Related papers: Term Graph Rewriting and Parallel Term Rewriting
Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However,…
Term graph rewriting provides a formalism for implementing term rewriting in an efficient manner by avoiding duplication. Infinitary term rewriting has been introduced to study infinite term reduction sequences. Such infinite reductions can…
In this extended abstract, we present a simple approach to convergence on term graphs that allows us to unify term graph rewriting and infinitary term rewriting. This approach is based on a partial order and a metric on term graphs. These…
Graphs, and graph transformation systems, are used in many areas within Computer Science: to represent data structures and algorithms, to define computation models, as a general modelling tool to study complex systems, etc. Research in term…
We tackle the problem of attributed graph transformations and propose a new algorithmic approach for defining parallel graph transformations allowing overlaps. We start by introducing some abstract operations over graph structures. Then, we…
Proof terms in term rewriting are a representation means for reduction sequences, and more in general for contraction activity, allowing to distinguish e.g simultaneous from sequential reduction. Proof terms for finitary, first-order,…
We tackle the problem of simultaneous transformations of networks represented as graphs. Roughly speaking, one may distinguish two kinds of simultaneous or parallel rewrite relations over complex structures such as graphs: (i) those which…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
Recently, Gavazzo has developed a relational theory of symbolic manipulation, that allows to study syntax-based rewriting systems without relying on specific notions of syntax. This theory was obtained by extending the algebra of relations…
Deduction systems and graph rewriting systems are compared within a common categorical framework. This leads to an improved deduction method in diagrammatic logics.
In order to define graph transformations by the simultaneous application of concurrent rules, we have adopted in previous work a structure of attributed graphs stable by unions. We analyze the consequences on parallel independence, a…
We report on work in progress on 'nested term graphs' for formalizing higher-order terms (e.g. finite or infinite lambda-terms), including those expressing recursion (e.g. terms in the lambda-calculus with letrec). The idea is to represent…
In this paper we present a new termination proof and complexity analysis of unfolding graph rewriting which is a specific kind of infinite graph rewriting expressing the general form of safe recursion. We introduce a termination order over…
The basic principle of graph rewriting is the stepwise replacement of subgraphs inside a host graph. A challenge in such replacement steps is the treatment of the patch graph, consisting of those edges of the host graph that touch the…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…
We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In…
Motivated by questions from program transformations, eight notions of isomorphisms between term rewriting systems are defined, analysed, and classified. The notions include global isomorphisms, where the renaming of variables and function…
We introduce a categorical formalism for rewriting surface-embedded graphs. Such graphs can represent string diagrams in a non-symmetric setting where we guarantee that the wires do not intersect each other. The main technical novelty is a…