A. Laville, Lazy Pattern Matching in the ML Language, Proc. of FST&TCS, Springer-Verlag LNCS, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....systems are restrictive. Therefore we now show how our results can be applied to functional or equational programming languages. ffl Most functional languages such as ML [HMT88] and Hope [BMS80] permit overlapping rewrite rules, but make use of priorities to disambiguate among them. Laville [Lav87] has shown how these rules can be transformed into equivalent constructorbased orthogonal system. The transformed programs must be strongly sequential (as they most often are) in order to have a complete lazy normalization procedure. We can now transform this system into a path sequential system ....

A. Laville, Lazy Pattern Matching in the ML Language, Proc. of FST&TCS, Springer-Verlag LNCS, 1987.

....the indices of l are exactly those fringe positions wherein l has a nonvariable. With priorities, however, we may have to inspect positions wherein l has a variable in order to rule out a match for higher priority patterns. To identify these variable positions (that are indices) Laville [17] proposed an indirect method. In this method the prioritized patterns are first transformed into an equivalent set of unprioritized patterns, and then indices are identified using this set. Specifically, for each pattern l, the transformation generates a set M l of its instances (called minimally ....

A. Laville, Lazy Pattern Matching in the ML Language, Foundations of Software Technology & Theoretical Computer Science, 1987.

....( #2 ( #1 #0 #2 ) 6 . 4 Pattern Matching Pattern matching is an operation which extracts (sub ) structures of particular shapes and elements from given structural contexts and substitutes them for place holders in other structural contexts. It is available in all modern functional languages [Turn86, Lavi87, HuWa88] and primarily used as an elegant way 6 Note that in order to get deBruijn indices as originally defined, these indices have to be incremented by one. of defining functions as ordered sets of alternative equations. However, its full potential lies in complex rule based modifications of ....

Laville, A.: Lazy Pattern Matching in the ML Language, INRIA Rapporte de Recherche, No. 664, 1987

....ground convergent constructor based rewrite system is equivalent to a (ground convergent constructor based) rewrite system where all the patterns are linear. Term subtraction and the previous results are also relevant to the compilation of pattern matching in functional languages, for example [24, 40]. Deciding whether a term is covered by a disjunction of terms is closely related to the concept of ground reducibility in term rewriting. Ground reducibility is important because it has application in proving that an algebraic specification is sufficiently complete and in proving inductive ....

A. Laville, Lazy Pattern Matching in the ML Language, Proc. Conf. on Foundations of Software Technology and Theoretical Computer Science, Pune, LNCS 287, 400--419, 1987.

.... Several authors have pursued studies of this reduction order with different Partially supported by grants from NWO, the Vrije Universiteit Amsterdam and the Katholieke Universiteit Nijmegen 1 Miranda TM is a trademark of Research Software Limited semantic transformations (Kennaway (1990) Laville (1987),Puel and Su arez (1990) The language Clean is close to its underlying computational model (i.e. term graph rewriting (Barendregt et al. 1987) Therefore, it seems natural to define the functional strategy directly in the computational model rather than using a transformation to an equivalent ....

Laville, A. (1987). Lazy pattern matching in the ml language, Proc. of 7th Conference on Software Technology and Theoretical Computer Science, Pune, India, Springer Verlag, 287, pp. 400--419.

....of naming conflicts. 4 Pattern Matching Pattern matching is an operation which extracts (sub ) structures of particular shapes and elements from given structural contexts and substitutes them for place holders in other structural contexts. It is available in all modern functional languages [Turn86, Lavi87, HuWa88] and primarily used as an elegant way of defining functions as ordered sets of alternative equations. However, its full potential lies in complex rule based modifications of structured objects. Pattern matches are in KiR defined as so called WHEN clauses which have the syntactical form WHEN pat 1 ....

Laville, A.: Lazy Pattern Matching in the ML Language, INRIA Rapporte de Recherche, No. 664, 1987

....rule, we know that the first one cannot be applied. Hence, we have some knowledge about the ground terms on which the second rule should be tried : they are in the complement of the first left hand side. This is effectively used in, for example [Sch88a] Another kind of term complements is used in [Lav87, Lav88, PS90] in order to produce a non ambiguous set of patterns . ffl There are basically two kinds of applications of complement problems in logic programming. Both rely on the fact that the declarative semantics of a logic program is its least Herbrand model. First, it is possible to statically deduce ....

A. Laville. Lazy pattern matching in the ML language. In Proc. 7th Conf. Found. of Software Technology and Theoretical Computer Science, Pune, INDIA, LNCS 287, December 1987.

....priorities, however, we may have to inspect positions wherein l has a variable in order to rule out a match for higher priority patterns. But it is not obvious which variable position of l must be inspected and so it is not clear how to compute indices in prioritized systems. Therefore Laville [8] proposed an indirect method for index computation that first transforms the prioritized patterns into an equivalent set of unprioritized patterns, which is then used for index computation. For each pattern l, the transformation generates a set M l of its instances that are not instances of any ....

A. Laville, Lazy Pattern Matching in the ML Language, FST&TCS '87.

....that they are correct, most notably for the notion of simulation from Kamperman and Walters. 1 Introduction Quite a number of papers deal with particular examples of transformations of rewrite systems, usually with the aim to obtain a rewrite system which satisfies some desirable property, e.g. [17, 12, 2, 18, 16, 20, 19, 23, 9, 10, 8]. In most of these papers, correctness of the transformation is stated, meaning that the original and the transformed rewrite system are in some sense equivalent . This claim is based on the observation either that desirable properties such as confluence and termination are preserved by the ....

....is studied. The conclusion is that for left linear weakly non overlapping term rewriting systems, the transformation into graph rewriting systems preserves normal forms. In order to obtain correctness, one additionally has to verify that termination is preserved, which is indeed the case. Laville [12] considered rewrite systems with priorities, which were first studied in [1] If two rewrite rules can be applied to the same term, then only the rule with the highest priority is applied. Priorities are a powerful means to capture intricate rewriting in a simple rewrite system, but they are ....

A. Laville. Lazy pattern matching in the ML language. In K.V. Nori, editor, Proceedings 7th Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS'87), Pune, India, LNCS 287, pages 400--419. Springer, 1987.

....of compilation steps for functional programming languages which stay inside the domain of rewrite systems. Quite a number of papers deal with particular examples of transformations of rewrite systems, usually with the aim to obtain a rewrite system which satisfies some desirable property, e.g. [17, 10, 18, 16, 19, 22, 7]. In most of these papers, correctness of the transformation is stated, meaning that the original and the transformed rewrite system are in some sense equivalent . This claim is based on the observation either that desirable properties such as confluence and termination are preserved by the ....

A. Laville. Lazy pattern matching in the ML language. In Proceedings FSTTCS'87, LNCS 287, pp. 400--419. Springer, 1987.

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