Results 21 to 30 of about 837,747 (262)
Idempotents in intensional type theory [PDF]
Logical Methods in Computer Science, 2017 We study idempotents in intensional Martin-L\"of type theory, and in particular the question of when and whether they split. We show that in the presence of propositional truncation and Voevodsky's univalence axiom, there exist idempotents that do not ...
Michael Shulman
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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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A dependent nominal type theory [PDF]
Logical Methods in Computer Science, 2012 Nominal abstract syntax is an approach to representing names and binding pioneered by Gabbay and Pitts. So far nominal techniques have mostly been studied using classical logic or model theory, not type theory. Nominal extensions to simple, dependent and
James Cheney
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Quantum Gauge Field Theory in Cohesive Homotopy Type Theory [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We implement in the formal language of homotopy type theory a new set of axioms called cohesion. Then we indicate how the resulting cohesive homotopy type theory naturally serves as a formal foundation for central concepts in quantum gauge field theory.
Urs Schreiber, Michael Shulman
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W-types in homotopy type theory [PDF]
Mathematical Structures in Computer Science, 2014 We will give a detailed account of why the simplicial sets model of the univalence axiom due to Voevodsky also models W-types. In addition, we will discuss W-types in categories of simplicial presheaves and an application to models of set theory.
van den Berg, B., Moerdijk, I.
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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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Visualizing Type-Checking Proofs: An Educational Web-Based System for an Extended Simply Typed Lambda Calculus [PDF]
Computer Science Journal of MoldovaUnderstanding simply typed lambda calculus is essential for learning type systems and formal semantics, but its abstract concepts are often challenging.
Ján Perháč, Vladyslav Futrak
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Explicit Substitutions for Contextual Type Theory [PDF]
Electronic Proceedings in Theoretical Computer Science, 2010 In this paper, we present an explicit substitution calculus which distinguishes between ordinary bound variables and meta-variables. Its typing discipline is derived from contextual modal type theory.
Andreas Abel, Brigitte Pientka
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Guarded Cubical Type Theory [PDF]
Journal of Automated Reasoning, 2018 This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning with coinductive types. We wish to implement GDTT with decidable
Lars Birkedal +5 more
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Web-Based Questionnaires for Type Theory Course [PDF]
Acta Electrotechnica et Informatica, 2017 This paper describes our effort on the usage of modern information and communication technologies as well as innovation process in the field of teaching.
Daniel MIHÁLYI +3 more
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