The generalised term graph rewriting computational model is exploited to implement concurrent languages based on Girard's Linear Logic (LL). In particular a fragment of LL is identified which is able to serve as a "process calculus" and on which the design of a number of languages can be based. It is then shown how this fragment can be mapped onto equivalent sets of graph rewriting rules that both preserve the functionality of the LL connectives and also exploit the properties of linearity for efficient implementation on a distributed architecture. Notions such as channels, production and consumption of messages, and N-to-N communication between agents, are interpreted in the world of (term) graph rewriting. This work serves two purposes: i) to extend the notion of Term Graph Rewriting as a generalised computational model for the case of linear concurrent languages, and ii) to act as an initial investigation towards a fully linear term graph rewriting model of computation able to be im...

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.

Two of the currently most promising programming paradigms, namely Object-Oriented Programming and Concurrent Constraint Programming are combined into a single, highly parallel computational model based on Term Graph Rewriting Systems. In particular, we show how multi-headed Term Graph rewrite rules provide a powerful tool able to manipulate Term Graphs which themselves represent in a homogeneous way objects, concurrently executing agents and constraints. Due to the inherent fine grain parallelism of Term Graph Rewriting the proposed model is highly parallel with all activities (object communication, agent execution and constraint solving) executing concurrently. 1. Introduction The generalised computational model of Term Graph Rewriting Systems (TGRS) ([5]) has been used extensively as an implementation vehicle for a number of, often divergent, programming paradigms ranging from the traditional functional programming ones ([12,15]) to the (concurrent) logic programming ones ([3,10,18])...

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...

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. Keywords Object Oriented Languages, Object Synchronisation, Term Graph Rewriting, MONSTR, Distributed Processing, Serialisability. 1 INTRODUCTION...

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 ...