DROPS

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DOI: 10.4230/LIPIcs.AFT.2025.5

Blockchain Governance via Sharp Anonymous Multisignatures

Authors: Wonseok Choi, Xiangyu Liu, and Vassilis Zikas

Published in: LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025)

Abstract

Electronic voting has occupied a large part of the cryptographic protocols literature. The recent reality of blockchains - in particular, their need for online governance mechanisms - has brought new parameters and requirements to the problem. We identify the key requirements of a blockchain governance mechanism, namely correctness (including eliminative double votes), voter anonymity, and traceability, and investigate mechanisms that can achieve them with minimal interaction and under assumptions that fit the blockchain setting. First, we define a signature-like primitive, which we term sharp anonymous multisignatures (in short, ♯AMS) that tightly meets the needs of blockchain governance. In a nutshell, ♯AMSs allow any set of parties to generate a signature, e.g., on a proposal to be voted upon, which, if posted on the blockchain, hides the identities of the signers/voters but reveals their number. This can be seen as a (strict) generalization of threshold ring signatures (TRS). We next turn to constructing such ♯AMSs and using them in various governance scenarios - e.g., single vote vs. multiple votes per voter. In this direction, although the definition of TRS does not imply ♯AMS, one can compile some existing TRS constructions into ♯AMS. This raises the question: What is the TRS structure that allows such a compilation? To answer the above, we devise templates for TRSs. Our templates encapsulate and abstract the structure that allows for the above compilation - most of the TRS schemes that can be compiled into ♯AMS are, in fact, instantiations of our template. This abstraction makes our template generic for instantiating TRSs and ♯AMSs from different cryptographic assumptions (e.g., DDH, LWE, etc.). One of our templates is based on chameleon hashes, and we explore a framework of lossy chameleon hashes to understand their nature fully. Finally, we turn to how ♯AMS schemes can be used in our applications. We provide fast (in some cases non-interactive) ♯AMS-based blockchain governance mechanisms for a wide spectrum of assumptions on the honesty (semi-honest vs malicious) and availability of voters and proposers.

Cite as

Wonseok Choi, Xiangyu Liu, and Vassilis Zikas. Blockchain Governance via Sharp Anonymous Multisignatures. In 7th Conference on Advances in Financial Technologies (AFT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 354, pp. 5:1-5:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{choi_et_al:LIPIcs.AFT.2025.5,
  author =	{Choi, Wonseok and Liu, Xiangyu and Zikas, Vassilis},
  title =	{{Blockchain Governance via Sharp Anonymous Multisignatures}},
  booktitle =	{7th Conference on Advances in Financial Technologies (AFT 2025)},
  pages =	{5:1--5:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-400-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{354},
  editor =	{Avarikioti, Zeta and Christin, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.5},
  URN =		{urn:nbn:de:0030-drops-247242},
  doi =		{10.4230/LIPIcs.AFT.2025.5},
  annote =	{Keywords: Blockchain, E-voting, Threshold Ring Signatures, Threshold Cryptography}
}

Document

DOI: 10.4230/LIPIcs.ITP.2025.29

Nanopass Back-Translation of Call-Return Trees for Mechanized Secure Compilation Proofs

Authors: Jérémy Thibault, Joseph Lenormand, and Cătălin Hriţcu

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

Abstract

Researchers aim to build secure compilation chains enforcing that if there is no attack a source context can mount against a source program then there is also no attack an adversarial target context can mount against the compiled program. Proving that these compilation chains are secure is, however, challenging, and involves a non-trivial back-translation step: for any attack a target context mounts against the compiled program one has to exhibit a source context mounting the same attack against the source program. We describe a novel back-translation technique, which results in simpler proofs that can be more easily mechanized in a proof assistant. Given a finite set of finite trace prefixes, capturing the interaction recorded during an attack between a target context and the compiled program, we build a call-return tree that we back-translate into a source context producing the same trace prefixes. We use state in the generated source context to record the current location in the call-return tree. The back-translation is done in several small steps, each adding to the tree new information describing how the location should change depending on how the context regains control. To prove this back-translation correct we give semantics to every intermediate call-return tree language, using ghost state to store information and explicitly enforce execution invariants. We prove several small forward simulations, basically seeing the back-translation as a verified nanopass compiler. Thanks to this modular structure, we are able to mechanize this complex back-translation and its correctness proof in the Rocq prover without too much effort.

Cite as

Jérémy Thibault, Joseph Lenormand, and Cătălin Hriţcu. Nanopass Back-Translation of Call-Return Trees for Mechanized Secure Compilation Proofs. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{thibault_et_al:LIPIcs.ITP.2025.29,
  author =	{Thibault, J\'{e}r\'{e}my and Lenormand, Joseph and Hri\c{t}cu, C\u{a}t\u{a}lin},
  title =	{{Nanopass Back-Translation of Call-Return Trees for Mechanized Secure Compilation Proofs}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{29:1--29:20},
  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.2025.29},
  URN =		{urn:nbn:de:0030-drops-246272},
  doi =		{10.4230/LIPIcs.ITP.2025.29},
  annote =	{Keywords: secure compilation, back-translation, machine-checked proofs, Rocq, Coq}
}

Document

DOI: 10.4230/LIPIcs.ITP.2025.4

A Formalization of Divided Powers in Lean

Authors: Antoine Chambert-Loir and María Inés de Frutos-Fernández

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

Abstract

Given an ideal I in a commutative ring A, a divided power structure on I is a collection of maps {γ_n : I → A}_{n ∈ ℕ}, subject to axioms that imply that it behaves like the family {x ↦ xⁿ/n!}_{n ∈ ℕ}, but which can be defined even when division by factorials is not possible in A. Divided power structures have important applications in diverse areas of mathematics, including algebraic topology, number theory and algebraic geometry. In this article we describe a formalization in Lean 4 of the basic theory of divided power structures, including divided power morphisms and sub-divided power ideals, and we provide several fundamental constructions, in particular quotients and sums. This constitutes the first formalization of this theory in any theorem prover. As a prerequisite of general interest, we expand the formalized theory of multivariate power series rings, endowing them with a topology and defining evaluation and substitution of power series.

Cite as

Antoine Chambert-Loir and María Inés de Frutos-Fernández. A Formalization of Divided Powers in Lean. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chambertloir_et_al:LIPIcs.ITP.2025.4,
  author =	{Chambert-Loir, Antoine and de Frutos-Fern\'{a}ndez, Mar{\'\i}a In\'{e}s},
  title =	{{A Formalization of Divided Powers in Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{4:1--4:17},
  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.2025.4},
  URN =		{urn:nbn:de:0030-drops-246038},
  doi =		{10.4230/LIPIcs.ITP.2025.4},
  annote =	{Keywords: Formal mathematics, algebraic number theory, commutative algebra, divided powers, Lean, Mathlib}
}

Document

DOI: 10.4230/LIPIcs.ITP.2025.1

A Certified Proof Checker for Deep Neural Network Verification in Imandra

Authors: Remi Desmartin, Omri Isac, Grant Passmore, Ekaterina Komendantskaya, Kathrin Stark, and Guy Katz

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

Abstract

Recent advances in the verification of deep neural networks (DNNs) have opened the way for a broader usage of DNN verification technology in many application areas, including safety-critical ones. However, DNN verifiers are themselves complex programs that have been shown to be susceptible to errors and numerical imprecision; this, in turn, has raised the question of trust in DNN verifiers. One prominent attempt to address this issue is enhancing DNN verifiers with the capability of producing certificates of their results that are subject to independent algorithmic checking. While formulations of Marabou certificate checking already exist on top of the state-of-the-art DNN verifier Marabou, they are implemented in C++, and that code itself raises the question of trust (e.g., in the precision of floating point calculations or guarantees for implementation soundness). Here, we present an alternative implementation of the Marabou certificate checking in Imandra - an industrial functional programming language and an interactive theorem prover (ITP) - that allows us to obtain full proof of certificate correctness. The significance of the result is two-fold. Firstly, it gives stronger independent guarantees for Marabou proofs. Secondly, it opens the way for the wider adoption of DNN verifiers in interactive theorem proving in the same way as many ITPs already incorporate SMT solvers.

Cite as

Remi Desmartin, Omri Isac, Grant Passmore, Ekaterina Komendantskaya, Kathrin Stark, and Guy Katz. A Certified Proof Checker for Deep Neural Network Verification in Imandra. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 1:1-1:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{desmartin_et_al:LIPIcs.ITP.2025.1,
  author =	{Desmartin, Remi and Isac, Omri and Passmore, Grant and Komendantskaya, Ekaterina and Stark, Kathrin and Katz, Guy},
  title =	{{A Certified Proof Checker for Deep Neural Network Verification in Imandra}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{1:1--1:21},
  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.2025.1},
  URN =		{urn:nbn:de:0030-drops-246000},
  doi =		{10.4230/LIPIcs.ITP.2025.1},
  annote =	{Keywords: Neural Network Verification, Farkas Lemma, Proof Certification}
}

Document

DOI: 10.4230/LIPIcs.ITP.2025.33

Scott’s Representation Theorem and the Univalent Karoubi Envelope

Authors: Arnoud van der Leer, Kobe Wullaert, and Benedikt Ahrens

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

Abstract

Lambek and Scott constructed a correspondence between simply-typed lambda calculi and Cartesian closed categories. Scott’s Representation Theorem is a cousin to this result for untyped lambda calculi. It states that every untyped lambda calculus arises from a reflexive object in some category. We present a formalization of Scott’s Representation Theorem in univalent foundations, in the (Rocq-)UniMath library. Specifically, we implement two proofs of that theorem, one by Scott and one by Hyland. We also explain the role of the Karoubi envelope - a categorical construction - in the proofs and the impact the chosen foundation has on this construction. Finally, we report on some automation we have implemented for the reduction of λ-terms.

Cite as

Arnoud van der Leer, Kobe Wullaert, and Benedikt Ahrens. Scott’s Representation Theorem and the Univalent Karoubi Envelope. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 33:1-33:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{vanderleer_et_al:LIPIcs.ITP.2025.33,
  author =	{van der Leer, Arnoud and Wullaert, Kobe and Ahrens, Benedikt},
  title =	{{Scott’s Representation Theorem and the Univalent Karoubi Envelope}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{33:1--33:20},
  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.2025.33},
  URN =		{urn:nbn:de:0030-drops-246318},
  doi =		{10.4230/LIPIcs.ITP.2025.33},
  annote =	{Keywords: Lambda calculi, algebraic theories, categorical semantics, Karoubi envelope, formalization, Rocq-UniMath, univalent foundations}
}

Document

DOI: 10.4230/LIPIcs.ITP.2025.23

Formalizing the Hidden Number Problem in Isabelle/HOL

Authors: Sage Binder, Eric Ren, and Katherine Kosaian

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

Abstract

We formalize the hidden number problem (HNP), as introduced in a seminal work by Boneh and Venkatesan in 1996, in Isabelle/HOL. Intuitively, the HNP involves demonstrating the existence of an algorithm (the "adversary") which can compute (with high probability) a hidden number α given access to a bit-leaking oracle. Originally developed to establish the security of Diffie-Hellman key exchange, the HNP has since been used not only for protocol security but also in cryptographic attacks, including notable ones on DSA and ECDSA. Further, as the HNP establishes an expressive paradigm for reasoning about security in the context of information leakage, many HNP variants for other specialized cryptographic applications have since been developed. A main contribution of our work is explicating and clarifying the HNP proof blueprint from the original source material; naturally, formalization forces us to make all assumptions and proof steps precise and transparent. For example, the source material did not explicitly define the adversary and only abstractly defined what information is being leaked; our formalization concretizes both definitions. Additionally, the HNP makes use of an instance of Babai’s nearest plane algorithm, which solves the approximate closest vector problem; we formalize this as a result of independent interest. Our formalizations of Babai’s algorithm and the HNP adversary are executable, setting up potential future work, e.g. in developing formally verified instances of cryptographic attacks.

Cite as

Sage Binder, Eric Ren, and Katherine Kosaian. Formalizing the Hidden Number Problem in Isabelle/HOL. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 23:1-23:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{binder_et_al:LIPIcs.ITP.2025.23,
  author =	{Binder, Sage and Ren, Eric and Kosaian, Katherine},
  title =	{{Formalizing the Hidden Number Problem in Isabelle/HOL}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{23:1--23:19},
  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.2025.23},
  URN =		{urn:nbn:de:0030-drops-246216},
  doi =		{10.4230/LIPIcs.ITP.2025.23},
  annote =	{Keywords: hidden number problem, Babai’s nearest plane algorithm, cryptography, interactive theorem proving, Isabelle/HOL}
}

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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.2025.15

Certified Implementability of Global Multiparty Protocols

Authors: Elaine Li and Thomas Wies

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

Abstract

Implementability is the decision problem at the heart of top-down approaches to protocol verification. In this paper, we present a mechanization of a recently proposed precise implementability characterization by Li et al. for a large class of protocols that subsumes many existing formalisms in the literature. Our protocols and implementations model asynchronous commmunication, and can exhibit infinite behavior. We improve upon their pen-and-paper results by unifying distinct formalisms, simplifying existing proof arguments, elaborating on the construction of canonical implementations, and even uncovering a subtle bug in the semantics for infinite words. As a corollary of our mechanization, we show that the original characterization of implementability applies even to protocols with infinitely many participants. We also contribute a reusable library for reasoning about generic communicating state machines. Our mechanization consists of about 15k lines of Rocq code. We believe that our mechanization can provide the foundation for deductively proving the implementability of protocols beyond the reach of prior work, extracting certified implementations for finite protocols, and investigating implementability under alternative asynchronous communication models.

Cite as

Elaine Li and Thomas Wies. Certified Implementability of Global Multiparty Protocols. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{li_et_al:LIPIcs.ITP.2025.15,
  author =	{Li, Elaine and Wies, Thomas},
  title =	{{Certified Implementability of Global Multiparty Protocols}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{15:1--15:20},
  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.2025.15},
  URN =		{urn:nbn:de:0030-drops-246139},
  doi =		{10.4230/LIPIcs.ITP.2025.15},
  annote =	{Keywords: Asynchronous protocols, communicating state machines, labeled transition systems, infinite semantics, realizability, multiparty session types, choreographies, deadlock freedom}
}

Document

DOI: 10.4230/LIPIcs.ITP.2025.22

Formalizing Splitting in Isabelle/HOL

Authors: Ghilain Bergeron, Florent Krasnopol, and Sophie Tourret

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

Abstract

We describe the formalization in Isabelle/HOL of a framework for splitting, a theorem proving technique that extends saturation-based calculi with branching abilities. The framework preserves the completeness of the original calculus. We focus here on the simplest splitting model and provide an extension of the ordered resolution calculus with a variant of splitting called Lightweight AVATAR.

Cite as

Ghilain Bergeron, Florent Krasnopol, and Sophie Tourret. Formalizing Splitting in Isabelle/HOL. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bergeron_et_al:LIPIcs.ITP.2025.22,
  author =	{Bergeron, Ghilain and Krasnopol, Florent and Tourret, Sophie},
  title =	{{Formalizing Splitting in Isabelle/HOL}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{22:1--22:19},
  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.2025.22},
  URN =		{urn:nbn:de:0030-drops-246208},
  doi =		{10.4230/LIPIcs.ITP.2025.22},
  annote =	{Keywords: Isabelle/HOL, saturation-based calculi, splitting}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2025.33

Solving Guarded Domain Equations in Presheaves over Ordinals and Mechanizing It

Authors: Sergei Stepanenko and Amin Timany

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

Abstract

Constructing solutions to recursive domain equations is a well-known, important problem in the study of programs and programming languages. Mathematically speaking, the problem is finding a fixed point (up to isomorphism) of a suitable functor over a suitable category. A particularly useful instance, inspired by the step-indexing technique, is where the functor is over (a subcategory of) the category of presheaves over the ordinal ω and the functors are locally-contractive, also known as guarded functors. This corresponds to step-indexing over natural numbers. However, for certain problems, e.g., when dealing with infinite non-determinism, one needs to employ trans-finite step-indexing, i.e., consider presheaf categories over higher ordinals. Prior work on trans-finite step-indexing either only considers a very narrow class of functors over a particularly restricted subcategory of presheaves over higher ordinals, or treats the problem very generally working with sheaves over an arbitrary complete Heyting algebra with a well-founded basis. In this paper we present a solution to the guarded domain equations problem over all guarded functors over the category of presheaves over ordinal numbers, as well as its mechanization in the Rocq Prover. As the categories of sheaves and presheaves over ordinals are equivalent, our main contribution is simplifying prior work from the setting of the category of sheaves to the setting of the category of presheaves and mechanizing it - presheaves are more amenable to mechanization in a proof assistant.

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Sergei Stepanenko and Amin Timany. Solving Guarded Domain Equations in Presheaves over Ordinals and Mechanizing It. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 33:1-33:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{stepanenko_et_al:LIPIcs.FSCD.2025.33,
  author =	{Stepanenko, Sergei and Timany, Amin},
  title =	{{Solving Guarded Domain Equations in Presheaves over Ordinals and Mechanizing It}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{33:1--33:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.33},
  URN =		{urn:nbn:de:0030-drops-236486},
  doi =		{10.4230/LIPIcs.FSCD.2025.33},
  annote =	{Keywords: Domain Equations, Guarded Fixed Points, Fixed Points, Category Theory, Rocq, Presheaves, Ordinals}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2025.17

Mechanized Undecidability of Higher-Order Beta-Matching

Authors: Andrej Dudenhefner

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

Abstract

Higher-order β-matching is the following decision problem: given two simply typed λ-terms, can the first term be instantiated to be β-equivalent to the second term? This problem was formulated by Huet in the 1970s and shown undecidable by Loader in 2003 by reduction from λ-definability. The present work provides a novel undecidability proof for higher-order β-matching, in an effort to verify this result by means of a proof assistant. Rather than starting from λ-definability, the presented proof encodes a restricted form of string rewriting as higher-order β-matching. The particular approach is similar to Urzyczyn’s undecidability result for intersection type inhabitation. The presented approach has several advantages. First, the proof is simpler to verify in full detail due to the simple form of rewriting systems, which serve as a starting point. Second, undecidability of the considered problem in string rewriting is already certified using the Coq proof assistant. As a consequence, we obtain a certified many-one reduction from the Halting Problem to higher-order β-matching. Third, the presented approach identifies a uniform construction which shows undecidability of higher-order β-matching, λ-definability, and intersection type inhabitation. The presented undecidability proof is mechanized in the Coq proof assistant and contributed to the existing Coq Library of Undecidability Proofs.

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Andrej Dudenhefner. Mechanized Undecidability of Higher-Order Beta-Matching. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 17:1-17:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dudenhefner:LIPIcs.FSCD.2025.17,
  author =	{Dudenhefner, Andrej},
  title =	{{Mechanized Undecidability of Higher-Order Beta-Matching}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{17:1--17:15},
  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.2025.17},
  URN =		{urn:nbn:de:0030-drops-236323},
  doi =		{10.4230/LIPIcs.FSCD.2025.17},
  annote =	{Keywords: lambda-calculus, simple types, undecidability, higher-order matching, mechanization, Coq}
}

Document

DOI: 10.4230/LIPIcs.ECOOP.2025.12

Automatic Goal Clone Detection in Rocq

Authors: Ali Ghanbari

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

Abstract

Proof engineering in Rocq is a labor-intensive process, and as proof developments grow in size, redundancy and maintainability become challenges. One such redundancy is goal cloning, i.e., proving α-equivalent goals multiple times, leading to wasted effort and bloated proof scripts. In this paper, we introduce clone-finder, a novel technique for detecting goal clones in Rocq proofs. By leveraging the formal notion of α-equivalence for Gallina terms, clone-finder systematically identifies duplicated proof goals across large Rocq codebases. We evaluate clone-finder on 40 real-world Rocq projects from the CoqGym dataset. Our results reveal that each project contains an average of 27.73 instances of goal clone. We observed that the clones can be categorized as either exact goal duplication, generalization, or α-equivalent goals with different proofs, each signifying varying levels duplicate effort. Our findings highlight significant untapped potential for proof reuse in Rocq-based formal verification projects, paving the way for future improvements in automated proof engineering.

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Ali Ghanbari. Automatic Goal Clone Detection in Rocq. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ghanbari:LIPIcs.ECOOP.2025.12,
  author =	{Ghanbari, Ali},
  title =	{{Automatic Goal Clone Detection in Rocq}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{12:1--12:19},
  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.2025.12},
  URN =		{urn:nbn:de:0030-drops-233055},
  doi =		{10.4230/LIPIcs.ECOOP.2025.12},
  annote =	{Keywords: Clone Detection, Goal, Proof, Rocq, Gallina}
}

Document

DOI: 10.4230/LIPIcs.ECOOP.2025.32

Compositional Static Value Analysis for Higher-Order Numerical Programs

Authors: Milla Valnet, Raphaël Monat, and Antoine Miné

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

Abstract

Static analyzers have been successfully developed to detect runtime errors in many languages. However, the automatic analysis of functional languages remains a challenge due to their recursive functions, recursive algebraic data types, and higher-order functions. Classic type systems provide compositional methods that are in general not precise enough to prove the absence of runtime errors such as assertion failures. At the other end of the spectrum, deductive methods are more expressive but may require user guidance to prove invariants. Our work describes a static value analysis by abstract interpretation for a higher-order pure functional language. This analysis provides a sound and automatic approach to discover invariants and prevent assertion and match failures. We have designed a compositional analysis: functions are analyzed only once, at their definition site, generating a summary of their behavior. The summaries can be viewed as input-output relations expressed with relational abstract domains. We present two new abstract domains. A first abstract domain summarizes recursive algebraic data types. A second abstract domain lifts existing disjunctive relational summaries to higher-order by formalizing them as domains able to abstract higher-order functions. Both abstractions are parameterized by the abstractions of basic types (strings, integers, ...). Thanks to this parametric nature, both domains can be combined, allowing the analysis of higher-order functions manipulating algebraic data types and, conversely, algebraic data types using functions as first-class values. We have implemented this analysis in the open-source MOPSA platform. Preliminary evaluation confirms the precision of our approach on a set of 40 handwritten toy programs as well as 20 programs from the state-of-the-art Salto analyzer benchmark.

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Milla Valnet, Raphaël Monat, and Antoine Miné. Compositional Static Value Analysis for Higher-Order Numerical Programs. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 32:1-32:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{valnet_et_al:LIPIcs.ECOOP.2025.32,
  author =	{Valnet, Milla and Monat, Rapha\"{e}l and Min\'{e}, Antoine},
  title =	{{Compositional Static Value Analysis for Higher-Order Numerical Programs}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{32:1--32:29},
  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.2025.32},
  URN =		{urn:nbn:de:0030-drops-233249},
  doi =		{10.4230/LIPIcs.ECOOP.2025.32},
  annote =	{Keywords: Static Value Analysis, Functional Programming, Abstract Interpretation}
}

Document

DOI: 10.4230/LIPIcs.CSL.2025.24

Propositional Logics of Overwhelming Truth

Authors: Thibaut Antoine and David Baelde

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

Abstract

Cryptographers consider that asymptotic security holds when, for any possible attacker running in polynomial time, the probability that the attack succeeds is negligible, i.e. that it tends fast enough to zero with the size of secrets. In order to reason formally about cryptographic truth, one may thus consider logics where a formula is satisfied when it is true with overwhelming probability, i.e. a probability that tends fast enough to one with the size of secrets. In such logics it is not always the case that either ϕ or ⌝ϕ is satisfied by a given model. However, security analyses will inevitably involve specific formulas, which we call determined, satisfying this property - typically because they are not probabilistic. The Squirrel proof assistant, which implements a logic of overwhelming truth, features ad-hoc proof rules for this purpose. In this paper, we study several propositional logics whose semantics rely on overwhelming truth. We first consider a modal logic of overwhelming truth, and show that it coincides with S5. In addition to providing an axiomatization, this brings a well-behaved proof system for our logic in the form of Poggiolesi’s hypersequent calculus. Further, we show that this system can be adapted to elegantly incorporate reasoning on determined atoms. We then consider a logic that is closer to Squirrel’s language, where the overwhelming truth modality cannot be nested. In that case, we show that a simple proof system, based on regular sequents, is sound and complete. This result justifies the core of Squirrel’s proof system.

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Thibaut Antoine and David Baelde. Propositional Logics of Overwhelming Truth. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{antoine_et_al:LIPIcs.CSL.2025.24,
  author =	{Antoine, Thibaut and Baelde, David},
  title =	{{Propositional Logics of Overwhelming Truth}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{24:1--24:19},
  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.2025.24},
  URN =		{urn:nbn:de:0030-drops-227818},
  doi =		{10.4230/LIPIcs.CSL.2025.24},
  annote =	{Keywords: Cryptography, Modal Logic, Sequent Calculus}
}

Document

DOI: 10.4230/DagRep.11.10.173

Secure Compilation (Dagstuhl Seminar 21481)

Authors: David Chisnall, Deepak Garg, Catalin Hritcu, and Mathias Payer

Published in: Dagstuhl Reports, Volume 11, Issue 10 (2022)

Abstract

Secure compilation is an emerging field that puts together advances in security, programming languages, compilers, verification, systems, and hardware architectures in order to devise more secure compilation chains that eliminate many of today’s security vulnerabilities and that allow sound reasoning about security properties in the source language. For a concrete example, all modern languages provide a notion of structured control flow and an invoked procedure is expected to return to the right place. However, today’s compilation chains (compilers, linkers, loaders, runtime systems, hardware) cannot efficiently enforce this abstraction against linked low-level code, which can call and return to arbitrary instructions or smash the stack, blatantly violating the high-level abstraction. Other problems arise because today’s languages fail to specify security policies, such as data confidentiality, and the compilation chains thus fail to enforce them, especially against powerful side-channel attacks. The emerging secure compilation community aims to address such problems by identifying precise security goals and attacker models, designing more secure languages, devising efficient enforcement and mitigation mechanisms, and developing effective verification techniques for secure compilation chains. This seminar strived to take a broad and inclusive view of secure compilation and to provide a forum for discussion on the topic. The goal was to identify interesting research directions and open challenges by bringing together people working on building secure compilation chains, on designing security enforcement and attack-mitigation mechanisms in both software and hardware, and on developing formal verification techniques for secure compilation.

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David Chisnall, Deepak Garg, Catalin Hritcu, and Mathias Payer. Secure Compilation (Dagstuhl Seminar 21481). In Dagstuhl Reports, Volume 11, Issue 10, pp. 173-204, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Article{chisnall_et_al:DagRep.11.10.173,
  author =	{Chisnall, David and Garg, Deepak and Hritcu, Catalin and Payer, Mathias},
  title =	{{Secure Compilation (Dagstuhl Seminar 21481)}},
  pages =	{173--204},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2022},
  volume =	{11},
  number =	{10},
  editor =	{Chisnall, David and Garg, Deepak and Hritcu, Catalin and Payer, Mathias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.11.10.173},
  URN =		{urn:nbn:de:0030-drops-159332},
  doi =		{10.4230/DagRep.11.10.173},
  annote =	{Keywords: secure compilation, low-level attacks, source-level reasoning, attacker models, full abstraction, hyperproperties, enforcement mechanisms, compartmentalization, security architectures, side-channels}
}

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