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In type theory, a branch of mathematical logic, in a given typed calculus, the type inhabitation problem for this calculus is the following problem: given a type and a typing environment , does there exist a -term M such that ? With an empty type environment, such an M is said to be an inhabitant of .

Attributes	Values
rdfs:label	住性 (型理論) (ja) Type inhabitation (en) 类型居留问题 (zh)
rdfs:comment	In type theory, a branch of mathematical logic, in a given typed calculus, the type inhabitation problem for this calculus is the following problem: given a type and a typing environment , does there exist a -term M such that ? With an empty type environment, such an M is said to be an inhabitant of . (en) 型理論において、型住性問題(type inhabitation problem)とは、型と型環境が与えられたとき、を満足する項tが存在するか否かの判定問題である。そのような項tが存在するとき、項tは型の住人であるといい、型は有項であるという。 (ja) 在简单类型lambda演算中，类型居留（Type inhabitation）问题是如下问题：给定一个类型，是否存在一个 -项 M 使得对于某个类型环境有？在空的类型环境中，如果回答是肯定的，则 M 被称为的居留元（inhabitant）。因为在简单类型的 lambda 演算中类型对应于极小蕴涵逻辑(参见 Curry-Howard 同构)，一个类型有一个居留元，当且仅当它是极小蕴涵逻辑的重言式。证明了在简单类型λ演算中类型居留问题是的。 (zh)
dcterms:subject	Lambda calculus Type theory
Wikipage page ID	14703193 (xsd:integer)
Wikipage revision ID	1120040038 (xsd:integer)
Link from a Wikipage to another Wikipage	Lambda calculus Richard Statman Decision problem Intuitionistic logic PSPACE-complete Mathematical logic Simply typed lambda calculus Typing environment Type theory Tautology (logic) Type theory System F Second-order logic Pure type system PSPACE-hard Curry-Howard Curry–Howard isomorphism
sameAs	Type inhabitation Type inhabitation Type inhabitation Type inhabitation Type inhabitation
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Type-theory-stub
has abstract	In type theory, a branch of mathematical logic, in a given typed calculus, the type inhabitation problem for this calculus is the following problem: given a type and a typing environment , does there exist a -term M such that ? With an empty type environment, such an M is said to be an inhabitant of . (en) 型理論において、型住性問題(type inhabitation problem)とは、型と型環境が与えられたとき、を満足する項tが存在するか否かの判定問題である。そのような項tが存在するとき、項tは型の住人であるといい、型は有項であるという。 (ja) 在简单类型lambda演算中，类型居留（Type inhabitation）问题是如下问题：给定一个类型，是否存在一个 -项 M 使得对于某个类型环境有？在空的类型环境中，如果回答是肯定的，则 M 被称为的居留元（inhabitant）。因为在简单类型的 lambda 演算中类型对应于极小蕴涵逻辑(参见 Curry-Howard 同构)，一个类型有一个居留元，当且仅当它是极小蕴涵逻辑的重言式。证明了在简单类型λ演算中类型居留问题是的。 (zh)
prov:wasDerivedFrom	wikipedia-en:Type_inhabitation?oldid=1120040038&ns=0
page length (characters) of wiki page	1816 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Type_inhabitation
is Link from a Wikipage to another Wikipage of	Intersection type discipline Simply typed lambda calculus Empty type Type system Type theory Logical framework Hindley–Milner type system Automath Pure type system Type inhabitation problem
is Wikipage redirect of	Type inhabitation problem
is foaf:primaryTopic of	wikipedia-en:Type_inhabitation

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