Tootfinder

This https://arxiv.org/abs/2108.03018 has been replaced.
link: https://scholar.google.com/scholar?q=a

Conditional Separation as a Binary Relation. A Coq Assisted Proof
The concept of d-separation holds a pivotal role in causality theory, serving as a fundamental tool for deriving conditional independence properties from causal graphs. Pearl defined the d-separation of two subsets conditionally on a third one. In this study, we present a novel perspective by showing i) how the d-separation can be extended beyond acyclic graphs, possibly infinite, and ii) how it can be expressed and characterized as a binary relation between vertices. Compared to the typ…

This https://arxiv.org/abs/2402.14485 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Machine-Checked Categorical Diagrammatic Reasoning
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.

[Le Parisien] - « #PouletsManipulésGénétiquement » : le groupe LDC, des volailles #LeGaulois et #MaîtreCoq, poursuit L214 en justice.
Le groupe qui co…

« Poulets manipulés génétiquement » : le groupe LDC, des volailles Le Gaulois et Maître Coq, poursuit L214 en justice
Le groupe qui commercialise les marques Le Gaulois et Maître Coq, se plaint d’être victime d’une campagne de « dénigrement » et de « désinformation » de la part de L214, qui dénonce ses poulets « manipulés génétiquement ».

This https://arxiv.org/abs/2108.03018 has been replaced.
link: https://scholar.google.com/scholar?q=a

Conditional Separation as a Binary Relation. A Coq Assisted Proof
The concept of d-separation holds a pivotal role in causality theory, serving as a fundamental tool for deriving conditional independence properties from causal graphs. Pearl defined the d-separation of two subsets conditionally on a third one. In this study, we present a novel perspective by showing i) how the d-separation can be extended beyond acyclic graphs, possibly infinite, and ii) how it can be expressed and characterized as a binary relation between vertices. Compared to the typ…

coq au vin pour le dîner

A Comprehensive Overview of the Lebesgue Differentiation Theorem in Coq
Reynald Affeldt, Zachary Stone
https://arxiv.org/abs/2403.18229 https://

A Comprehensive Overview of the Lebesgue Differentiation Theorem in Coq
Formalization of real analysis offers a chance to rebuild traditional proofs of important theorems as unambiguous theories that can be interactively explored. This paper provides a comprehensive overview of the Lebesgue Differentiation Theorem formalized in the Coq proof assistant, from which the first Fundamental Theorem of Calculus (FTC) for the Lebesgue integral is obtained as a corollary. Proving the first FTC in this way has the advantage of decomposing into loosely-coupled theories of mod…

A Coq Mechanization of JavaScript Regular Expression Semantics
No\'e De Santo, Aur\`ele Barri\`ere, Cl\'ement Pit-Claudel
https://arxiv.org/abs/2403.11919

A Coq Mechanization of JavaScript Regular Expression Semantics
We present an executable, proven-safe, faithful, and future-proof Coq mechanization of JavaScript regular expression (regex) matching, as specified by the last published edition of ECMA-262 section 22.2. This is, to our knowledge, the first time that an industrial-strength regex language has been faithfully mechanized in an interactive theorem prover. We highlight interesting challenges that arose in the process (including issues of encoding, corner cases, and executability), and we document th…

A Comprehensive Overview of the Lebesgue Differentiation Theorem in Coq
Reynald Affeldt, Zachary Stone
https://arxiv.org/abs/2403.18229 https://

A Comprehensive Overview of the Lebesgue Differentiation Theorem in Coq
Formalization of real analysis offers a chance to rebuild traditional proofs of important theorems as unambiguous theories that can be interactively explored. This paper provides a comprehensive overview of the Lebesgue Differentiation Theorem formalized in the Coq proof assistant, from which the first Fundamental Theorem of Calculus (FTC) for the Lebesgue integral is obtained as a corollary. Proving the first FTC in this way has the advantage of decomposing into loosely-coupled theories of mod…

[Le Parisien] - « #PouletsManipulésGénétiquement » : le groupe LDC, des volailles #LeGaulois et #MaîtreCoq, poursuit L214 en justice.
Le groupe qui co…

« Poulets manipulés génétiquement » : le groupe LDC, des volailles Le Gaulois et Maître Coq, poursuit L214 en justice
Le groupe qui commercialise les marques Le Gaulois et Maître Coq, se plaint d’être victime d’une campagne de « dénigrement » et de « désinformation » de la part de L214, qui dénonce ses poulets « manipulés génétiquement ».

This https://arxiv.org/abs/2402.14485 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Machine-Checked Categorical Diagrammatic Reasoning
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.

ViCAR: Visualizing Categories with Automated Rewriting in Coq
Bhakti Shah, William Spencer, Laura Zielinski, Ben Caldwell, Adrian Lehmann, Robert Rand
https://arxiv.org/abs/2404.08163

ViCAR: Visualizing Categories with Automated Rewriting in Coq
We present ViCAR, a library for working with monoidal categories in the Coq proof assistant. ViCAR provides definitions for categorical structures that users can instantiate with their own verification projects. Upon verifying relevant coherence conditions, ViCAR gives a set of lemmas and tactics for manipulating categorical structures. We also provide a visualizer that can display any composition and tensor product of morphisms as a string diagram, showing its categorical structure. This enabl…

This https://arxiv.org/abs/2402.10494 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLO_…

Mechanised uniform interpolation for modal logics K, GL, and iSL
The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) Gödel-Löb logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Löb logic iSL, for…

Samma, ihr, die in Deutschland aufgewachsen sind; ihr kennt doch alle (also wirklich ALLE) das Lied "Der Hahn ist tot" bzw. "Le coq est mort", ja?
Angeblich kommt es aus Frankreich, allerdings kannte keine*r (also wirklich KEINE*R) der Franzos*innen, die ich gefragt habe, dieses Lied.
Ich glaube daher nicht, daß das Lied frz. Ursprungs ist. Vielmehr denke ich, daß es ein Hohnlied dt. Soldaten im WK1 war (der Hahn ist frz. Wappentier).
Später unkritisch ent…

A Coq Library of Sets for Teaching Denotational Semantics
Qinxiang Cao, Xiwei Wu, Yalun Liang
https://arxiv.org/abs/2404.05459 https://

A Coq Library of Sets for Teaching Denotational Semantics
Sets and relations are very useful concepts for defining denotational semantics. In the Coq proof assistant, curried functions to Prop are used to represent sets and relations, e.g. A -> Prop, A -> B -> Prop, A -> B -> C -> Prop, etc. Further, the membership relation can be encoded by function applications, e.g. X a represents a in X if X: A -> Prop. This is very convenient for developing formal definitions and proofs for professional users, but it makes propositions more difficult to read for …

This https://arxiv.org/abs/2108.03018 has been replaced.
link: https://scholar.google.com/scholar?q=a

Conditional Separation as a Binary Relation. A Coq Assisted Proof
The concept of d-separation holds a pivotal role in causality theory, serving as a fundamental tool for deriving conditional independence properties from causal graphs. Pearl defined the d-separation of two subsets conditionally on a third one. In this study, we present a novel perspective by showing i) how the d-separation can be extended beyond acyclic graphs, possibly infinite, and ii) how it can be expressed and characterized as a binary relation between vertices. Compared to the typ…

Verified Multi-Step Synthesis using Large Language Models and Monte Carlo Tree Search
David Brandfonbrener, Sibi Raja, Tarun Prasad, Chloe Loughridge, Jianang Yang, Simon Henniger, William E. Byrd, Robert Zinkov, Nada Amin
https://arxiv.org/abs/2402.08147

Verified Multi-Step Synthesis using Large Language Models and Monte Carlo Tree Search
We present an approach using Monte Carlo Tree Search (MCTS) to guide Large Language Models (LLMs) to generate verified programs in Dafny, Lean and Coq. Our method, which we call VMCTS, leverages the verifier inside the search algorithm by checking partial programs at each step. In combination with the LLM prior, the verifier feedback raises the synthesis capabilities of open source models. On a set of five verified programming problems, we find that in four problems where the base model cannot …

Models for Storage in Database Backends
Edgard Schiebelbein (Amazon Web Services), Saalik Hatia (Amazon Web Services), Annette Bieniusa (Amazon Web Services), Gustavo Petri (Amazon Web Services), Carla Ferreira (NOVA), Marc Shapiro (DELYS)
https://arxiv.org/abs/2403.11716

Models for Storage in Database Backends
This paper describes ongoing work on developing a formal specification of a database backend. We present the formalisation of the expected behaviour of a basic transactional system that calls into a simple store API, and instantiate in two semantic models. The first one is a map-based, classical versioned key-value store; the second one, journal-based, appends individual transaction effects to a journal. We formalise a significant part of the specification in the Coq proof assistant. This work …

This https://arxiv.org/abs/2310.06959 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csPL_…

Towards Proof Repair in Cubical Agda
Proofs in proof assistants like Coq can be brittle, breaking easily in response to changes in the terms and types those proofs depend on. To address this, recent work introduced an algorithm and tool in Coq to automatically repair broken proofs in response to changes that correspond to type equivalences. However, many changes remained out of the scope of this algorithm and tool -- especially changes in underlying behavior. We extend this proof repair algorithm so that it can express certain cha…

Taming Differentiable Logics with Coq Formalisation
Reynald Affeldt, Alessandro Bruni, Ekaterina Komendantskaya, Natalia \'Slusarz, Kathrin Stark
https://arxiv.org/abs/2403.13700

Taming Differentiable Logics with Coq Formalisation
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to translate propositional or first-order formulae into loss functions deployed for optimisation in machine learning. At the same time, recent attempts to give programming language support for verification of neural networks showed that DLs can be used to compile ve…

This https://arxiv.org/abs/2310.06959 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csPL_…

Towards Proof Repair in Cubical Agda
Proofs in proof assistants like Coq can be brittle, breaking easily in response to changes in the terms and types those proofs depend on. To address this, recent work introduced an algorithm and tool in Coq to automatically repair broken proofs in response to changes that correspond to type equivalences. However, many changes remained out of the scope of this algorithm and tool -- especially changes in underlying behavior. We extend this proof repair algorithm so that it can express certain cha…

This https://arxiv.org/abs/2211.13513 has been replaced.
link: https://scholar.google.com/scholar?q=a

Waterproof: Educational Software for Learning How to Write Mathematical Proofs
In order to help students learn how to write mathematical proofs, we adapt the Coq proof assistant into an educational tool we call Waterproof. Like with other interactive theorem provers, students write out their proofs inside the software using a specific syntax, and the software provides feedback on the logical validity of each step. Waterproof consists of two components: a custom proof language that allows formal, machine-verified proofs to be written in a style that closely resembles handw…

This https://arxiv.org/abs/2311.14347 has been replaced.
link: https://scholar.google.com/scholar?q=a

Typed compositional quantum computation with lenses
We propose a type-theoretic framework for describing and proving properties of quantum computations, in particular those presented as quantum circuits. Our proposal is based on an observation that, in the polymorphic type system of Coq, currying on quantum states allows us to apply quantum gates directly inside a complex circuit. By introducing a discrete notion of lens to control this currying, we are further able to separate the combinatorics of the circuit structure from the computational co…

Machine-Checked Categorical Diagrammatic Reasoning
Beno\^it Guillemet, Assia Mahboubi, Matthieu Piquerez
https://arxiv.org/abs/2402.14485 https://

Machine-Checked Categorical Diagrammatic Reasoning
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.

This https://arxiv.org/abs/2311.14347 has been replaced.
link: https://scholar.google.com/scholar?q=a

Typed compositional quantum computation with lenses
We propose a type-theoretic framework for describing and proving properties of quantum computations, in particular those presented as quantum circuits. Our proposal is based on an observation that, in the polymorphic type system of Coq, currying on quantum states allows us to apply quantum gates directly inside a complex circuit. By introducing a discrete notion of lens to control this currying, we are further able to separate the combinatorics of the circuit structure from the computational co…

This https://arxiv.org/abs/2204.02643 has been replaced.
link: https://scholar.google.com/scholar?q=a

Compositional pre-processing for automated reasoning in dependent type theory
In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical fragment. This very often prevents users from applying these tactics in other contexts, even similar ones. This paper discusses the design and the implementation of pre-processing operations for automating formal proofs in the Coq proof assistant. It presents the …

This https://arxiv.org/abs/2204.02643 has been replaced.
link: https://scholar.google.com/scholar?q=a

Compositional pre-processing for automated reasoning in dependent type theory
In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical fragment. This very often prevents users from applying these tactics in other contexts, even similar ones. This paper discusses the design and the implementation of pre-processing operations for automating formal proofs in the Coq proof assistant. It presents the …

Mechanised uniform interpolation for modal logics K, GL and iSL
Hugo F\'er\'ee, Iris van der Giessen, Sam van Gool, Ian Shillito
https://arxiv.org/abs/2402.10494

Mechanised uniform interpolation for modal logics K, GL and iSL
The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) Gödel-Löb logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Löb logic iSL, for…