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Lambda calculus

In mathematical logic, the lambda calculus (also written as λ-calculus) is a formal system for expressing computation based on function abstraction and application using variable binding and substitution. Untyped lambda calculus, the topic of this article, is a universal machine, i.

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Overview

Definition

Explanation and applications

History

Motivation

Normal forms and confluence

Encoding datatypes

Additional programming techniques

Typed lambda calculus

Computability

Complexity

Lambda calculus and programming languages

Semantics

Variations and extensions

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Lambda calculus

Nodes149
Edges148
Triples291
Avg. degree1.99
Density0.013423
Components1

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Lambda calculus

Top relations

related to Further reading · 103
Lambda calculus → Abelson, ACM, Alonzo, Alonzo Church, American Journal, American Mathematical Society, An, An Introduction, April, Available, Barendregt, Benjamin, Bulletin, Calculus, Chris, Church, Church's Lambda-Notation, Combinatory Logic Archived, Communications, Computer Programs
related to External links · 34
Lambda calculus → Alligator Eggs, Allison, Animated ReductionL, Bret Victor, Calculus, Computerphile, David, EMS Press, Encyclopedia, Graham Hutton, Graphical Notation, Implementing, Internet Encyclopedia, Java, Keenan, Lambda, Lambda Animator, Lambda Calculi, Lambda CalculusHelmut Brandl, Lambda CalculusLCI Lambda Interpreter
see also · 21
Lambda calculus → An, Applicative, Bruijn, Curry, Formal, Howard, Let, LISP, Mathematics, Minimalism, Mock, Mockingbird, Rewriting, Rosser, Rules, Scheme, Study, The, Transformation, Treatment
related to Computability · 17
Lambda calculus → As, Building, Church, Church's, FALSE, Gödel, Gödel's, If, In, Kleene, More, See, Then, There, This, TRUE, Turing
related to Origin of the λ symbol · 11
Lambda calculus → According, Addison Jr, Cardone, Church, Church's, Dana Scott, Greek, Hindley, John, Scott, There
related to Recursion and fixed points · 11
Lambda calculus → As, For, If, It, Lambda, Other, Recursion, Since, This, Thus, What
has application · 9
Lambda calculus → For, Greek, In, Its, Lambda, On, One, Turing, Typed
related to history · 9
Lambda calculus → Alonzo Church, Church, In, Kleene, Lambda, Rosser, Stephen Kleene, Subsequently, The
related to Complexity · 8
Lambda calculus → Director, In, It, More, The, This, To, Turing
related to Normal forms and confluence · 7
Lambda calculus → By, Church, Considering, For, However, It, Rosser

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Important terminology

lambda calculus function displaystyle text church terms functions term one argument defined expression programming reduction typed example used abstraction β-reduction

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Lambda calculusis atyped formalism that uses the lambda-symbol0.90text
Lambda calculusis alanguage of a Cartesian closed category0.90text
Lambda calculusis abit tricky0.90text
.mw-parser-output .monospacedinstance ofthere are terms with no normal form0.80text
MLinstance ofthey can also be considered the more fundamental theory and untyped lambda calculus a special case with only one type.Typed lambda calculi are foundational programming languages…0.80text
Haskell andinstance ofthey can also be considered the more fundamental theory and untyped lambda calculus a special case with only one type.Typed lambda calculi are foundational programming languages…0.80text
more indirectlyinstance ofthey can also be considered the more fundamental theory and untyped lambda calculus a special case with only one type.Typed lambda calculi are foundational programming languages…0.80text
typed imperative programming languagesinstance ofthey can also be considered the more fundamental theory and untyped lambda calculus a special case with only one type.Typed lambda calculi are foundational programming languages…0.80text
the number of leftmost-outermost steps to normal forminstance ofIt is not known if optimal reduction implementations are reasonable when measured with respect to a reasonable cost model0.80text
but it has been shown for fragments of the lambda calculus that the optimal reduction algorithm is efficientinstance ofIt is not known if optimal reduction implementations are reasonable when measured with respect to a reasonable cost model0.80text
has at most a quadratic overhead compared to leftmost-outermostinstance ofIt is not known if optimal reduction implementations are reasonable when measured with respect to a reasonable cost model0.80text
futures to the lambda calculusinstance ofOne can add constructs0.80text

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