Term rewriting systems with priorities

Baeten, J.C.M.; Bergstra, Jan A.; Klop, Jan Willem

doi:10.1007/3-540-17220-3_8

Cited by 14 publications

(13 citation statements)

References 10 publications

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“…This strategy, which has been defined precisely, is c-normalizing and optimal for the class of admissible termgraphs. In [21], a lazy graph rewriting strategy close to ours is described, namely the annotated functional strategy, which combines the discriminating position strategy [24] and rewriting with priority [4]. To our knowledge, no formal result has been proved regarding this strategy.…”

Section: Resultsmentioning

confidence: 98%

On Term-Graph Rewrite Strategies

Echahed

2008

Electronic Notes in Theoretical Computer Science

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We tackle the problem of cyclic term-graph rewriting. We first revisit the classical algorithmic approach to term-graph rewriting by providing a definition of rewrite rules of the form lhs → rhs where the lefthand sides are term-graphs and the right-hand sides are sequences of actions. Such actions, which specify how to rewrite a term-graph in a stepwise manner, contribute to simplify substantially the definition of cyclic term-graph rewriting. Then we define a new class of term-graph rewrite systems which are confluent over the so-called admissible term-graphs. Finally, we provide an efficient rewrite strategy which contracts only needed redexes and give pointers to other results regarding optimal rewrite strategies of admissible term-graphs.

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Section: Resultsmentioning

confidence: 98%

On Term-Graph Rewrite Strategies

Echahed

2008

Electronic Notes in Theoretical Computer Science

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“…In rewrite systems, each step of a reduction can be faced with choices among several candidate redex (reducible expressions) and rewrite rules. PRS [21,2] impose an order of priority among rewrite rules and always apply the highest priority rule at each reduction step:…”

Section: Definition 3 a Rewrite Relation -+ Is A Binary Relation Overmentioning

confidence: 99%

“…The tremendous potential for new applications ensures a continuous quest for understanding its foundations. The goal of this paper is to propose a minimal model of behavioral reflection for a prototype-based language, to study it in depth and to provide it with a formal semantics using the theory of priority rewrite systems (PRS) [2,21,5]. We propose a complete prototype-based language, but our formal study is restricted to the reflective protocol only; hence our results can be applied to other reflective object-oriented programming languages, provided they use a similar reflective protocol.…”

Section: Introductionmentioning

confidence: 99%

A semantics of introspection in a reflective prototype-based language

Malenfant

Cointe²,

Dony

1996

Lisp and Symbolic Computation

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Abstract. In Malenfant et aI. [19], we have described a reflective model for a prototype-based language based on the lookup o apply reflective introspection protocol, tn this paper, we augment our previous protocol by converting it to handle continuations reified as first-class objects. First-class continuations provide much more control over the current computation; during the introspection phase fired by message sending, they make it possible not only to change the behavior of the program for that message but also for the entire future computation. In this paper, we provide this introspection protocol with a formal semantics. This result is obtained by exhibiting a mapping A from program configurations to priority rewrite systems (PRS) as well as a mapping from message expressions to ground first-order terms used to query the PRS. Other advantages of this approach are: to ensure the termination of the introspection using the smallest set of formally justified conditions and to provide a clear declarative account of this reflective protocol. The PRS also appears as a recta-level to the base tanguage~ independent of the implementation, but from which we derive fundamental clues to obtain an efficient language processor. By our new model, we finally highlight the link between reflection in object-oriented languages and the one originally proposed by 3-Lisp [24], although object-orientation provides reusability to reflection, making it easier to use.

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“…In [1,2], priority rewriting systems (PRSs in short) have been introduced. A PRS is a term rewrite system (TRS in short) with a partial ordering on rules, determining a priority between some of them.…”

Section: Introductionmentioning

confidence: 99%

“…In [1], a semantics is proposed, relying on a notion of unique sound and complete set of closed instances of the rules of the PRS, and it is shown that bounded -the bounded property is weaker than termination-PRSs have a semantics. In [12], a fixed point based technique is proposed to compute the semantics of a PRS.…”

Section: Introductionmentioning

confidence: 99%

Termination of Priority Rewriting

Gnaedig

2009

Language and Automata Theory and Applications

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Abstract. Introducing priorities in rewriting increases the expressive power of rules and helps to limit computations. Priority rewriting is used in rule-based programming as well as in functional programming. Termination of priority rewriting is then important to guarantee that programs give a result. We describe an inductive proof method for termination of priority rewriting, relying on an explicit induction on the termination property and working by generating proof trees, which model the rewriting relation by using abstraction and narrowing.

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Term rewriting systems with priorities

Abstract: Term rewriting systems with rules of different priority are introduced.The semantics are explained in detail and several examples are discussed.

Cited by 14 publications

References 10 publications

On Term-Graph Rewrite Strategies

On Term-Graph Rewrite Strategies

A semantics of introspection in a reflective prototype-based language

Termination of Priority Rewriting

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