Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory, the latter abbreviated as MLTT) is a type theory and an alternative foundation of mathematics.
Intuitionistic type theory was created by Per Martin-Löf, a Swedish mathematician and philosopher, who first published it in 1972. There are multiple versions of the type theory: Martin-Löf proposed both intensional and extensional variants of the theory and early impredicative versions, shown to be inconsistent by Girard's paradox, gave way to predicative versions. However, all versions keep the core design of constructive logic using dependent types.
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λ-calculus of Alonzo Church Intuitionistictypetheory of Per Martin-Löf Most computerized proof-writing systems use a typetheory for their foundation. A...
systems Arity or type, the number of operands a function takes Type, any proposition or set in the intuitionistictypetheoryType, of an entire function...
dependent type is a type whose definition depends on a value. It is an overlapping feature of typetheory and type systems. In intuitionistictypetheory, dependent...
science, homotopy typetheory (HoTT) refers to various lines of development of intuitionistictypetheory, based on the interpretation of types as objects to...
calculus and beta reduction in the typed lambda calculus. This provides the foundation for the intuitionistictypetheory developed by Per Martin-Löf, and...
types, which became known as intuitionistictypetheory or Martin-Löf typetheory. Martin-Löf's theory uses inductive types to represent unbounded data...
Heyting arithmetic Impredicativity Intuitionistictypetheory Law of excluded middle Ordinal analysis Set theory Subcountability Troelstra, A. S., van...
familiar induction principle for natural numbers. W-types are well-founded types in intuitionistictypetheory (ITT). They generalize natural numbers, lists...
Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical...
Martin-Löf for a treatment of the concept of assertion inside intuitionistictypetheory, and by Carlo Dalla Pozza, with a proposal of a formal pragmatics...
proofs and programs, and such logical systems as Per Martin-Löf's intuitionistictypetheory, and Thierry Coquand and Gérard Huet's calculus of constructions...
various ways of interpreting intuitionistic logic, including the Brouwer–Heyting–Kolmogorov interpretation. See also Intuitionistic logic § Semantics. Multi-valued...
occupants of armoured vehicles. Intuitionistictypetheory, other name of Martin-Löf TypeTheory Intensional typetheory ITT Inc. (formerly International...
Peter Dybjer, "The Interpretation of IntuitionisticTypeTheory in Locally Cartesian Closed Categories—an Intuitionistic Perspective", Electronic Notes in...
programming. In the 1980s, Per Martin-Löf developed intuitionistictypetheory (also called constructive typetheory), which associated functional programs with...
base of intuitionistictypetheory, the calculus of constructions and the logical framework (LF), a pure lambda calculus with dependent types. Based on...
08467. Per Martin-Löf, Intuitionistictypetheory, 1980. Anne Sjerp Troelstra, Metamathematical investigation of intuitionistic arithmetic and analysis...
semantics, the intuitionistic existential quantifier and intuitionistictypetheory. combining these, discussion of the intuitionistictheory of real numbers...
and its Cubical typetheory. "Identity Type". nLab. Retrieved 19 January 2022. Martin-Löf, Per (June 1980). IntuitionisticTypeTheory (PDF). Streicher...
as natural deduction, can be directly interpreted in its intuitionistic version as a typed variant of the model of computation known as lambda calculus...
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