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DOI: 10.4230/LIPIcs.FSCD.2022.21

Linear Lambda-Calculus is Linear

Authors: Alejandro Díaz-Caro and Gilles Dowek

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract

We prove a linearity theorem for an extension of linear logic with addition and multiplication by a scalar: the proofs of some propositions in this logic are linear in the algebraic sense. This work is part of a wider research program that aims at defining a logic whose proof language is a quantum programming language.

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Alejandro Díaz-Caro and Gilles Dowek. Linear Lambda-Calculus is Linear. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{diazcaro_et_al:LIPIcs.FSCD.2022.21,
  author =	{D{\'\i}az-Caro, Alejandro and Dowek, Gilles},
  title =	{{Linear Lambda-Calculus is Linear}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{21:1--21:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.21},
  URN =		{urn:nbn:de:0030-drops-163024},
  doi =		{10.4230/LIPIcs.FSCD.2022.21},
  annote =	{Keywords: Proof theory, Lambda calculus, Linear logic, Quantum computing}
}

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DOI: 10.4230/LIPIcs.FSCD.2019.14

Proof Normalisation in a Logic Identifying Isomorphic Propositions

Authors: Alejandro Díaz-Caro and Gilles Dowek

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

Abstract

We define a fragment of propositional logic where isomorphic propositions, such as A wedge B and B wedge A, or A ==> (B wedge C) and (A ==> B) wedge (A ==> C) are identified. We define System I, a proof language for this logic, and prove its normalisation and consistency.

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Alejandro Díaz-Caro and Gilles Dowek. Proof Normalisation in a Logic Identifying Isomorphic Propositions. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 14:1-14:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{diazcaro_et_al:LIPIcs.FSCD.2019.14,
  author =	{D{\'\i}az-Caro, Alejandro and Dowek, Gilles},
  title =	{{Proof Normalisation in a Logic Identifying Isomorphic Propositions}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{14:1--14:23},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2019.14},
  URN =		{urn:nbn:de:0030-drops-105210},
  doi =		{10.4230/LIPIcs.FSCD.2019.14},
  annote =	{Keywords: Simply typed lambda calculus, Isomorphisms, Logic, Cut-elimination, Proof-reduction}
}

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Documents authored by Díaz-Caro, Alejandro

Linear Lambda-Calculus is Linear

Abstract

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Proof Normalisation in a Logic Identifying Isomorphic Propositions

Abstract

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