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• Intuitionistic_type_theory abstract "Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics based on the principles of mathematical constructivism. Intuitionistic type theory was introduced by Per Martin-Löf, a Swedish mathematician and philosopher, in 1972. Martin-Löf has modified his proposal a few times; his 1971 impredicative formulation was inconsistent as demonstrated by Girard's paradox. Later formulations were predicative. He proposed both intensional and extensional variants of the theory. For more detail see the section on Martin-Löf type theories below.Intuitionistic type theory is based on a certain analogy or isomorphism between propositions and types: a proposition is identified with the type of its proofs. This identification is usually called the Curry–Howard isomorphism, which was originally formulated for intuitionistic logic and simply typed lambda calculus. Type theory extends this identification to predicate logic by introducing dependent types, that is types which contain values.Type theory internalizes the interpretation of intuitionistic logic proposed by Brouwer, Heyting and Kolmogorov, the so-called BHK interpretation. The types in type theory play a similar role to sets in set theory but functions definable in type theory are always computable.".
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• Intuitionistic_type_theory wikiPageExternalLink tutorials.html.
• Intuitionistic_type_theory wikiPageExternalLink book.
• Intuitionistic_type_theory wikiPageExternalLink TTFP.
• Intuitionistic_type_theory wikiPageExternalLink 978-94-007-1735-0.
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• Intuitionistic_type_theory wikiPageWikiLink ATS_(programming_language).
• Intuitionistic_type_theory wikiPageWikiLink Agda_(programming_language).
• Intuitionistic_type_theory wikiPageWikiLink Andrey_Kolmogorov.
• Intuitionistic_type_theory wikiPageWikiLink Arend_Heyting.
• Intuitionistic_type_theory wikiPageWikiLink Boolean_data_type.
• Intuitionistic_type_theory wikiPageWikiLink Bottom_type.
• Intuitionistic_type_theory wikiPageWikiLink Brouwer–Heyting–Kolmogorov_interpretation.
• Intuitionistic_type_theory wikiPageWikiLink Calculus_of_constructions.
• Intuitionistic_type_theory wikiPageWikiLink Cartesian_closed_category.
• Intuitionistic_type_theory wikiPageWikiLink Cartesian_product.
• Intuitionistic_type_theory wikiPageWikiLink Category:Constructivism_(mathematics).
• Intuitionistic_type_theory wikiPageWikiLink Category:Dependently_typed_programming.
• Intuitionistic_type_theory wikiPageWikiLink Category:Intuitionism.
• Intuitionistic_type_theory wikiPageWikiLink Category:Logic_in_computer_science.
• Intuitionistic_type_theory wikiPageWikiLink Category:Type_theory.
• Intuitionistic_type_theory wikiPageWikiLink Category_of_families.
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• Intuitionistic_type_theory wikiPageWikiLink Coq.
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• Intuitionistic_type_theory wikiPageWikiLink Decision_problem.
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• Intuitionistic_type_theory wikiPageWikiLink Epigram_(programming_language).
• Intuitionistic_type_theory wikiPageWikiLink Existential_quantification.
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• Intuitionistic_type_theory wikiPageWikiLink Idris_(programming_language).
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• Intuitionistic_type_theory wikiPageWikiLink Intuitionism.
• Intuitionistic_type_theory wikiPageWikiLink Intuitionistic_logic.
• Intuitionistic_type_theory wikiPageWikiLink Jean-Yves_Girard.
• Intuitionistic_type_theory wikiPageWikiLink L._E._J._Brouwer.
• Intuitionistic_type_theory wikiPageWikiLink LEGO_(programming).
• Intuitionistic_type_theory wikiPageWikiLink Logical_conjunction.
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• Intuitionistic_type_theory wikiPageWikiLink Material_conditional.
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• Intuitionistic_type_theory wikiPageWikiLink Natural_number.
• Intuitionistic_type_theory wikiPageWikiLink Negation.
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• Intuitionistic_type_theory wikiPageWikiLink Path_(topology).
• Intuitionistic_type_theory wikiPageWikiLink Per_Martin-Löf.
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• Intuitionistic_type_theory wikiPageWikiLink Predicate_logic.
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• Intuitionistic_type_theory wikiPageWikiLink Set_theory.
• Intuitionistic_type_theory wikiPageWikiLink Setoid.
• Intuitionistic_type_theory wikiPageWikiLink Simply_typed_lambda_calculus.
• Intuitionistic_type_theory wikiPageWikiLink Sweden.
• Intuitionistic_type_theory wikiPageWikiLink System_F.
• Intuitionistic_type_theory wikiPageWikiLink System_U.
• Intuitionistic_type_theory wikiPageWikiLink Truth_value.
• Intuitionistic_type_theory wikiPageWikiLink Tuple.
• Intuitionistic_type_theory wikiPageWikiLink Type_system.
• Intuitionistic_type_theory wikiPageWikiLink Type_theory.
• Intuitionistic_type_theory wikiPageWikiLink Typed_lambda_calculus.
• Intuitionistic_type_theory wikiPageWikiLink Undecidable_problem.
• Intuitionistic_type_theory wikiPageWikiLink Unit_type.
• Intuitionistic_type_theory wikiPageWikiLink Universal_quantification.
• Intuitionistic_type_theory wikiPageWikiLink Value_(computer_science).
• Intuitionistic_type_theory wikiPageWikiLink Well-founded_relation.
• Intuitionistic_type_theory wikiPageWikiLinkText "1971 type theory".
• Intuitionistic_type_theory wikiPageWikiLinkText "Intuitionistic type theory".
• Intuitionistic_type_theory wikiPageWikiLinkText "Intuitionistic type theory#Equality type".
• Intuitionistic_type_theory wikiPageWikiLinkText "Intuitionistic type theory#Extensional versus intensional".
• Intuitionistic_type_theory wikiPageWikiLinkText "Intuitionistic type theory#Inductive types".
• Intuitionistic_type_theory wikiPageWikiLinkText "Intuitionistic_type_theory#Equality_type".
• Intuitionistic_type_theory wikiPageWikiLinkText "dependent sum type".
• Intuitionistic_type_theory wikiPageWikiLinkText "equality type".
• Intuitionistic_type_theory wikiPageWikiLinkText "identity type".

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