This paper gives some examples of how computation in a number of languages may be described as graph rewriting, giving the Dactl notation for the examples shown. It goes on to present the Dactl model more formally before giving a formal definition of the syntax and semantics of the language. 2 Examples of Computation by Graph Rewriting

Abstract: A translation of the π-calculus into the MONSTR graph rewriting language is described and proved correct. The translation illustrates the heavy cost in practice of faithfully implementing the communication primitive of the π-calculus and similar process calculi. It also illustrates the convenience of representing an evolving network of communicating agents directly within a graph manipulation formalism, both because the necessity to use delicate notions of bound variables and of scopes is avoided, and also because the standard model of graphs in set theory automatically yields a useful semantics for the process calculus. The correctness proof illustrates many features typically encountered in reasoning about graph rewriting systems, and particularly how serialisation techniques can be used to reorder an arbitrary execution into one having stated desirable properties.

Abstract: This is the first in a series of papers dealing with the implementation of an extended term graph rewriting model of computation (described by the DACTL language) on a distributed store architecture. In this paper we set out the high level model, and under some simple packet store model is compared to a more realistic and finegrained packet store model, more closely related to the properties of a genuine distributed store architecture, and the differences are used to inspire the definition of the MONSTR sublanguage of DACTL, intended for direct execution on the machine. Various alternative operational semantics for MONSTR are proposed to reflect more closely the finegrained packet store model, and the prospects for establishing correctness are discussed. The detailed treatment of the alternative models, in the context of suitable sublanguages of MONSTR where appropriate, are subjects for subsequent papers.

A methodology for polymorphic type inference for general term graph rewriting systems is presented. This requires modified notions of type and of type inference due to the absence of structural induction over graphs. Induction over terms is replaced by dataflow analysis. 1 Introduction Term graphs are objects that locally look like terms, but globally have a general directed graph structure. Since their introduction in Barendregt et al. (1987), they have served the purpose of defining a rigorous framework for graph reduction implementations of functional languages (Peyton-Jones (1987)). This was the original intention. However the rewriting of term graphs defined in the operational semantics of the model, makes term graph rewriting systems (TGRSs) interesting models of computation in their own right. One can thus study all sorts of issues in the specific TGRS context. Typically one might be interested in how close TGRSs are to TRSs and this problem is examined in Barendregt et al. (19...

Two superficially similar graph rewriting formalisms, Interaction Nets and MONSTR, are studied. Interaction Nets come from multiplicative Linear Logic and feature undirected graph edges, while MONSTR arose from the desire to implement generalized term graph rewriting efficiently on a distributed architecture and utilizes directed graph arcs. Both formalisms feature rules with small left-hand sides consisting of two main graph nodes. A translation of Interaction Nets into MONSTR is described for both typed and untyped nets, while the impossibility of the opposite translation rests on the fact that net rewriting is always Church–Rosser while MONSTR rewriting is not. Some extensions to the net formalism suggested by the relationship with MONSTR are discussed, as well as some related implementation issues.

this paper we try to bridge the gap between the two formalisms by showing how concurrent logic languages can be implemented using graph rewriting. In particular, we develop techniques for mapping a wide class of CLLs including Parlog, GHC, Strand, Janus and a restricted subset of the Concurrent Prolog family onto Dactl, a compiler target language based on graph rewriting. We discuss the problems found in the process and the adopted solutions. The paper contributes to related research by: # examining the potential of graph reduction as a suitable model for implementing CLLs in terms of expressiveness and efficiency

The extended term graph rewriting formalism of MONSTR is described, together with some of its more important rigorously established properties, particularly regarding serialisability and acyclicity. This basis is used for giving a convenient description of the global runtime structure of a concurrent object oriented language. The formalism proves especially convenient for describing very precisely a variety of intended synchronisation properties of objects in a concurrent OOL, and this flexibility is illustrated by considering a variety of possible operational semantics for a simple counter object. A lower bound object example illustrates that even more extreme synchronisation properties for objects may be contemplated without stretching the capabilities of the MONSTR formalism. The presentation is independent of any specific high level OOL. Key Words: Object Oriented Languages, Object Synchronisation, Term Graph Rewriting, MONSTR, Distributed Processing, Serialisability. 1 Introductio...

: A translation of the p-calculus into the MONSTR graph rewriting language is described and proved correct. The translation illustrates the heavy cost in practice of faithfully implementing the communication primitive of the p-calculus and similar process calculi. It also illustrates the convenience of representing an evolving network of communicating agents directly within a graph manipulation formalism, both because the necessity to use delicate notions of bound variables and of scopes is avoided, and also because the standard model of graphs in set theory automatically yields a useful semantics for the process calculus. The correctness proof illustrates many features typically encountered in reasoning about graph rewriting systems, and particularly how serialisation techniques can be used to reorder an arbitrary execution into one having stated desirable properties. Key Words: Concurrency, Pi-Calculus, Term Graph Rewriting, MONSTR, Process Networks, Simulation, Serialisability. Ca...

MONSTR Rule Systems R. Banach UMCS-96-7-3 Computer Science University of Manchester Technical Report Series University of Manchester Department of Computer Science ISSN 1361 - 6161 2 A Fibration Semantics for Pi-Calculus Modules via Abstract MONSTR Rule Systems* R. Banach Department of Computer Science University of Manchester Oxford Road, Manchester, U.K. banach@cs.man.ac.uk 31 July 1996 Copyright 1996. All rights reserved. Reproduction of all or part of this work is permitted for educational or research purposes on condition that: (1) this copyright notice is included, (2) proper attribution to the author or authors is made, and (3) no commercial gain is involved. Recent technical reports issued by the Department of Computer Science, Manchester University, are available by anonymous ftp from ftp.cs.man.ac.uk in the directory pub/TR. The files are stored as PostScript, in compressed form, with the report number as filename. They can also be obtained on WWW via ...