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Intuitionistic Type Theory - Formalisation of Type Theory | | Intuitionistic Type Theory - Formalisation of Type Theory: 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 | | | Intuitionistic Type Theory, Intuitionistic Type Theory - Π-types, Intuitionistic Type Theory - Σ-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 | | |
| | | Intuitionistic Type Theory: Encyclopedia II - Intuitionistic Type Theory - Formalisation of Type Theory
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 τ are equal types in context Γ.
- , t and u are equal terms of type σ in context Γ.
Of special importance is the conversion rule, which says that given and then .
Other related archives1972, BHK interpretation, Booleans, Brouwer, Calculus of constructions, Cartesian product, Coq, Curry Howard isomorphism, Curry-Howard isomorphism, Dependent ML, Epigram, Girard, Heyting, Intuitionistic logic, Kolmogorov, Per Martin-Löf, Swedish, System F, Type Theory, Typed lambda calculus, calculus of constructions, category theory, commutative, conjunction, connective, decidable, dependent types, disjoint union, disjunction, existential quantification, extensional, function space, functional programming language, implication, impredicative, induction, intensional, intuitionistic logic, logic, mathematical constructivism, mathematician, natural number, natural numbers, negation, philosopher, predicate logic, predicative, primitive recursion, programming languages, propositional logic, propositions, propositions as types principle, real number, real numbers, set theory, simply typed lambda calculus, tuple, type checking, typed lambda calculus, types, undecidable, unit type, universal quantification, well-founded
 Adapted from the Wikipedia article "Formalisation of Type Theory", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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