相关论文: Canonized Rewriting and Ground AC Completion Modul…

We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC;…

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…

Algorithms for computing congruence closure of ground equations over uninterpreted symbols and interpreted symbols satisfying associativity and commutativity (AC) properties are proposed. The algorithms are based on a framework for…

This paper presents a new framework for constructing congruence closure of a finite set of ground equations over uninterpreted symbols and interpreted symbols for the group axioms. In this framework, ground equations are flattened into…

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…

Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new correctness proofs of abstract completion, both for finite and infinite runs. For the…

The Homeomorphic Embedding relation has been amply used for defining termination criteria of symbolic methods for program analysis, transformation, and verification. However, homeomorphic embedding has never been investigated in the context…

Adding rewriting to a proof assistant based on the Curry-Howard isomorphism, such as Coq, may greatly improve usability of the tool. Unfortunately adding an arbitrary set of rewrite rules may render the underlying formal system undecidable…

An inductive theorem proving method for constrained term rewriting systems, which is based on rewriting induction, needs a decision procedure for reduction-completeness of constrained terms. In addition, the sufficient complete property of…

Analysis of (partial) groundness is an important application of abstract interpretation. There are several proposals for improving the precision of such an analysis by exploiting type information, icluding our own work with Hill and King,…

We study the termination of rewriting modulo a set of equations in the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined by higher-order rewrite rules. In a previous…

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…

Generative models, widely utilized in various applications, can often struggle with prompts corresponding to partial tokens. This struggle stems from tokenization, where partial tokens fall out of distribution during inference, leading to…

Coalgebras provide a uniform framework to study dynamical systems, including several types of automata. In this paper, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are…

We explore the Collatz conjecture and its variants through the lens of termination of string rewriting. We construct a rewriting system that simulates the iterated application of the Collatz function on strings corresponding to mixed…

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…

A general method is established to derive a ground-complete axiomatization for a weak semantics from such an axiomatization for its concrete counterpart, in the context of the process algebra BCCS. This transformation moreover preserves…

Canonical models are of central importance in modal logic, in particular as they witness strong completeness and hence compactness. While the canonical model construction is well understood for Kripke semantics, non-normal modal logics…

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating…

We provide a complete axiomatization of modal inclusion logic - team-based modal logic extended with inclusion atoms. We review and refine an expressive completeness and normal form theorem for the logic, define a natural deduction proof…