21 Search Results for "Zdancewic, Steve"

Document
DOI: 10.4230/LIPIcs.CSL.2026.45
Reasoning About Quality in Hyperproperties

Authors: Samuel Graepler, Benjamin Monmege, and Jean-Marc Talbot

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

Abstract
Hyperproperties allow one to specify properties of systems that inherently involve not single executions of the system, but several of them at once: observational determinism and non-inference are two examples of such properties used to study the security of systems. Logics like HyperLTL have been studied in the past to model check hyperproperties of systems. However, most of the time, requiring strict security properties is actually ineffective as systems do not meet such requirements. To overcome this issue, we introduce qualitative reasoning in HyperLTL, inspired by a similar work on LTL by Almagor, Boker and Kupferman [Almagor et al., 2016] where a formula has a value in the interval [0, 1], obtained by considering either a propositional quality (how much the specification is satisfied), or a temporal quality (when the specification is satisfied). We show decidability of the approximated model checking problem, as well as the model checking of large fragments.
Cite as

Samuel Graepler, Benjamin Monmege, and Jean-Marc Talbot. Reasoning About Quality in Hyperproperties. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 45:1-45:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{graepler_et_al:LIPIcs.CSL.2026.45,
  author =	{Graepler, Samuel and Monmege, Benjamin and Talbot, Jean-Marc},
  title =	{{Reasoning About Quality in Hyperproperties}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{45:1--45:18},
  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.2026.45},
  URN =		{urn:nbn:de:0030-drops-254704},
  doi =		{10.4230/LIPIcs.CSL.2026.45},
  annote =	{Keywords: Hyperlogics, Automata-based model checking, Quantitative verification}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.7
A Verified Cost Model for Call-By-Push-Value

Authors: Zhuo Zoey Chen, Johannes Åman Pohjola, and Christine Rizkallah

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

Abstract
The call-by-push-value λ-calculus allows for syntactically specifying the order of evaluation as part of the term language. Hence, it serves as a unifying language for embedding various evaluation strategies including call-by-value and call-by-name. Given the impact of call-by-push-value, it is remarkable that its adequacy as a model for computational complexity theory has not yet been studied. In this paper, we show that the call-by-push-value λ-calculus is reasonable for both time and space complexity. A reasonable cost model can encode other reasonable cost models with polynomial overhead in time and constant factor overhead in space. We achieve this by encoding call-by-push-value λ-calculus into Turing machines, following a simulation strategy by Forster et al.; for the converse direction, we prove that Levy’s encoding of the call-by-value λ-calculus has reasonable complexity bounds. The main results have been formalised in the HOL4 theorem prover.
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Zhuo Zoey Chen, Johannes Åman Pohjola, and Christine Rizkallah. A Verified Cost Model for Call-By-Push-Value. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 7:1-7:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ITP.2025.7,
  author =	{Chen, Zhuo Zoey and \r{A}man Pohjola, Johannes and Rizkallah, Christine},
  title =	{{A Verified Cost Model for Call-By-Push-Value}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{7:1--7:19},
  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.2025.7},
  URN =		{urn:nbn:de:0030-drops-246067},
  doi =		{10.4230/LIPIcs.ITP.2025.7},
  annote =	{Keywords: lambda calculus, formalizations of computational models, computability theory, HOL, call-by-push-value reduction, time and space complexity, abstract machines}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.8
Abstract, Compositional Consistency: Isabelle/HOL Locales for Completeness à la Fitting

Authors: Asta Halkjær From and Anders Schlichtkrull

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

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

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

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@InProceedings{from_et_al:LIPIcs.ITP.2025.8,
  author =	{From, Asta Halkj{\ae}r and Schlichtkrull, Anders},
  title =	{{Abstract, Compositional Consistency: Isabelle/HOL Locales for Completeness \`{a} la Fitting}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.8},
  URN =		{urn:nbn:de:0030-drops-246406},
  doi =		{10.4230/LIPIcs.ITP.2025.8},
  annote =	{Keywords: Logic, completeness, abstract consistency property, Isabelle/HOL, locales}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.30
Nondeterministic Asynchronous Dataflow in Isabelle/HOL

Authors: Rafael Castro Gonçalves Silva, Laouen Fernet, and Dmitriy Traytel

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

Abstract
We formalize nondeterministic asynchronous dataflow networks in Isabelle/HOL. Dataflow networks are comprised of operators that are capable of communicating with the network, performing silent computations, and making nondeterministic choices. We represent operators using a shallow embedding as codatatypes. Using this representation, we define standard asynchronous dataflow primitives, including sequential and parallel composition and a feedback operator. These primitives adhere to a number of laws from the literature, which we prove by coinduction using weak bisimilarity as our equality. Albeit coinductive and nondeterministic, our model is executable via code extraction to Haskell.
Cite as

Rafael Castro Gonçalves Silva, Laouen Fernet, and Dmitriy Traytel. Nondeterministic Asynchronous Dataflow in Isabelle/HOL. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 30:1-30:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{silva_et_al:LIPIcs.ITP.2025.30,
  author =	{Silva, Rafael Castro Gon\c{c}alves and Fernet, Laouen and Traytel, Dmitriy},
  title =	{{Nondeterministic Asynchronous Dataflow in Isabelle/HOL}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{30:1--30:20},
  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.2025.30},
  URN =		{urn:nbn:de:0030-drops-246280},
  doi =		{10.4230/LIPIcs.ITP.2025.30},
  annote =	{Keywords: dataflow, verification, coinduction, Isabelle/HOL}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ITP.2025.40
Autosubst: On Mechanising Binders in a General-Purpose Proof Assistant (Invited Talk)

Authors: Kathrin Stark

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

Abstract
The question of handling binders effectively regularly comes up when mechanising results in a proof assistant. Since the beginning of proof assistants, many solutions have been suggested: these include de Bruijn syntax, locally nameless binders, nominal syntax or HOAS. But even today - 20 years after the POPLMark Challenge [Brian E. Aydemir et al., 2005] - new tools and approaches to binding are still being published. Binders are still mentioned as being a complication of mechanised proofs over pen-and-paper proofs and the source of uninteresting technicalities and heaps of boilerplate - particularly, when working in a proof assistant without native support for binders or quotients. Autosubst [Steven Schäfer et al., 2015; Steven Schäfer et al., 2015], initially developed a decade ago as a teaching tool, addresses this problem by automating boilerplate code generation for a de Bruijn representation in the Rocq prover. Autosubst translates a specification into the corresponding pure or scoped de Bruijn algebra: It hence generates a corresponding instantiation operation for parallel substitutions, and several equational substitution lemmas. Central to its usability is a rewriting tactic that automatically decides equality up to substitutions, requiring minimal input and knowledge from the user’s side. This greatly simplifies using the otherwise notoriously difficult de Bruijn representation. Since then, Autosubst has been successfully used in several projects. In this talk, I will give an overview of the background and history of Autosubst and give an overview on the work, tools, and formalisations around it [Kathrin Stark et al., 2019; Kathrin Stark, 2020; Andreas Abel et al., 2019]. Moreover, this talk will highlight some of the more recent extensions [Yannick Forster and Kathrin Stark, 2020] as well as outline future challenges and directions.
Cite as

Kathrin Stark. Autosubst: On Mechanising Binders in a General-Purpose Proof Assistant (Invited Talk). In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 40:1-40:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{stark:LIPIcs.ITP.2025.40,
  author =	{Stark, Kathrin},
  title =	{{Autosubst: On Mechanising Binders in a General-Purpose Proof Assistant}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{40:1--40:2},
  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.2025.40},
  URN =		{urn:nbn:de:0030-drops-246385},
  doi =		{10.4230/LIPIcs.ITP.2025.40},
  annote =	{Keywords: Syntax, binders, Rocq}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.13
Barendregt’s Theory of the λ-Calculus, Refreshed and Formalized

Authors: Adrienne Lancelot, Beniamino Accattoli, and Maxime Vemclefs

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

Abstract
Barendregt’s book on the untyped λ-calculus refines the inconsistent view of β-divergence as representation of the undefined via the key concept of head reduction. In this paper, we put together recent revisitations of some key theorems laid out in Barendregt’s book, and we formalize them in the Abella proof assistant. Our work provides a compact and refreshed presentation of the core of the book. The formalization faithfully mimics pen-and-paper proofs. Two interesting aspects are the manipulation of contexts for the study of contextual equivalence and a formal alternative to the informal trick at work in Takahashi’s proof of the genericity lemma. As a by-product, we obtain an alternative definition of contextual equivalence that does not mention contexts.
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Adrienne Lancelot, Beniamino Accattoli, and Maxime Vemclefs. Barendregt’s Theory of the λ-Calculus, Refreshed and Formalized. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 13:1-13:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lancelot_et_al:LIPIcs.ITP.2025.13,
  author =	{Lancelot, Adrienne and Accattoli, Beniamino and Vemclefs, Maxime},
  title =	{{Barendregt’s Theory of the \lambda-Calculus, Refreshed and Formalized}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{13:1--13:22},
  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.2025.13},
  URN =		{urn:nbn:de:0030-drops-246114},
  doi =		{10.4230/LIPIcs.ITP.2025.13},
  annote =	{Keywords: lambda-calculus, head reduction, equational theory}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.11
Animating MRBNFs: Truly Modular Binding-Aware Datatypes in Isabelle/HOL

Authors: Jan van Brügge, Andrei Popescu, and Dmitriy Traytel

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

Abstract
Nominal Isabelle provides powerful tools for meta-theoretic reasoning about syntax of logics or programming languages, in which variables are bound. It has been instrumental to major verification successes, such as Gödel’s incompleteness theorems. However, the existing tooling is not compositional. In particular, it does not support nested recursion, linear binding patterns, or infinitely branching syntax. These limitations are fundamental in the way nominal datatypes and functions on them are constructed within Nominal Isabelle. Taking advantage of recent theoretical advancements that overcome these limitations through a modular approach using the concept of map-restricted bounded natural functor (MRBNF), we develop and implement a new definitional package for binding-aware datatypes in Isabelle/HOL, called MrBNF. We describe the journey from the user specification to the end-product types, constants and theorems the tool generates. We validate MrBNF in two formalization case studies that so far were out of reach of nominal approaches: (1) Mazza’s isomorphism between the finitary and the infinitary affine λ-calculus, and (2) the POPLmark 2B challenge, which involves non-free binders for linear pattern matching.
Cite as

Jan van Brügge, Andrei Popescu, and Dmitriy Traytel. Animating MRBNFs: Truly Modular Binding-Aware Datatypes in Isabelle/HOL. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vanbrugge_et_al:LIPIcs.ITP.2025.11,
  author =	{van Br\"{u}gge, Jan and Popescu, Andrei and Traytel, Dmitriy},
  title =	{{Animating MRBNFs: Truly Modular Binding-Aware Datatypes in Isabelle/HOL}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{11:1--11:20},
  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.2025.11},
  URN =		{urn:nbn:de:0030-drops-246091},
  doi =		{10.4230/LIPIcs.ITP.2025.11},
  annote =	{Keywords: syntax with bindings, datatypes, inductive predicates, Isabelle/HOL}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.4
Substructural Parametricity

Authors: C. B. Aberlé, Karl Crary, Chris Martens, and Frank Pfenning

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

Abstract
Ordered, linear, and other substructural type systems allow us to expose deep properties of programs at the syntactic level of types. In this paper, we develop a family of unary logical relations that allow us to prove consequences of parametricity for a range of substructural type systems. A key idea is to parameterize the relation by an algebra, which we exemplify with a monoid and commutative monoid to interpret ordered and linear type systems, respectively. We prove the fundamental theorem of logical relations and apply it to deduce extensional properties of inhabitants of certain types. Examples include demonstrating that the ordered types for list append and reversal are inhabited by exactly one function, as are types of some tree traversals. Similarly, the linear type of the identity function on lists is inhabited only by permutations of the input. Our most advanced example shows that the ordered type of the list fold function is inhabited only by the fold function.
Cite as

C. B. Aberlé, Karl Crary, Chris Martens, and Frank Pfenning. Substructural Parametricity. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 4:1-4:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{aberle_et_al:LIPIcs.FSCD.2025.4,
  author =	{Aberl\'{e}, C. B. and Crary, Karl and Martens, Chris and Pfenning, Frank},
  title =	{{Substructural Parametricity}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{4:1--4:21},
  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.2025.4},
  URN =		{urn:nbn:de:0030-drops-236193},
  doi =		{10.4230/LIPIcs.FSCD.2025.4},
  annote =	{Keywords: Substructural type systems, logical relations, ordered logic}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2025.2
Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs (Invited Talk)

Authors: Matthew L. Daggitt, Wen Kokke, Robert Atkey, Ekaterina Komendantskaya, Natalia Slusarz, and Luca Arnaboldi

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

Abstract
Neuro-symbolic programs, i.e. programs containing both machine learning components and traditional symbolic code, are becoming increasingly widespread. Finding a general methodology for verifying such programs is challenging due to both the number of different tools involved and the intricate interface between the "neural" and "symbolic" program components. In this paper we present a general decomposition of the neuro-symbolic verification problem into parts, and examine the problem of the embedding gap that occurs when one tries to combine proofs about the neural and symbolic components. To address this problem we then introduce Vehicle - standing as an abbreviation for a "verification condition language" - an intermediate programming language interface between machine learning frameworks, automated theorem provers, and dependently-typed formalisations of neuro-symbolic programs. Vehicle allows users to specify the properties of the neural components of neuro-symbolic programs once, and then safely compile the specification to each interface using a tailored typing and compilation procedure. We give a high-level overview of Vehicle’s overall design, its interfaces and compilation & type-checking procedures, and then demonstrate its utility by formally verifying the safety of a simple autonomous car controlled by a neural network, operating in a stochastic environment with imperfect information.
Cite as

Matthew L. Daggitt, Wen Kokke, Robert Atkey, Ekaterina Komendantskaya, Natalia Slusarz, and Luca Arnaboldi. Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs (Invited Talk). In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 2:1-2:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{daggitt_et_al:LIPIcs.FSCD.2025.2,
  author =	{Daggitt, Matthew L. and Kokke, Wen and Atkey, Robert and Komendantskaya, Ekaterina and Slusarz, Natalia and Arnaboldi, Luca},
  title =	{{Vehicle: Bridging the Embedding Gap in the Verification of Neuro-Symbolic Programs}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{2:1--2:20},
  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.2025.2},
  URN =		{urn:nbn:de:0030-drops-236172},
  doi =		{10.4230/LIPIcs.FSCD.2025.2},
  annote =	{Keywords: Neural Network Verification, Types, Interactive Theorem Provers}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.23
∞-Categorical Models of Linear Logic

Authors: Eliès Harington and Samuel Mimram

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

Abstract
The notion of categorical model of linear logic is now well studied and established around the notion of linear-non-linear adjunction, which encompasses the earlier notions of Seely categories, Lafont categories and linear categories. These categorical structures have counterparts in the realm of ∞-categories, which can thus be thought of as weak forms of models of linear logic. The goal of this article is to formally introduce them and study their relationships. We show that ∞-linear-non-linear adjunctions still play the role of a unifying notion of model in this setting. Moreover, we provide a sufficient condition for a symmetric monoidal ∞-category to be Lafont. Finally, we illustrate our constructions by providing models: we construct linear-non-linear adjunctions that generalize well-known models in relations (and variants based on profunctors or spans), domains and vector spaces. In particular, we introduce a model based on spectra, a homotopical variant of abelian groups.
Cite as

Eliès Harington and Samuel Mimram. ∞-Categorical Models of Linear Logic. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{harington_et_al:LIPIcs.FSCD.2025.23,
  author =	{Harington, Eli\`{e}s and Mimram, Samuel},
  title =	{{∞-Categorical Models of Linear Logic}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{23:1--23:20},
  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.2025.23},
  URN =		{urn:nbn:de:0030-drops-236381},
  doi =		{10.4230/LIPIcs.FSCD.2025.23},
  annote =	{Keywords: linear logic, linear-non-linear adjunction, ∞-category, spectrum}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2025.2
The Algebra of Patterns

Authors: David Binder and Lean Ermantraut

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

Abstract
Pattern matching is a popular feature in functional, imperative and object-oriented programming languages. Language designers should therefore invest effort in a good design for pattern matching. Most languages choose a first-match semantics for pattern matching; that is, clauses are tried in the order in which they appear in the program until the first one matches. As a consequence, the order in which the clauses appear cannot be arbitrarily changed, which results in a less declarative programming model. The declarative alternative to this is an order-independent semantics for pattern matching, which is not implemented in most programming languages since it requires more verbose patterns. The reason for this verbosity is that the syntax of patterns is usually not expressive enough to express the complement of a pattern. In this paper, we show a principled way to make order-independent pattern matching practical. Our solution consists of two parts: First, we introduce a boolean algebra of patterns which can express the complement of a pattern. Second, we introduce default clauses to pattern matches. These default clauses capture the essential idea of a fallthrough case without sacrificing the property of order-independence.
Cite as

David Binder and Lean Ermantraut. The Algebra of Patterns. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 2:1-2:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{binder_et_al:LIPIcs.ECOOP.2025.2,
  author =	{Binder, David and Ermantraut, Lean},
  title =	{{The Algebra of Patterns}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{2:1--2:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-373-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{333},
  editor =	{Aldrich, Jonathan and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2025.2},
  URN =		{urn:nbn:de:0030-drops-232959},
  doi =		{10.4230/LIPIcs.ECOOP.2025.2},
  annote =	{Keywords: functional programming, pattern matching, algebraic data types, equational reasoning}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2025.10
Bottom-Up Synthesis of Memory Mutations with Separation Logic

Authors: Kasra Ferdowsi and Hila Peleg

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

Abstract
Programming-by-Example (PBE) is the paradigm of program synthesis specified via input-output pairs. It is commonly used because examples are easy to provide and collect from the environment. A popular optimization for enumerative synthesis with examples is Observational Equivalence (OE), which groups programs into equivalence classes according to their evaluation on example inputs. Current formulations of OE, however, are severely limited by the assumption that the synthesizer’s target language contains only pure components with no side-effects, either enforcing this in their target language, or ignoring it, leading to an incorrect enumeration. This limits their ability to use realistic component sets. We address this limitation by borrowing from Separation Logic, which can compositionally reason about heap mutations. We reformulate PBE using a restricted Separation Logic: Concrete Heap Separation Logic (CHSL), transforming the search for programs into a proof search in CHSL. This lets us perform bottom-up enumerative synthesis without the need for expert-provided annotations or domain-specific inferences, but with three key advantages: we (i) preserve correctness in the presence of memory-mutating operations, (ii) compact the search space by representing many concrete programs as one under CHSL, and (iii) perform a provably correct OE-reduction. We present SObEq (Side-effects in OBservational EQuivalence), a bottom-up enumerative algorithm that, given a PBE task, searches for its CHSL derivation. The SObEq algorithm is proved correct with no purity assumptions: we show it is guaranteed to lose no solutions. We also evaluate our implementation of SObEq on benchmarks from the literature and online sources, and show that it produces high-quality results quickly.
Cite as

Kasra Ferdowsi and Hila Peleg. Bottom-Up Synthesis of Memory Mutations with Separation Logic. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 10:1-10:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ferdowsi_et_al:LIPIcs.ECOOP.2025.10,
  author =	{Ferdowsi, Kasra and Peleg, Hila},
  title =	{{Bottom-Up Synthesis of Memory Mutations with Separation Logic}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{10:1--10:32},
  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.2025.10},
  URN =		{urn:nbn:de:0030-drops-233036},
  doi =		{10.4230/LIPIcs.ECOOP.2025.10},
  annote =	{Keywords: Program synthesis, observational equivalence}
}
Document
DOI: 10.4230/OASIcs.FMBC.2025.8
Formal Verification of a Fail-Safe Cross-Chain Bridge

Authors: Filip Marić, Bernhard Scholz, and Pavle Subotić

Published in: OASIcs, Volume 129, 6th International Workshop on Formal Methods for Blockchains (FMBC 2025)

Abstract
Cross-chain bridges are financial services that interconnect blockchains. High monetary values flow through these bridges, and their security must be safeguarded. However, designing real-world cross-chain bridges is a difficult endeavor. Due to blockchain’s closed-world nature, tokens cannot be transferred from a sender to a receiver chain; on the contrary, they need complex logic that maintains an equilibrium on both chains, even if either the chains or the bridge fail. This paper formally verifies a model of a novel fail-safe cross-chain bridge to ensure correctness. We define formal requirements and prove the bridge is safe using the Isabelle/HOL proof assistant.
Cite as

Filip Marić, Bernhard Scholz, and Pavle Subotić. Formal Verification of a Fail-Safe Cross-Chain Bridge. In 6th International Workshop on Formal Methods for Blockchains (FMBC 2025). Open Access Series in Informatics (OASIcs), Volume 129, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{maric_et_al:OASIcs.FMBC.2025.8,
  author =	{Mari\'{c}, Filip and Scholz, Bernhard and Suboti\'{c}, Pavle},
  title =	{{Formal Verification of a Fail-Safe Cross-Chain Bridge}},
  booktitle =	{6th International Workshop on Formal Methods for Blockchains (FMBC 2025)},
  pages =	{8:1--8:18},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-371-3},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{129},
  editor =	{Marmsoler, Diego and Xu, Meng},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.FMBC.2025.8},
  URN =		{urn:nbn:de:0030-drops-230342},
  doi =		{10.4230/OASIcs.FMBC.2025.8},
  annote =	{Keywords: Cross-Chain Bridge, Formal Verification, Logic, Security}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.47
A Rewriting Theory for Quantum λ-Calculus

Authors: Claudia Faggian, Gaetan Lopez, and Benoît Valiron

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

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

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@InProceedings{faggian_et_al:LIPIcs.CSL.2025.47,
  author =	{Faggian, Claudia and Lopez, Gaetan and Valiron, Beno\^{i}t},
  title =	{{A Rewriting Theory for Quantum \lambda-Calculus}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{47:1--47:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.47},
  URN =		{urn:nbn:de:0030-drops-228046},
  doi =		{10.4230/LIPIcs.CSL.2025.47},
  annote =	{Keywords: quantum lambda-calculus, probabilistic rewriting, operational semantics, asymptotic normalization, principles of quantum programming languages}
}
Document
DOI: 10.4230/LIPIcs.CSL.2025.32
A Mixed Linear and Graded Logic: Proofs, Terms, and Models

Authors: Victoria Vollmer, Danielle Marshall, Harley Eades III, and Dominic Orchard

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

Abstract
Graded modal logics generalise standard modal logics via families of modalities indexed by an algebraic structure whose operations mediate between the different modalities. The graded "of-course" modality !_r captures how many times a proposition is used and has an analogous interpretation to the of-course modality from linear logic; the of-course modality from linear logic can be modelled by a linear exponential comonad and graded of-course can be modelled by a graded linear exponential comonad. Benton showed in his seminal paper on Linear/Non-Linear logic that the of-course modality can be split into two modalities connecting intuitionistic logic with linear logic, forming a symmetric monoidal adjunction. Later, Fujii et al. demonstrated that every graded comonad can be decomposed into an adjunction and a "strict action". We give a similar result to Benton, leveraging Fujii et al.’s decomposition, showing that graded modalities can be split into two modalities connecting a graded logic with a graded linear logic. We propose a sequent calculus, its proof theory and categorical model, and a natural deduction system which we show is isomorphic to the sequent calculus system. Interestingly, our system can also be understood as Linear/Non-Linear logic composed with an action that adds the grading, further illuminating the shared principles between linear logic and a class of graded modal logics.
Cite as

Victoria Vollmer, Danielle Marshall, Harley Eades III, and Dominic Orchard. A Mixed Linear and Graded Logic: Proofs, Terms, and Models. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 32:1-32:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vollmer_et_al:LIPIcs.CSL.2025.32,
  author =	{Vollmer, Victoria and Marshall, Danielle and Eades III, Harley and Orchard, Dominic},
  title =	{{A Mixed Linear and Graded Logic: Proofs, Terms, and Models}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{32:1--32:21},
  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.2025.32},
  URN =		{urn:nbn:de:0030-drops-227892},
  doi =		{10.4230/LIPIcs.CSL.2025.32},
  annote =	{Keywords: linear logic, graded modal logic, adjoint decomposition}
}
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