arXiv subjects

Denis Cousineau

Publications and source records attributed to Denis Cousineau.

5 recordsLinked to original sources

arXiv2024

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 implementation of a wide variety of predictible, atomic goal transformations, which can be composed in various ways to target different backends. A gallery of examples illustrates how it helps to expand significantly the power of automation engines.

cs.LO↗

arXiv2023

Embedding Pure Type Systems in the lambda-Pi-calculus modulo

The lambda-Pi-calculus allows to express proofs of minimal predicate logic. It can be extended, in a very simple way, by adding computation rules. This leads to the lambda-Pi-calculus modulo. We show in this paper that this simple extension is surprisingly expressive and, in particular, that all functional Pure Type Systems, such as the system F, or the Calculus of Constructions, can be embedded in it. And, moreover, that this embedding is conservative under termination hypothesis.

cs.LO↗

arXiv2019

Automated Deductive Verification for Ladder Programming

Ladder Logics is a programming language standardized in IEC 61131-3 and widely used for programming industrial Programmable Logic Controllers (PLC). A PLC program consists of inputs (whose values are given at runtime by factory sensors), outputs (whose values are given at runtime to factory actuators), and the logical expressions computing output values from input values. Due to the graphical form of Ladder programs, and the amount of inputs and outputs in typical industrial programs, debugging such programs is time-consuming and error-prone. We present, in this paper, a Why3-based tool prototype we have implemented for automating the use of deductive verification in order to provide an easy-to-use and robust debugging tool for Ladder programmers.

cs.SE↗

arXiv2012

TLA+ Proofs

TLA+ is a specification language based on standard set theory and temporal logic that has constructs for hierarchical proofs. We describe how to write TLA+ proofs and check them with TLAPS, the TLA+ Proof System. We use Peterson's mutual exclusion algorithm as a simple example to describe the features of TLAPS and show how it and the Toolbox (an IDE for TLA+) help users to manage large, complex proofs.

cs.SE↗

arXiv2012

On completeness of reducibility candidates as a semantics of strong normalization

This paper defines a sound and complete semantic criterion, based on reducibility candidates, for strong normalization of theories expressed in minimal deduction modulo à la Curry. The use of Curry-style proof-terms allows to build this criterion on the classic notion of pre-Heyting algebras and makes that criterion concern all theories expressed in minimal deduction modulo. Compared to using Church-style proof-terms, this method provides both a simpler definition of the criterion and a simpler proof of its completeness.

cs.LO↗