25 Search Results for "de'Liguoro, Ugo"

Volume

LIPIcs, Volume 188

26th International Conference on Types for Proofs and Programs (TYPES 2020)

TYPES 2020, March 2-5, 2020, University of Turin, Italy

Editors: Ugo de'Liguoro, Stefano Berardi, and Thorsten Altenkirch

Document
DOI: 10.4230/LIPIcs.ITP.2025.8
Abstract, Compositional Consistency: Isabelle/HOL Locales for Completeness à la Fitting

Authors: Asta Halkjær From and Anders Schlichtkrull

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

Abstract
Smullyan and Fitting have used abstract consistency properties to great effect in unifying meta-theoretical results in logic. In this paper, we generalize these developments with the help of Isabelle/HOL. We use locales to decompose abstract consistency into general parts, and provide the textbook variants as special cases. Users can assemble their own consistency property for a given logic. The compositionality alleviates the absence of dependent types in Isabelle/HOL. We use our development to mechanize completeness of calculi for three logics: (1) first-order logic where we only instantiate universal quantifiers with already occurring terms, (2) second-order logic over general models, and (3) a recently developed strong hybrid logic with propositional quantification.
Cite as

Asta Halkjær From and Anders Schlichtkrull. Abstract, Compositional Consistency: Isabelle/HOL Locales for Completeness à la Fitting. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{from_et_al:LIPIcs.ITP.2025.8,
  author =	{From, Asta Halkj{\ae}r and Schlichtkrull, Anders},
  title =	{{Abstract, Compositional Consistency: Isabelle/HOL Locales for Completeness \`{a} la Fitting}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{8:1--8:20},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-246406},
  doi =		{10.4230/LIPIcs.ITP.2025.8},
  annote =	{Keywords: Logic, completeness, abstract consistency property, Isabelle/HOL, locales}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.10
Abstract Subtyping for Asynchronous Multiparty Sessions

Authors: Laura Bocchi, Andy King, Maurizio Murgia, and Simon Thompson

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
Session subtyping answers the question of whether a program in a communicating system can be safely substituted for another, when their communication behaviour is described by session types. Asynchronous session subtyping is undecidable, even for two participants, hence the interest in sound, but incomplete, subtyping algorithms. Asynchronous multiparty subtyping can be formulated by decomposing session types into single input and output types which preclude, respectively, external and internal choice. This paper shows how abstract interpretation can sit atop this approach and how it leads to an algorithm that can prove subtyping for intricate communication patterns.
Cite as

Laura Bocchi, Andy King, Maurizio Murgia, and Simon Thompson. Abstract Subtyping for Asynchronous Multiparty Sessions. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 10:1-10:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bocchi_et_al:LIPIcs.CONCUR.2025.10,
  author =	{Bocchi, Laura and King, Andy and Murgia, Maurizio and Thompson, Simon},
  title =	{{Abstract Subtyping for Asynchronous Multiparty Sessions}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{10:1--10:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.10},
  URN =		{urn:nbn:de:0030-drops-239605},
  doi =		{10.4230/LIPIcs.CONCUR.2025.10},
  annote =	{Keywords: asynchrony, session subtyping, automata, abstract interpretation}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.12
Ohana Trees and Taylor Expansion for the λI-Calculus: No variable gets left behind or forgotten!

Authors: Rémy Cerda, Giulio Manzonetto, and Alexis Saurin

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Although the λI-calculus is a natural fragment of the λ-calculus, obtained by forbidding the erasure, its equational theories did not receive much attention. The reason is that all proper denotational models studied in the literature equate all non-normalizable λI-terms, whence the associated theory is not very informative. The goal of this paper is to introduce a previously unknown theory of the λI-calculus, induced by a notion of evaluation trees that we call "Ohana trees". The Ohana tree of a λI-term is an annotated version of its Böhm tree, remembering all free variables that are hidden within its meaningless subtrees, or pushed into infinity along its infinite branches. We develop the associated theories of program approximation: the first approach - more classic - is based on finite trees and continuity, the second adapts Ehrhard and Regnier’s Taylor expansion. We then prove a Commutation Theorem stating that the normal form of the Taylor expansion of a λI-term coincides with the Taylor expansion of its Ohana tree. As a corollary, we obtain that the equality induced by Ohana trees is compatible with abstraction and application. We conclude by discussing the cases of Lévy-Longo and Berarducci trees, and generalizations to the full λ-calculus.
Cite as

Rémy Cerda, Giulio Manzonetto, and Alexis Saurin. Ohana Trees and Taylor Expansion for the λI-Calculus: No variable gets left behind or forgotten!. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cerda_et_al:LIPIcs.FSCD.2025.12,
  author =	{Cerda, R\'{e}my and Manzonetto, Giulio and Saurin, Alexis},
  title =	{{Ohana Trees and Taylor Expansion for the \lambdaI-Calculus: No variable gets left behind or forgotten!}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.12},
  URN =		{urn:nbn:de:0030-drops-236277},
  doi =		{10.4230/LIPIcs.FSCD.2025.12},
  annote =	{Keywords: \lambda-calculus, program approximation, Taylor expansion, \lambdaI-calculus, persistent free variables, B\"{o}hm trees, Ohana trees}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.29
Linear Logic Using Negative Connectives

Authors: Dale Miller

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
In linear logic, the invertibility of a connective’s right-introduction rule is equivalent to the non-invertibility of its left-introduction rule. This duality motivates the concept of polarity: a connective is termed negative if its right-introduction rule is invertible, and positive otherwise. A two-sided sequent calculus for first-order linear logic featuring only negative connectives exhibits a compelling proof theory. Proof search in such a system unfolds through alternating phases of invertible (right-introduction) rules and non-invertible (left-introduction) rules, mirroring the processes of goal-reduction and backchaining, respectively. These phases are formalized here using the framework of multifocused proofs. We analyze linear logic by dissecting it into three sublogics: L₀ (first-order intuitionistic logic with conjunction, implication, and universal quantification); L₁ (an extension of L₀ incorporating linear implication which preserves its intuitionistic nature); and L₂ (which includes multiplicative falsity ⊥ and encompasses classical linear logic). It is worth noting that the single-conclusion restriction on sequents, a constraint imposed by Gentzen, is not a prerequisite for defining intuitionistic logic proofs within this framework, as it emerges naturally by restricting the formulas to those of L₀ and L₁. While multifocused proofs of L₂ sequents can accommodate parallel applications of left-introduction rules, proofs of L₀ and L₁ sequents cannot leverage such parallel rule applications. This notion of parallelism within proofs enables a novel approach to handling disjunctions and existential quantifiers in the natural deduction system for intuitionistic logic.
Cite as

Dale Miller. Linear Logic Using Negative Connectives. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 29:1-29:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{miller:LIPIcs.FSCD.2025.29,
  author =	{Miller, Dale},
  title =	{{Linear Logic Using Negative Connectives}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{29:1--29:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.29},
  URN =		{urn:nbn:de:0030-drops-236442},
  doi =		{10.4230/LIPIcs.FSCD.2025.29},
  annote =	{Keywords: Linear logic, multifocused proofs, sequent calculus}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2025.17
Contrasting Deadlock-Free Session Processes

Authors: Juan C. Jaramillo and Jorge A. Pérez

Published in: LIPIcs, Volume 333, 39th European Conference on Object-Oriented Programming (ECOOP 2025)

Abstract
Deadlock freedom is a crucial property for message-passing programs. Over the years, several different type systems for concurrent processes that ensure deadlock freedom have been proposed; this diversity raises the question of how they compare. We address this question, considering two type systems not covered in prior work: Kokke et al.’s HCP, a type system based on a linear logic with hypersequents, and Padovani’s priority-based type system for asynchronous processes, dubbed 𝖯. Their distinctive features make formal comparisons relevant and challenging. Our findings are two-fold: (1) the hypersequent setting does not drastically change the class of deadlock-free processes induced by linear logic, and (2) we relate the classes of deadlock-free processes induced by HCP and 𝖯. We prove that our results hold under both synchronous and asynchronous communication. Our results provide new insights into the essential mechanisms involved in statically avoiding deadlocks in concurrency.
Cite as

Juan C. Jaramillo and Jorge A. Pérez. Contrasting Deadlock-Free Session Processes. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 17:1-17:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jaramillo_et_al:LIPIcs.ECOOP.2025.17,
  author =	{Jaramillo, Juan C. and P\'{e}rez, Jorge A.},
  title =	{{Contrasting Deadlock-Free Session Processes}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{17:1--17:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-373-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{333},
  editor =	{Aldrich, Jonathan and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2025.17},
  URN =		{urn:nbn:de:0030-drops-233103},
  doi =		{10.4230/LIPIcs.ECOOP.2025.17},
  annote =	{Keywords: session types, process calculi, deadlock freedom}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.31
Simple Types for Probabilistic Termination

Authors: Willem Heijltjes and Georgina Majury

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

Abstract
We present a new typing discipline to guarantee the probability of termination in probabilistic lambda-calculi. The main contribution is a particular naturality and simplicity: our probabilistic types are as simple types, but generated from probabilities as base types, representing a least probability of termination. Simple types are recovered by restricting probabilities to one. Our vehicle is the Probabilistic Event Lambda-Calculus by Dal Lago, Guerrieri, and Heijltjes, which presents a solution to the issue of confluence in probabilistic lambda-calculi. Our probabilistic type system provides an alternative solution to that using counting quantifiers by Antonelli, Dal Lago, and Pistone, for the same calculus. The problem that both type systems address is to give a lower bound on the probability that terms head-normalize. Following the recent Functional Machine Calculus by Heijltjes, our development takes the (simplified) Krivine machine as primary, and proceeds via an extension of the calculus with sequential composition and identity on the machine. Our type system then gives a natural account of termination probability on the Krivine machine, reflected back onto head-normalization for the original calculus. In this way we are able to avoid the use of counting quantifiers, while improving on the termination bounds given by Antonelli, Dal Lago, and Pistone.
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Willem Heijltjes and Georgina Majury. Simple Types for Probabilistic Termination. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 31:1-31:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{heijltjes_et_al:LIPIcs.CSL.2025.31,
  author =	{Heijltjes, Willem and Majury, Georgina},
  title =	{{Simple Types for Probabilistic Termination}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{31:1--31:21},
  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.2025.31},
  URN =		{urn:nbn:de:0030-drops-227885},
  doi =		{10.4230/LIPIcs.CSL.2025.31},
  annote =	{Keywords: lambda-calculus, probabilistic termination, simple types}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.47
A Rewriting Theory for Quantum λ-Calculus

Authors: Claudia Faggian, Gaetan Lopez, and Benoît Valiron

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

Abstract
Quantum lambda calculus has been studied mainly as an idealized programming language - the evaluation essentially corresponds to a deterministic abstract machine. Very little work has been done to develop a rewriting theory for quantum lambda calculus. Recent advances in the theory of probabilistic rewriting give us a way to tackle this task with tools unavailable a decade ago. Our primary focus are standardization and normalization results.
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Claudia Faggian, Gaetan Lopez, and Benoît Valiron. A Rewriting Theory for Quantum λ-Calculus. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 47:1-47:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{faggian_et_al:LIPIcs.CSL.2025.47,
  author =	{Faggian, Claudia and Lopez, Gaetan and Valiron, Beno\^{i}t},
  title =	{{A Rewriting Theory for Quantum \lambda-Calculus}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{47:1--47:22},
  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.2025.47},
  URN =		{urn:nbn:de:0030-drops-228046},
  doi =		{10.4230/LIPIcs.CSL.2025.47},
  annote =	{Keywords: quantum lambda-calculus, probabilistic rewriting, operational semantics, asymptotic normalization, principles of quantum programming languages}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.TYPES.2020
LIPIcs, Volume 188, TYPES 2020, Complete Volume

Authors: Ugo de'Liguoro, Stefano Berardi, and Thorsten Altenkirch

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

Abstract
LIPIcs, Volume 188, TYPES 2020, Complete Volume
Cite as

26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 1-204, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Proceedings{deliguoro_et_al:LIPIcs.TYPES.2020,
  title =	{{LIPIcs, Volume 188, TYPES 2020, Complete Volume}},
  booktitle =	{26th International Conference on Types for Proofs and Programs (TYPES 2020)},
  pages =	{1--204},
  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},
  URN =		{urn:nbn:de:0030-drops-138785},
  doi =		{10.4230/LIPIcs.TYPES.2020},
  annote =	{Keywords: LIPIcs, Volume 188, TYPES 2020, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.TYPES.2020.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Ugo de'Liguoro, Stefano Berardi, and Thorsten Altenkirch

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

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

26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 0:i-0:viii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{deliguoro_et_al:LIPIcs.TYPES.2020.0,
  author =	{de'Liguoro, Ugo and Berardi, Stefano and Altenkirch, Thorsten},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{26th International Conference on Types for Proofs and Programs (TYPES 2020)},
  pages =	{0:i--0:viii},
  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.2020.0},
  URN =		{urn:nbn:de:0030-drops-138792},
  doi =		{10.4230/LIPIcs.TYPES.2020.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2020.1
On Model-Theoretic Strong Normalization for Truth-Table Natural Deduction

Authors: Andreas Abel

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

Abstract
Intuitionistic truth table natural deduction (ITTND) by Geuvers and Hurkens (2017), which is inherently non-confluent, has been shown strongly normalizing (SN) using continuation-passing-style translations to parallel lambda calculus by Geuvers, van der Giessen, and Hurkens (2019). We investigate the applicability of standard model-theoretic proof techniques and show (1) SN of detour reduction (β) using Girard’s reducibility candidates, and (2) SN of detour and permutation reduction (βπ) using biorthogonals. In the appendix, we adapt Tait’s method of saturated sets to β, clarifying the original proof of 2017, and extend it to βπ.
Cite as

Andreas Abel. On Model-Theoretic Strong Normalization for Truth-Table Natural Deduction. In 26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 1:1-1:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{abel:LIPIcs.TYPES.2020.1,
  author =	{Abel, Andreas},
  title =	{{On Model-Theoretic Strong Normalization for Truth-Table Natural Deduction}},
  booktitle =	{26th International Conference on Types for Proofs and Programs (TYPES 2020)},
  pages =	{1:1--1:21},
  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.2020.1},
  URN =		{urn:nbn:de:0030-drops-138805},
  doi =		{10.4230/LIPIcs.TYPES.2020.1},
  annote =	{Keywords: Natural deduction, Permutative conversion, Reducibility, Strong normalization, Truth table}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2020.2
Extending Equational Monadic Reasoning with Monad Transformers

Authors: Reynald Affeldt and David Nowak

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

Abstract
There is a recent interest for the verification of monadic programs using proof assistants. This line of research raises the question of the integration of monad transformers, a standard technique to combine monads. In this paper, we extend Monae, a Coq library for monadic equational reasoning, with monad transformers and we explain the benefits of this extension. Our starting point is the existing theory of modular monad transformers, which provides a uniform treatment of operations. Using this theory, we simplify the formalization of models in Monae and we propose an approach to support monadic equational reasoning in the presence of monad transformers. We also use Monae to revisit the lifting theorems of modular monad transformers by providing equational proofs and explaining how to patch a known bug using a non-standard use of Coq that combines impredicative polymorphism and parametricity.
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Reynald Affeldt and David Nowak. Extending Equational Monadic Reasoning with Monad Transformers. In 26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 2:1-2:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{affeldt_et_al:LIPIcs.TYPES.2020.2,
  author =	{Affeldt, Reynald and Nowak, David},
  title =	{{Extending Equational Monadic Reasoning with Monad Transformers}},
  booktitle =	{26th International Conference on Types for Proofs and Programs (TYPES 2020)},
  pages =	{2:1--2:21},
  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.2020.2},
  URN =		{urn:nbn:de:0030-drops-138810},
  doi =		{10.4230/LIPIcs.TYPES.2020.2},
  annote =	{Keywords: monads, monad transformers, Coq, impredicativity, parametricity}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2020.3
Towards a Certified Reference Monitor of the Android 10 Permission System

Authors: Guido De Luca and Carlos Luna

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

Abstract
Android is a platform for mobile devices that captures more than 85% of the total market share [International Data Corporation (IDC), 2020]. Currently, mobile devices allow people to develop multiple tasks in different areas. Regrettably, the benefits of using mobile devices are counteracted by increasing security risks. The important and critical role of these systems makes them a prime target for formal verification. In our previous work [Betarte et al., 2018], we exhibited a formal specification of an idealized formulation of the permission model of version 6 of Android. In this paper we present an enhanced version of the model in the proof assistant Coq, including the most relevant changes concerning the permission system introduced in versions Nougat, Oreo, Pie and 10. The properties that we had proved earlier for the security model have been either revalidated or refuted, and new ones have been formulated and proved. Additionally, we make observations on the security of the most recent versions of Android. Using the programming language of Coq we have developed a functional implementation of a reference validation mechanism and certified its correctness. The formal development is about 23k LOC of Coq, including proofs.
Cite as

Guido De Luca and Carlos Luna. Towards a Certified Reference Monitor of the Android 10 Permission System. In 26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{deluca_et_al:LIPIcs.TYPES.2020.3,
  author =	{De Luca, Guido and Luna, Carlos},
  title =	{{Towards a Certified Reference Monitor of the Android 10 Permission System}},
  booktitle =	{26th International Conference on Types for Proofs and Programs (TYPES 2020)},
  pages =	{3:1--3:18},
  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.2020.3},
  URN =		{urn:nbn:de:0030-drops-138821},
  doi =		{10.4230/LIPIcs.TYPES.2020.3},
  annote =	{Keywords: Android, Permission model, Formal idealized model, Reference monitor, Formal proofs, Certified implementation, Coq}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2020.4
Coinductive Proof Search for Polarized Logic with Applications to Full Intuitionistic Propositional Logic

Authors: José Espírito Santo, Ralph Matthes, and Luís Pinto

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

Abstract
The approach to proof search dubbed "coinductive proof search", and previously developed by the authors for implicational intuitionistic logic, is in this paper extended to LJP, a focused sequent-calculus presentation of polarized intuitionistic logic, including an array of positive and negative connectives. As before, this includes developing a coinductive description of the search space generated by a sequent, an equivalent inductive syntax describing the same space, and decision procedures for inhabitation problems in the form of predicates defined by recursion on the inductive syntax. We prove the decidability of existence of focused inhabitants, and of finiteness of the number of focused inhabitants for polarized intuitionistic logic, by means of such recursive procedures. Moreover, the polarized logic can be used as a platform from which proof search for other logics is understood. We illustrate the technique with LJT, a focused sequent calculus for full intuitionistic propositional logic (including disjunction). For that, we have to work out the "negative translation" of LJT into LJP (that sees all intuitionistic types as negative types), and verify that the translation gives a faithful representation of proof search in LJT as proof search in the polarized logic. We therefore inherit decidability of both problems studied for LJP and thus get new proofs of these results for LJT.
Cite as

José Espírito Santo, Ralph Matthes, and Luís Pinto. Coinductive Proof Search for Polarized Logic with Applications to Full Intuitionistic Propositional Logic. In 26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 4:1-4:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{espiritosanto_et_al:LIPIcs.TYPES.2020.4,
  author =	{Esp{\'\i}rito Santo, Jos\'{e} and Matthes, Ralph and Pinto, Lu{\'\i}s},
  title =	{{Coinductive Proof Search for Polarized Logic with Applications to Full Intuitionistic Propositional Logic}},
  booktitle =	{26th International Conference on Types for Proofs and Programs (TYPES 2020)},
  pages =	{4:1--4:24},
  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.2020.4},
  URN =		{urn:nbn:de:0030-drops-138837},
  doi =		{10.4230/LIPIcs.TYPES.2020.4},
  annote =	{Keywords: Inhabitation problems, Coinduction, Lambda-calculus, Polarized logic}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2020.5
Synthetic Completeness for a Terminating Seligman-Style Tableau System

Authors: Asta Halkjær From

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

Abstract
Hybrid logic extends modal logic with nominals that name worlds. Seligman-style tableau systems for hybrid logic divide branches into blocks named by nominals to achieve a local proof style. We present a Seligman-style tableau system with a formalization in the proof assistant Isabelle/HOL. Our system refines an existing system to simplify formalization and we claim termination from this relationship. Existing completeness proofs that account for termination are either analytic or based on translation, but synthetic proofs have been shown to generalize to richer logics and languages. Our main result is the first synthetic completeness proof for a terminating hybrid logic tableau system. It is also the first formalized completeness proof for any hybrid logic proof system.
Cite as

Asta Halkjær From. Synthetic Completeness for a Terminating Seligman-Style Tableau System. In 26th International Conference on Types for Proofs and Programs (TYPES 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 188, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{from:LIPIcs.TYPES.2020.5,
  author =	{From, Asta Halkj{\ae}r},
  title =	{{Synthetic Completeness for a Terminating Seligman-Style Tableau System}},
  booktitle =	{26th International Conference on Types for Proofs and Programs (TYPES 2020)},
  pages =	{5:1--5:17},
  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.2020.5},
  URN =		{urn:nbn:de:0030-drops-138847},
  doi =		{10.4230/LIPIcs.TYPES.2020.5},
  annote =	{Keywords: Hybrid logic, Seligman-style tableau, synthetic completeness, Isabelle/HOL}
}
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