35 Search Results for "Uustalu, Tarmo"

Volume

LIPIcs, Volume 69

21st International Conference on Types for Proofs and Programs (TYPES 2015)

TYPES 2015, May 18-21, 2015, Tallinn, Estonia

Editors: Tarmo Uustalu

Document
DOI: 10.4230/LIPIcs.STACS.2026.65
Demystifying Codensity Monads via Duality

Authors: Fabian Lenke, Nico Wittrock, Stefan Milius, and Henning Urbat

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Codensity monads provide a universal method to generate complex monads from simple functors. Recently, a wide range of important monads in logic, denotational semantics, and probabilistic computation, such as several incarnations of the ultrafilter monad, the Vietoris monad, and the Giry monad, have been presented as codensity monads, using complex arguments. We propose a unifying categorical approach to codensity presentations of monads, based on the idea of relating the presenting functor to a dense functor via a suitable duality between categories. We prove a general presentation result applying to every such situation and demonstrate that most codensity presentations known in the literature emerge from this strikingly simple duality-based setup, drastically alleviating the complexity of their proofs and in many cases completely reducing them to standard duality results. Additionally, we derive a number of novel codensity presentations using our framework, including the first non-trivial codensity presentations for the filter monads on sets and topological spaces, the lower Vietoris monad on topological spaces, and the expectation monad on sets.
Cite as

Fabian Lenke, Nico Wittrock, Stefan Milius, and Henning Urbat. Demystifying Codensity Monads via Duality. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 65:1-65:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{lenke_et_al:LIPIcs.STACS.2026.65,
  author =	{Lenke, Fabian and Wittrock, Nico and Milius, Stefan and Urbat, Henning},
  title =	{{Demystifying Codensity Monads via Duality}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{65:1--65:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.65},
  URN =		{urn:nbn:de:0030-drops-255549},
  doi =		{10.4230/LIPIcs.STACS.2026.65},
  annote =	{Keywords: Codensity, Monad, Duality}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.19
A Unifying Conservation Theorem

Authors: Giulio Fellin

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

Abstract
The relationship between classical and constructive logics has long been illuminated by a series of conservation results, beginning with Kolmogorov’s negative translation and Glivenko’s double negation theorem, and later extended by Kuroda and Segerberg to first-order and minimal logics respectively. These results reveal how certain classical principles can be interpreted or recovered within weaker constructive frameworks, either via translations or through minimal extensions that satisfy specific logical properties. In this paper, we propose a unifying generalisation of these conservation theorems, that consolidates and expands the abstract methods introduced in earlier studies, offering a unified perspective on the interplay between classical provability and constructive reasoning.
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Giulio Fellin. A Unifying Conservation Theorem. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 19:1-19:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fellin:LIPIcs.CSL.2026.19,
  author =	{Fellin, Giulio},
  title =	{{A Unifying Conservation Theorem}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{19:1--19:23},
  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.2026.19},
  URN =		{urn:nbn:de:0030-drops-254431},
  doi =		{10.4230/LIPIcs.CSL.2026.19},
  annote =	{Keywords: double negation, negative translation, conservation, minimal logic, Glivenko’s theorem}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.24
Well-Founded Coalgebras Meet Kőnig’s Lemma

Authors: Henning Urbat and Thorsten Wißmann

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

Abstract
Kőnig’s lemma is a fundamental result about trees with countless applications in mathematics and computer science. In contrapositive form, it states that if a tree is finitely branching and well-founded (i.e. has no infinite paths), then it is finite. We present a coalgebraic version of Kőnig’s lemma featuring two dimensions of generalization: from finitely branching trees to coalgebras for a finitary endofunctor H, and from the base category of sets to a locally finitely presentable category ℂ, such as the category of posets, nominal sets, or convex sets. Our coalgebraic Kőnig’s lemma states that, under mild assumptions on ℂ and H, every well-founded coalgebra for H is the directed join of its well-founded subcoalgebras with finitely generated state space - in particular, the category of well-founded coalgebras is locally presentable. As applications, we derive versions of Kőnig’s lemma for graphs in a topos as well as for nominal and convex transition systems. Additionally, we show that the key construction underlying the proof gives rise to two simple constructions of the initial algebra (equivalently, the final recursive coalgebra) for the functor H: The initial algebra is both the colimit of all well-founded and of all recursive coalgebras with finitely presentable state space. Remarkably, this result holds even in settings where well-founded coalgebras form a proper subclass of recursive ones. The first construction of the initial algebra is entirely new, while for the second one our approach yields a short and transparent new correctness proof.
Cite as

Henning Urbat and Thorsten Wißmann. Well-Founded Coalgebras Meet Kőnig’s Lemma. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{urbat_et_al:LIPIcs.CSL.2026.24,
  author =	{Urbat, Henning and Wi{\ss}mann, Thorsten},
  title =	{{Well-Founded Coalgebras Meet K\H{o}nig’s Lemma}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{24:1--24:19},
  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.2026.24},
  URN =		{urn:nbn:de:0030-drops-254485},
  doi =		{10.4230/LIPIcs.CSL.2026.24},
  annote =	{Keywords: K\H{o}nig’s Lemma, Well-Foundedness, Coalgebra}
}
Document
DOI: 10.4230/LIPIcs.CSL.2026.38
The Biequivalence of Path Categories and Axiomatic Martin-Löf Type Theories

Authors: Daniël Otten and Matteo Spadetto

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

Abstract
The semantics of extensional type theory has an elegant categorical description: models of extensional =-types, 𝟙-types, and Σ-types are biequivalent to finitely complete categories, while adding Π-types yields locally Cartesian closed categories. We establish parallel results for axiomatic type theory, which includes systems like cubical type theory, where the computation rule of the =-types only holds as a propositional axiom instead of a definitional reduction. In particular, we prove that models of axiomatic =-types, and standard 𝟙- and Σ-types are biequivalent to certain path categories, while adding axiomatic Π-types yields dependent homotopy exponents. This biequivalence simplifies axiomatic =-types, which are more intricate than extensional ones since they permit higher dimensional structure. Specifically, path categories use a primitive notion of equivalence instead of a direct reproduction of the syntactic elimination rules and computation axioms. We apply our correspondence to prove a coherence theorem: we show that these weak homotopical models can be turned into equivalent strict models of axiomatic type theory. In addition, we introduce a more modular notion, that of a display map path category, which only models axiomatic =-types by default, while leaving room to add other axiomatic type formers such as 𝟙-, Σ-, and Π-types.
Cite as

Daniël Otten and Matteo Spadetto. The Biequivalence of Path Categories and Axiomatic Martin-Löf Type Theories. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 38:1-38:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{otten_et_al:LIPIcs.CSL.2026.38,
  author =	{Otten, Dani\"{e}l and Spadetto, Matteo},
  title =	{{The Biequivalence of Path Categories and Axiomatic Martin-L\"{o}f Type Theories}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{38:1--38:23},
  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.2026.38},
  URN =		{urn:nbn:de:0030-drops-254633},
  doi =		{10.4230/LIPIcs.CSL.2026.38},
  annote =	{Keywords: Axiomatic type theory, cubical type theory, propositional equality, biequivalence, display map categories, path categories, homotopy theory, coherence}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.14
Canonical for Automated Theorem Proving in Lean

Authors: Chase Norman and Jeremy Avigad

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

Abstract
Canonical is a solver for type inhabitation in dependent type theory, that is, the problem of producing a term of a given type. We present a Lean tactic which invokes Canonical to generate proof terms and synthesize programs. The tactic supports higher-order and dependently-typed goals, structural recursion over indexed inductive types, and definitional equality. Canonical finds proofs for 84% of Natural Number Game problems in 51 seconds total.
Cite as

Chase Norman and Jeremy Avigad. Canonical for Automated Theorem Proving in Lean. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{norman_et_al:LIPIcs.ITP.2025.14,
  author =	{Norman, Chase and Avigad, Jeremy},
  title =	{{Canonical for Automated Theorem Proving in Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{14:1--14:20},
  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.2025.14},
  URN =		{urn:nbn:de:0030-drops-246128},
  doi =		{10.4230/LIPIcs.ITP.2025.14},
  annote =	{Keywords: Automated Reasoning, Interactive Theorem Proving, Dependent Type Theory, Inhabitation, Unification, Program Synthesis, Formal Methods}
}
Document
DOI: 10.4230/OASIcs.Programming.2025.19
Is There Hypothesis for Attribute Grammars?

Authors: Emanuel Rodrigues, José Nuno Macedo, and João Saraiva

Published in: OASIcs, Volume 134, Companion Proceedings of the 9th International Conference on the Art, Science, and Engineering of Programming (Programming 2025)

Abstract
Software testing is essential to ensure software reliability and functionality. Numerous testing techniques have been proposed, and most programming languages provide built-in support for testing. However, these techniques have yet to be integrated into the powerful attribute grammar formalism. This paper introduces a method to incorporate property-based testing into attribute grammars. We achieve this by embedding attribute grammars in Python which is combined with its powerful Hypothesis property-based testing framework. To validate our approach, we express properties of scope rules in a (nested) block-structured language, commonly found in many (functional) languages.
Cite as

Emanuel Rodrigues, José Nuno Macedo, and João Saraiva. Is There Hypothesis for Attribute Grammars?. In Companion Proceedings of the 9th International Conference on the Art, Science, and Engineering of Programming (Programming 2025). Open Access Series in Informatics (OASIcs), Volume 134, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rodrigues_et_al:OASIcs.Programming.2025.19,
  author =	{Rodrigues, Emanuel and Macedo, Jos\'{e} Nuno and Saraiva, Jo\~{a}o},
  title =	{{Is There Hypothesis for Attribute Grammars?}},
  booktitle =	{Companion Proceedings of the 9th International Conference on the Art, Science, and Engineering of Programming (Programming 2025)},
  pages =	{19:1--19:15},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-382-9},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{134},
  editor =	{Edwards, Jonathan and Perera, Roly and Petricek, Tomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Programming.2025.19},
  URN =		{urn:nbn:de:0030-drops-243036},
  doi =		{10.4230/OASIcs.Programming.2025.19},
  annote =	{Keywords: Property-based Testing, Attribute Grammars, Strategic Term Rewriting}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2025.4
Distributive Laws of Monadic Containers

Authors: Chris Purdy and Stefania Damato

Published in: LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)

Abstract
Containers are used to carve out a class of strictly positive data types in terms of shapes and positions. They can be interpreted via a fully-faithful functor into endofunctors on Set. Monadic containers are those containers whose interpretation as a Set functor carries a monad structure. The category of containers is closed under container composition and is a monoidal category, whereas monadic containers do not in general compose. In this paper, we develop a characterisation of distributive laws of monadic containers. Distributive laws were introduced as a sufficient condition for the composition of the underlying functors of two monads to also carry a monad structure. Our development parallels Ahman and Uustalu’s characterisation of distributive laws of directed containers, i.e. containers whose Set functor interpretation carries a comonad structure. Furthermore, by combining our work with theirs, we construct characterisations of mixed distributive laws (i.e. of directed containers over monadic containers and vice versa), thereby completing the "zoo" of container characterisations of (co)monads and their distributive laws. We have found these characterisations amenable to development of existence and uniqueness proofs of distributive laws, particularly in the mechanised setting of Cubical Agda, in which most of the theory of this paper has been formalised.
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Chris Purdy and Stefania Damato. Distributive Laws of Monadic Containers. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{purdy_et_al:LIPIcs.CALCO.2025.4,
  author =	{Purdy, Chris and Damato, Stefania},
  title =	{{Distributive Laws of Monadic Containers}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{4:1--4:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-383-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{342},
  editor =	{C\^{i}rstea, Corina and Knapp, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.4},
  URN =		{urn:nbn:de:0030-drops-235633},
  doi =		{10.4230/LIPIcs.CALCO.2025.4},
  annote =	{Keywords: distributive laws, monadic containers, monads, dependent types, cubical agda}
}
Document
DOI: 10.4230/LIPIcs.CALCO.2025.7
A Coinductive Representation of Computable Functions

Authors: Alvin Tang and Dirk Pattinson

Published in: LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)

Abstract
We investigate a representation of computable functions as total functions over 2^∞, the set of finite and infinite sequences over {0,1}. In this model, infinite sequences are interpreted as non-terminating computations whilst finite sequences represent the sum of their digits. We introduce a new definition principle, function space corecursion, that simultaneously generalises minimisation and primitive recursion. This defines the class of computable corecursive functions that is closed under composition and function space corecursion. We prove computable corecursive functions represent all partial recursive functions, and show that all computable corecursive functions are indeed computable by translation into the untyped λ-calculus.
Cite as

Alvin Tang and Dirk Pattinson. A Coinductive Representation of Computable Functions. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{tang_et_al:LIPIcs.CALCO.2025.7,
  author =	{Tang, Alvin and Pattinson, Dirk},
  title =	{{A Coinductive Representation of Computable Functions}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-383-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{342},
  editor =	{C\^{i}rstea, Corina and Knapp, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.7},
  URN =		{urn:nbn:de:0030-drops-235662},
  doi =		{10.4230/LIPIcs.CALCO.2025.7},
  annote =	{Keywords: Computability, Coinduction}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.5
The Cost of Skeletal Call-By-Need, Smoothly

Authors: Beniamino Accattoli, Francesco Magliocca, Loïc Peyrot, and Claudio Sacerdoti Coen

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

Abstract
Skeletal call-by-need is an optimization of call-by-need evaluation also known as "fully lazy sharing": when the duplication of a value has to take place, it is first split into "skeleton", which is then duplicated, and "flesh" which is instead kept shared. Here, we provide two cost analyses of skeletal call-by-need. Firstly, we provide a family of terms showing that skeletal call-by-need can be asymptotically exponentially faster than call-by-need in both time and space; it is the first such evidence, to our knowledge. Secondly, we prove that skeletal call-by-need can be implemented efficiently, that is, with bi-linear overhead. This result is obtained by providing a new smooth presentation of ideas by Shivers and Wand for the reconstruction of skeletons, which is then smoothly plugged into the study of an abstract machine following the distillation technique by Accattoli et al.
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Beniamino Accattoli, Francesco Magliocca, Loïc Peyrot, and Claudio Sacerdoti Coen. The Cost of Skeletal Call-By-Need, Smoothly. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{accattoli_et_al:LIPIcs.FSCD.2025.5,
  author =	{Accattoli, Beniamino and Magliocca, Francesco and Peyrot, Lo\"{i}c and Sacerdoti Coen, Claudio},
  title =	{{The Cost of Skeletal Call-By-Need, Smoothly}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{5:1--5:22},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-236206},
  doi =		{10.4230/LIPIcs.FSCD.2025.5},
  annote =	{Keywords: \lambda-calculus, abstract machines, call-by-need, cost models}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.10
Categorical Continuation Semantics for Concurrency

Authors: Flavien Breuvart and Hugo Paquet

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

Abstract
Continuation semantics for simple programming languages can be axiomatized as a dialogue category: a symmetric monoidal category equipped with a negation operation. This axiomatization makes clear the relationship between game semantics, CPS transformations, and continuation monads. In this paper we extend dialogue categories with 2-categorical structure and concurrent primitives. This is inspired by a recent analysis of concurrency based on 2-categorical monads. We show that the fine-grained structure of dialogue categories, not generally available in other semantic models, can be exploited to give a type to concurrent primitives join and fork. Our main theorem is that this simple axiomatization induces a concurrent continuation 2-monad. We also show that this framework is expressive beyond call-by-value monadic programming. The definitions in this paper are illustrated by concrete constructions in concurrent game semantics, and our results give a formal categorical basis for concurrent strategies. From a more practical perspective, our approach suggests a candidate target language for linear CPS transformations of concurrent programming languages.
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Flavien Breuvart and Hugo Paquet. Categorical Continuation Semantics for Concurrency. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 10:1-10:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{breuvart_et_al:LIPIcs.FSCD.2025.10,
  author =	{Breuvart, Flavien and Paquet, Hugo},
  title =	{{Categorical Continuation Semantics for Concurrency}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{10:1--10:21},
  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.2025.10},
  URN =		{urn:nbn:de:0030-drops-236251},
  doi =		{10.4230/LIPIcs.FSCD.2025.10},
  annote =	{Keywords: denotational semantics, 2-categories, concurrency, continuations, game semantics}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.21
An Expressive Trace Logic for Recursive Programs

Authors: Dilian Gurov and Reiner Hähnle

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

Abstract
We present an expressive logic over trace formulas, based on binary state predicates, chop, and least fixed points, for precise specification of programs with recursive procedures. Both programs and trace formulas are equipped with a direct-style, fully compositional, denotational semantics that on programs coincides with the standard SOS of recursive programs. We design a compositional proof calculus for proving finite-trace program properties, and prove soundness as well as (relative) completeness. We show that each program can be mapped to a semantics-preserving trace formula and, vice versa, each trace formula can be mapped to a canonical program over slightly extended programs, resulting in a Galois connection between programs and formulas. Our results shed light on the correspondence between programming constructs and logical connectives.
Cite as

Dilian Gurov and Reiner Hähnle. An Expressive Trace Logic for Recursive Programs. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gurov_et_al:LIPIcs.FSCD.2025.21,
  author =	{Gurov, Dilian and H\"{a}hnle, Reiner},
  title =	{{An Expressive Trace Logic for Recursive Programs}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{21:1--21:22},
  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.2025.21},
  URN =		{urn:nbn:de:0030-drops-236360},
  doi =		{10.4230/LIPIcs.FSCD.2025.21},
  annote =	{Keywords: Denotational semantics, compositional semantics, program specification, compositional verification, fixed point logic, trace logic}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2025.14
IsaBIL: A Framework for Verifying (In)correctness of Binaries in Isabelle/HOL

Authors: Matt Griffin, Brijesh Dongol, and Azalea Raad

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

Abstract
This paper presents IsaBIL, a binary analysis framework in Isabelle/HOL that is based on the widely used Binary Analysis Platform (BAP). Specifically, in IsaBIL, we formalise BAP’s intermediate language, called BIL and integrate it with Hoare logic (to enable proofs of correctness) as well as incorrectness logic (to enable proofs of incorrectness). IsaBIL inherits the full flexibility of BAP, allowing us to verify binaries for a wide range of languages (C, C++, Rust), toolchains (LLVM, Ghidra) and target architectures (x86, RISC-V), and can also be used when the source code for a binary is unavailable. To make verification tractable, we develop a number of big-step rules that combine BIL’s existing small-step rules at different levels of abstraction to support reuse. We develop high-level reasoning rules for RISC-V instructions (our main target architecture) to further optimise verification. Additionally, we develop Isabelle proof tactics that exploit common patterns in C binaries for RISC-V to discharge large numbers of proof goals (often in the 100s) automatically. IsaBIL includes an Isabelle/ML based parser for BIL programs, allowing one to automatically generate the associated Isabelle/HOL program locale from a BAP output. Taken together, IsaBIL provides a highly flexible proof environment for program binaries. As examples, we prove correctness of key examples from the Joint Strike Fighter coding standards and the MITRE database.
Cite as

Matt Griffin, Brijesh Dongol, and Azalea Raad. IsaBIL: A Framework for Verifying (In)correctness of Binaries in Isabelle/HOL. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 14:1-14:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{griffin_et_al:LIPIcs.ECOOP.2025.14,
  author =	{Griffin, Matt and Dongol, Brijesh and Raad, Azalea},
  title =	{{IsaBIL: A Framework for Verifying (In)correctness of Binaries in Isabelle/HOL}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{14:1--14:30},
  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.2025.14},
  URN =		{urn:nbn:de:0030-drops-233070},
  doi =		{10.4230/LIPIcs.ECOOP.2025.14},
  annote =	{Keywords: Binary Analysis Platform, Isabelle/HOL, Hoare Logic, Incorrectness Logic}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.28
Strong Induction Is an Up-To Technique

Authors: Filippo Bonchi, Elena Di Lavore, and Anna Ricci

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

Abstract
Up-to techniques are enhancements of the coinduction proof principle which, in lattice theoretic terms, is the dual of induction. What is the dual of coinduction up-to? By means of duality, we illustrate a theory of induction up-to and we observe that an elementary proof technique, commonly known as strong induction, is an instance of induction up-to. We also show that, when generalising our theory from lattices to categories, one obtains an enhancement of the induction definition principle known in the literature as comonadic recursion.
Cite as

Filippo Bonchi, Elena Di Lavore, and Anna Ricci. Strong Induction Is an Up-To Technique. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonchi_et_al:LIPIcs.CSL.2025.28,
  author =	{Bonchi, Filippo and Di Lavore, Elena and Ricci, Anna},
  title =	{{Strong Induction Is an Up-To Technique}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{28:1--28:21},
  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.2025.28},
  URN =		{urn:nbn:de:0030-drops-227856},
  doi =		{10.4230/LIPIcs.CSL.2025.28},
  annote =	{Keywords: Induction, Coinduction, Up-to Techniques, Induction up-to, Lattices, Algebras}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.29
Correspondences Between Codensity and Coupling-Based Liftings, a Practical Approach

Authors: Samuel Humeau, Daniela Petrisan, and Jurriaan Rot

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

Abstract
The Kantorovich distance is a widely used metric between probability distributions. The Kantorovich-Rubinstein duality states that it can be defined in two equivalent ways: as a supremum, based on non-expansive functions into [0,1], and as an infimum, based on probabilistic couplings. Orthogonally, there are categorical generalisations of both presentations proposed in the literature, in the form of codensity liftings and what we refer to as coupling-based liftings. Both lift endofunctors on the category Set of sets and functions to that of pseudometric spaces, and both are parameterised by modalities from coalgebraic modal logic. A generalisation of the Kantorovich-Rubinstein duality has been more nebulous - it is known not to work in some cases. In this paper we propose a compositional approach for obtaining such generalised dualities for a class of functors, which is closed under coproducts and products. Our approach is based on an explicit construction of modalities and also applies to and extends known cases such as that of the powerset functor.
Cite as

Samuel Humeau, Daniela Petrisan, and Jurriaan Rot. Correspondences Between Codensity and Coupling-Based Liftings, a Practical Approach. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{humeau_et_al:LIPIcs.CSL.2025.29,
  author =	{Humeau, Samuel and Petrisan, Daniela and Rot, Jurriaan},
  title =	{{Correspondences Between Codensity and Coupling-Based Liftings, a Practical Approach}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{29:1--29:18},
  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.2025.29},
  URN =		{urn:nbn:de:0030-drops-227861},
  doi =		{10.4230/LIPIcs.CSL.2025.29},
  annote =	{Keywords: Kantorovich distance, behavioural metrics, Kantorovich-Rubinstein duality, functor liftings}
}
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