About: Simply typed lambda calculus

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The simply typed lambda calculus, a formof type theory, is a typed interpretation of the lambda calculus with only one type constructor that builds function types. It is the canonical and simplest example of a typed lambda calculus. The simply typed lambda calculus was originally introduced by Alonzo Church in 1940 as an attempt to avoid paradoxical use of the untyped lambda calculus.

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rdfs:label	Λ-λογισμός με απλούς τύπους (el) Cálculo lambda simplemente tipado (es) Simply typed lambda calculus (en) Cálculo lambda simplesmente tipado (pt) Просто типизированное лямбда-исчисление (ru) 简单类型λ演算 (zh)
rdfs:comment	Просто типизированное лямбда-исчисление (простое типизированное лямбда-исчисление, лямбда-исчисление с простыми типами, система ) — система типизированного лямбда-исчисления, в которой лямбда-абстракции приписывается специальный «стрелочный» тип. Эта система была предложена Алонзо Чёрчем в 1940 году. Для близкого к лямбда-исчислению формализма комбинаторной логики похожая система рассматривалась Хаскеллом Карри в 1934 году. (ru) 简单类型 lambda 演算是连接词只有 (函数类型)的有类型 lambda 演算。这使它成为规范的、在很多方面是最简单的有类型 lambda 演算的例子。简单类型也被用来称呼对简单类型 lambda 演算的扩展比如积、或自然数(系统 T)甚至完全的递归(如)。相反的，介入了多态类型(如系统F)或依赖类型(如逻辑框架)的系统不被当作是简单类型。简单类型 lambda 演算最初由阿隆佐·邱奇在 1940 年介入来尝试避免无类型 lambda 演算的悖论性使用。 (zh) Ο λ-λογισμός με απλούς τύπους είναι μια θεωρίας τύπων, είναι μια ερμηνεία τύπων του λ-λογισμού με ένα μοναδικό κατασκευαστή τύπων (type constructor): , ο οποίος κατασκευάζει . Είναι το κανονικό και το πιο απλό παράδειγμα λ-λογισμού με τύπους, και εμφανίζει πολλές επιθυμητές και ενδιαφέρουσες ιδιότητες. (el) El cálculo lambda simplemente tipado es una teoría de tipos basada en el cálculo de lambda con un único , , que construye . Es el ejemplo canónico y más sencillo de un cálculo lambda tipado. El cálculo lambda simplemente tipado fue originalmente introducido por Alonzo Church en el 1940 como un intento de evitar la aparición de paradojas en el cálculo lambda sin tipos. (es) The simply typed lambda calculus, a formof type theory, is a typed interpretation of the lambda calculus with only one type constructor that builds function types. It is the canonical and simplest example of a typed lambda calculus. The simply typed lambda calculus was originally introduced by Alonzo Church in 1940 as an attempt to avoid paradoxical use of the untyped lambda calculus. (en) O cálculo lambda simplesmente tipado, ou cálculo lambda com tipagem simples, é um modelo da teoria dos tipos que adiciona o conceito de tipagem ao cálculo lambda. Isso é possível com adição de apenas um elemento (o construtor de tipos: ) para construir tipos de funções. Esse é o exemplo mais simples e canônico de um cálculo lambda com tipagem. O cálculo lambda simplesmente tipado foi introduzido originalmente por Alonzo Church em 1940 como uma tentativa de evitar o uso paradoxal do , o qual mostrou várias propriedades interessantes e desejadas. (pt)
dcterms:subject	Lambda calculus Theory of computation Type theory
Wikipage page ID	1986011 (xsd:integer)
Wikipage revision ID	1122932982 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartesian product Normalisation by evaluation Typed lambda calculus Principal type Beta reduction Dependent type Lambda calculus Apply Currying Call by name Call by value Decidability (logic) Intuitionistic logic Combinatory logic Morphism Coproduct Equivalence class Operational semantics Linear type system Simply typed lambda calculus Closed monoidal category Completeness (logic) Function space Function type Functor Parametric polymorphism Turing complete Typing environment Backus–Naur form Category of sets Type system Type theory Eta reduction Minimal logic Alonzo Church Church encoding Dialectica interpretation Natural deduction Type erasure Product (category theory) Recursion Tautology (logic) Theory of computation Type theory Joachim Lambek LF (logical framework) Lambda calculus Topos System F Polynomial Grzegorczyk hierarchy Typing rule Natural number Set (mathematics) Set theory Type safety Type inference Untyped lambda calculus Type inhabitation Evaluation strategy Fixed-point combinator Internal language Type constructor Normalization property (lambda-calculus) Elementary recursive Church numeral Equational theory Strong normalization Cartesian closed categories Final object Programming language for Computable Functions Recursive type Object (category theory) Unification (computing) Curry–Howard isomorphism Hindley–Milner type inference
Link from a Wikipage to an external page	ftp://ftp.cs.ru.nl/pub/CompMath.Found/HBK.ps http://www.lfcs.inf.ed.ac.uk/reports/98/ECS-LFCS-98-381/
sameAs	Simply typed lambda calculus Simply typed lambda calculus Simply typed lambda calculus Simply typed lambda calculus Simply typed lambda calculus

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