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   Articles with "type theory" as a keyword



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An Adequacy Theorem for Dependent Type Theory

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recommendations! Published in 2018 at "Theory of Computing Systems"

DOI: 10.1007/s00224-018-9879-9

Abstract: We present a domain model of dependent type theory and use it to prove basic metatheoretic properties. In particular, we prove that two convertible terms have the same Böhm tree. The method used is reminiscent… read more here.

Keywords: adequacy theorem; theory; type theory; theorem dependent ... See more keywords

Expressing ‘the structure of’ in homotopy type theory

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recommendations! Published in 2017 at "Synthese"

DOI: 10.1007/s11229-017-1569-7

Abstract: As a new foundational language for mathematics with its very different idea as to the status of logic, we should expect homotopy type theory to shed new light on some of the problems of philosophy… read more here.

Keywords: type theory; homotopy type; type; mathematics ... See more keywords
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The Justification of Identity Elimination in Martin-Löf’s Type Theory

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recommendations! Published in 2017 at "Topoi"

DOI: 10.1007/s11245-017-9509-1

Abstract: On the basis of Martin-Löf’s meaning explanations for his type theory a detailed justification is offered of the rule of identity elimination. Brief discussions are thereafter offered of how the univalence axiom fares with respect… read more here.

Keywords: theory; type theory; justification; martin ... See more keywords
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Finiteness and rational sequences, constructively*

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recommendations! Published in 2017 at "Journal of Functional Programming"

DOI: 10.1017/s0956796817000041

Abstract: Abstract Rational sequences are possibly infinite sequences with a finite number of distinct suffixes. In this paper, we present different implementations of rational sequences in Martin–Löf type theory. First, we literally translate the above definition… read more here.

Keywords: finiteness rational; lists backpointers; type theory; sequences constructively ... See more keywords

Cubical Agda: A dependently typed programming language with univalence and higher inductive types

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recommendations! Published in 2021 at "Journal of Functional Programming"

DOI: 10.1017/s0956796821000034

Abstract: Abstract Proof assistants based on dependent type theory provide expressive languages for both programming and proving within the same system. However, all of the major implementations lack powerful extensionality principles for reasoning about equality, such… read more here.

Keywords: dependently typed; higher inductive; univalence; type theory ... See more keywords

Gradual type theory

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recommendations! Published in 2021 at "Journal of Functional Programming"

DOI: 10.1017/s0956796821000125

Abstract: Abstract Gradually typed languages are designed to support both dynamically typed and statically typed programming styles while preserving the benefits of each. Sound gradually typed languages dynamically check types at runtime at the boundary between… read more here.

Keywords: type theory; gradual type; semantics; eta equality ... See more keywords

Model structure on the universe of all types in interval type theory

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recommendations! Published in 2020 at "Mathematical Structures in Computer Science"

DOI: 10.1017/s0960129520000213

Abstract: Abstract Model categories constitute the major context for doing homotopy theory. More recently, homotopy type theory (HoTT) has been introduced as a context for doing syntactic homotopy theory. In this paper, we show that a… read more here.

Keywords: model; type theory; universe types; model structure ... See more keywords

Symmetric monoidal smash products in homotopy type theory

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recommendations! Published in 2024 at "Mathematical Structures in Computer Science"

DOI: 10.1017/s0960129524000318

Abstract: Abstract In homotopy type theory, few constructions have proved as troublesome as the smash product. While its definition is just as direct as in classical mathematics, one quickly realises that in order to define and… read more here.

Keywords: homotopy type; smash; smash products; symmetric monoidal ... See more keywords
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Groupoidal realizability for intensional type theory

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recommendations! Published in 2024 at "Mathematical Structures in Computer Science"

DOI: 10.1017/s0960129524000343

Abstract: Abstract We develop realizability models of intensional type theory, based on groupoids, wherein realizers themselves carry non-trivial (non-discrete) homotopical structure. In the spirit of realizability, this is intended to formalize a homotopical BHK interpretation, whereby… read more here.

Keywords: intensional type; groupoid; realizability; type theory ... See more keywords

Preface: Advances in Homotopy Type Theory

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recommendations! Published in 2024 at "Mathematical Structures in Computer Science"

DOI: 10.1017/s0960129524000410

Abstract: Abstract We give a brief overview of the special issue of MSCS “Advances in Homotopy Type Theory.” read more here.

Keywords: preface advances; homotopy type; advances homotopy; type theory ... See more keywords

A topological reading of coinductive predicates in dependent type theory

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recommendations! Published in 2025 at "Mathematical Structures in Computer Science"

DOI: 10.1017/s0960129525100182

Abstract: Abstract In the context of dependent type theory, we show that coinductive predicates have an equivalent topological counterpart in terms of coinductively generated positivity relations, introduced by G. Sambin to represent closed subsets in point-free… read more here.

Keywords: coinductive predicates; type; dependent type; topological reading ... See more keywords