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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.2026.24

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.2026.26

ε-Distance via Lévy-Prokhorov Lifting

Authors: Josée Desharnais and Ana Sokolova

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

Abstract

The most studied and accepted pseudometric for probabilistic processes is one based on the Kantorovich distance between distributions. It comes with many theoretical and motivating results, in particular it is the fixpoint of a given functional and defines a functor on (complete) pseudometric spaces. It is also the foundation for a categorical lifting of pseudometrics. Other notions of behavioural pseudometrics have also been proposed, one of them (ε-distance) based on ε-bisimulation. ε-Distance has the advantages that it is intuitively easy to understand, it relates systems that are conceptually close (for example, an imperfect implementation is close to its specification), and it comes equipped with a natural notion of ε-coupling. Finally, this distance is easy to compute. We show that ε-distance is also the greatest fixpoint of a functional and provides a functor. The latter is obtained by replacing the Kantorovich distance in the lifting functor with the Lévy-Prokhorov distance. In addition, we show that ε-couplings and ε-bisimulations have an appealing coalgebraic characterization.

Cite as

Josée Desharnais and Ana Sokolova. ε-Distance via Lévy-Prokhorov Lifting. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 26:1-26:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{desharnais_et_al:LIPIcs.CSL.2026.26,
  author =	{Desharnais, Jos\'{e}e and Sokolova, Ana},
  title =	{{\epsilon-Distance via L\'{e}vy-Prokhorov Lifting}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{26:1--26:24},
  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.2026.26},
  URN =		{urn:nbn:de:0030-drops-254506},
  doi =		{10.4230/LIPIcs.CSL.2026.26},
  annote =	{Keywords: L\'{e}vy-Prokhorov metric, behavioural distance, epsilon-bisimulation, reactive probabilistic transition systems, discrete labelled Markov processes, coalgebraic epsilon-(bi)simulation}
}

Document

DOI: 10.4230/LIPIcs.CSL.2026.47

Useful Call-by-Value: A Semantic Interpretation via Quantitative Types

Authors: Pablo Barenbaum, Delia Kesner, and Mariana Milicich

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

Abstract

Useful evaluation is an optimised evaluation mechanism for functional programming languages. It relies on representing terms with sharing and imposing a restricted notion of useful substitutions, that intuitively disallows copying subterms that do not contribute to the progress of the computation. In particular, useful call-by-value evaluation optimises the standard call-by-value strategy by preserving its original semantics. This preservation result has been shown by means of syntactical rewriting techniques, difficult to adapt to alternative variants of the calculi at play. In this work, we present the first semantic model of useful call-by-value evaluation through the non-idempotent intersection type system 𝒰. Our first contribution is a characterisation of termination for useful call-by-value evaluation via system 𝒰. That is, a term is typable in system 𝒰 if and only if it terminates in the useful call-by-value strategy. As a second contribution, we show that system 𝒰 provides a quantitative interpretation for useful call-by-value evaluation, offering exact step-count information for program evaluation. Our third contribution is that termination in call-by-value and useful call-by-value are equivalent. This ensures in particular that call-by-value, which is (potentially) erasing, and useful call-by-value, which is non-erasing, are observationally equivalent. Even though the specification of the operational semantics of useful evaluation is highly complex, system 𝒰 is notably simple. As far as we know, system 𝒰 is one of the scarce quantitative type systems capturing exactly the substitution step-count for variables and abstractions in an open call-by-value strategy.

Cite as

Pablo Barenbaum, Delia Kesner, and Mariana Milicich. Useful Call-by-Value: A Semantic Interpretation via Quantitative Types. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 47:1-47:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{barenbaum_et_al:LIPIcs.CSL.2026.47,
  author =	{Barenbaum, Pablo and Kesner, Delia and Milicich, Mariana},
  title =	{{Useful Call-by-Value: A Semantic Interpretation via Quantitative Types}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{47:1--47:24},
  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.2026.47},
  URN =		{urn:nbn:de:0030-drops-254721},
  doi =		{10.4230/LIPIcs.CSL.2026.47},
  annote =	{Keywords: Lambda calculus, Evaluation strategies, Call-by-Value, Useful Evaluation, Intersection types, Quantitative models}
}

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

DOI: 10.4230/LIPIcs.MFCS.2025.61

Quantum Relaxations of CSP and Structure Isomorphism

Authors: Amin Karamlou

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract

We investigate quantum relaxations of two key decision problems in computer science: the constraint satisfaction problem (CSP) and the structure isomorphism problem. CSP asks whether a homomorphism exists between two relational structures, while structure isomorphism seeks an isomorphism between them. In recent years, it has become increasingly apparent that many special cases of CSP can be reformulated in terms of the existence of perfect classical strategies in non-local games, a key topic of study in quantum information theory. These games have allowed us to study quantum advantage in relation to many important decision problems, such as the k-colouring problem, and the problem of solving binary constraint systems. Abramsky et al. (2017) have shown that all of these games can be seen as special instances of a non-local CSP game. Moreover, they show that perfect quantum strategies in this CSP game can be viewed as Kleisli morphisms of a graded monad on the category of relational structures, which they dub the quantum monad. In this way, the quantum monad provides a categorical characterisation of quantum advantage for the non-local CSP game. In this work we solidify and expand the results of Abramsky et al., answering several of their open questions. Firstly, we compare the definition of quantum graph homomorphisms arising from this work with an earlier definition of the concept due to Mančinska and Roberson and show that there are graphs which exhibit quantum advantage under one definition but not the other. Our second contribution is to extend the results of Abramsky et al. which only hold in the tensor product framework of quantum mechanics to the commuting operator framework. Next, we study a non-local structure isomorphism game, which generalises the well-studied graph isomorphism game. We show how the construction of the quantum monad can be refined to provide categorical semantics for quantum strategies in this game. This results in a category where morphisms coincide with quantum homomorphisms and isomorphisms coincide with quantum isomorphisms.

Cite as

Amin Karamlou. Quantum Relaxations of CSP and Structure Isomorphism. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 61:1-61:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{karamlou:LIPIcs.MFCS.2025.61,
  author =	{Karamlou, Amin},
  title =	{{Quantum Relaxations of CSP and Structure Isomorphism}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{61:1--61:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.61},
  URN =		{urn:nbn:de:0030-drops-241686},
  doi =		{10.4230/LIPIcs.MFCS.2025.61},
  annote =	{Keywords: CSP, graph isomorphism, quantum information, non-local game, quantum graph homomorphism, monad}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2025.34

New Fault Domains for Conformance Testing of Finite State Machines

Authors: Frits Vaandrager and Ivo Melse

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

Abstract

A fault domain reflects a tester’s assumptions about faults that may occur in an implementation and that need to be detected during testing. A fault domain that has been widely studied in the literature on black-box conformance testing is the class of finite state machines (FSMs) with at most m states. Numerous strategies for generating test suites have been proposed that guarantee fault coverage for this class. These so-called m-complete test suites grow exponentially in m-n, where n is the number of states of the specification, so one can only run them for small values of m-n. But the assumption that m-n is small is not realistic in practice. In his seminal paper from 1964, Hennie raised the challenge to design checking experiments in which the number of states may increase appreciably. In order to solve this long-standing open problem, we propose (much larger) fault domains that capture the assumption that all states in an implementation can be reached by first performing a sequence from some set A (typically a state cover for the specification), followed by k arbitrary inputs, for some small k. The number of states of FSMs in these fault domains grows exponentially in k. We present a sufficient condition for k-A-completeness of test suites with respect to these fault domains. Our condition implies k-A-completeness of two prominent m-complete test suite generation strategies, the Wp and HSI methods. Thus these strategies are complete for much larger fault domains than those for which they were originally designed, and thereby solve Hennie’s challenge. We show that three other prominent m-complete methods (H, SPY and SPYH) do not always generate k-A-complete test suites.

Cite as

Frits Vaandrager and Ivo Melse. New Fault Domains for Conformance Testing of Finite State Machines. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 34:1-34:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vaandrager_et_al:LIPIcs.CONCUR.2025.34,
  author =	{Vaandrager, Frits and Melse, Ivo},
  title =	{{New Fault Domains for Conformance Testing of Finite State Machines}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{34:1--34:22},
  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.2025.34},
  URN =		{urn:nbn:de:0030-drops-239843},
  doi =		{10.4230/LIPIcs.CONCUR.2025.34},
  annote =	{Keywords: conformance testing, finite state machines, Mealy machines, apartness, observation tree, fault domains, k-A-complete test suites}
}

Document

DOI: 10.4230/LIPIcs.CALCO.2025.8

Drawing and Recolouring

Authors: Bart Jacobs and Márk Széles

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

Abstract

Drawing a ball from an urn filled with balls of different colours is one of the basic models in probability theory. The probability of drawing a ball of a particular colour is determined by the proportion / fraction of balls of that colour. This paper introduces a new stochastic model for such urns: draw a ball, recolour (repaint) it, and put it back into the urn. One can distinguish four modes of drawing-and-recolouring, namely whether done proportionally or uniformly (both for drawing and recolouring). These modes can be reformulated in financial terms as redistribution of wealth or in biological terms as evolutionary drift. The resulting four operations form a coalgebra for the distribution monad, on the set of multisets of a fixed size. In fact they form a Markov chain and even a hidden Markov model, in combination with the frequentist learning map as emission channel. This paper identifies fixed points, capturing stable situations, for these four modes of drawing-and-recolouring.

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Bart Jacobs and Márk Széles. Drawing and Recolouring. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 8:1-8:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jacobs_et_al:LIPIcs.CALCO.2025.8,
  author =	{Jacobs, Bart and Sz\'{e}les, M\'{a}rk},
  title =	{{Drawing and Recolouring}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{8:1--8:15},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-235674},
  doi =		{10.4230/LIPIcs.CALCO.2025.8},
  annote =	{Keywords: Markov-chain, Urn model, Multiset}
}

Document

(Co)algebraic pearl

DOI: 10.4230/LIPIcs.CALCO.2025.16

Active Learning of Upward-Closed Sets of Words ((Co)algebraic pearl)

Authors: Quentin Aristote

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

Abstract

We give a new proof of a result from well quasi-order theory on the computability of bases for upwards-closed sets of words. This new proof is based on Angluin’s L* algorithm, that learns an automaton from a minimally adequate teacher. This relates in particular two results from the 1980s: Angluin’s L* algorithm, and a result from Valk and Jantzen on the computability of bases for upwards-closed sets of tuples of integers. Along the way, we describe an algorithm for learning quasi-ordered automata from a minimally adequate teacher, and extend a generalization of Valk and Jantzen’s result, encompassing both words and integers, to finitely generated monoids.

Cite as

Quentin Aristote. Active Learning of Upward-Closed Sets of Words ((Co)algebraic pearl). In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 16:1-16:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aristote:LIPIcs.CALCO.2025.16,
  author =	{Aristote, Quentin},
  title =	{{Active Learning of Upward-Closed Sets of Words}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{16:1--16:12},
  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.2025.16},
  URN =		{urn:nbn:de:0030-drops-235751},
  doi =		{10.4230/LIPIcs.CALCO.2025.16},
  annote =	{Keywords: active learning, well quasi-orders, Valk-Jantzen lemma, piecewise-testable languages, monoids}
}

Document

DOI: 10.4230/LIPIcs.CALCO.2025.12

Cancellative Convex Semilattices

Authors: Ana Sokolova and Harald Woracek

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

Abstract

Convex semilattices are algebras that are at the same time a convex algebra and a semilattice, together with a distributivity axiom. These algebras have attracted some attention in the last years as suitable algebras for probability and nondeterminism, in particular by being the Eilenberg-Moore algebras of the nonempty finitely-generated convex subsets of the distributions monad. A convex semilattice is cancellative if the underlying convex algebra is cancellative. Cancellative convex algebras have been characterized by M. H. Stone and by H. Kneser: A convex algebra is cancellative if and only if it is isomorphic to a convex subset of a vector space (with canonical convex algebra operations). We prove an analogous theorem for convex semilattices: A convex semilattice is cancellative if and only if it is isomorphic to a convex subset of a Riesz space, i.e., a lattice-ordered vector space (with canonical convex semilattice operations).

Cite as

Ana Sokolova and Harald Woracek. Cancellative Convex Semilattices. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sokolova_et_al:LIPIcs.CALCO.2025.12,
  author =	{Sokolova, Ana and Woracek, Harald},
  title =	{{Cancellative Convex Semilattices}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{12:1--12:15},
  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.2025.12},
  URN =		{urn:nbn:de:0030-drops-235714},
  doi =		{10.4230/LIPIcs.CALCO.2025.12},
  annote =	{Keywords: convex semilattice, cancellativity, Riesz space}
}

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Invited Talk

DOI: 10.4230/LIPIcs.CALCO.2025.1

Effectful Mealy Machines: Coalgebraic and Causal Traces (Invited Talk)

Authors: Filippo Bonchi, Elena Di Lavore, and Mario Román

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

Abstract

We introduce effectful Mealy machines - a general notion of Mealy machine with global effects - and give them semantics in terms of both bisimilarity and traces. Bisimilarity of effectful Mealy machines is characterized syntactically, via free uniform feedback. Their traces are given a novel semantic coinductive universe in terms of effectful streams. We prove that this framework generalizes standard causal processes and captures existing flavours of Mealy machine, bisimilarity, and trace. This is an extended abstract for the manuscript Effectful Mealy Machines: Bisimulation and Trace that will appear in the proceedings of LiCS 2025 [Bonchi et al., 2025]; an extended version with proofs is also available (arxiv.org/abs/2410.10627) [Bonchi et al., 2025]. We additionally characterise causal processes as lax-natural transformations.

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Filippo Bonchi, Elena Di Lavore, and Mario Román. Effectful Mealy Machines: Coalgebraic and Causal Traces (Invited Talk). In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 1:1-1:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonchi_et_al:LIPIcs.CALCO.2025.1,
  author =	{Bonchi, Filippo and Di Lavore, Elena and Rom\'{a}n, Mario},
  title =	{{Effectful Mealy Machines: Coalgebraic and Causal Traces}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{1:1--1:7},
  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.2025.1},
  URN =		{urn:nbn:de:0030-drops-235596},
  doi =		{10.4230/LIPIcs.CALCO.2025.1},
  annote =	{Keywords: Mealy machines, coinduction, copy-discard categories, premonoidal categories}
}

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.

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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.ECRTS.2025.9

DAMA: A Dual Arbitration Mechanism for Mixed-Criticality Applications

Authors: Wafic Lawand and Rodolfo Pellizzoni

Published in: LIPIcs, Volume 335, 37th Euromicro Conference on Real-Time Systems (ECRTS 2025)

Abstract

We discuss hardware resource management in mixed-criticality systems, where requestors may issue latency-critical (LTC) and non-latency-critical (NLTC) requests. LTC requests must adhere to strict latency bounds imposed by safety-critical applications, but timely servicing NLTC requests is necessary to maximize overall system performance in the average case. In this paper, we address this tradeoff for a shared memory resource by proposing DAMA, a dual arbitration mechanism that imposes an upper bound on the cumulative latency of LTC requests without unduly impacting NLTC performance. DAMA comprises a high-performance arbiter, a real-time arbiter, and a mechanism that constantly monitors the cumulative latency of requests suffered by each requestor. DAMA primarily executes in high-performance mode and only switches to real-time mode in the rare instances when its incorporated mechanism detects a violation of a task’s timing guarantee. We demonstrate the effectiveness of our arbitration scheme by adapting a predictable prefetcher that issues NLTC requests and attaching it to the L1 caches of our cores. We show both formally and experimentally that DAMA provides timing guarantees for LTC requests while processing other NLTC requests. We also demonstrate that with a negligible overhead of less than 1.5% on the cumulative latency bound of LTC requests, DAMA can achieve an equivalent average performance to a prefetcher that processes requests under a high-performance arbitration scheme.

Cite as

Wafic Lawand and Rodolfo Pellizzoni. DAMA: A Dual Arbitration Mechanism for Mixed-Criticality Applications. In 37th Euromicro Conference on Real-Time Systems (ECRTS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 335, pp. 9:1-9:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lawand_et_al:LIPIcs.ECRTS.2025.9,
  author =	{Lawand, Wafic and Pellizzoni, Rodolfo},
  title =	{{DAMA: A Dual Arbitration Mechanism for Mixed-Criticality Applications}},
  booktitle =	{37th Euromicro Conference on Real-Time Systems (ECRTS 2025)},
  pages =	{9:1--9:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-377-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{335},
  editor =	{Mancuso, Renato},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2025.9},
  URN =		{urn:nbn:de:0030-drops-235875},
  doi =		{10.4230/LIPIcs.ECRTS.2025.9},
  annote =	{Keywords: Real-time Systems, Mixed-criticality Applications, Memory controllers, Prefetchers}
}

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.

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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.2025.5

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}
}

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