49 Search Results for "Gaboardi, Marco"

Volume

LIPIcs, Volume 260

8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

FSCD 2023, July 3-6, 2023, Rome, Italy

Editors: Marco Gaboardi and Femke van Raamsdonk

Document
DOI: 10.4230/LIPIcs.CSL.2025.35
A Kleene Algebra with Tests for Union Bound Reasoning About Probabilistic Programs

Authors: Leandro Gomes, Patrick Baillot, and Marco Gaboardi

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
Kleene Algebra with Tests (KAT) provides a framework for algebraic equational reasoning about imperative programs. The recent variant Guarded KAT (GKAT) allows to reason on non-probabilistic properties of probabilistic programs. Here we introduce an extension of this framework called approximate GKAT (aGKAT), which equips GKAT with a partially ordered monoid (real numbers) enabling to express satisfaction of (deterministic) properties except with a probability up to a certain bound. This allows to represent in equational reasoning "à la KAT" proofs of probabilistic programs based on the union bound, a technique from basic probability theory. We show how a propositional variant of approximate Hoare Logic (aHL), a program logic for union bound, can be soundly encoded in our system aGKAT. We then illustrate the use of aGKAT with an example of accuracy analysis from the field of differential privacy.
Cite as

Leandro Gomes, Patrick Baillot, and Marco Gaboardi. A Kleene Algebra with Tests for Union Bound Reasoning About Probabilistic Programs. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 35:1-35:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gomes_et_al:LIPIcs.CSL.2025.35,
  author =	{Gomes, Leandro and Baillot, Patrick and Gaboardi, Marco},
  title =	{{A Kleene Algebra with Tests for Union Bound Reasoning About Probabilistic Programs}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{35:1--35:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.35},
  URN =		{urn:nbn:de:0030-drops-227929},
  doi =		{10.4230/LIPIcs.CSL.2025.35},
  annote =	{Keywords: Kleene algebras with tests, Hoare logic, equational reasoning, probabilistic programs, union bound, formal verification}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.36
Kleene Algebra with Commutativity Conditions Is Undecidable

Authors: Arthur Azevedo de Amorim, Cheng Zhang, and Marco Gaboardi

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
We prove that the equational theory of Kleene algebra with commutativity conditions on primitives (or atomic terms) is undecidable, thereby settling a longstanding open question in the theory of Kleene algebra. While this question has also been recently solved independently by Kuznetsov, our results hold even for weaker theories that do not support the induction axioms of Kleene algebra.
Cite as

Arthur Azevedo de Amorim, Cheng Zhang, and Marco Gaboardi. Kleene Algebra with Commutativity Conditions Is Undecidable. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 36:1-36:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{azevedodeamorim_et_al:LIPIcs.CSL.2025.36,
  author =	{Azevedo de Amorim, Arthur and Zhang, Cheng and Gaboardi, Marco},
  title =	{{Kleene Algebra with Commutativity Conditions Is Undecidable}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{36:1--36:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.36},
  URN =		{urn:nbn:de:0030-drops-227933},
  doi =		{10.4230/LIPIcs.CSL.2025.36},
  annote =	{Keywords: Kleene Algebra, Hypotheses, Complexity}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.157
Domain Reasoning in TopKAT

Authors: Cheng Zhang, Arthur Azevedo de Amorim, and Marco Gaboardi

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
TopKAT is the algebraic theory of Kleene algebra with tests (KAT) extended with a top element. Compared to KAT, one pleasant feature of TopKAT is that, in relational models, the top element allows us to express the domain and codomain of a relation. This enables several applications in program logics, such as proving under-approximate specifications or reachability properties of imperative programs. However, while TopKAT inherits many pleasant features of KATs, such as having a decidable equational theory, it is incomplete with respect to relational models. In other words, there are properties that hold true of all relational TopKATs but cannot be proved with the axioms of TopKAT. This issue is potentially worrisome for program-logic applications, in which relational models play a key role. In this paper, we further investigate the completeness properties of TopKAT with respect to relational models. We show that TopKAT is complete with respect to (co)domain comparison of KAT terms, but incomplete when comparing the (co)domain of arbitrary TopKAT terms. Since the encoding of under-approximate specifications in TopKAT hinges on this type of formula, the aforementioned incompleteness results have a limited impact when using TopKAT to reason about such specifications.
Cite as

Cheng Zhang, Arthur Azevedo de Amorim, and Marco Gaboardi. Domain Reasoning in TopKAT. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 157:1-157:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{zhang_et_al:LIPIcs.ICALP.2024.157,
  author =	{Zhang, Cheng and de Amorim, Arthur Azevedo and Gaboardi, Marco},
  title =	{{Domain Reasoning in TopKAT}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{157:1--157:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.157},
  URN =		{urn:nbn:de:0030-drops-203003},
  doi =		{10.4230/LIPIcs.ICALP.2024.157},
  annote =	{Keywords: Kleene algebra, Kleene Algebra With Tests, Kleene Algebra With Domain, Kleene Algebra With Top and Tests, Completeness, Decidability}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.FSCD.2023
LIPIcs, Volume 260, FSCD 2023, Complete Volume

Authors: Marco Gaboardi and Femke van Raamsdonk

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
LIPIcs, Volume 260, FSCD 2023, Complete Volume
Cite as

8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 1-658, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Proceedings{gaboardi_et_al:LIPIcs.FSCD.2023,
  title =	{{LIPIcs, Volume 260, FSCD 2023, Complete Volume}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{1--658},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023},
  URN =		{urn:nbn:de:0030-drops-179830},
  doi =		{10.4230/LIPIcs.FSCD.2023},
  annote =	{Keywords: LIPIcs, Volume 260, FSCD 2023, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.FSCD.2023.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Marco Gaboardi and Femke van Raamsdonk

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

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

8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{gaboardi_et_al:LIPIcs.FSCD.2023.0,
  author =	{Gaboardi, Marco and van Raamsdonk, Femke},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{0:i--0:xviii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.0},
  URN =		{urn:nbn:de:0030-drops-179849},
  doi =		{10.4230/LIPIcs.FSCD.2023.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2023.1
Nominal Techniques for Software Specification and Verification (Invited Talk)

Authors: Maribel Fernández

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
In this talk we discuss the nominal approach to the specification of languages with binders and some applications to programming languages and verification.
Cite as

Maribel Fernández. Nominal Techniques for Software Specification and Verification (Invited Talk). In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 1:1-1:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fernandez:LIPIcs.FSCD.2023.1,
  author =	{Fern\'{a}ndez, Maribel},
  title =	{{Nominal Techniques for Software Specification and Verification}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{1:1--1:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.1},
  URN =		{urn:nbn:de:0030-drops-179855},
  doi =		{10.4230/LIPIcs.FSCD.2023.1},
  annote =	{Keywords: Binding operator, Nominal Logic, Nominal Rewriting, Unification, Equational Theories, Type Systems}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2023.2
How Can We Make Trustworthy AI? (Invited Talk)

Authors: Mateja Jamnik

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
Not too long ago most headlines talked about our fear of AI. Today, AI is ubiquitous, and the conversation has moved on from whether we should use AI to how we can trust the AI systems that we use in our daily lives. In this talk I look at some key technical ingredients that help us build confidence and trust in using intelligent technology. I argue that intuitiveness, interaction, explainability and inclusion of human domain knowledge are essential in building this trust. I present some of the techniques and methods we are building for making AI systems that think and interact with humans in more intuitive and personalised ways, enabling humans to better understand the solutions produced by machines, and enabling machines to incorporate human domain knowledge in their reasoning and learning processes.
Cite as

Mateja Jamnik. How Can We Make Trustworthy AI? (Invited Talk). In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{jamnik:LIPIcs.FSCD.2023.2,
  author =	{Jamnik, Mateja},
  title =	{{How Can We Make Trustworthy AI?}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.2},
  URN =		{urn:nbn:de:0030-drops-179869},
  doi =		{10.4230/LIPIcs.FSCD.2023.2},
  annote =	{Keywords: AI, human-centric computing, knowledge representation, reasoning, machine learning}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2023.3
A Lambda Calculus Satellite (Invited Talk)

Authors: Giulio Manzonetto

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
We shortly summarize the contents of the book "A Lambda Calculus Satellite", presented at the 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023).
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Giulio Manzonetto. A Lambda Calculus Satellite (Invited Talk). In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 3:1-3:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{manzonetto:LIPIcs.FSCD.2023.3,
  author =	{Manzonetto, Giulio},
  title =	{{A Lambda Calculus Satellite}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{3:1--3:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.3},
  URN =		{urn:nbn:de:0030-drops-179878},
  doi =		{10.4230/LIPIcs.FSCD.2023.3},
  annote =	{Keywords: \lambda-calculus, rewriting, denotational models, equational theories}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2023.4
Termination of Term Rewriting: Foundation, Formalization, Implementation, and Competition (Invited Talk)

Authors: Akihisa Yamada

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
Automated termination analysis is a central topic in the research of term rewriting. In this talk, I will first review the theoretical foundation of termination of term rewriting, leading to the recently established tuple interpretation method. Then I will present an Isabelle/HOL formalization of the theory. Although the formalization is based on the existing library IsaFoR (Isabelle Formalization of Rewriting), the present work takes another approach of representing relations (predicates rather than sets) so that the notation is more human friendly. Then I will present a unified implementation of the termination analysis techniques via SMT encoding, leading to the termination prover NaTT. Many tools have been developed for termination analysis and have been competing annually in termCOMP (Termination Competition) for two decades. At the end of the talk, I will share my experience in organizing termCOMP in the last five years.
Cite as

Akihisa Yamada. Termination of Term Rewriting: Foundation, Formalization, Implementation, and Competition (Invited Talk). In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 4:1-4:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{yamada:LIPIcs.FSCD.2023.4,
  author =	{Yamada, Akihisa},
  title =	{{Termination of Term Rewriting: Foundation, Formalization, Implementation, and Competition}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{4:1--4:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.4},
  URN =		{urn:nbn:de:0030-drops-179882},
  doi =		{10.4230/LIPIcs.FSCD.2023.4},
  annote =	{Keywords: Term rewriting, Termination, Isabelle/HOL, Competition}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2023.5
Homotopy Type Theory as Internal Languages of Diagrams of ∞-Logoses

Authors: Taichi Uemura

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
We show that certain diagrams of ∞-logoses are reconstructed in internal languages of their oplax limits via lex, accessible modalities, which enables us to use plain homotopy type theory to reason about not only a single ∞-logos but also a diagram of ∞-logoses. This also provides a higher dimensional version of Sterling’s synthetic Tait computability - a type theory for higher dimensional logical relations.
Cite as

Taichi Uemura. Homotopy Type Theory as Internal Languages of Diagrams of ∞-Logoses. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 5:1-5:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{uemura:LIPIcs.FSCD.2023.5,
  author =	{Uemura, Taichi},
  title =	{{Homotopy Type Theory as Internal Languages of Diagrams of ∞-Logoses}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{5:1--5:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.5},
  URN =		{urn:nbn:de:0030-drops-179897},
  doi =		{10.4230/LIPIcs.FSCD.2023.5},
  annote =	{Keywords: Homotopy type theory, ∞-logos, ∞-topos, oplax limit, Artin gluing, modality, synthetic Tait computability, logical relation}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2023.6
The Formal Theory of Monads, Univalently

Authors: Niels van der Weide

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
We develop the formal theory of monads, as established by Street, in univalent foundations. This allows us to formally reason about various kinds of monads on the right level of abstraction. In particular, we define the bicategory of monads internal to a bicategory, and prove that it is univalent. We also define Eilenberg-Moore objects, and we show that both Eilenberg-Moore categories and Kleisli categories give rise to Eilenberg-Moore objects. Finally, we relate monads and adjunctions in arbitrary bicategories. Our work is formalized in Coq using the https://github.com/UniMath/UniMath library.
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Niels van der Weide. The Formal Theory of Monads, Univalently. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{vanderweide:LIPIcs.FSCD.2023.6,
  author =	{van der Weide, Niels},
  title =	{{The Formal Theory of Monads, Univalently}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.6},
  URN =		{urn:nbn:de:0030-drops-179904},
  doi =		{10.4230/LIPIcs.FSCD.2023.6},
  annote =	{Keywords: bicategory theory, univalent foundations, formalization, monads, Coq}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2023.7
Automata-Based Verification of Relational Properties of Functions over Algebraic Data Structures

Authors: Théo Losekoot, Thomas Genet, and Thomas Jensen

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
This paper is concerned with automatically proving properties about the input-output relation of functional programs operating over algebraic data types. Recent results show how to approximate the image of a functional program using a regular tree language. Though expressive, those techniques cannot prove properties relating the input and the output of a function, e.g., proving that the output of a function reversing a list has the same length as the input list. In this paper, we built upon those results and define a procedure to compute or over-approximate such a relation. Instead of representing the image of a function by a regular set of terms, we represent (an approximation of) the input-output relation by a regular set of tuples of terms. Regular languages of tuples of terms are recognized using a tree automaton recognizing convolutions of terms, where a convolution transforms a tuple of terms into a term built on tuples of symbols. Both the program and the properties are transformed into predicates and Constrained Horn clauses (CHCs). Then, using an Implication Counter Example procedure (ICE), we infer a model of the clauses, associating to each predicate a regular relation. In this ICE procedure, checking if a given model satisfies the clauses is undecidable in general. We overcome undecidability by proposing an incomplete but sound inference procedure for such relational regular properties. Though the procedure is incomplete, its implementation performs well on 120 examples. It efficiently proves non-trivial relational properties or finds counter-examples.
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Théo Losekoot, Thomas Genet, and Thomas Jensen. Automata-Based Verification of Relational Properties of Functions over Algebraic Data Structures. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 7:1-7:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{losekoot_et_al:LIPIcs.FSCD.2023.7,
  author =	{Losekoot, Th\'{e}o and Genet, Thomas and Jensen, Thomas},
  title =	{{Automata-Based Verification of Relational Properties of Functions over Algebraic Data Structures}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{7:1--7:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.7},
  URN =		{urn:nbn:de:0030-drops-179915},
  doi =		{10.4230/LIPIcs.FSCD.2023.7},
  annote =	{Keywords: Formal verification, Tree automata, Constrained Horn Clauses, Model inference, Relational properties, Algebraic datatypes}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2023.8
The Sum-Product Algorithm For Quantitative Multiplicative Linear Logic

Authors: Thomas Ehrhard, Claudia Faggian, and Michele Pagani

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
We consider an extension of multiplicative linear logic which encompasses bayesian networks and expresses samples sharing and marginalisation with the polarised rules of contraction and weakening. We introduce the necessary formalism to import exact inference algorithms from bayesian networks, giving the sum-product algorithm as an example of calculating the weighted relational semantics of a multiplicative proof-net improving runtime performance by storing intermediate results.
Cite as

Thomas Ehrhard, Claudia Faggian, and Michele Pagani. The Sum-Product Algorithm For Quantitative Multiplicative Linear Logic. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ehrhard_et_al:LIPIcs.FSCD.2023.8,
  author =	{Ehrhard, Thomas and Faggian, Claudia and Pagani, Michele},
  title =	{{The Sum-Product Algorithm For Quantitative Multiplicative Linear Logic}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.8},
  URN =		{urn:nbn:de:0030-drops-179926},
  doi =		{10.4230/LIPIcs.FSCD.2023.8},
  annote =	{Keywords: Linear Logic, Proof-Nets, Denotational Semantics, Probabilistic Programming}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2023.9
Generalized Newman’s Lemma for Discrete and Continuous Systems

Authors: Ievgen Ivanov

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract
We propose a generalization of Newman’s lemma which gives a criterion of confluence for a wide class of not-necessarily-terminating abstract rewriting systems. We show that ordinary Newman’s lemma for terminating systems can be considered as a corollary of this criterion. We describe a formalization of the proposed generalized Newman’s lemma in Isabelle proof assistant using HOL logic.
Cite as

Ievgen Ivanov. Generalized Newman’s Lemma for Discrete and Continuous Systems. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ivanov:LIPIcs.FSCD.2023.9,
  author =	{Ivanov, Ievgen},
  title =	{{Generalized Newman’s Lemma for Discrete and Continuous Systems}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.9},
  URN =		{urn:nbn:de:0030-drops-179936},
  doi =		{10.4230/LIPIcs.FSCD.2023.9},
  annote =	{Keywords: abstract rewriting system, confluence, discrete-continuous systems, proof assistant, formal proof}
}
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