction elimination into the SKI calculus as binary trees whose leaves are one of the three symbols S, K, and I (called combinators).

  9. Beta normal form - Wikipedia

    en.wikipedia.org/wiki/Beta_normal_form

    In the lambda calculus, a beta redex is a term of the form: [3] [4] (.). A redex is in head position in a term , if has the following shape (note that application has higher priority than abstraction, and that the formula below is meant to be a lambda-abstraction, not an application):