Towards an intermediate language based on Graph Rewriting

1997

The lambda calculus forms without any question* the* theoretical backbone of functional programming languages. For the design and implementation of the lazy functional language Concurrent Clean we have used a related computational model: Term Graph Rewriting Systems (TGRS's). This paper wraps up our main conclusions after 10 years of experience with graph rewriting semantics for functional programming languages.

1993

In a declarative programming language a computation is expressed in a static fashion, as a list of declarations. A program in such a language is regarded as a specification that happens to be executable as well. In this textbook we focus on a subclass of the declarative languages, the functional programming languages, sometimes called applicative languages. In these languages a program consists of a list of function definitions. The execution of a program consists of the evaluation of a function application given the functions that have been defined.

Proceedings of the 1995 ACM symposium on Applied computing - SAC '95, 1995

et al. ([18]) gives an accurate reflection of contemporary interest in this area. 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-toN 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 implemented efficiently on distributed architectures.

1997

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.

Theoretical Computer Science, 1993

Electronic Notes in Theoretical Computer Science, 1995

The main features of the lazy functional language Concurrent Clean and of its semantics based on Term Graph Rewriting are presented.

Theoretical Computer Science, 1988

In 1984, Raoult has given a description of graph rewriting. His description is operational, despite the similarity which his constructions have to the category-theoretic concept of a pushout. We describe a modification to Raoult's description of graph rewriting which allows the reduction of a redex to be described as a pushout, in a category of graphs where morphisms are not required to preserve graph structure.

IEEE Access

The ability to handle evolving graph structures is important both for programming languages and modeling languages. Of various languages that adopt graphs as primary data structures, a graph rewriting language LMNtal provides features of both (concurrent) programming languages and modeling languages, and its implementation unifies ordinary program execution and model checking functionalities. Unlike pointer manipulation in imperative languages, LMNtal allows us to manipulate graph structures in such a way that the well-formedness of graphs is guaranteed by the language itself. However, since the shapes of graphs can be complex and diverse compared to algebraic data structures such as lists and trees, it is a non-obvious important task to formulate types of graphs to verify individual programs. With this motivation, this paper discusses LMNtal ShapeType, a type checking framework that applies the basic idea of Structured Gamma to a concrete graph rewriting language. Types are defined by generative grammars written as LMNtal rules, and type checking of LMNtal programs can accordingly be done by exploiting the model checking features of LMNtal itself. We gave a full implementation of type checking exploiting the features of the LMNtal meta-interpreter and confirmed that it works for practical operations on various graph structures, including single-step and multi-step operations on non-algebraic data structures and data structures with numerical shape constraints. INDEX TERMS Dynamic data structures, graph grammars, graph rewriting, type checking.

Visual Languages/Human-Centric Computing Languages and Environments, 1995

The multi-paradigm language PROGRES is the first rule-ori- ented visual language which has a well-defined type concept and supports programming with graph rewriting systems. To some extent, it has the flavor of a visual database program- ming language with powerful pattern matching and replac- ing facilities as well as backtracking capabilities. Until now, it was mainly used for specifying and

1995

This note presents a new formalization of graph rewritings which generalizes traditional graph rewritings. Relational notions of graphs and their rewritings are introduced and several properties about graph rewritings are discussed using relational calculus (theory of binary relations). Single pushout approaches to graph rewritings proposed by Raoult and Kennaway are compared with our rewritings of relational (labeled) graph. Moreover a more general sufficient condition for two rewritings to commute and a theorem concerning critical pairs useful to demonstrate the confluency of graph rewriting systems are also given. 1 Introduction There are many researches [1-7,9,13,14,16-18,20-22] on graph grammars and graph rewritings which have a lot of applications including software specification, data bases, analysis of concurrent systems, developmental biology and many others. In these one of the advantages of categorical graph rewritings is to produce a universal reduction which eases theor...

Theoretical Computer Science, 1988

In 1984, Raoult has given a description of graph rewriting. His description is operational, despite the similarity which his constructions have to the category-theoretic concept of a pushout. We describe a modification to Raoult's description of graph rewriting which allows the reduction of a redex to be described as a pushout, in a category of graphs where morphisms are not required to preserve graph structure.

Theoretical Computer Science, 2015

Higher-order functions-the ones which manipulate other functions-have a fundamental role in Computer Science, specially in areas such as functional programming and theory of computation. Graph transformation-the rule-based modification of graphs-is also an important approach used in many contexts, as for instance, the definition of syntax and semantics of visual languages and the modelling and analysis of concurrent and non-deterministic systems. Although the algebraic double-pushout (DPO) approach to graph transformation has a vast theory, it does not present a notion of higher-order transformation, i.e., transformation of graph rewriting rules themselves. Higher-order would be required, for instance, to ease the modelling of dynamic systems through graph transformation systems, and to describe model transformations that modify graph rewriting rules. The main contribution of this work is a notion of double-pushout transformation for graph rewriting rules, where the result of the rewriting is a valid graph rule. We use DPO diagrams in the category of graph spans to describe rule transformations, and negative application conditions (NACs) in the second-order rules to enforce preservation of the rule structure. We define a model named second-order graph grammars, capable of first-and secondorder derivations. Finally, we discuss alternative ways of defining second-order transformations.

Lecture Notes in Computer Science, 2004

We propose a faithful encoding of Java programs (written in a suitable fragment of the language) to Graph Transformation Systems. Every program is translated to a set of rules including some basic rules, common to all programs and providing the operational semantics of Java (data and control) operators, and the program specific rules, namely one rule for each method or constructor declared in the program. Besides sketching some potential applications of the proposed translation, we discuss some desing choices that ensure its correctness, and we report on how do we intend to extend it in order to handle several other features of the Java language.

Lecture Notes in Computer Science, 2001

We identify a set of programming constructs ensuring that a programming language based on graph transformation is computationally complete. These constructs are (1) nondeterministic application of a set of graph transformation rules, (2) sequential composition and (3) iteration. This language is minimal in that omitting either sequential composition or iteration results in a computationally incomplete language. By computational completeness we refer to the ability to compute every computable partial function on labelled graphs. Our completeness proof is based on graph transformation programs which encode arbitrary graphs as strings, simulate Turing machines on these strings, and decode the resulting strings back into graphs.

2001

Abstract. This paper advocates need for a formal foundation for refactoring object-oriented software. More specifically, it investigates the potential of graph rewriting as candidate formalism. Using a small Java application as a case study, it shows how a range of different notions of behaviour preservation can be expressed in a formal, yet intuitive, way. A number of other open research topics that can benefit from a graph rewriting formalism are discussed as well. Keywords.