4 Search Results for "Frumin, Dan"

Document
DOI: 10.4230/LIPIcs.ITP.2023.30
Certifying Higher-Order Polynomial Interpretations

Authors: Niels van der Weide, Deivid Vale, and Cynthia Kop

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

Abstract
Higher-order rewriting is a framework in which one can write higher-order programs and study their properties. One such property is termination: the situation that for all inputs, the program eventually halts its execution and produces an output. Several tools have been developed to check whether higher-order rewriting systems are terminating. However, developing such tools is difficult and can be error-prone. In this paper, we present a way of certifying termination proofs of higher-order term rewriting systems. We formalize a specific method that is used to prove termination, namely the polynomial interpretation method. In addition, we give a program that processes proof traces containing a high-level description of a termination proof into a formal Coq proof script that can be checked by Coq. We demonstrate the usability of this approach by certifying higher-order polynomial interpretation proofs produced by Wanda, a termination analysis tool for higher-order rewriting.
Cite as

Niels van der Weide, Deivid Vale, and Cynthia Kop. Certifying Higher-Order Polynomial Interpretations. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 30:1-30:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{vanderweide_et_al:LIPIcs.ITP.2023.30,
  author =	{van der Weide, Niels and Vale, Deivid and Kop, Cynthia},
  title =	{{Certifying Higher-Order Polynomial Interpretations}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{30:1--30:20},
  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.2023.30},
  URN =		{urn:nbn:de:0030-drops-184051},
  doi =		{10.4230/LIPIcs.ITP.2023.30},
  annote =	{Keywords: higher-order rewriting, Coq, termination, formalization}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2022.23
A Self-Dual Distillation of Session Types

Authors: Jules Jacobs

Published in: LIPIcs, Volume 222, 36th European Conference on Object-Oriented Programming (ECOOP 2022)

Abstract
We introduce ƛ ("lambda-barrier"), a minimal extension of linear λ-calculus with concurrent communication, which adds only a single new fork construct for spawning threads. It is inspired by GV, a session-typed functional language also based on linear λ-calculus. Unlike GV, ƛ strives to be as simple as possible, and adds no new operations other than fork, no new type formers, and no explicit definition of session type duality. Instead, we use linear function function type τ₁ -∘ τ₂ for communication between threads, which is dual to τ₂ -∘ τ₁, i.e., the function type constructor is dual to itself. Nevertheless, we can encode session types as ƛ types, GV’s channel operations as ƛ terms, and show that this encoding is type-preserving. The linear type system of ƛ ensures that all programs are deadlock-free and satisfy global progress, which we prove in Coq. Because of ƛ’s minimality, these proofs are simpler than mechanized proofs of deadlock freedom for GV.
Cite as

Jules Jacobs. A Self-Dual Distillation of Session Types. In 36th European Conference on Object-Oriented Programming (ECOOP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 222, pp. 23:1-23:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{jacobs:LIPIcs.ECOOP.2022.23,
  author =	{Jacobs, Jules},
  title =	{{A Self-Dual Distillation of Session Types}},
  booktitle =	{36th European Conference on Object-Oriented Programming (ECOOP 2022)},
  pages =	{23:1--23:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-225-9},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{222},
  editor =	{Ali, Karim and Vitek, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2022.23},
  URN =		{urn:nbn:de:0030-drops-162518},
  doi =		{10.4230/LIPIcs.ECOOP.2022.23},
  annote =	{Keywords: Linear types, concurrency, lambda calculus, session types}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2019.41
Kleene Algebra with Observations

Authors: Tobias Kappé, Paul Brunet, Jurriaan Rot, Alexandra Silva, Jana Wagemaker, and Fabio Zanasi

Published in: LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)

Abstract
Kleene algebra with tests (KAT) is an algebraic framework for reasoning about the control flow of sequential programs. Generalising KAT to reason about concurrent programs is not straightforward, because axioms native to KAT in conjunction with expected axioms for concurrency lead to an anomalous equation. In this paper, we propose Kleene algebra with observations (KAO), a variant of KAT, as an alternative foundation for extending KAT to a concurrent setting. We characterise the free model of KAO, and establish a decision procedure w.r.t. its equational theory.
Cite as

Tobias Kappé, Paul Brunet, Jurriaan Rot, Alexandra Silva, Jana Wagemaker, and Fabio Zanasi. Kleene Algebra with Observations. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 41:1-41:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{kappe_et_al:LIPIcs.CONCUR.2019.41,
  author =	{Kapp\'{e}, Tobias and Brunet, Paul and Rot, Jurriaan and Silva, Alexandra and Wagemaker, Jana and Zanasi, Fabio},
  title =	{{Kleene Algebra with Observations}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{41:1--41:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Fokkink, Wan and van Glabbeek, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.41},
  URN =		{urn:nbn:de:0030-drops-109431},
  doi =		{10.4230/LIPIcs.CONCUR.2019.41},
  annote =	{Keywords: Concurrent Kleene algebra, Kleene algebra with tests, free model, axiomatisation, decision procedure}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2019.5
Bicategories in Univalent Foundations

Authors: Benedikt Ahrens, Dan Frumin, Marco Maggesi, and Niels van der Weide

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

Abstract
We develop bicategory theory in univalent foundations. Guided by the notion of univalence for (1-)categories studied by Ahrens, Kapulkin, and Shulman, we define and study univalent bicategories. To construct examples of those, we develop the notion of "displayed bicategories", an analog of displayed 1-categories introduced by Ahrens and Lumsdaine. Displayed bicategories allow us to construct univalent bicategories in a modular fashion. To demonstrate the applicability of this notion, we prove several bicategories are univalent. Among these are the bicategory of univalent categories with families and the bicategory of pseudofunctors between univalent bicategories. Our work is formalized in the UniMath library of univalent mathematics.
Cite as

Benedikt Ahrens, Dan Frumin, Marco Maggesi, and Niels van der Weide. Bicategories in Univalent Foundations. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 5:1-5:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{ahrens_et_al:LIPIcs.FSCD.2019.5,
  author =	{Ahrens, Benedikt and Frumin, Dan and Maggesi, Marco and van der Weide, Niels},
  title =	{{Bicategories in Univalent Foundations}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{5:1--5:17},
  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.2019.5},
  URN =		{urn:nbn:de:0030-drops-105124},
  doi =		{10.4230/LIPIcs.FSCD.2019.5},
  annote =	{Keywords: bicategory theory, univalent mathematics, dependent type theory, Coq}
}
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