Towards an intermediate language based on Graph Rewriting

Barendregt, Henk; Eekelen, M.C.J.D. van; Glauert, John; Kennaway, Richard; Plasmeijer, M.J.; Sleep, M. R.

doi:10.1007/3-540-17945-3_9

Cited by 29 publications

(8 citation statements)

References 5 publications

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“…The need for a less restrictive notion of confluence arises in practice if one wants to provide a more accurate foundation of programming languages. To reason about either execution or optimizations one has to deal with the notion of sharing and cyclic structures [12,31,2]. As pointed out by Wadsworth [35], these concerns can be accommodated by considering term graph rewriting as opposed to term (or tree) rewriting.…”

Section: Lack Of Confluence In Term Graph Rewritingmentioning

confidence: 99%

Skew and ω-Skew Confluence and Abstract Böhm Semantics

Ariola

Blom

2005

Processes, Terms and Cycles: Steps on the Road to Infinity

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Skew confluence was introduced as a characterization of nonconfluent term rewriting systems that had unique infinite normal forms or Böhm like trees. This notion however is not expressive enough to deal with all possible sources of non-confluence in the context of infinite terms or terms extended with letrec. We present a new notion called ωskew confluence which constitutes a sufficient and necessary condition for uniqueness. We also present a theory that can lift uniqueness results from term rewriting systems to rewriting systems on terms with letrec. We present our results in the setting of Abstract Böhm Semantics, which is a generalization of Böhm like trees to abstract reduction systems.

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Section: Lack Of Confluence In Term Graph Rewritingmentioning

confidence: 99%

Skew and ω-Skew Confluence and Abstract Böhm Semantics

Ariola

Blom

2005

Processes, Terms and Cycles: Steps on the Road to Infinity

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“…In graph rewriting systems (Barendregt et al (1987b)) a program is represented by a set of rewrite rules. Each rewrite rule consists of a left-band-side graph (thepattern), an optional fight-hand-side graph (the contractum) and one or more redirections.…”

Section: Graph Rewritingmentioning

confidence: 99%

“…He proposes a call-byname parameter passing mechanism (which must involve copying of some nodes) between mutual reeorsive functions. In DACTL (Glanert et al (1987)), also based on Graph Rewriting Systems (Barendregt et al (1987b)) there is no overall reduction strategy. This means that the reduction order is completely controlled by the annotations in the rewrite rules.…”

Section: Related Workmentioning

confidence: 99%

Parallel graph rewriting on loosely coupled machine architectures

Eekelen

Plasmeijer

Smetsers

1991

Conditional and Typed Rewriting Systems

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Graph rewriting models are very suited to serve as the basic computational model for functional languages and their implementation. Graphs are used to share computations which is needed to make efficient implementations of functional languages on sequential hardware possible. When graphs are rewritten (reduced) on parallel loosely coupled machine architectures, subgraphs have to be copied from one processor to another such that sharing is lost. In this paper we introduce the notion of lazy copying. With lazy copying it is possible to duplicate a graph without duplicating work. Lazy copying can be combined with simple mmotations which control the order of reduction. In principle, only interleaved execution of the individual reduction steps is possible. However, a condition is deduced under which parallel execution is allowed. When only certain combinations of lazy copying and annotations are used it is guarantied that this so-called non-interference condition is fulfilled. Abbreviations for these combinations are introduced. Now complex process behavlours, such as process communication on a loosely coupled parallel machine architecture, can be modelled. This also includes a special case: modelling mnltlprocessing on a single processor. Arbitrary process topologies can be created. Synchronous and asyncbronons process communication can be modelled. The implementation of the language Concurrent Clean, which is based on the proposed graph rewriting model, has shown that complicated parallel algorithms which can go far beyond divide-and-conquar like applications can be expressed. 1 I n t r o d u c t i o n Ideally, a computational model of a language is a formal model as close as possible to both its semantics and its implementation, still it models only the essential aspects of them. In the following paragraphs it is explained why Graph Rewriting Systems (GRS*s) are suited to serve as a computational model of functional languages and their implementations. After that, GRS's are extended in order to deal with parallel evaluation. Graph rewriting systems and functional languages Our prime interests are functional languages and their implementation on sequential and parallel hardware. Traditionally. the pure lambda calculus (Church (1932/3). Barendregt (1984)) is considered to be a suitable model for these languages. However, in our opinion, some important aspects of functional languages and the way they are usually implemented, cannot be modelled with this calculus. In particular, the calculus itself lacks pattern matching and the notion of sharing of computations. Patterns contain in'tportant information for strictness analyTers (Ntcker (1988)). Sharing of computations is essential to obtain efficient implementations on traditional hardware (Fasel & Keller (1986)). Graph Rewriting systems are based on pattern matching and sharing. We believe that compared to the X-calculus graph rewriting systems (Barendregt et al. (1987a,b)) are better suited to serve as computational model for functional languages. In the past we have...

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“…A thorough introduction to TRS's is given in [KLO85]. TRS based languages like DACTL [GLA85] and Lean [BAR86a] are used as a computational model for implementations of new languages such as Miranda [TUR85] and OBJ [FUT84]. Currently various attempts ( [BAR86b] based on [RAO84] and [BRO86] based on [EHR78]) are made to extend TRS's to a calculus for Graph Rewriting Systems (GRS's), in order to make them serve as a computational model of (parallel) graph reducing implementations.…”

Section: Introductionmentioning

confidence: 99%