2 Search Results for "Manighetti, Matteo"

Document
DOI: 10.4230/LIPIcs.TYPES.2020.10
Two Applications of Logic Programming to Coq

Authors: Matteo Manighetti, Dale Miller, and Alberto Momigliano

Published in: LIPIcs, Volume 188, 26th International Conference on Types for Proofs and Programs (TYPES 2020)

Abstract
The logic programming paradigm provides a flexible setting for representing, manipulating, checking, and elaborating proof structures. This is particularly true when the logic programming language allows for bindings in terms and proofs. In this paper, we make use of two recent innovations at the intersection of logic programming and proof checking. One of these is the foundational proof certificate (FPC) framework which provides a flexible means of defining the semantics of a range of proof structures for classical and intuitionistic logic. A second innovation is the recently released Coq-Elpi plugin for Coq in which the Elpi implementation of λProlog can send and retrieve information to and from the Coq kernel. We illustrate the use of both this Coq plugin and FPCs with two example applications. First, we implement an FPC-driven sequent calculus for a fragment of the Calculus of Inductive Constructions and we package it into a tactic to perform property-based testing of inductive types corresponding to Horn clauses. Second, we implement in Elpi a proof checker for first-order intuitionistic logic and demonstrate how proof certificates can be supplied by external (to Coq) provers and then elaborated into the fully detailed proof terms that can be checked by the Coq kernel.
Cite as

Matteo Manighetti, Dale Miller, and Alberto Momigliano. Two Applications of Logic Programming to Coq. In 26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{manighetti_et_al:LIPIcs.TYPES.2020.10,
  author =	{Manighetti, Matteo and Miller, Dale and Momigliano, Alberto},
  title =	{{Two Applications of Logic Programming to Coq}},
  booktitle =	{26th International Conference on Types for Proofs and Programs (TYPES 2020)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-182-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{188},
  editor =	{de'Liguoro, Ugo and Berardi, Stefano and 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.TYPES.2020.10},
  URN =		{urn:nbn:de:0030-drops-138896},
  doi =		{10.4230/LIPIcs.TYPES.2020.10},
  annote =	{Keywords: Proof assistants, logic programming, Coq, \lambdaProlog, property-based testing}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2016.4
On Natural Deduction for Herbrand Constructive Logics II: Curry-Howard Correspondence for Markov's Principle in First-Order Logic and Arithmetic

Authors: Federico Aschieri and Matteo Manighetti

Published in: LIPIcs, Volume 97, 22nd International Conference on Types for Proofs and Programs (TYPES 2016)

Abstract
Intuitionistic first-order logic extended with a restricted form of Markov's principle is constructive and admits a Curry-Howard correspondence, as shown by Herbelin. We provide a simpler proof of that result and then we study intuitionistic first-order logic extended with unrestricted Markov's principle. Starting from classical natural deduction, we restrict the excluded middle and we obtain a natural deduction system and a parallel Curry-Howard isomorphism for the logic. We show that proof terms for existentially quantified formulas reduce to a list of individual terms representing all possible witnesses. As corollary, we derive that the logic is Herbrand constructive: whenever it proves any existential formula, it proves also an Herbrand disjunction for the formula. Finally, using the techniques just introduced, we also provide a new computational interpretation of Arithmetic with Markov's principle.
Cite as

Federico Aschieri and Matteo Manighetti. On Natural Deduction for Herbrand Constructive Logics II: Curry-Howard Correspondence for Markov's Principle in First-Order Logic and Arithmetic. In 22nd International Conference on Types for Proofs and Programs (TYPES 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 97, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{aschieri_et_al:LIPIcs.TYPES.2016.4,
  author =	{Aschieri, Federico and Manighetti, Matteo},
  title =	{{On Natural Deduction for Herbrand Constructive Logics II: Curry-Howard Correspondence for Markov's Principle in First-Order Logic and Arithmetic}},
  booktitle =	{22nd International Conference on Types for Proofs and Programs (TYPES 2016)},
  pages =	{4:1--4:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-065-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{97},
  editor =	{Ghilezan, Silvia and Geuvers, Herman and Ivetic, Jelena},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2016.4},
  URN =		{urn:nbn:de:0030-drops-98590},
  doi =		{10.4230/LIPIcs.TYPES.2016.4},
  annote =	{Keywords: Markov's Principle, first-order logic, natural deduction, Curry-Howard}
}
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