Shostak's congruence closure algorithm is demystiied, using the framework of ground completion on (possibly nonterminating, non-reduced) rewrite rules. In particular, the canonical rewriting relation induced by the algorithm on ground terms by a given set of ground equations is precisely constructed. The main idea is to extend the signature of the original input to include new constant symbols ...

Adhesive categories provide an abstract setting for the doublepushout approach to rewriting, generalising classical approaches to graph transformation. Fundamental results about parallelism and confluence, including the local Church-Rosser theorem, can be proven in adhesive categories, provided that one restricts to linear rules. We identify a class of categories, including most adhesive catego...

This paper discusses a deterministic version of #-rewriting systems with context-free rules. It demonstrates that classical form of determinism does not affect the generative power of #rewriting systems. The result concerning deterministic #-rewriting systems of index k is given too. The conclusion discusses even the stronger type of determinism.

The formal framework of Logically Constrained Term Rewriting Systems (LCTRSs), introduced in [Kop and Nishida 2013], combines term rewriting with constraints and calculations over an arbitrary theory. This for instance allows users to specify rules with integers, arrays and strings, and can be used to analyze both imperative and functional programs (without higher-order variables) in a natural ...

Instruction selection (mapping IR trees to machine instructions) can be expressed by means of rewrite rules. Typically, such sets of rewrite rules are highly ambiguous. Therefore, standard rewriting engines based on fixed, exhaustive strategies are not appropriate for the execution of instruction selection. Code generator generators use special purpose implementations employing dynamic programm...

Rippling is a special type of rewriting developed for induct-ive theorem proving. Bundy et. al. have shown that rippling terminates by providing a well-founded order for the annotated rewrite rules used by rippling. Here, we simplify and generalize this order, thereby enlarging the class of rewrite rules that can be used. In addition, we extend the power of rippling by proposing new domain depe...

We propose to use Graph Rewriting for parsing syntactic dependencies. We present a system of rewriting rules dedicated to French and we evaluate it by parsing the SEQUOIA corpus.

We present a Haskell library for first-order term rewriting covering basic operations on positions, terms, contexts, substitutions and rewrite rules. This effort is motivated by the increasing number of term rewriting tools that are written in Haskell.

Rippling is a special type of rewriting developed for inductive theorem proving Bundy et al have shown that rippling terminates by providing a well founded order for the annotated rewrite rules used by rippling Here we simplify and generalize this order thereby enlarging the class of rewrite rules that can be used In addition we extend the power of rippling by proposing new domain dependent ord...

Nominal rewriting (Fernández, Gabbay & Mackie, 2004; Fernández & Gabbay, 2007) is a framework that extends first-order term rewriting by a binding mechanism based on the nominal approach (Gabbay & Pitts, 2002; Pitts, 2003). In this paper, we investigate confluence properties of nominal rewriting, following the study of orthogonal systems in (Suzuki et al., 2015), but here we treat systems in wh...