12 Search Results for "Tassi, Enrico"

Document
DOI: 10.4230/LIPIcs.ITP.2025.27
Inductive Predicates via Least Fixpoints in Higher-Order Separation Logic

Authors: Robbert Krebbers, Luko van der Maas, and Enrico Tassi

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Inductive predicates play a key role in program verification using separation logic. There are many methods for defining such predicates in separation logic, which all have different conditions and thus support different classes of predicates. The most common methods are: (1) through a structurally-recursive definition (commonly used to define representation predicates for the verification of data structures), and (2) through step-indexing (commonly used to give a semantics of Hoare triples for partial program correctness). A lesser-known method is to define such inductive predicates internally in higher-order separation logic through a least fixpoint of a monotone function. The contributions of this paper are fourfold. First, we present the folklore result (from the Iris library) that one can define least (and greatest) fixpoints internally in separation logic by extending the standard second-order impredicative encoding with some modalities. Second, we show that these fixpoints are useful to define representation predicates where the mathematical and in-memory data structures do not correspond. Third, we show that these fixpoints can be used to define Hoare triples and weakest preconditions for total program correctness in Iris. Fourth, we present a prototype command (akin to Rocq’s Inductive), written in Rocq-Elpi, to generate the least fixpoint and its reasoning principles (constructors and induction principles) from a high-level specification.
Cite as

Robbert Krebbers, Luko van der Maas, and Enrico Tassi. Inductive Predicates via Least Fixpoints in Higher-Order Separation Logic. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 27:1-27:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{krebbers_et_al:LIPIcs.ITP.2025.27,
  author =	{Krebbers, Robbert and van der Maas, Luko and Tassi, Enrico},
  title =	{{Inductive Predicates via Least Fixpoints in Higher-Order Separation Logic}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{27:1--27:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.27},
  URN =		{urn:nbn:de:0030-drops-246258},
  doi =		{10.4230/LIPIcs.ITP.2025.27},
  annote =	{Keywords: Separation Logic, Program Verification, Data Structures, Iris, Rocq prover}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.24
Formally Verifying a Vertical Cell Decomposition Algorithm

Authors: Yves Bertot and Thomas Portet

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
The broad context of this work is the application of formal methods to geometry and robotics. We describe an algorithm to decompose a working area containing obstacles into a collection of safe cells and the formal proof that this algorithm is correct. We expect such an algorithm will be useful to compute safe trajectories. To our knowledge, this is one of the first formalization of such an algorithm to decompose a working space into elementary cells that are suitable for later applications, with the proof of correctness that guarantees that large parts of the working space are safe. Techniques to perform this proof go from algebraic reasoning on coordinates and determinants to sorting. The main difficulty comes from the possible existence of degenerate cases, which are treated in a principled way.
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Yves Bertot and Thomas Portet. Formally Verifying a Vertical Cell Decomposition Algorithm. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bertot_et_al:LIPIcs.ITP.2025.24,
  author =	{Bertot, Yves and Portet, Thomas},
  title =	{{Formally Verifying a Vertical Cell Decomposition Algorithm}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{24:1--24:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.24},
  URN =		{urn:nbn:de:0030-drops-246222},
  doi =		{10.4230/LIPIcs.ITP.2025.24},
  annote =	{Keywords: Formal Verification, Motion planning, algorithmic geometry}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.18
Formalising New Mathematics in Isabelle: Diagonal Ramsey

Authors: Lawrence C. Paulson

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
The formalisation of mathematics is becoming routine, but its value to research mathematicians remains unproven. There are few examples of using proof assistants to verify new work. This paper reports the formalisation - inspired by a Lean one by Bhavik Mehta - of a major new result [Marcelo Campos et al., 2023] about Ramsey numbers. One unexpected finding was a heavy role for computer algebra techniques.
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Lawrence C. Paulson. Formalising New Mathematics in Isabelle: Diagonal Ramsey. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{paulson:LIPIcs.ITP.2025.18,
  author =	{Paulson, Lawrence C.},
  title =	{{Formalising New Mathematics in Isabelle: Diagonal Ramsey}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.18},
  URN =		{urn:nbn:de:0030-drops-246163},
  doi =		{10.4230/LIPIcs.ITP.2025.18},
  annote =	{Keywords: Isabelle, formalisation of mathematics, Ramsey’s theorem, computer algebra}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.14
Canonical for Automated Theorem Proving in Lean

Authors: Chase Norman and Jeremy Avigad

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Canonical is a solver for type inhabitation in dependent type theory, that is, the problem of producing a term of a given type. We present a Lean tactic which invokes Canonical to generate proof terms and synthesize programs. The tactic supports higher-order and dependently-typed goals, structural recursion over indexed inductive types, and definitional equality. Canonical finds proofs for 84% of Natural Number Game problems in 51 seconds total.
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Chase Norman and Jeremy Avigad. Canonical for Automated Theorem Proving in Lean. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{norman_et_al:LIPIcs.ITP.2025.14,
  author =	{Norman, Chase and Avigad, Jeremy},
  title =	{{Canonical for Automated Theorem Proving in Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.14},
  URN =		{urn:nbn:de:0030-drops-246128},
  doi =		{10.4230/LIPIcs.ITP.2025.14},
  annote =	{Keywords: Automated Reasoning, Interactive Theorem Proving, Dependent Type Theory, Inhabitation, Unification, Program Synthesis, Formal Methods}
}
Document
DOI: 10.4230/LITES.10.1.2
Towards a Coq-verified Chain of Esterel Semantics

Authors: Lionel Rieg and Gérard Berry

Published in: LITES, Volume 10, Issue 1 (2025). Leibniz Transactions on Embedded Systems, Volume 10, Issue 1

Abstract
This article focuses on formally specifying and verifying the chain of formal semantics of the Esterel synchronous programming language using the Coq proof assistant. In particular, in addition to the standard logical (LBS) semantics, constructive semantics (CBS) and constructive state semantics (CSS), we introduce a novel microstep semantics that gets rid of the Must/Can potential function pair of the constructive semantics and can be viewed as an abstract version of Esterel’s circuit semantics used by compilers to generate software code and hardware designs. The article also comes with formal proofs in Coq of the equivalence between the CBS and CSS semantics and of the refinement of the CSS by the microstep semantics, except for the loop construct of Esterel.
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Lionel Rieg and Gérard Berry. Towards a Coq-verified Chain of Esterel Semantics. In LITES, Volume 10, Issue 1 (2025). Leibniz Transactions on Embedded Systems, Volume 10, Issue 1, pp. 2:1-2:54, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{rieg_et_al:LITES.10.1.2,
  author =	{Rieg, Lionel and Berry, G\'{e}rard},
  title =	{{Towards a Coq-verified Chain of Esterel Semantics}},
  journal =	{Leibniz Transactions on Embedded Systems},
  pages =	{2:1--2:54},
  ISSN =	{2199-2002},
  year =	{2025},
  volume =	{10},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES.10.1.2},
  URN =		{urn:nbn:de:0030-drops-230144},
  doi =		{10.4230/LITES.10.1.2},
  annote =	{Keywords: Esterel programming language, formal verification, Coq proof assistant}
}
Document
DOI: 10.4230/LIPIcs.ITP.2023.12
Lessons for Interactive Theorem Proving Researchers from a Survey of Coq Users

Authors: Ana de Almeida Borges, Annalí Casanueva Artís, Jean-Rémy Falleri, Emilio Jesús Gallego Arias, Érik Martin-Dorel, Karl Palmskog, Alexander Serebrenik, and Théo Zimmermann

Published in: LIPIcs, Volume 268, 14th International Conference on Interactive Theorem Proving (ITP 2023)

Abstract
The Coq Community Survey 2022 was an online public survey of users of the Coq proof assistant conducted during February 2022. Broadly, the survey asked about use of Coq features, user interfaces, libraries, plugins, and tools, views on renaming Coq and Coq improvements, and also demographic data such as education and experience with Coq and other proof assistants and programming languages. The survey received 466 submitted responses, making it the largest survey of users of an interactive theorem prover (ITP) so far. We present the design of the survey, a summary of key results, and analysis of answers relevant to ITP technology development and usage. In particular, we analyze user characteristics associated with adoption of tools and libraries and make comparisons to adjacent software communities. Notably, we find that experience has significant impact on Coq user behavior, including on usage of tools, libraries, and integrated development environments.
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Ana de Almeida Borges, Annalí Casanueva Artís, Jean-Rémy Falleri, Emilio Jesús Gallego Arias, Érik Martin-Dorel, Karl Palmskog, Alexander Serebrenik, and Théo Zimmermann. Lessons for Interactive Theorem Proving Researchers from a Survey of Coq Users. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 12:1-12:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dealmeidaborges_et_al:LIPIcs.ITP.2023.12,
  author =	{de Almeida Borges, Ana and Casanueva Art{\'\i}s, Annal{\'\i} and Falleri, Jean-R\'{e}my and Gallego Arias, Emilio Jes\'{u}s and Martin-Dorel, \'{E}rik and Palmskog, Karl and Serebrenik, Alexander and Zimmermann, Th\'{e}o},
  title =	{{Lessons for Interactive Theorem Proving Researchers from a Survey of Coq Users}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{12:1--12:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-284-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{268},
  editor =	{Naumowicz, Adam and Thiemann, Ren\'{e}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.12},
  URN =		{urn:nbn:de:0030-drops-183875},
  doi =		{10.4230/LIPIcs.ITP.2023.12},
  annote =	{Keywords: Coq, Community, Survey, Statistical Analysis}
}
Document
DOI: 10.4230/LIPIcs.ITP.2022.4
Use and Abuse of Instance Parameters in the Lean Mathematical Library

Authors: Anne Baanen

Published in: LIPIcs, Volume 237, 13th International Conference on Interactive Theorem Proving (ITP 2022)

Abstract
The Lean mathematical library mathlib features extensive use of the typeclass pattern for organising mathematical structures, based on Lean’s mechanism of instance parameters. Related mechanisms for typeclasses are available in other provers including Agda, Coq and Isabelle with varying degrees of adoption. This paper analyses representative examples of design patterns involving instance parameters in the current Lean 3 version of mathlib, focussing on complications arising at scale and how the mathlib community deals with them.
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Anne Baanen. Use and Abuse of Instance Parameters in the Lean Mathematical Library. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 4:1-4:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{baanen:LIPIcs.ITP.2022.4,
  author =	{Baanen, Anne},
  title =	{{Use and Abuse of Instance Parameters in the Lean Mathematical Library}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{4:1--4:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-252-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{237},
  editor =	{Andronick, June and de Moura, Leonardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2022.4},
  URN =		{urn:nbn:de:0030-drops-167131},
  doi =		{10.4230/LIPIcs.ITP.2022.4},
  annote =	{Keywords: formalization of mathematics, dependent type theory, typeclasses, algebraic hierarchy, Lean prover}
}
Document
DOI: 10.4230/LIPIcs.ITP.2022.29
Reflexive Tactics for Algebra, Revisited

Authors: Kazuhiko Sakaguchi

Published in: LIPIcs, Volume 237, 13th International Conference on Interactive Theorem Proving (ITP 2022)

Abstract
Computational reflection allows us to turn verified decision procedures into efficient automated reasoning tools in proof assistants. The typical applications of such methodology include decidable algebraic theories such as equational theories of commutative rings and lattices. However, such existing tools are known not to cooperate with packed classes, a methodology to define mathematical structures in dependent type theory, that allows for the sharing of vocabulary across the inheritance hierarchy. Moreover, such tools do not support homomorphisms whose domain and codomain types may differ. This paper demonstrates how to implement reflexive tactics that support packed classes and homomorphisms. As applications of our methodology, we adapt the ring and field tactics of Coq to the commutative ring and field structures of the Mathematical Components library, and apply the resulting tactics to the formal proof of the irrationality of ζ(3) by Chyzak, Mahboubi, and Sibut-Pinote. As a result, the lines of code in the proof scripts have been reduced by 8%, and the time required for proof checking has been decreased by 27%.
Cite as

Kazuhiko Sakaguchi. Reflexive Tactics for Algebra, Revisited. In 13th International Conference on Interactive Theorem Proving (ITP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 237, pp. 29:1-29:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{sakaguchi:LIPIcs.ITP.2022.29,
  author =	{Sakaguchi, Kazuhiko},
  title =	{{Reflexive Tactics for Algebra, Revisited}},
  booktitle =	{13th International Conference on Interactive Theorem Proving (ITP 2022)},
  pages =	{29:1--29:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-252-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{237},
  editor =	{Andronick, June and de Moura, Leonardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2022.29},
  URN =		{urn:nbn:de:0030-drops-167385},
  doi =		{10.4230/LIPIcs.ITP.2022.29},
  annote =	{Keywords: Coq, Elpi, \lambdaProlog, Mathematical Components, algebraic structures, packed classes, canonical structures, proof by reflection}
}
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.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
System Description
DOI: 10.4230/LIPIcs.FSCD.2020.34
Hierarchy Builder: Algebraic hierarchies Made Easy in Coq with Elpi (System Description)

Authors: Cyril Cohen, Kazuhiko Sakaguchi, and Enrico Tassi

Published in: LIPIcs, Volume 167, 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)

Abstract
It is nowadays customary to organize libraries of machine checked proofs around hierarchies of algebraic structures. One influential example is the Mathematical Components library on top of which the long and intricate proof of the Odd Order Theorem could be fully formalized. Still, building algebraic hierarchies in a proof assistant such as Coq requires a lot of manual labor and often a deep expertise in the internals of the prover. Moreover, according to our experience, making a hierarchy evolve without causing breakage in client code is equally tricky: even a simple refactoring such as splitting a structure into two simpler ones is hard to get right. In this paper we describe HB, a high level language to build hierarchies of algebraic structures and to make these hierarchies evolve without breaking user code. The key concepts are the ones of factory, builder and abbreviation that let the hierarchy developer describe an actual interface for their library. Behind that interface the developer can provide appropriate code to ensure backward compatibility. We implement the HB language in the hierarchy-builder addon for the Coq system using the Elpi extension language.
Cite as

Cyril Cohen, Kazuhiko Sakaguchi, and Enrico Tassi. Hierarchy Builder: Algebraic hierarchies Made Easy in Coq with Elpi (System Description). In 5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 167, pp. 34:1-34:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cohen_et_al:LIPIcs.FSCD.2020.34,
  author =	{Cohen, Cyril and Sakaguchi, Kazuhiko and Tassi, Enrico},
  title =	{{Hierarchy Builder: Algebraic hierarchies Made Easy in Coq with Elpi}},
  booktitle =	{5th International Conference on Formal Structures for Computation and Deduction (FSCD 2020)},
  pages =	{34:1--34:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-155-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{167},
  editor =	{Ariola, Zena M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2020.34},
  URN =		{urn:nbn:de:0030-drops-123562},
  doi =		{10.4230/LIPIcs.FSCD.2020.34},
  annote =	{Keywords: Algebraic Hierarchy, Packed Classes, Coq, Elpi, Metaprogramming, \lambdaProlog}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.26
Ornaments for Proof Reuse in Coq

Authors: Talia Ringer, Nathaniel Yazdani, John Leo, and Dan Grossman

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
Ornaments express relations between inductive types with the same inductive structure. We implement fully automatic proof reuse for a particular class of ornaments in a Coq plugin, and show how such a tool can give programmers the rewards of using indexed inductive types while automating away many of the costs. The plugin works directly on Coq code; it is the first ornamentation tool for a non-embedded dependently typed language. It is also the first tool to automatically identify ornaments: To lift a function or proof, the user must provide only the source type, the destination type, and the source function or proof. In taking advantage of the mathematical properties of ornaments, our approach produces faster functions and smaller terms than a more general approach to proof reuse in Coq.
Cite as

Talia Ringer, Nathaniel Yazdani, John Leo, and Dan Grossman. Ornaments for Proof Reuse in Coq. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 26:1-26:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{ringer_et_al:LIPIcs.ITP.2019.26,
  author =	{Ringer, Talia and Yazdani, Nathaniel and Leo, John and Grossman, Dan},
  title =	{{Ornaments for Proof Reuse in Coq}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{26:1--26:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.26},
  URN =		{urn:nbn:de:0030-drops-110816},
  doi =		{10.4230/LIPIcs.ITP.2019.26},
  annote =	{Keywords: ornaments, proof reuse, proof automation}
}
Document
DOI: 10.4230/LIPIcs.ITP.2019.29
Deriving Proved Equality Tests in Coq-Elpi: Stronger Induction Principles for Containers in Coq

Authors: Enrico Tassi

Published in: LIPIcs, Volume 141, 10th International Conference on Interactive Theorem Proving (ITP 2019)

Abstract
We describe a procedure to derive equality tests and their correctness proofs from inductive type declarations in Coq. Programs and proofs are derived compositionally, reusing code and proofs derived previously. The key steps are two. First, we design appropriate induction principles for data types defined using parametric containers. Second, we develop a technique to work around the modularity limitations imposed by the purely syntactic termination check Coq performs on recursive proofs. The unary parametricity translation of inductive data types turns out to be the key to both steps. Last but not least, we provide an implementation of the procedure for the Coq proof assistant based on the Elpi [Dunchev et al., 2015] extension language.
Cite as

Enrico Tassi. Deriving Proved Equality Tests in Coq-Elpi: Stronger Induction Principles for Containers in Coq. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{tassi:LIPIcs.ITP.2019.29,
  author =	{Tassi, Enrico},
  title =	{{Deriving Proved Equality Tests in Coq-Elpi: Stronger Induction Principles for Containers in Coq}},
  booktitle =	{10th International Conference on Interactive Theorem Proving (ITP 2019)},
  pages =	{29:1--29:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-122-1},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{141},
  editor =	{Harrison, John and O'Leary, John and Tolmach, Andrew},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2019.29},
  URN =		{urn:nbn:de:0030-drops-110841},
  doi =		{10.4230/LIPIcs.ITP.2019.29},
  annote =	{Keywords: Coq, Containers, Induction, Equality test, Parametricity translation}
}
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