2 Search Results for "Frey, Jonas"

Document
DOI: 10.4230/LIPIcs.FSCD.2019.31
Cubical Syntax for Reflection-Free Extensional Equality

Authors: Jonathan Sterling, Carlo Angiuli, and Daniel Gratzer

Published in: LIPIcs, Volume 131, 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)

Abstract
We contribute XTT, a cubical reconstruction of Observational Type Theory [Altenkirch et al., 2007] which extends Martin-Löf’s intensional type theory with a dependent equality type that enjoys function extensionality and a judgmental version of the unicity of identity proofs principle (UIP): any two elements of the same equality type are judgmentally equal. Moreover, we conjecture that the typing relation can be decided in a practical way. In this paper, we establish an algebraic canonicity theorem using a novel extension of the logical families or categorical gluing argument inspired by Coquand and Shulman [Coquand, 2018; Shulman, 2015]: every closed element of boolean type is derivably equal to either true or false.
Cite as

Jonathan Sterling, Carlo Angiuli, and Daniel Gratzer. Cubical Syntax for Reflection-Free Extensional Equality. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 31:1-31:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{sterling_et_al:LIPIcs.FSCD.2019.31,
  author =	{Sterling, Jonathan and Angiuli, Carlo and Gratzer, Daniel},
  title =	{{Cubical Syntax for Reflection-Free Extensional Equality}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{31:1--31:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-107-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{131},
  editor =	{Geuvers, Herman},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2019.31},
  URN =		{urn:nbn:de:0030-drops-105387},
  doi =		{10.4230/LIPIcs.FSCD.2019.31},
  annote =	{Keywords: Dependent type theory, extensional equality, cubical type theory, categorical gluing, canonicity}
}
Document
DOI: 10.4230/LIPIcs.TLCA.2015.196
Realizability Toposes from Specifications

Authors: Jonas Frey

Published in: LIPIcs, Volume 38, 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)

Abstract
We investigate a framework of Krivine realizability with I/O effects, and present a method of associating realizability models to specifications on the I/O behavior of processes, by using ad- equate interpretations of the central concepts of pole and proof-like term. This method does in particular allow to associate realizability models to computable functions. Following recent work of Streicher and others we show how these models give rise to triposes and toposes.
Cite as

Jonas Frey. Realizability Toposes from Specifications. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 196-210, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{frey:LIPIcs.TLCA.2015.196,
  author =	{Frey, Jonas},
  title =	{{Realizability Toposes from Specifications}},
  booktitle =	{13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
  pages =	{196--210},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-87-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{38},
  editor =	{Altenkirch, Thorsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TLCA.2015.196},
  URN =		{urn:nbn:de:0030-drops-51645},
  doi =		{10.4230/LIPIcs.TLCA.2015.196},
  annote =	{Keywords: Krivine machine, classical realizability, realizability topos, bisimulation}
}
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