16 Search Results for "Jouannaud, Jean-Pierre"

Document
DOI: 10.4230/LIPIcs.CSL.2026.18
A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light

Authors: Antonella Bilotta, Marco Maggesi, and Cosimo Perini Brogi

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
We extend the existing HOL Light Library for Modal Systems (HOLMS) to support a modular implementation of modal reasoning within the HOL Light proof assistant. We deeply embed axiomatic calculi and relational semantics for seven normal modal logics (K, T, B, K4, S4, S5, GL) and formalise modal adequacy theorems for these systems. We then leverage those formalisations to implement a mechanism for automated reasoning via proof-search in the associated labelled sequent calculi, which we shallowly embed in HOL Light’s goal-stack mechanism. This way, we equip the general-purpose proof assistant with (semi)decision procedures for these logics that, in case of failure to construct a proof for the input formula, return a certified countermodel within the appropriate class for the logic under consideration. On the methodological side, we propose a precise measure of the modularity of our approach by systematically adopting Christopher Strachey’s distinction between ad hoc and parametric polymorphism throughout the library.
Cite as

Antonella Bilotta, Marco Maggesi, and Cosimo Perini Brogi. A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 18:1-18:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bilotta_et_al:LIPIcs.CSL.2026.18,
  author =	{Bilotta, Antonella and Maggesi, Marco and Perini Brogi, Cosimo},
  title =	{{A Modular Framework for Proof-Search via Formalised Modal Completeness in HOL Light}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{18:1--18:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.18},
  URN =		{urn:nbn:de:0030-drops-254427},
  doi =		{10.4230/LIPIcs.CSL.2026.18},
  annote =	{Keywords: Modal logic, HOL Light, Labelled sequent calculi, Logical verification, Interactive theorem proving, Automated proof-search}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.39
A Canonical Form for Universe Levels in Impredicative Type Theory

Authors: Yoan Géran

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract
The 0-imax-successor algebra, where imax: ℕ × ℕ → ℕ is the function defined by imax(n, 0) = 0 and imax(n, S(m)) = max(n, S(m)), is used to represent universe levels in impredicative type theory, in particular with universe polymorphism which introduces level variables, so it is present in proof systems such as Rocq and Lean. In particular, we need to know when two elements of this algebra are equivalent, and we may also want to decide the inequality. In this article, we introduce a canonical form for the terms of this algebra, and we provide a canonization algorithm. It permits deciding level equivalence by checking the canonical form equality, and also permits easily checking if a level is smaller than another one.
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Yoan Géran. A Canonical Form for Universe Levels in Impredicative Type Theory. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 39:1-39:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{geran:LIPIcs.CSL.2026.39,
  author =	{G\'{e}ran, Yoan},
  title =	{{A Canonical Form for Universe Levels in Impredicative Type Theory}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{39:1--39:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.39},
  URN =		{urn:nbn:de:0030-drops-254640},
  doi =		{10.4230/LIPIcs.CSL.2026.39},
  annote =	{Keywords: universe levels, canonical form, impredicativity, imax algebra}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.5
A Mechanized First-Order Theory of Algebraic Data Types with Pattern Matching

Authors: Joshua M. Cohen

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

Abstract
Algebraic data types (ADTs) and pattern matching are widely used to write elegant functional programs and to specify program behavior. These constructs are critical to most general-purpose interactive theorem provers (e.g. Lean, Rocq/Coq), first-order SMT-based deductive verifiers (e.g. Dafny, VeriFast), and intermediate verification languages (e.g. Why3). Such features require layers of compilation - in Rocq, pattern matches are compiled to remove nesting, while SMT-based tools further axiomatize ADTs with a first-order specification. However, these critical steps have been omitted from prior formalizations of such toolchains (e.g. MetaRocq). We give the first proved-sound sophisticated pattern matching compiler (based on Maranget’s compilation to decision trees) and first-order axiomatization of ADTs, both based on Why3 implementations. We prove the soundness of exhaustiveness checking, extending pen-and-paper proofs from the literature, and formulate a robustness property with which we find an exhaustiveness-related bug in Why3. We show that many of our proofs could be useful for reasoning about any first-order program verifier supporting ADTs.
Cite as

Joshua M. Cohen. A Mechanized First-Order Theory of Algebraic Data Types with Pattern Matching. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cohen:LIPIcs.ITP.2025.5,
  author =	{Cohen, Joshua M.},
  title =	{{A Mechanized First-Order Theory of Algebraic Data Types with Pattern Matching}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{5:1--5:20},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-246046},
  doi =		{10.4230/LIPIcs.ITP.2025.5},
  annote =	{Keywords: Pattern Matching Compilation, Algebraic Data Types, First-Order Logic}
}
Document
Short Paper
DOI: 10.4230/LIPIcs.ITP.2025.39
Towards Automating Permutation Proofs in Rocq: A Reflexive Approach with Iterative Deepening Search (Short Paper)

Authors: Nadeem Abdul Hamid

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

Abstract
The concept of permutations is fundamental in computer science, and is useful for specifying and reasoning about a variety of data structures and algorithms. This paper presents the implementation of a fully automated tactic for proving complex permutation goals within the Rocq Prover (formerly, Coq proof assistant). Our approach leverages proof by reflection and an iterative deepening search procedure to establish permutation relations on arbitrary lists composed of concatenation operations. We detail the construction of mapping/substitution environments, a unification algorithm, and metaprogramming tactics to automate the proof process. The potential impact of the tactic for goals involving permutations is demonstrated by significant reduction in proof script length for an existing non-trivial development.
Cite as

Nadeem Abdul Hamid. Towards Automating Permutation Proofs in Rocq: A Reflexive Approach with Iterative Deepening Search (Short Paper). In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 39:1-39:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{abdulhamid:LIPIcs.ITP.2025.39,
  author =	{Abdul Hamid, Nadeem},
  title =	{{Towards Automating Permutation Proofs in Rocq: A Reflexive Approach with Iterative Deepening Search}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{39:1--39:7},
  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.2025.39},
  URN =		{urn:nbn:de:0030-drops-246378},
  doi =		{10.4230/LIPIcs.ITP.2025.39},
  annote =	{Keywords: permutations, reflection, tactics, Rocq, Coq}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.10
An Isabelle/HOL Formalization of Semi-Thue and Conditional Semi-Thue Systems

Authors: Dohan Kim

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

Abstract
We present a formalized framework for semi-Thue and conditional semi-Thue systems for studying monoids and their word problem using the Isabelle/HOL proof assistant. We provide a formalized decision procedure for the word problem of monoids if they are finitely presented by complete semi-Thue systems. In particular, we present a new formalized method for checking confluence using (conditional) critical pairs for certain conditional semi-Thue systems. We propose and formalize an inference system for generating conditional equational theories and Thue congruences using conditional semi-Thue systems. Then we provide a new formalized decision procedure for the word problem of monoids which have finite complete (reductive) conditional presentations.
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Dohan Kim. An Isabelle/HOL Formalization of Semi-Thue and Conditional Semi-Thue Systems. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kim:LIPIcs.ITP.2025.10,
  author =	{Kim, Dohan},
  title =	{{An Isabelle/HOL Formalization of Semi-Thue and Conditional Semi-Thue Systems}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{10:1--10:20},
  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.2025.10},
  URN =		{urn:nbn:de:0030-drops-246081},
  doi =		{10.4230/LIPIcs.ITP.2025.10},
  annote =	{Keywords: semi-Thue systems, conditional semi-Thue systems, conditional string rewriting, monoids, word problem}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.7
Combining Generalization Algorithms in Regular Collapse-Free Theories

Authors: Mauricio Ayala-Rincón, David M. Cerna, Temur Kutsia, and Christophe Ringeissen

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

Abstract
We look at the generalization problem modulo some equational theories. This problem is dual to the unification problem: given two input terms, we want to find a common term whose respective two instances are equivalent to the original terms modulo the theory. There exist algorithms for finding generalizations over various equational theories. We focus on modular construction of equational generalization algorithms for the union of signature-disjoint theories. Specifically, we consider the class of regular and collapse-free theories, showing how to combine existing generalization algorithms to produce specific solutions in these cases. Additionally, we identify a class of theories that admit a generalization algorithm based on the application of axioms to resolve the problem. To define this class, we rely on the notion of syntactic theories, a concept originally introduced to develop unification procedures similar to the one known for syntactic unification. We demonstrate that syntactic theories are also helpful in developing generalization procedures similar to those used for syntactic generalization.
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Mauricio Ayala-Rincón, David M. Cerna, Temur Kutsia, and Christophe Ringeissen. Combining Generalization Algorithms in Regular Collapse-Free Theories. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ayalarincon_et_al:LIPIcs.FSCD.2025.7,
  author =	{Ayala-Rinc\'{o}n, Mauricio and Cerna, David M. and Kutsia, Temur and Ringeissen, Christophe},
  title =	{{Combining Generalization Algorithms in Regular Collapse-Free Theories}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{7:1--7:18},
  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.2025.7},
  URN =		{urn:nbn:de:0030-drops-236228},
  doi =		{10.4230/LIPIcs.FSCD.2025.7},
  annote =	{Keywords: Generalization, Anti-unification, Equational theories, Combination}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.8
The Unification Type of an Equational Theory May Depend on the Instantiation Preorder

Authors: Franz Baader and Oliver Fernández Gil

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

Abstract
The unification type of an equational theory is defined using a preorder on substitutions, called the instantiation preorder, whose scope is either restricted to the variables occurring in the unification problem, or unrestricted such that all variables are considered. It has been known for more than three decades that the unification type of an equational theory may vary, depending on which instantiation preorder is used. More precisely, it was shown in 1991 that the theory ACUI of an associative, commutative, and idempotent binary function symbol with a unit is unitary w.r.t. the restricted instantiation preorder, but not unitary w.r.t. the unrestricted one. In 2016 this result was strengthened by showing that the unrestricted type of this theory also cannot be finitary. Here, we considerably improve on this result by proving that ACUI is infinitary w.r.t. the unrestricted instantiation preorder, thus precluding type zero. We also show that, w.r.t. this preorder, the unification type of ACU (where idempotency is removed from the axioms) and of AC (where additionally the unit is removed) is infinitary, though it is respectively unitary and finitary in the restricted case. In the other direction, we prove (using the example of unification in the description logic EL) that the unification type may actually improve from type zero to infinitary when switching from the restricted instantiation preorder to the unrestricted one. In addition, we establish some general results on the relationship between the two instantiation preorders.
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Franz Baader and Oliver Fernández Gil. The Unification Type of an Equational Theory May Depend on the Instantiation Preorder. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 8:1-8:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{baader_et_al:LIPIcs.FSCD.2025.8,
  author =	{Baader, Franz and Fern\'{a}ndez Gil, Oliver},
  title =	{{The Unification Type of an Equational Theory May Depend on the Instantiation Preorder}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{8:1--8:24},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-236230},
  doi =		{10.4230/LIPIcs.FSCD.2025.8},
  annote =	{Keywords: Unification type, Instantiation preorder, Equational theories, Modal and Description Logics}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2025.2
The Algebra of Patterns

Authors: David Binder and Lean Ermantraut

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

Abstract
Pattern matching is a popular feature in functional, imperative and object-oriented programming languages. Language designers should therefore invest effort in a good design for pattern matching. Most languages choose a first-match semantics for pattern matching; that is, clauses are tried in the order in which they appear in the program until the first one matches. As a consequence, the order in which the clauses appear cannot be arbitrarily changed, which results in a less declarative programming model. The declarative alternative to this is an order-independent semantics for pattern matching, which is not implemented in most programming languages since it requires more verbose patterns. The reason for this verbosity is that the syntax of patterns is usually not expressive enough to express the complement of a pattern. In this paper, we show a principled way to make order-independent pattern matching practical. Our solution consists of two parts: First, we introduce a boolean algebra of patterns which can express the complement of a pattern. Second, we introduce default clauses to pattern matches. These default clauses capture the essential idea of a fallthrough case without sacrificing the property of order-independence.
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David Binder and Lean Ermantraut. The Algebra of Patterns. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 2:1-2:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{binder_et_al:LIPIcs.ECOOP.2025.2,
  author =	{Binder, David and Ermantraut, Lean},
  title =	{{The Algebra of Patterns}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{2:1--2:28},
  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.2025.2},
  URN =		{urn:nbn:de:0030-drops-232959},
  doi =		{10.4230/LIPIcs.ECOOP.2025.2},
  annote =	{Keywords: functional programming, pattern matching, algebraic data types, equational reasoning}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.26
The Complexity of Deciding Characteristic Formulae in Van Glabbeek’s Branching-Time Spectrum

Authors: Luca Aceto, Antonis Achilleos, Aggeliki Chalki, and Anna Ingólfsdóttir

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

Abstract
Characteristic formulae give a complete logical description of the behaviour of processes modulo some chosen notion of behavioural semantics. They allow one to reduce equivalence or preorder checking to model checking, and are exactly the formulae in the modal logics characterizing classic behavioural equivalences and preorders for which model checking can be reduced to equivalence or preorder checking. This paper studies the complexity of determining whether a formula is characteristic for some process in each of the logics providing modal characterizations of the simulation-based semantics in van Glabbeek’s branching-time spectrum. Since characteristic formulae in each of those logics are exactly the satisfiable and prime ones, this article presents complexity results for the satisfiability and primality problems, and investigates the boundary between modal logics for which those problems can be solved in polynomial time and those for which they become computationally hard. Amongst other contributions, this article also studies the complexity of constructing characteristic formulae in the modal logics characterizing simulation-based semantics, both when such formulae are presented in explicit form and via systems of equations.
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Luca Aceto, Antonis Achilleos, Aggeliki Chalki, and Anna Ingólfsdóttir. The Complexity of Deciding Characteristic Formulae in Van Glabbeek’s Branching-Time Spectrum. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aceto_et_al:LIPIcs.CSL.2025.26,
  author =	{Aceto, Luca and Achilleos, Antonis and Chalki, Aggeliki and Ing\'{o}lfsd\'{o}ttir, Anna},
  title =	{{The Complexity of Deciding Characteristic Formulae in Van Glabbeek’s Branching-Time Spectrum}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{26:1--26:18},
  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.2025.26},
  URN =		{urn:nbn:de:0030-drops-227836},
  doi =		{10.4230/LIPIcs.CSL.2025.26},
  annote =	{Keywords: Characteristic formulae, prime formulae, bisimulation, simulation relations, modal logics, complexity theory, satisfiability}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.30
A Complete Inference System for Probabilistic Infinite Trace Equivalence

Authors: Corina Cîrstea, Lawrence S. Moss, Victoria Noquez, Todd Schmid, Alexandra Silva, and Ana Sokolova

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

Abstract
We present the first sound and complete axiomatization of infinite trace semantics for generative probabilistic transition systems. Our approach is categorical, and we build on recent results on proper functors over convex sets. At the core of our proof is a characterization of infinite traces as the final coalgebra of a functor over convex algebras. Somewhat surprisingly, our axiomatization of infinite trace semantics coincides with that of finite trace semantics, even though the techniques used in the completeness proof are significantly different.
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Corina Cîrstea, Lawrence S. Moss, Victoria Noquez, Todd Schmid, Alexandra Silva, and Ana Sokolova. A Complete Inference System for Probabilistic Infinite Trace Equivalence. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 30:1-30:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cirstea_et_al:LIPIcs.CSL.2025.30,
  author =	{C\^{i}rstea, Corina and Moss, Lawrence S. and Noquez, Victoria and Schmid, Todd and Silva, Alexandra and Sokolova, Ana},
  title =	{{A Complete Inference System for Probabilistic Infinite Trace Equivalence}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{30:1--30:23},
  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.2025.30},
  URN =		{urn:nbn:de:0030-drops-227870},
  doi =		{10.4230/LIPIcs.CSL.2025.30},
  annote =	{Keywords: Coalgebra, infinite trace, semantics, logic, convex sets}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2024.21
Impredicativity, Cumulativity and Product Covariance in the Logical Framework Dedukti

Authors: Thiago Felicissimo and Théo Winterhalter

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
Proof assistants such as Coq implement a type theory featuring three important features: impredicativity, cumulativity and product covariance. This combination has proven difficult to be expressed in the logical framework Dedukti, and previous attempts have failed in providing an encoding that is proven confluent, sound and conservative. In this work we solve this longstanding open problem by providing an encoding of these three features that we prove to be confluent, sound and to satisfy a restricted (but, we argue, strong enough) form of conservativity. Our proof of confluence is a contribution by itself, and combines various criteria and proof techniques from rewriting theory. Our proof of soundness also contributes a new strategy in which the result is shown in terms of an inverse translation function, fixing a common flaw made in some previous encoding attempts.
Cite as

Thiago Felicissimo and Théo Winterhalter. Impredicativity, Cumulativity and Product Covariance in the Logical Framework Dedukti. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 21:1-21:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{felicissimo_et_al:LIPIcs.FSCD.2024.21,
  author =	{Felicissimo, Thiago and Winterhalter, Th\'{e}o},
  title =	{{Impredicativity, Cumulativity and Product Covariance in the Logical Framework Dedukti}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{21:1--21:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.21},
  URN =		{urn:nbn:de:0030-drops-203503},
  doi =		{10.4230/LIPIcs.FSCD.2024.21},
  annote =	{Keywords: Dedukti, Rewriting, Confluence, Dependent types, Cumulativity, Universes}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.21
Linear Lambda-Calculus is Linear

Authors: Alejandro Díaz-Caro and Gilles Dowek

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

Abstract
We prove a linearity theorem for an extension of linear logic with addition and multiplication by a scalar: the proofs of some propositions in this logic are linear in the algebraic sense. This work is part of a wider research program that aims at defining a logic whose proof language is a quantum programming language.
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Alejandro Díaz-Caro and Gilles Dowek. Linear Lambda-Calculus is Linear. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{diazcaro_et_al:LIPIcs.FSCD.2022.21,
  author =	{D{\'\i}az-Caro, Alejandro and Dowek, Gilles},
  title =	{{Linear Lambda-Calculus is Linear}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{21:1--21:17},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.21},
  URN =		{urn:nbn:de:0030-drops-163024},
  doi =		{10.4230/LIPIcs.FSCD.2022.21},
  annote =	{Keywords: Proof theory, Lambda calculus, Linear logic, Quantum computing}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.28
Compositional Confluence Criteria

Authors: Kiraku Shintani and Nao Hirokawa

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

Abstract
We show how confluence criteria based on decreasing diagrams are generalized to ones composable with other criteria. For demonstration of the method, the confluence criteria of orthogonality, rule labeling, and critical pair systems for term rewriting are recast into composable forms. In addition to them, we prove that Toyama’s parallel closedness result based on parallel critical pairs subsumes his almost parallel closedness theorem.
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Kiraku Shintani and Nao Hirokawa. Compositional Confluence Criteria. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 28:1-28:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{shintani_et_al:LIPIcs.FSCD.2022.28,
  author =	{Shintani, Kiraku and Hirokawa, Nao},
  title =	{{Compositional Confluence Criteria}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{28:1--28:19},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.28},
  URN =		{urn:nbn:de:0030-drops-163095},
  doi =		{10.4230/LIPIcs.FSCD.2022.28},
  annote =	{Keywords: term rewriting, confluence, decreasing diagrams}
}
Document
DOI: 10.4230/LIPIcs.CSL.2015.423
Confluence of Layered Rewrite Systems

Authors: Jiaxiang Liu, Jean-Pierre Jouannaud, and Mizuhito Ogawa

Published in: LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)

Abstract
We investigate a new, Turing-complete class of layered systems, whose linearized lefthand sides of rules can only be overlapped at the root position. Layered systems define a natural notion of rank for terms: the maximal number of redexes along a path from the root to a leaf. Overlappings are allowed in finite or infinite trees. Rules may be non-terminating, non-left-linear, or non-right- linear. Using a novel unification technique, cyclic unification, we show that rank non-increasing layered systems are confluent provided their cyclic critical pairs have cyclic-joinable decreasing diagrams.
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Jiaxiang Liu, Jean-Pierre Jouannaud, and Mizuhito Ogawa. Confluence of Layered Rewrite Systems. In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 423-440, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{liu_et_al:LIPIcs.CSL.2015.423,
  author =	{Liu, Jiaxiang and Jouannaud, Jean-Pierre and Ogawa, Mizuhito},
  title =	{{Confluence of Layered Rewrite Systems}},
  booktitle =	{24th EACSL Annual Conference on Computer Science Logic (CSL 2015)},
  pages =	{423--440},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-90-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{41},
  editor =	{Kreutzer, Stephan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.423},
  URN =		{urn:nbn:de:0030-drops-54293},
  doi =		{10.4230/LIPIcs.CSL.2015.423},
  annote =	{Keywords: Layers, confluence, decreasing diagrams, critical pairs, cyclic unification}
}
Document
DOI: 10.4230/LIPIcs.TLCA.2015.257
Termination of Dependently Typed Rewrite Rules

Authors: Jean-Pierre Jouannaud and Jianqi Li

Published in: LIPIcs, Volume 38, 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)

Abstract
Our interest is in automated termination proofs of higher-order rewrite rules in presence of dependent types modulo a theory T on base types. We first describe an original transformation to a type discipline without type dependencies which preserves non-termination. Since the user must reason on expressions of the transformed language, we then introduce an extension of the computability path ordering CPO for comparing dependently typed expressions named DCPO. Using the previous result, we show that DCPO is a well-founded order, behaving well in practice.
Cite as

Jean-Pierre Jouannaud and Jianqi Li. Termination of Dependently Typed Rewrite Rules. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 257-272, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{jouannaud_et_al:LIPIcs.TLCA.2015.257,
  author =	{Jouannaud, Jean-Pierre and Li, Jianqi},
  title =	{{Termination of Dependently Typed Rewrite Rules}},
  booktitle =	{13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015)},
  pages =	{257--272},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-87-3},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{38},
  editor =	{Altenkirch, Thorsten},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TLCA.2015.257},
  URN =		{urn:nbn:de:0030-drops-51684},
  doi =		{10.4230/LIPIcs.TLCA.2015.257},
  annote =	{Keywords: rewriting, dependent types, strong normalization, path orderings}
}
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