Related papers: Formalizing Higher-Order Termination in Coq
This paper explores the idea of using defunctionalization as a proof technique for higher-order programs. Defunctionalization builds on substituting functional values by a first-order representation. Thus, its interest is that one can use…
Xavier Leroy and Sandrine Blazy in 2007 conducted a formal verification, using the Coq proof assistant, of a memory model for low-level imperative languages such as C. Considering their formalization was performed essentially in first-order…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
As deep neural models in NLP become more complex, and as a consequence opaque, the necessity to interpret them becomes greater. A burgeoning interest has emerged in rationalizing explanations to provide short and coherent justifications for…
Arts and Giesl proved that the termination of a first-order rewrite system can be reduced to the study of its "dependency pairs". We extend these results to rewrite systems on simply typed lambda-terms by using Tait's computability…
PyLog is a minimal experimental proof assistant based on linearised natural deduction for intuitionistic and classical first-order logic extended with a comprehension operator. PyLog is interesting as a tool to be used in conjunction with…
This document reports on the use of an algebraic, visual, formal approach to the specification of patterns for the formalization of the GoF design patterns. The approach is based on graphs, morphisms and operations from category theory and…
Dependently typed languages such as Coq are used to specify and verify the full functional correctness of source programs. Type-preserving compilation can be used to preserve these specifications and proofs of correctness through…
In this work, we investigate whether improving task clarity can enhance reasoning ability of large language models, focusing on theorem proving in Coq. We introduce a concept-level metric to evaluate task clarity and show that adding…
In domain theory every finite computable object can be represented by a single mathematical object instead of a set of objects, using the notion of finitary-basis. In this article we report on our effort to formalize domain theory in Coq in…
A prominent approach to implementing ontology-mediated queries (OMQs) is to rewrite into a first-order query, which is then executed using a conventional SQL database system. We consider the case where the ontology is formulated in the…
In mathematics, it is common practice to have several constructions for the same objects. Mathematicians will identify them modulo isomorphism and will not worry later on which construction they use, as theorems proved for one construction…
We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…
Computational content encoded into constructive type theory proofs can be used to make computing experiments over concrete data structures. In this paper, we explore this possibility when working in Coq with chain complexes of infinite type…
This work studies the applicability of automatic AI agent optimization methods to real-world agents in formal verification settings, focusing on automated theorem proving in Rocq as a representative and challenging domain. We evaluate how…
In this paper we give a preliminary formalization of the p-adic numbers, in the context of the second author's univalent foundations program. We also provide the corresponding code verifying the construction in the proof assistant Coq.…
We propose a new library to model and verify hardware circuits in the Coq proof assistant. This library allows one to easily build circuits by following the usual pen-and-paper diagrams. We define a deep-embedding: we use a (dependently…
Context-free language theory is a subject of high importance in computer language processing technology as well as in formal language theory. This paper presents a formalization, using the Coq proof assistant, of fundamental results related…
Dirac notation is widely used in quantum physics and quantum programming languages to define, compute and reason about quantum states. This paper considers Dirac notation from the perspective of automated reasoning. We prove two main…
Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a…