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Intuitionistic Type Theory - Extensional versus intensional | A Wisdom Archive on Intuitionistic Type Theory - Extensional versus intensional | | Intuitionistic Type Theory - Extensional versus intensional A selection of articles related to Intuitionistic Type Theory - Extensional versus intensional | |
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More material related to Intuitionistic Type Theory can be found here:
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Intuitionistic Type Theory, Intuitionistic Type Theory - <span class=texhtml>Π</span>-types, Intuitionistic Type Theory - <span class=texhtml>Σ</span>-types, Intuitionistic Type Theory - Categorical models of Type Theory, Intuitionistic Type Theory - Connectives of Type Theory, Intuitionistic Type Theory - Equality type, Intuitionistic Type Theory - Extensional versus intensional, Intuitionistic Type Theory - Finite types, Intuitionistic Type Theory - Formalisation of Type Theory, Intuitionistic Type Theory - Implementations of Type Theory, Intuitionistic Type Theory - Inductive types, Intuitionistic Type Theory - Universes, Typed lambda calculus, Curry-Howard isomorphism, Intuitionistic logic, Calculus of constructions, Per Martin-Löf, Type Theory
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ARTICLES RELATED TO Intuitionistic Type Theory - Extensional versus intensional | | | |  Intuitionistic Type Theory - Extensional versus intensional: Encyclopedia II - Intuitionistic Type Theory - Connectives of Type TheoryIn the context of Type Theory a connective is a way of constructing types, possibly using already given types. The basic connectives of Type Theory are:
Intuitionistic Type Theory - Π-types.
Π-types, also called dependent function types, generalize the normal function space to model functions whose result type may vary on their input. E.g. writing for n-tuples of real numbers, stands for the type of functions wh ...
See also:Intuitionistic Type Theory, Intuitionistic Type Theory - Connectives of Type Theory, Intuitionistic Type Theory - Π-types, Intuitionistic Type Theory - Σ-types, Intuitionistic Type Theory - Finite types, Intuitionistic Type Theory - Equality type, Intuitionistic Type Theory - Inductive types, Intuitionistic Type Theory - Universes, Intuitionistic Type Theory - Formalisation of Type Theory, Intuitionistic Type Theory - Categorical models of Type Theory, Intuitionistic Type Theory - Extensional versus intensional, Intuitionistic Type Theory - Implementations of Type Theory Read more here: » Intuitionistic Type Theory: Encyclopedia II - Intuitionistic Type Theory - Connectives of Type Theory |
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| | | | Intuitionistic Type Theory - Extensional versus intensional: Encyclopedia II - Intuitionistic Type Theory - Categorical models of Type Theory Using the language of category theory, Seely introduced the notion of a locally cartesian closed category (LCCC) as the basic model of Type Theory. This has been refined by Hofmann and Dybjer to Categories with Families or Categories with Attributes based on earlier work by Cartmell.
A category with families is a category C of contexts (in which the objects are contexts, and the context morphisms are substitutions), together with a functor T : C^op -> Fam(Set). Fam(Set) is the category in which the objects are pa ...
See also:Intuitionistic Type Theory, Intuitionistic Type Theory - Connectives of Type Theory, Intuitionistic Type Theory - Π-types, Intuitionistic Type Theory - Σ-types, Intuitionistic Type Theory - Finite types, Intuitionistic Type Theory - Equality type, Intuitionistic Type Theory - Inductive types, Intuitionistic Type Theory - Universes, Intuitionistic Type Theory - Formalisation of Type Theory, Intuitionistic Type Theory - Categorical models of Type Theory, Intuitionistic Type Theory - Extensional versus intensional, Intuitionistic Type Theory - Implementations of Type Theory Read more here: » Intuitionistic Type Theory: Encyclopedia II - Intuitionistic Type Theory - Categorical models of Type Theory |
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| | | | Intuitionistic Type Theory - Extensional versus intensional: Encyclopedia II - Intuitionistic Type Theory - Formalisation of Type Theory Type Theory is usually presented as a dependently typed lambda calculus, using the judgements:
, Γ is a well-formed context of typing assumptions.
, σ is a well-formed type in context Γ.
, t is a well-formed term of type σ in context Γ.
, σ and ...
See also:Intuitionistic Type Theory, Intuitionistic Type Theory - Connectives of Type Theory, Intuitionistic Type Theory - Π-types, Intuitionistic Type Theory - Σ-types, Intuitionistic Type Theory - Finite types, Intuitionistic Type Theory - Equality type, Intuitionistic Type Theory - Inductive types, Intuitionistic Type Theory - Universes, Intuitionistic Type Theory - Formalisation of Type Theory, Intuitionistic Type Theory - Categorical models of Type Theory, Intuitionistic Type Theory - Extensional versus intensional, Intuitionistic Type Theory - Implementations of Type Theory Read more here: » Intuitionistic Type Theory: Encyclopedia II - Intuitionistic Type Theory - Formalisation of Type Theory |
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