D. Bert and R. Echahed. Abstraction of Conditional Term Rewriting Systems. In J. Lloyd, editor, International Symposium on Logic Programming, ILPS-95, Portland, Oregon, pages 162-176. MIT Press, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....for each generator profile Furthermore, they satisfy the syntactic criteria of Theorem 4, except sum of Example 8 (due to the lack of the splitting property) and some Boolean functions in Section 3. 2 (due to non trivial use of #, #, #) Another approach to signature completion is given in [2] taking the least fixed point of a rewrite system transformation, using a notion of abstract domains. Thus, this method is based on rewriting rather than type analysis. Soundness, but not optimality results, are proved. 4. Semantic subtypes A semantic subtype definition has the following format, ....

D. Bert, R. Echahed: "Abstraction of conditional term rewriting systems." Research Report 942, LGI-IMAG, Grenoble, France, 1995.

....condition on the rhs s of the rules, which prevented our methods from coping with many interesting examples, such as the program of Example 1. In this paper we provide two di erent, novel criteria for recognizing redundancy, which are based on inductionless induction [10] and abstract rewriting [8], respectively. The combination of these methods catches redundancy in many new practical cases, including Example 1. Of course, in exchange for the conditions of [2] di erent extra conditions are required, which are also discussed in the paper. 1.1 Plan of the paper After some preliminaries in ....

....which the problem of detection of redundant arguments is decidable. This class is di erent from the one identi ed in [2] and hence also the decidability results in this paper and those in [2] are incomparable and complement each other. In Section 5, we show how the abstract rewriting technique of [8], for approximating normal forms of terms, can be used to prove inductive theorems, and thus to detect new redundancies. Section 6 concludes the paper. 2 Preliminaries Let us rst introduce the main notations used in the paper. For full or missing de nitions about term rewriting, we refer to ....

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D. Bert and R. Echahed. Abstraction of Conditional Term Rewriting Systems. In J. Lloyd, editor, International Symposium on Logic Programming, ILPS-95, Portland, Oregon, pages 162-176. MIT Press, 1995.

....systems as a fixed point calculus and we state the soundness of the approximation we propose. At last, we compare our work with other approaches and we show some possible applications in the concluding section 5. Due to lack of space, the proofs have been omitted. They may be consulted in [2]. 2 Preliminaries We start by giving some basic definitions needed for the understanding of the paper. Concepts not defined here can be found for example in [7] 13] or [9] A signature is a pair Sigma = S; Omega ) where S is a set of sort names, and Omega is a family of sets of operator names ....

....t 1 p t 2 iff there exists a term t 3 such that t 1 rewrites into t 3 at position p according to Definition 3. 7 and t 2 = up(t 3 ) Coming back to term t, we have t rewrites into t 00 = head(t 0 ) s a ( nat ) From the definition of R up , the following properties can be easily shown [2]. Theorem 3.11 (Properties of R up ) Let SP be a constructor based specification SP = Sigma; R) up a finite upper closure. Then 1. R up is terminating, 2. 8s 2 S; 8t 1 ; t 2 2 TA( Omega Gamma ;s ; t 1 s t 2 ) up(t 1 )# R up s up(t 2 )# R up; 3. 8f 2 Omega s 1 Delta Delta Delta sn ;s ; ....

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Didier Bert and Rachid Echahed. Abstraction of conditional term rewriting systems. Technical report RR942.I., IMAG-LGI, January 1995.

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