31 Search Results for "Jacobs, Bart"

Document
DOI: 10.4230/LIPIcs.ECOOP.2024.16
Mover Logic: A Concurrent Program Logic for Reduction and Rely-Guarantee Reasoning

Authors: Cormac Flanagan and Stephen N. Freund

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract
Rely-guarantee (RG) logic uses thread interference specifications (relies and guarantees) to reason about the correctness of multithreaded software. Unfortunately, RG logic requires each function postcondition to be "stabilized" or specialized to the behavior of other threads, making it difficult to write function specifications that are reusable at multiple call sites. This paper presents mover logic, which extends RG logic to address this problem via the notion of atomic functions. Atomic functions behave as if they execute serially without interference from concurrent threads, and so they can be assigned more general and reusable specifications that avoid the stabilization requirement of RG logic. Several practical verifiers (Calvin-R, QED, CIVL, Armada, Anchor, etc.) have demonstrated the modularity benefits of atomic function specifications. However, the complexity of these systems and their correctness proofs makes it challenging to understand and extend these systems. Mover logic formalizes the central ideas of reduction in a declarative program logic that provides a foundation for future work in this area.
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Cormac Flanagan and Stephen N. Freund. Mover Logic: A Concurrent Program Logic for Reduction and Rely-Guarantee Reasoning. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 16:1-16:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{flanagan_et_al:LIPIcs.ECOOP.2024.16,
  author =	{Flanagan, Cormac and Freund, Stephen N.},
  title =	{{Mover Logic: A Concurrent Program Logic for Reduction and Rely-Guarantee Reasoning}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{16:1--16:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.16},
  URN =		{urn:nbn:de:0030-drops-208654},
  doi =		{10.4230/LIPIcs.ECOOP.2024.16},
  annote =	{Keywords: concurrent program verification, reduction, rely-guarantee reasoning, synchronization}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2024.25
Compositional Symbolic Execution for Correctness and Incorrectness Reasoning

Authors: Andreas Lööw, Daniele Nantes-Sobrinho, Sacha-Élie Ayoun, Caroline Cronjäger, Petar Maksimović, and Philippa Gardner

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract
The introduction of separation logic has led to the development of symbolic execution techniques and tools that are (functionally) compositional with function specifications that can be used in broader calling contexts. Many of the compositional symbolic execution tools developed in academia and industry have been grounded on a formal foundation, but either the function specifications are not validated with respect to the underlying separation logic of the theory, or there is a large gulf between the theory and the implementation of the tool. We introduce a formal compositional symbolic execution engine which creates and uses function specifications from an underlying separation logic and provides a sound theoretical foundation for, and indeed was partially inspired by, the Gillian symbolic execution platform. This is achieved by providing an axiomatic interface which describes the properties of the consume and produce operations used in the engine to update compositionally the symbolic state, for example when calling function specifications. This consume-produce technique is used by VeriFast, Viper, and Gillian, but has not been previously characterised independently of the tool. As part of our result, we give consume and produce operations inspired by the Gillian implementation that satisfy the properties described by our axiomatic interface. A surprising property is that our engine semantics provides a common foundation for both correctness and incorrectness reasoning, with the difference in the underlying engine only amounting to the choice to use satisfiability or validity. We use this property to extend the Gillian platform, which previously only supported correctness reasoning, with incorrectness reasoning and automatic true bug-finding using incorrectness bi-abduction. We evaluate our new Gillian platform by using the Gillian instantiation to C. This instantiation is the first tool grounded on a common formal compositional symbolic execution engine to support both correctness and incorrectness reasoning.
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Andreas Lööw, Daniele Nantes-Sobrinho, Sacha-Élie Ayoun, Caroline Cronjäger, Petar Maksimović, and Philippa Gardner. Compositional Symbolic Execution for Correctness and Incorrectness Reasoning. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 25:1-25:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{loow_et_al:LIPIcs.ECOOP.2024.25,
  author =	{L\"{o}\"{o}w, Andreas and Nantes-Sobrinho, Daniele and Ayoun, Sacha-\'{E}lie and Cronj\"{a}ger, Caroline and Maksimovi\'{c}, Petar and Gardner, Philippa},
  title =	{{Compositional Symbolic Execution for Correctness and Incorrectness Reasoning}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{25:1--25:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.25},
  URN =		{urn:nbn:de:0030-drops-208741},
  doi =		{10.4230/LIPIcs.ECOOP.2024.25},
  annote =	{Keywords: separation logic, incorrectness logic, symbolic execution, bi-abduction}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2024.26
Matching Plans for Frame Inference in Compositional Reasoning

Authors: Andreas Lööw, Daniele Nantes-Sobrinho, Sacha-Élie Ayoun, Petar Maksimović, and Philippa Gardner

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract
The use of function specifications to reason about function calls and the manipulation of user-defined predicates are two essential ingredients of modern compositional verification tools based on separation logic. To execute these operations successfully, these tools must be able to solve the frame inference problem, that is, to understand which parts of the state are relevant for the operation at hand. We introduce matching plans, a concept that is used in the Gillian verification platform to automate frame inference efficiently. We extract matching plans and their automation machinery from the Gillian implementation and present them in a tool-agnostic way, making the Gillian approach available to the broader verification community as a verification-tool design pattern.
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Andreas Lööw, Daniele Nantes-Sobrinho, Sacha-Élie Ayoun, Petar Maksimović, and Philippa Gardner. Matching Plans for Frame Inference in Compositional Reasoning. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 26:1-26:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{loow_et_al:LIPIcs.ECOOP.2024.26,
  author =	{L\"{o}\"{o}w, Andreas and Nantes-Sobrinho, Daniele and Ayoun, Sacha-\'{E}lie and Maksimovi\'{c}, Petar and Gardner, Philippa},
  title =	{{Matching Plans for Frame Inference in Compositional Reasoning}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{26:1--26:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.26},
  URN =		{urn:nbn:de:0030-drops-208751},
  doi =		{10.4230/LIPIcs.ECOOP.2024.26},
  annote =	{Keywords: Compositional reasoning, separation logic, frame inference}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2024.30
Verifying Lock-Free Search Structure Templates

Authors: Nisarg Patel, Dennis Shasha, and Thomas Wies

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract
We present and verify template algorithms for lock-free concurrent search structures that cover a broad range of existing implementations based on lists and skiplists. Our linearizability proofs are fully mechanized in the concurrent separation logic Iris. The proofs are modular and cover the broader design space of the underlying algorithms by parameterizing the verification over aspects such as the low-level representation of nodes and the style of data structure maintenance. As a further technical contribution, we present a mechanization of a recently proposed method for reasoning about future-dependent linearization points using hindsight arguments. The mechanization builds on Iris' support for prophecy reasoning and user-defined ghost resources. We demonstrate that the method can help to reduce the proof effort compared to direct prophecy-based proofs.
Cite as

Nisarg Patel, Dennis Shasha, and Thomas Wies. Verifying Lock-Free Search Structure Templates. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 30:1-30:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{patel_et_al:LIPIcs.ECOOP.2024.30,
  author =	{Patel, Nisarg and Shasha, Dennis and Wies, Thomas},
  title =	{{Verifying Lock-Free Search Structure Templates}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{30:1--30:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.30},
  URN =		{urn:nbn:de:0030-drops-208797},
  doi =		{10.4230/LIPIcs.ECOOP.2024.30},
  annote =	{Keywords: skiplists, lock-free, separation logic, linearizability, future-dependent linearization points, hindsight reasoning}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2024.39
Formalizing, Mechanizing, and Verifying Class-Based Refinement Types

Authors: Ke Sun, Di Wang, Sheng Chen, Meng Wang, and Dan Hao

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract
Refinement types have been extensively used in class-based languages to specify and verify fine-grained logical specifications. Despite the advances in practical aspects such as applicability and usability, two fundamental issues persist. First, the soundness of existing class-based refinement type systems is inadequately explored, casting doubts on their reliability. Second, the expressiveness of existing systems is limited, restricting the depiction of semantic properties related to object-oriented constructs. This work tackles these issues through a systematic framework. We formalize a declarative class-based refinement type calculus (named RFJ), that is expressive and concise. We rigorously develop the soundness meta-theory of this calculus, followed by its mechanization in Coq. Finally, to ensure the calculus’s verifiability, we propose an algorithmic verification approach based on a fragment of first-order logic (named LFJ), and implement this approach as a type checker.
Cite as

Ke Sun, Di Wang, Sheng Chen, Meng Wang, and Dan Hao. Formalizing, Mechanizing, and Verifying Class-Based Refinement Types. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 39:1-39:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{sun_et_al:LIPIcs.ECOOP.2024.39,
  author =	{Sun, Ke and Wang, Di and Chen, Sheng and Wang, Meng and Hao, Dan},
  title =	{{Formalizing, Mechanizing, and Verifying Class-Based Refinement Types}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{39:1--39:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.39},
  URN =		{urn:nbn:de:0030-drops-208881},
  doi =		{10.4230/LIPIcs.ECOOP.2024.39},
  annote =	{Keywords: Refinement Types, Program Verification, Object-oriented Programming}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2024.43
Inductive Predicate Synthesis Modulo Programs

Authors: Scott Wesley, Maria Christakis, Jorge A. Navas, Richard Trefler, Valentin Wüstholz, and Arie Gurfinkel

Published in: LIPIcs, Volume 313, 38th European Conference on Object-Oriented Programming (ECOOP 2024)

Abstract
A growing trend in program analysis is to encode verification conditions within the language of the input program. This simplifies the design of analysis tools by utilizing off-the-shelf verifiers, but makes communication with the underlying solver more challenging. Essentially, the analysis tools operates at the level of input programs, whereas the solver operates at the level of problem encodings. To bridge this gap, the verifier must pass along proof-rules from the analysis tool to the solver. For example, an analysis tool for concurrent programs built on an inductive program verifier might need to declare Owicki-Gries style proof-rules for the underlying solver. Each such proof-rule further specifies how a program should be verified, meaning that the problem of passing proof-rules is a form of invariant synthesis. Similarly, many program analysis tasks reduce to the synthesis of pure, loop-free Boolean functions (i.e., predicates), relative to a program. From this observation, we propose Inductive Predicate Synthesis Modulo Programs (IPS-MP) which extends high-level languages with minimal synthesis features to guide analysis. In IPS-MP, unknown predicates appear under assume and assert statements, acting as specifications modulo the program semantics. Existing synthesis solvers are inefficient at IPS-MP as they target more general problems. In this paper, we show that IPS-MP admits an efficient solution in the Boolean case, despite being generally undecidable. Moreover, we show that IPS-MP reduces to the satisfiability of constrained Horn clauses, which is less general than existing synthesis problems, yet expressive enough to encode verification tasks. We provide reductions from challenging verification tasks - such as parameterized model checking - to IPS-MP. We realize these reductions with an efficient IPS-MP-solver based on SeaHorn, and describe a real-world application to smart-contract verification.
Cite as

Scott Wesley, Maria Christakis, Jorge A. Navas, Richard Trefler, Valentin Wüstholz, and Arie Gurfinkel. Inductive Predicate Synthesis Modulo Programs. In 38th European Conference on Object-Oriented Programming (ECOOP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 313, pp. 43:1-43:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{wesley_et_al:LIPIcs.ECOOP.2024.43,
  author =	{Wesley, Scott and Christakis, Maria and Navas, Jorge A. and Trefler, Richard and W\"{u}stholz, Valentin and Gurfinkel, Arie},
  title =	{{Inductive Predicate Synthesis Modulo Programs}},
  booktitle =	{38th European Conference on Object-Oriented Programming (ECOOP 2024)},
  pages =	{43:1--43:30},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-341-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{313},
  editor =	{Aldrich, Jonathan and Salvaneschi, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2024.43},
  URN =		{urn:nbn:de:0030-drops-208926},
  doi =		{10.4230/LIPIcs.ECOOP.2024.43},
  annote =	{Keywords: Software Verification, Invariant Synthesis, Model-Checking}
}
Document
DOI: 10.4230/LIPIcs.ITP.2024.19
Modular Verification of Intrusive List and Tree Data Structures in Separation Logic

Authors: Marc Hermes and Robbert Krebbers

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract
Intrusive linked data structures are commonly used in low-level programming languages such as C for efficiency and to enable a form of generic types. Notably, intrusive versions of linked lists and search trees are used in the Linux kernel and the Boost C++ library. These data structures differ from ordinary data structures in the way that nodes contain only the meta data (i.e. pointers to other nodes), but not the data itself. Instead the programmer needs to embed nodes into the data, thereby avoiding pointer indirections, and allowing data to be part of several data structures. In this paper we address the challenge of specifying and verifying intrusive data structures using separation logic. We aim for modular verification, where we first specify and verify the operations on the nodes (without the data) and then use these specifications to verify clients that attach data. We achieve this by employing a representation predicate that separates the data structure’s node structure from the data that is attached to it. We apply our methodology to singly-linked lists - from which we build cyclic and doubly-linked lists - and binary trees - from which we build binary search trees. All verifications are conducted using the Coq proof assistant, making use of the Iris framework for separation logic.
Cite as

Marc Hermes and Robbert Krebbers. Modular Verification of Intrusive List and Tree Data Structures in Separation Logic. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hermes_et_al:LIPIcs.ITP.2024.19,
  author =	{Hermes, Marc and Krebbers, Robbert},
  title =	{{Modular Verification of Intrusive List and Tree Data Structures in Separation Logic}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{19:1--19:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.19},
  URN =		{urn:nbn:de:0030-drops-207478},
  doi =		{10.4230/LIPIcs.ITP.2024.19},
  annote =	{Keywords: Separation Logic, Program Verification, Data Structures, Iris, Coq}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.16
Effect Semantics for Quantum Process Calculi

Authors: Lorenzo Ceragioli, Fabio Gadducci, Giuseppe Lomurno, and Gabriele Tedeschi

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
The development of quantum communication protocols sparked the interest in quantum extensions of process calculi and behavioural equivalences, but defining a bisimilarity that matches the observational properties of a quantum-capable system is a surprisingly difficult task. The two proposals explicitly addressing this issue, qCCS and lqCCS, do not define an algorithmic verification scheme: the bisimilarity of two processes is proven by comparing their behaviour under all input states. We introduce a new semantic model based on effects, i.e. probabilistic predicates on quantum states that represent their observable properties. We define and investigate the properties of effect distributions and effect labelled transition systems (eLTSs), generalizing probability distributions and probabilistic labelled transition systems (pLTSs), respectively. As a proof of concept, we provide an eLTS-based semantics for a minimal quantum process algebra, which we prove sound and complete with respect to the observable probabilistic behaviour of quantum processes. To the best of our knowledge, ours is the first algorithmically verifiable proposal that abides to the properties of quantum theory.
Cite as

Lorenzo Ceragioli, Fabio Gadducci, Giuseppe Lomurno, and Gabriele Tedeschi. Effect Semantics for Quantum Process Calculi. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 16:1-16:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ceragioli_et_al:LIPIcs.CONCUR.2024.16,
  author =	{Ceragioli, Lorenzo and Gadducci, Fabio and Lomurno, Giuseppe and Tedeschi, Gabriele},
  title =	{{Effect Semantics for Quantum Process Calculi}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{16:1--16:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak 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.CONCUR.2024.16},
  URN =		{urn:nbn:de:0030-drops-207886},
  doi =		{10.4230/LIPIcs.CONCUR.2024.16},
  annote =	{Keywords: Quantum process calculi, probabilistic LTSs, effect LTSs}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.20
Behavioural Metrics: Compositionality of the Kantorovich Lifting and an Application to Up-To Techniques

Authors: Keri D'Angelo, Sebastian Gurke, Johanna Maria Kirss, Barbara König, Matina Najafi, Wojciech Różowski, and Paul Wild

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
Behavioural distances of transition systems modelled via coalgebras for endofunctors generalize traditional notions of behavioural equivalence to a quantitative setting, in which states are equipped with a measure of how (dis)similar they are. Endowing transition systems with such distances essentially relies on the ability to lift functors describing the one-step behavior of the transition systems to the category of pseudometric spaces. We consider the category theoretic generalization of the Kantorovich lifting from transportation theory to the case of lifting functors to quantale-valued relations, which subsumes equivalences, preorders and (directed) metrics. We use tools from fibred category theory, which allow one to see the Kantorovich lifting as arising from an appropriate fibred adjunction. Our main contributions are compositionality results for the Kantorovich lifting, where we show that that the lifting of a composed functor coincides with the composition of the liftings. In addition, we describe how to lift distributive laws in the case where one of the two functors is polynomial (with finite coproducts). These results are essential ingredients for adapting up-to-techniques to the case of quantale-valued behavioural distances. Up-to techniques are a well-known coinductive technique for efficiently showing lower bounds for behavioural distances. We illustrate the results of our paper in two case studies.
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Keri D'Angelo, Sebastian Gurke, Johanna Maria Kirss, Barbara König, Matina Najafi, Wojciech Różowski, and Paul Wild. Behavioural Metrics: Compositionality of the Kantorovich Lifting and an Application to Up-To Techniques. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dangelo_et_al:LIPIcs.CONCUR.2024.20,
  author =	{D'Angelo, Keri and Gurke, Sebastian and Kirss, Johanna Maria and K\"{o}nig, Barbara and Najafi, Matina and R\'{o}\.{z}owski, Wojciech and Wild, Paul},
  title =	{{Behavioural Metrics: Compositionality of the Kantorovich Lifting and an Application to Up-To Techniques}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{20:1--20:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak 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.CONCUR.2024.20},
  URN =		{urn:nbn:de:0030-drops-207921},
  doi =		{10.4230/LIPIcs.CONCUR.2024.20},
  annote =	{Keywords: behavioural metrics, coalgebra, Galois connections, quantales, Kantorovich lifting, up-to techniques}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.25
A Unifying Categorical View of Nondeterministic Iteration and Tests

Authors: Sergey Goncharov and Tarmo Uustalu

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
We study Kleene iteration in the categorical context. A celebrated completeness result by Kozen introduced Kleene algebra (with tests) as a ubiquitous tool for lightweight reasoning about program equivalence, and yet, numerous variants of it came along afterwards to answer the demand for more refined flavors of semantics, such as stateful, concurrent, exceptional, hybrid, branching time, etc. We detach Kleene iteration from Kleene algebra and analyze it from the categorical perspective. The notion, we arrive at is that of Kleene-iteration category (with coproducts and tests), which we show to be general and robust in the sense of compatibility with programming language features, such as exceptions, store, concurrent behaviour, etc. We attest the proposed notion w.r.t. various yardsticks, most importantly, by characterizing the free model as a certain category of (nondeterministic) rational trees.
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Sergey Goncharov and Tarmo Uustalu. A Unifying Categorical View of Nondeterministic Iteration and Tests. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 25:1-25:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{goncharov_et_al:LIPIcs.CONCUR.2024.25,
  author =	{Goncharov, Sergey and Uustalu, Tarmo},
  title =	{{A Unifying Categorical View of Nondeterministic Iteration and Tests}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{25:1--25:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak 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.CONCUR.2024.25},
  URN =		{urn:nbn:de:0030-drops-207979},
  doi =		{10.4230/LIPIcs.CONCUR.2024.25},
  annote =	{Keywords: Kleene iteration, Elgot iteration, Kleene algebra, coalgebraic resumptions}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.31
Bi-Reachability in Petri Nets with Data

Authors: Łukasz Kamiński and Sławomir Lasota

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
We investigate Petri nets with data, an extension of plain Petri nets where tokens carry values from an infinite data domain, and executability of transitions is conditioned by equalities between data values. We provide a decision procedure for the bi-reachability problem: given a Petri net and its two configurations, we ask if each of the configurations is reachable from the other. This pushes forward the decidability borderline, as the bi-reachability problem subsumes the coverability problem (which is known to be decidable) and is subsumed by the reachability problem (whose decidability status is unknown).
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Łukasz Kamiński and Sławomir Lasota. Bi-Reachability in Petri Nets with Data. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 31:1-31:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kaminski_et_al:LIPIcs.CONCUR.2024.31,
  author =	{Kami\'{n}ski, {\L}ukasz and Lasota, S{\l}awomir},
  title =	{{Bi-Reachability in Petri Nets with Data}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{31:1--31:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak 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.CONCUR.2024.31},
  URN =		{urn:nbn:de:0030-drops-208038},
  doi =		{10.4230/LIPIcs.CONCUR.2024.31},
  annote =	{Keywords: Petri nets, Petri nets with data, reachability, bi-reachability, reversible reachability, mutual reachability, orbit-finite sets}
}
Document
DOI: 10.4230/LIPIcs.TYPES.2023.3
Categorical Models of Subtyping

Authors: Greta Coraglia and Jacopo Emmenegger

Published in: LIPIcs, Volume 303, 29th International Conference on Types for Proofs and Programs (TYPES 2023)

Abstract
Most categorical models for dependent types have traditionally been heavily set based: contexts form a category, and for each we have a set of types in said context - and for each type a set of terms of said type. This is the case for categories with families, categories with attributes, and natural models; in particular, all of them can be traced back to certain discrete Grothendieck fibrations. We extend this intuition to the case of general, not necessarily discrete, fibrations, so that over a given context one has not only a set but a category of types. We argue that the added structure can be attributed to a notion of subtyping that shares many features with that of coercive subtyping, in the sense that it is the product of thinking about subtyping as an abbreviation mechanism: we say that a given type A' is a subtype of A if there is a unique coercion from A' to A. Whenever we need a term of type A, then, it suffices to have a term of type A', which we can "plug-in" into A. For this version of subtyping we provide rules, coherences, and explicit models, and we compare and contrast it to coercive subtyping as introduced by Z. Luo and others. We conclude by suggesting how the tools we present can be employed in finding appropriate rules relating subtyping and certain type constructors.
Cite as

Greta Coraglia and Jacopo Emmenegger. Categorical Models of Subtyping. In 29th International Conference on Types for Proofs and Programs (TYPES 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 303, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{coraglia_et_al:LIPIcs.TYPES.2023.3,
  author =	{Coraglia, Greta and Emmenegger, Jacopo},
  title =	{{Categorical Models of Subtyping}},
  booktitle =	{29th International Conference on Types for Proofs and Programs (TYPES 2023)},
  pages =	{3:1--3:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-332-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{303},
  editor =	{Kesner, Delia and Reyes, Eduardo Hermo and van den Berg, Benno},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2023.3},
  URN =		{urn:nbn:de:0030-drops-204811},
  doi =		{10.4230/LIPIcs.TYPES.2023.3},
  annote =	{Keywords: dependent types, subtyping, coercive subtyping, categorical semantics, categories with families, monad}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2024.7
Machine-Checked Categorical Diagrammatic Reasoning

Authors: Benoît Guillemet, Assia Mahboubi, and Matthieu Piquerez

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

Abstract
This paper describes a formal proof library, developed using the Coq proof assistant, designed to assist users in writing correct diagrammatic proofs, for 1-categories. This library proposes a deep-embedded, domain-specific formal language, which features dedicated proof commands to automate the synthesis, and the verification, of the technical parts often eluded in the literature.
Cite as

Benoît Guillemet, Assia Mahboubi, and Matthieu Piquerez. Machine-Checked Categorical Diagrammatic Reasoning. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 7:1-7:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{guillemet_et_al:LIPIcs.FSCD.2024.7,
  author =	{Guillemet, Beno\^{i}t and Mahboubi, Assia and Piquerez, Matthieu},
  title =	{{Machine-Checked Categorical Diagrammatic Reasoning}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{7:1--7:19},
  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.2024.7},
  URN =		{urn:nbn:de:0030-drops-203363},
  doi =		{10.4230/LIPIcs.FSCD.2024.7},
  annote =	{Keywords: Interactive theorem proving, categories, diagrams, formal proof automation}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2024.17
A Categorical Approach to DIBI Models

Authors: Tao Gu, Jialu Bao, Justin Hsu, Alexandra Silva, and Fabio Zanasi

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

Abstract
The logic of Dependence and Independence Bunched Implications (DIBI) is a logic to reason about conditional independence (CI); for instance, DIBI formulas can characterise CI in discrete probability distributions and in relational databases, using a probabilistic DIBI model and a similarly-constructed relational model. Despite the similarity of the two models, there lacks a uniform account. As a result, the laborious case-by-case verification of the frame conditions required for constructing new models hinders them from generalising the results to CI in other useful models such that continuous distribution. In this paper, we develop an abstract framework for systematically constructing DIBI models, using category theory as the unifying mathematical language. We show that DIBI models arise from arbitrary symmetric monoidal categories with copy-discard structure. In particular, we use string diagrams - a graphical presentation of monoidal categories - to give a uniform definition of the parallel composition and subkernel relation in DIBI models. Our approach not only generalises known models, but also yields new models of interest and reduces properties of DIBI models to structures in the underlying categories. Furthermore, our categorical framework enables a comparison between string diagrammatic approaches to CI in the literature and a logical notion of CI, defined in terms of the satisfaction of specific DIBI formulas. We show that the logical notion is an extension of string diagrammatic CI under reasonable conditions.
Cite as

Tao Gu, Jialu Bao, Justin Hsu, Alexandra Silva, and Fabio Zanasi. A Categorical Approach to DIBI Models. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gu_et_al:LIPIcs.FSCD.2024.17,
  author =	{Gu, Tao and Bao, Jialu and Hsu, Justin and Silva, Alexandra and Zanasi, Fabio},
  title =	{{A Categorical Approach to DIBI Models}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{17:1--17:20},
  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.2024.17},
  URN =		{urn:nbn:de:0030-drops-203469},
  doi =		{10.4230/LIPIcs.FSCD.2024.17},
  annote =	{Keywords: Conditional Independence, Dependence Independence Bunched Implications, String Diagrams, Markov Categories}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2024.19
Semantics for a Turing-Complete Reversible Programming Language with Inductive Types

Authors: Kostia Chardonnet, Louis Lemonnier, and Benoît Valiron

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

Abstract
This paper is concerned with the expressivity and denotational semantics of a functional higher-order reversible programming language based on Theseus. In this language, pattern-matching is used to ensure the reversibility of functions. We show how one can encode any Reversible Turing Machine in said language. We then build a sound and adequate categorical semantics based on join inverse categories, with additional structures to capture pattern-matching and to interpret inductive types and recursion. We then derive a notion of completeness in the sense that any computable, partial, first-order injective function is the image of a term in the language.
Cite as

Kostia Chardonnet, Louis Lemonnier, and Benoît Valiron. Semantics for a Turing-Complete Reversible Programming Language with Inductive Types. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chardonnet_et_al:LIPIcs.FSCD.2024.19,
  author =	{Chardonnet, Kostia and Lemonnier, Louis and Valiron, Beno\^{i}t},
  title =	{{Semantics for a Turing-Complete Reversible Programming Language with Inductive Types}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{19:1--19:19},
  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.2024.19},
  URN =		{urn:nbn:de:0030-drops-203487},
  doi =		{10.4230/LIPIcs.FSCD.2024.19},
  annote =	{Keywords: Reversible programming, functional programming, Computability, Denotational Semantics}
}
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