Related papers: Tactics for Reasoning modulo AC in Coq
AC-completion efficiently handles equality modulo associative and commutative function symbols. When the input is ground, the procedure terminates and provides a decision algorithm for the word problem. In this paper, we present a modular…
We define a lazy pattern-matching mechanism modulo associativity and commutativity. The solutions of a pattern-matching problem are stored in a lazy list composed of a first substitution at the head and a non-evaluated object that encodes…
Reasoning modulo equivalences is natural for everyone, including mathematicians. Unfortunately, in proof assistants based on type theory, equality is appallingly syntactic and, as a result, exploiting equivalences is cumbersome at best.…
Equational Unification is a critical problem in many areas such as automated theorem proving and security protocol analysis. In this paper, we focus on XOR-Unification, that is, unification modulo the theory of exclusive-or. This theory…
Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…
We describe a formalization of higher-order rewriting theory and formally prove that an AFS is strongly normalizing if it can be interpreted in a well-founded domain. To do so, we use Coq, which is a proof assistant based on dependent type…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
Symmetric monoidal categories (SMCs) are a common framework for reasoning about computation, focusing on the parallel and sequential compositionality of operations. String diagrams are a ubiquitous and powerful tool for reasoning about…
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…
Computational reflection allows us to turn verified decision procedures into efficient automated reasoning tools in proof assistants. The typical applications of such methodology include mathematical structures that have decidable theory…
In a previous work, we proved that an important part of the Calculus of Inductive Constructions (CIC), the basis of the Coq proof assistant, can be seen as a Calculus of Algebraic Constructions (CAC), an extension of the Calculus of…
We propose the first steps in the development of a tool to automate the translation of Redex models into a (hopefully) semantically equivalent model in Coq, and to provide tactics to help in the certification of fundamental properties of…
In a previous work, we proved that almost all of the Calculus of Inductive Constructions (CIC), which is the basis of the proof assistant Coq, can be seen as a Calculus of Algebraic Constructions (CAC), an extension of the Calculus of…
We revisit completion modulo equational theories for left-linear term rewrite systems where unification modulo the theory is avoided and the normal rewrite relation can be used in order to decide validity questions. To that end, we give a…
Reasoning in the presence of associativity and commutativity (AC) is well known to be challenging due to prolific nature of these axioms. Specialised treatment of AC axioms is mainly supported by provers for unit equality which are based on…
Proofs in proof assistants like Rocq can be brittle, breaking easily in response to changes. To address this, recent work introduced an algorithm and tool in Rocq to automatically repair broken proofs in response to changes that correspond…
In this paper we consider the problem of certified static checking of module-like constructs of programming languages. We argue that there are algorithms and properties related to modules that can be defined and proven in an abstract way.…
The modelling, specification and study of the semantics of concurrent reactive systems have been interesting research topics for many years now. The aim of this thesis is to exploit the strengths of the (co)algebraic framework in modelling…
Inductive and coinductive specifications are widely used in formalizing computational systems. Such specifications have a natural rendition in logics that support fixed-point definitions. Another useful formalization device is that of…
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…