40 Search Results for "Cohen, Liron"

Volume

LIPIcs, Volume 193

12th International Conference on Interactive Theorem Proving (ITP 2021)

ITP 2021, June 29 to July 1, 2021, Rome, Italy (Virtual Conference)

Editors: Liron Cohen and Cezary Kaliszyk

Document
DOI: 10.4230/LIPIcs.MFCS.2023.37
Inductive Continuity via Brouwer Trees

Authors: Liron Cohen, Bruno da Rocha Paiva, Vincent Rahli, and Ayberk Tosun

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
Continuity is a key principle of intuitionistic logic that is generally accepted by constructivists but is inconsistent with classical logic. Most commonly, continuity states that a function from the Baire space to numbers, only needs approximations of the points in the Baire space to compute. More recently, another formulation of the continuity principle was put forward. It states that for any function F from the Baire space to numbers, there exists a (dialogue) tree that contains the values of F at its leaves and such that the modulus of F at each point of the Baire space is given by the length of the corresponding branch in the tree. In this paper we provide the first internalization of this "inductive" continuity principle within a computational setting. Concretely, we present a class of intuitionistic theories that validate this formulation of continuity thanks to computations that construct such dialogue trees internally to the theories using effectful computations. We further demonstrate that this inductive continuity principle implies other forms of continuity principles.
Cite as

Liron Cohen, Bruno da Rocha Paiva, Vincent Rahli, and Ayberk Tosun. Inductive Continuity via Brouwer Trees. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 37:1-37:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cohen_et_al:LIPIcs.MFCS.2023.37,
  author =	{Cohen, Liron and da Rocha Paiva, Bruno and Rahli, Vincent and Tosun, Ayberk},
  title =	{{Inductive Continuity via Brouwer Trees}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{37:1--37:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.37},
  URN =		{urn:nbn:de:0030-drops-185718},
  doi =		{10.4230/LIPIcs.MFCS.2023.37},
  annote =	{Keywords: Continuity, Dialogue trees, Stateful computations, Intuitionistic Logic, Extensional Type Theory, Constructive Type Theory, Realizability, Theorem proving, Agda}
}
Document
DOI: 10.4230/LIPIcs.CSL.2023.15
Realizing Continuity Using Stateful Computations

Authors: Liron Cohen and Vincent Rahli

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)

Abstract
The principle of continuity is a seminal property that holds for a number of intuitionistic theories such as System T. Roughly speaking, it states that functions on real numbers only need approximations of these numbers to compute. Generally, continuity principles have been justified using semantical arguments, but it is known that the modulus of continuity of functions can be computed using effectful computations such as exceptions or reference cells. This paper presents a class of intuitionistic theories that features stateful computations, such as reference cells, and shows that these theories can be extended with continuity axioms. The modulus of continuity of the functionals on the Baire space is directly computed using the stateful computations enabled in the theory.
Cite as

Liron Cohen and Vincent Rahli. Realizing Continuity Using Stateful Computations. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cohen_et_al:LIPIcs.CSL.2023.15,
  author =	{Cohen, Liron and Rahli, Vincent},
  title =	{{Realizing Continuity Using Stateful Computations}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.15},
  URN =		{urn:nbn:de:0030-drops-174761},
  doi =		{10.4230/LIPIcs.CSL.2023.15},
  annote =	{Keywords: Continuity, Stateful computations, Intuitionism, Extensional Type Theory, Constructive Type Theory, Realizability, Theorem proving, Agda}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.10
Constructing Unprejudiced Extensional Type Theories with Choices via Modalities

Authors: Liron Cohen and Vincent Rahli

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

Abstract
Time-progressing expressions, i.e., expressions that compute to different values over time such as Brouwerian choice sequences or reference cells, are a common feature in many frameworks. For type theories to support such elements, they usually employ sheaf models. In this paper, we provide a general framework in the form of an extensional type theory incorporating various time-progressing elements along with a general possible-worlds forcing interpretation parameterized by modalities. The modalities can, in turn, be instantiated with topological spaces of bars, leading to a general sheaf model. This parameterized construction allows us to capture a distinction between theories that are "agnostic", i.e., compatible with classical reasoning in the sense that classical axioms can be validated, and those that are "intuitionistic", i.e., incompatible with classical reasoning in the sense that classical axioms can be proven false. This distinction is made via properties of the modalities selected to model the theory and consequently via the space of bars instantiating the modalities. We further identify a class of time-progressing elements that allows deriving "intuitionistic" theories that include not only choice sequences but also simpler operators, namely reference cells.
Cite as

Liron Cohen and Vincent Rahli. Constructing Unprejudiced Extensional Type Theories with Choices via Modalities. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 10:1-10:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{cohen_et_al:LIPIcs.FSCD.2022.10,
  author =	{Cohen, Liron and Rahli, Vincent},
  title =	{{Constructing Unprejudiced Extensional Type Theories with Choices via Modalities}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{10:1--10:23},
  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.2022.10},
  URN =		{urn:nbn:de:0030-drops-162917},
  doi =		{10.4230/LIPIcs.FSCD.2022.10},
  annote =	{Keywords: Intuitionism, Extensional Type Theory, Constructive Type Theory, Realizability, Choice sequences, References, Classical Logic, Theorem proving, Agda}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.ITP.2021
LIPIcs, Volume 193, ITP 2021, Complete Volume

Authors: Liron Cohen and Cezary Kaliszyk

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
LIPIcs, Volume 193, ITP 2021, Complete Volume
Cite as

12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 1-560, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Proceedings{cohen_et_al:LIPIcs.ITP.2021,
  title =	{{LIPIcs, Volume 193, ITP 2021, Complete Volume}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{1--560},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021},
  URN =		{urn:nbn:de:0030-drops-138943},
  doi =		{10.4230/LIPIcs.ITP.2021},
  annote =	{Keywords: LIPIcs, Volume 193, ITP 2021, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.ITP.2021.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Liron Cohen and Cezary Kaliszyk

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 0:i-0:viii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cohen_et_al:LIPIcs.ITP.2021.0,
  author =	{Cohen, Liron and Kaliszyk, Cezary},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{0:i--0:viii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.0},
  URN =		{urn:nbn:de:0030-drops-138955},
  doi =		{10.4230/LIPIcs.ITP.2021.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.ITP.2021.1
The CakeML Project’s Quest for Ever Stronger Correctness Theorems (Invited Paper)

Authors: Magnus O. Myreen

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
The CakeML project has developed a proof-producing code generation mechanism for the HOL4 theorem prover, a verified compiler for ML and, using these, a number of verified application programs that are proved correct down to the machine code that runs them (in some cases, even down to the underlying hardware). The purpose of this extended abstract is to tell the story of the project and to point curious readers to publications where they can read more about specific contributions.
Cite as

Magnus O. Myreen. The CakeML Project’s Quest for Ever Stronger Correctness Theorems (Invited Paper). In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 1:1-1:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{myreen:LIPIcs.ITP.2021.1,
  author =	{Myreen, Magnus O.},
  title =	{{The CakeML Project’s Quest for Ever Stronger Correctness Theorems}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{1:1--1:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.1},
  URN =		{urn:nbn:de:0030-drops-138963},
  doi =		{10.4230/LIPIcs.ITP.2021.1},
  annote =	{Keywords: Program verification, interactive theorem proving}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ITP.2021.2
Synthesis of Safe Pointer-Manipulating Programs (Invited Talk)

Authors: Nadia Polikarpova

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
Low-level pointer-manipulating code is ubiquitous in operating systems, networking stacks, and browsers, which form the backbone of our digital infrastructure. Unfortunately, this code is susceptible to many kinds of bugs, which lead to crashes and security vulnerabilities. A promising approach to eliminating bugs and reducing programmer effort at the same time is to use program synthesis technology to generate provably correct low-level code automatically from high-level specifications. In this talk I will present a program synthesizer SuSLik, which accepts as input a specification written in separation logic, and produces as output a provably correct C program. SuSLik is the first synthesizer capable of generating a wide range of operations on linked data structures (such as singly- and doubly-linked lists, binary trees, and rose trees) without additional hints from the user. It is also the first synthesizer to automatically discover recursive auxiliary functions required for nested data structure traversal. To make this possible, SuSLik relies on a novel proof system - synthetic separation logic - to derive correct-by-construction programs directly from their specifications. Program proofs generated by SuSLik can be automatically translated into three foundational verification frameworks embedded in Coq: Hoare Type Theory (HTT), Iris, and Verified Software Toolchain (VST).
Cite as

Nadia Polikarpova. Synthesis of Safe Pointer-Manipulating Programs (Invited Talk). In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{polikarpova:LIPIcs.ITP.2021.2,
  author =	{Polikarpova, Nadia},
  title =	{{Synthesis of Safe Pointer-Manipulating Programs}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.2},
  URN =		{urn:nbn:de:0030-drops-138975},
  doi =		{10.4230/LIPIcs.ITP.2021.2},
  annote =	{Keywords: Program Synthesis, Separation Logic, Proof Search}
}
Document
Invited Paper
DOI: 10.4230/LIPIcs.ITP.2021.3
Bounded-Deducibility Security (Invited Paper)

Authors: Andrei Popescu, Thomas Bauereiss, and Peter Lammich

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
We describe Bounded-Deducibility (BD) security, an expressive framework for the specification and verification of information-flow security. The framework grew by confronting concrete challenges of specifying and verifying fine-grained confidentiality properties in some realistic web-based systems. The concepts and theorems that constitute this framework have an eventful history of such "confrontations", often involving trial and error, which are reported in previous papers. This paper is the first to focus on the framework itself rather than the case studies, gathering in one place all the abstract results about BD security.
Cite as

Andrei Popescu, Thomas Bauereiss, and Peter Lammich. Bounded-Deducibility Security (Invited Paper). In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{popescu_et_al:LIPIcs.ITP.2021.3,
  author =	{Popescu, Andrei and Bauereiss, Thomas and Lammich, Peter},
  title =	{{Bounded-Deducibility Security}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{3:1--3:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.3},
  URN =		{urn:nbn:de:0030-drops-138982},
  doi =		{10.4230/LIPIcs.ITP.2021.3},
  annote =	{Keywords: Information-flow security, Unwinding proof method, Compositionality, Verification}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.4
A Graphical User Interface Framework for Formal Verification

Authors: Edward W. Ayers, Mateja Jamnik, and W. T. Gowers

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
We present the "ProofWidgets" framework for implementing general user interfaces (UIs) within an interactive theorem prover. The framework uses web technology and functional reactive programming, as well as metaprogramming features of advanced interactive theorem proving (ITP) systems to allow users to create arbitrary interactive UIs for representing the goal state. Users of the framework can create GUIs declaratively within the ITP’s metaprogramming language, without having to develop in multiple languages and without coordinated changes across multiple projects, which improves development time for new designs of UI. The ProofWidgets framework also allows UIs to make use of the full context of the theorem prover and the specialised libraries that ITPs offer, such as methods for dealing with expressions and tactics. The framework includes an extensible structured pretty-printing engine that enables advanced interaction with expressions such as interactive term rewriting. We exemplify the framework with an implementation for the https://leanprover-community.github.io. The framework is already in use by hundreds of contributors to the Lean mathematical library.
Cite as

Edward W. Ayers, Mateja Jamnik, and W. T. Gowers. A Graphical User Interface Framework for Formal Verification. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ayers_et_al:LIPIcs.ITP.2021.4,
  author =	{Ayers, Edward W. and Jamnik, Mateja and Gowers, W. T.},
  title =	{{A Graphical User Interface Framework for Formal Verification}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{4:1--4:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.4},
  URN =		{urn:nbn:de:0030-drops-138996},
  doi =		{10.4230/LIPIcs.ITP.2021.4},
  annote =	{Keywords: User Interfaces, ITP}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.5
A Formalization of Dedekind Domains and Class Groups of Global Fields

Authors: Anne Baanen, Sander R. Dahmen, Ashvni Narayanan, and Filippo A. E. Nuccio Mortarino Majno di Capriglio

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
Dedekind domains and their class groups are notions in commutative algebra that are essential in algebraic number theory. We formalized these structures and several fundamental properties, including number theoretic finiteness results for class groups, in the Lean prover as part of the mathlib mathematical library. This paper describes the formalization process, noting the idioms we found useful in our development and mathlib’s decentralized collaboration processes involved in this project.
Cite as

Anne Baanen, Sander R. Dahmen, Ashvni Narayanan, and Filippo A. E. Nuccio Mortarino Majno di Capriglio. A Formalization of Dedekind Domains and Class Groups of Global Fields. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{baanen_et_al:LIPIcs.ITP.2021.5,
  author =	{Baanen, Anne and Dahmen, Sander R. and Narayanan, Ashvni and Nuccio Mortarino Majno di Capriglio, Filippo A. E.},
  title =	{{A Formalization of Dedekind Domains and Class Groups of Global Fields}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.5},
  URN =		{urn:nbn:de:0030-drops-139004},
  doi =		{10.4230/LIPIcs.ITP.2021.5},
  annote =	{Keywords: formal math, algebraic number theory, commutative algebra, Lean, mathlib}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.6
A Formally Verified Checker for First-Order Proofs

Authors: Seulkee Baek

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
The Verified TESC Verifier (VTV) is a formally verified checker for the new Theory-Extensible Sequent Calculus (TESC) proof format for first-order ATPs. VTV accepts a TPTP problem and a TESC proof as input, and uses the latter to verify the unsatisfiability of the former. VTV is written in Agda, and the soundness of its proof-checking kernel is verified in respect to a first-order semantics formalized in Agda. VTV shows robust performance in a comprehensive test using all eligible problems from the TPTP problem library, successfully verifying all but the largest 5 of 12296 proofs, with >97% of the proofs verified in less than 1 second.
Cite as

Seulkee Baek. A Formally Verified Checker for First-Order Proofs. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{baek:LIPIcs.ITP.2021.6,
  author =	{Baek, Seulkee},
  title =	{{A Formally Verified Checker for First-Order Proofs}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{6:1--6:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.6},
  URN =		{urn:nbn:de:0030-drops-139010},
  doi =		{10.4230/LIPIcs.ITP.2021.6},
  annote =	{Keywords: TESC, TPTP, TSTP, ATP}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.7
Value-Oriented Legal Argumentation in Isabelle/HOL

Authors: Christoph Benzmüller and David Fuenmayor

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
Literature in AI & Law contemplates argumentation in legal cases as an instance of theory construction. The task of a lawyer in a legal case is to construct a theory containing: (a) relevant generic facts about the world, (b) relevant legal rules such as precedents and statutes, and (c) contingent facts describing or interpreting the situation at hand. Lawyers then elaborate convincing arguments starting from these facts and rules, deriving into a positive decision in favour of their client, often employing sophisticated argumentation techniques involving such notions as burden of proof, stare decisis, legal balancing, etc. In this paper we exemplarily show how to harness Isabelle/HOL to model lawyer’s argumentation using value-oriented legal balancing, while drawing upon shallow embeddings of combinations of expressive modal logics in HOL. We highlight the essential role of model finders (Nitpick) and "hammers" (Sledgehammer) in assisting the task of legal theory construction and share some thoughts on the practicability of extending the catalogue of ITP applications towards legal informatics.
Cite as

Christoph Benzmüller and David Fuenmayor. Value-Oriented Legal Argumentation in Isabelle/HOL. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{benzmuller_et_al:LIPIcs.ITP.2021.7,
  author =	{Benzm\"{u}ller, Christoph and Fuenmayor, David},
  title =	{{Value-Oriented Legal Argumentation in Isabelle/HOL}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{7:1--7:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.7},
  URN =		{urn:nbn:de:0030-drops-139028},
  doi =		{10.4230/LIPIcs.ITP.2021.7},
  annote =	{Keywords: Higher order logic, preference logic, shallow embedding, legal reasoning}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.8
Unsolvability of the Quintic Formalized in Dependent Type Theory

Authors: Sophie Bernard, Cyril Cohen, Assia Mahboubi, and Pierre-Yves Strub

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
In this paper, we describe an axiom-free Coq formalization that there does not exists a general method for solving by radicals polynomial equations of degree greater than 4. This development includes a proof of Galois' Theorem of the equivalence between solvable extensions and extensions solvable by radicals. The unsolvability of the general quintic follows from applying this theorem to a well chosen polynomial with unsolvable Galois group.
Cite as

Sophie Bernard, Cyril Cohen, Assia Mahboubi, and Pierre-Yves Strub. Unsolvability of the Quintic Formalized in Dependent Type Theory. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bernard_et_al:LIPIcs.ITP.2021.8,
  author =	{Bernard, Sophie and Cohen, Cyril and Mahboubi, Assia and Strub, Pierre-Yves},
  title =	{{Unsolvability of the Quintic Formalized in Dependent Type Theory}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.8},
  URN =		{urn:nbn:de:0030-drops-139038},
  doi =		{10.4230/LIPIcs.ITP.2021.8},
  annote =	{Keywords: Galois theory, Coq, Mathematical Components, Dependent Type Theory, Abel-Ruffini, General quintic}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.9
Itauto: An Extensible Intuitionistic SAT Solver

Authors: Frédéric Besson

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
We present the design and implementation of itauto, a Coq reflexive tactic for intuitionistic propositional logic. The tactic inherits features found in modern SAT solvers: definitional conjunctive normal form; lazy unit propagation and conflict driven backjumping. Formulae are hash-consed using native integers thus enabling a fast equality test and a pervasive use of Patricia Trees. We also propose a hybrid proof by reflection scheme whereby the extracted solver calls user-defined tactics on the leaves of the propositional proof search thus enabling theory reasoning and the generation of conflict clauses. The solver has decent efficiency and is more scalable than existing tactics on synthetic benchmarks and preliminary experiments are encouraging for existing developments.
Cite as

Frédéric Besson. Itauto: An Extensible Intuitionistic SAT Solver. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{besson:LIPIcs.ITP.2021.9,
  author =	{Besson, Fr\'{e}d\'{e}ric},
  title =	{{Itauto: An Extensible Intuitionistic SAT Solver}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.9},
  URN =		{urn:nbn:de:0030-drops-139043},
  doi =		{10.4230/LIPIcs.ITP.2021.9},
  annote =	{Keywords: SAT solver, proof by reflection}
}
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