P. Lescanne, Completion Procedures as Transition Rules + Control:ORME. In 2nd Intern. Workshop Algebraic and Logic Programming, Lecture Notes in Computer Science, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... x 3 y y, and the second definition is obtained by choosing to simplify first with the definition of h(x; u) 3 Conclusion We choose to use a partial unfailing completion process as the central part of a transformation system. For that we use the toolkit of rewriting tools provided by ORME [16]. With this simple initial implementation we have tested the well known examples and the kwic example given in the appendix. The kwic example is interesting because it requires 3 steps of transformation and therefore shows the potential for transformation of larger specifications by composition of ....

P. Lescanne, Completion Procedures as Transition Rules + Control:ORME. In 2nd Intern. Workshop Algebraic and Logic Programming, Lecture Notes in Computer Science, 1990.

....issues pertaining to strategy and control. As we shall see, this is precisely what reflection and a convenient internal strategy language allow us to accomplish. There have been several attempts to use this abstract view of completion in actual rewrite rule implementations of completion procedures [22, 20]. The challenge has been to control the rewriting inference process generated by the rules in C which in principle could go in many undesired directions by means of adequate strategies. Unfortunately, these implementations have not been able to preserve the separation between the logical and ....

....control of the rewriting process is deeply embedded in the data structure on which the inference rules operate. As a consequence, improvements in the control of the rewriting process require changes in the original data structure and consequently in the original inference system C as shown in [22]. In particular, proofs of correctness based on the original inference system need to be redone for the new inference rules combining inference and control. We believe that the difficulties encountered in previous approaches are quite intrinsic and probably cannot be overcome without the use of ....

P. Lescanne. Completion procedures as transition rules + control. In M. Diaz and F. Orejas, editors, TAPSOFT'89, volume 351 of Lecture Notes in Computer Science, pages 28--41. Springer-Verlag, 1989.

....treats the case of unsorted and unconditional rewrite theories; the extension to sorted and conditional theories is unproblematic and will appear elsewhere. There have been several attempts to use this abstract view of completion in actual rewrite rule implementations of completion procedures [15, 13]. The challenge has been to control the rewriting inference process generated by the rules in C which in principle could go in many undesired directions by means of adequate strategies. Unfortunately, these implementations have not been able to preserve the separation between the logical and ....

....For example, control of the rewriting process is deeply based on the data structure on which the inference rules operate. As a consequence, improvements in the control of the rewriting process required changes in the original data structure and consequently in the inference system C as shown in [15]. In particular, proofs of correctness based on the original inference system need to be redone for the new inference rules combining inference and control. We believe that the difficulties encountered in previous approaches are quite intrinsic and probably cannot be overcome without the use of ....

P. Lescanne. Completion procedures as transition rules + control. In M. Diaz and F. Orejas, editors, TAPSOFT'89, volume 351 of Lecture Notes in Computer Science, pages 28--41. Springer-Verlag, 1989.

....rule generates new constrained formulas. But in standard (i.e. without constraints) completion procedures, the use of simplification eliminates redundant equalities or rewrite rules. Simplification is crucial for efficiency as shown in the experiments with different completion strategies in Orme [6] and especially the ANS completion that gives high priority to simplification. However using simplification in conjunction with constrained superposition may lead to lose completeness, as in the next example [10] Example 1 Let F = ff; k; a; bg with f k a b and assume given the following ....

....given in Figure 1. The kind of simplification used in the three last rules is left unspecified and can be any of the previously defined simplification relations. In order to design a completion process giving priority to simplification, we just adapt the ideas of the ANS completion, described in [6] as a set of transition rules transforming a specific data structure. This mainly consists in splitting the set of rules R into five components and to use a data structure composed of six fields: E is the set of generated critical pairs. S is the set of rewrite rules used to simplify other ....

P. Lescanne. Completion procedures as transition rules + control. In M. Diaz and F. Orejas, editors, TAPSOFT'89, volume 351 of Lecture Notes in Computer Science, pages 28--41. Springer-Verlag, 1989.

....three concepts can be found in [11] The inference rules KB can be applied in many different ways, but all of them fair, correct, and sound. We choose two of them. The rst is a general completion procedure complete as it was presented e.g. by Huet [26] or in a more sophisticated way by Lescanne [41], the second is a nonreducing completion process nr complete, generating all critical pair consequences without interreduction. For corresponding control strategies see [20] Summarizing the possible performances, the completion procedure can succeed in generating a nite convergent canonical ....

P. Lescanne. Completion procedures as transition rules + control. In J. D#az and F. Orejas, editors, Proceedings of TAPSOFT '89, Volume 1: CAAP '89; Barcelona (Spain), volume 351 of Lecture Notes in Computer Science, pages 28 41. Springer-Verlag, March 1989.

....the normalization time for that term. This is quite different from our implementation, which emphasizes larger grained parallelism; it allows parallel rewriting during internormalization, but does not intentionally schedule multiple rewrites of the same term. Some sequential completion procedures [11, 14, 15] also divide the state into components, either to achieve better performance or to facilitate reasoning about correctness. The data structures used for our state components differ from these, however, because they are concurrent and have more control information to allow for the additional ....

P. Lescanne. Completion procedures as transition rules + control. In TAPSOFT '89, pages 28--41. LNCS 351, 1989.

....a function f w.r. t C is when for all ground term f( 1 ; 1 1 1 ; n ) there exists a constructor term s such that f( 1 ; 1 1 1 ; n ) 3 s R a s ste for ro ra transfor ation ASTRE has been written in CAML [10] The implementation uses largely all the functions CAML provided by the system ORME [18, 19] A functional language like CAML can be considered as a good specification language and it is easy to translate a program written in a pure functional language into a set of first order equations. Let us consider a simple CAML program to computes permutations which can be found in [12] Example ....

....[3] ASTRE can verify the ground convergence of R and R 0 by using an unfailing completion procedure. The transformation process also involves a (partial) unfailing completion procedure. The original code of an unfailing completion procedure is borrowed from the system ORME. It is described in [18, 19]. For the transformation, the user provides definitions of new function symbols. Example For example, a transformation of permu can be initiated by introducing the new definition: fmp(x,y) flatten(mapperms(x,y) The result of the transformation process given by ASTRE is then: ....

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P. Lescanne, Completion Procedures as Transition Rules + Control,In Proceedings of the Colloquium Current Concept In Programming Languages, TAPSOFT, Springer Verlag, Lectures Notes in Computer Science 351, pages 28-41, Barcelone, Spain, 1989.

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Pierre Lescanne. Completion procedures as transition rules + control. Centre de Recherche en Informatique de Nancy, France (unpublished).

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