Results 11 to 20 of about 13,143,476 (301)
Manuscrito, 2023 It is often claimed that the theory of function levels proposed by Frege in Grundgesetze der Arithmetik anticipates the hierarchy of types that underlies Church’s simple theory of types.
Bruno Bentzen
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Decidability of conversion for type theory in type theory [PDF]
Proceedings of the ACM on Programming Languages, 2017 Type theory should be able to handle its own meta-theory, both to justify its foundational claims and to obtain a verified implementation. At the core of a type checker for intensional type theory lies an algorithm to check equality of types, or in other words, to check whether two types are convertible.
Andreas Abel 0001 +2 more
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Type theory in a type theory with quotient inductive types [PDF]
, 2017 Type theory (with dependent types) was introduced by Per Martin-Löf with the intention of providing a foundation for constructive mathematics. A part of constructive mathematics is type theory itself, hence we should be able to say what type theory is using the formal language of type theory. In addition, metatheoretic properties of type theory such as
Kaposi, Ambrus
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Mind, 1896 THE 'TYPE-THEORY' OF REACTION The 'type-theory' of reaction (21) (-
Baldwin, James B.
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Type Theory with Opposite Types: A Paraconsistent Type Theory
Logic Journal of the IGPL, 2021 Abstract A version of intuitionistic type theory is extended with opposite types, allowing a different formalization of negation and obtaining a paraconsistent type theory ($\textsf{PTT} $). The rules for opposite types in $\textsf{PTT} $ are based on the rules of the so-called constructible falsity.
Juan Carlos Agudelo Agudelo +1 more
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Dualized Simple Type Theory [PDF]
Logical Methods in Computer Science, 2017 We propose a new bi-intuitionistic type theory called Dualized Type Theory (DTT). It is a simple type theory with perfect intuitionistic duality, and corresponds to a single-sided polarized sequent calculus.
Harley Eades III +2 more
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Multi-level Contextual Type Theory [PDF]
Electronic Proceedings in Theoretical Computer Science, 2011 Contextual type theory distinguishes between bound variables and meta-variables to write potentially incomplete terms in the presence of binders. It has found good use as a framework for concise explanations of higher-order unification, characterize ...
Mathieu Boespflug, Brigitte Pientka
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Cellular Cohomology in Homotopy Type Theory [PDF]
Logical Methods in Computer Science, 2020 We present a development of cellular cohomology in homotopy type theory. Cohomology associates to each space a sequence of abelian groups capturing part of its structure, and has the advantage over homotopy groups in that these abelian groups of many ...
Ulrik Buchholtz, Kuen-Bang Hou
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Type theories in category theory
CoRR, 2021 We introduce basic notions in category theory to type theorists, including comprehension categories, categories with attributes, contextual categories, type categories, and categories with families along with additional discussions that are not very closely related to type theories by listing definitions, lemmata (with detailed, diagram-rich proofs ...
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Inductive Types in Homotopy Type Theory [PDF]
2012 27th Annual IEEE Symposium on Logic in Computer Science, 2012 Homotopy type theory is an interpretation of Martin-Löf's constructive type theory into abstract homotopy theory. There results a link between constructive mathematics and algebraic topology, providing topological semantics for intensional systems of type theory as well as a computational approach to algebraic topology via type theory-based proof ...
Awodey, S, GAMBINO, Nicola, Sojakova, K.
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