G. Boudol. Computational semantics of term rewriting systems. Algebraic methods in Semantics, Maurice Nivat and John C. Reynolds (eds). Cambridge University Press, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....= #, then src(#) src(#) and tgt(#) tgt(#) and similarly for reductions (i.e. modulo the reduction identities) Remark 3.5 Permutation equivalence is of a relatively recent origin. It was introduced for the # calculus in [24] Some important further developments of the notion can be traced in [21,16,5,18,27,23,30,2]. Owing to the tight connexion between permutation equivalence and concurrency, permutation equivalence appears in many guises in areas where concurrency is important. For instance, in trace theory the notion of Mazurkiewicz trace as a trace up to the order of independent actions was introduced in ....

G. Boudol. Computational semantics of term rewriting systems. In M. Nivat and J.C. Reynolds, editors, Algebraic Methods in Semantics, pages 169--236. Cambridge University Press, 1985.

....synthetic exposition of which can be found in [20] has since been followed by various authors, and in particular by the group of Jaco de Bakker in Holland. However it is fair to say that this was not a complete success, as the coincidence with operational semantics (as proposed by G erard Boudol [16] following works by G erard Berry and Jean Jacques L evy [17] does not hold any more, except in some special cases. This chapter of Maurice s scienti c activity ends with the publication of [18] based on a joint French US meeting held in Fontainebleau in 1982. Next, Maurice addressed the ....

....le plus synth etique est [20] sera reprise par de nombreux auteurs par la suite, notamment par le groupe de Jaco de Bakker en Hollande. Mais il est juste de dire que le succ es ici n est pas complet, car la co ncidence avec la s emantique op erationnelle (telle que d e nie par G erard Boudol [16] a la suite des travaux de G erard Berry et Jean Jacques L evy [17] ne subsiste que dans certains cas particuliers. Ce chapitre de l activit e scienti que de Maurice se cl ot avec la publication de [18] qui collecte les communications faites a un s eminaire franco am ericain tenu a ....

G. Boudol, Computational semantics of term rewriting systems, in [18].

....t under each possible valuation 2 D Var(t) of its variables on a domain D. This is called a non ground value (ngv) in [Red85] and a derived operator in [GTW78, GTWW77] It is also essentially the same as in other algebraic approaches to semantics of TRS s and recursive program schemes such as [Bou85, Cou90, Gue81, Niv75]. Given domains D and E, the set [D E] D E] of (strict) continuous functions from D to E (pointwise) ordered by f v g i 8x 2 D; f(x) v 9 g(x) is a domain [Gun92, SLG94] Given a set W V of variables, for proving that [D W D] is a domain whenever D is, we note that W = W ]f g ....

G. Boudol. Computational semantics of term rewriting systems. In M. Nivat and J. Reynolds, editors, Algebraic Methods in Semantics, pages 169-236, Cambridge University Press, Cambridge, 1985.

....in disguise. The theorem (claim 3) justifies giving up a narrowing attempt as soon as the failure to find a rule occurs without further attempts to narrow t at other positions with the hope that a different rule might be found after other narrowing steps or that the position might be deleted [7] by another narrowing step. If (p; oe) 2 (t; T ) no equation having oe(t) as one side can be solved. Any amount of work applied toward finding a solution would be wasted. This is an opportunity for optimization. In fact oe(t) may be narrowable at other positions different from p and an ....

....(1) the concept of need as the foundation of laziness, 2) strategies for using narrowing in programming, and (3) implementations of narrowing in Prolog. 6. 1 Narrowing and need Seminal studies on the concept of need in rewriting appear in [24, 39] Subsequent variations and extensions, e.g. [7, 21, 27, 30, 33, 40, 41, 45, 48], do not address narrowing, but limit the discussion to rewriting. We have introduced a concept of need for narrowing that extends a similar concept for rewriting. We have shown that the concept of need for narrowing is inherently more complicated than that for rewriting. In orthogonal systems, a ....

G. Boudol. Computational semantics of term rewriting systems. In M. Nivat and J. C. Reynolds, editors, Algebraic methods in semantics, chapter 5. Cambridge University Press, Cambridge, UK, 1985.

....term rewriting, and investigate two different orderings between semantics aimed at approximating semantics and (hence) at properties of programs. Our notion of semantics is aimed at couching both operational and denotational aspects in the style of computational, algebraic, or evaluation semantics [Bou85,Cou90,Pit97]. Since many definitions and relationships among our semantics do not depend on any computational mechanism, we consider rewriting issues later (Section 5.1) Definition 1. A (ground) term semantics for a signature Sigma is a mapping S : T ( Sigma) P(T ( Sigma) A trivial example of term ....

....orthogonal TRSs eval ( nf ( GammaSeval ( GammaSnf ( Table 1. Semantics for computing different canonical forms; means determinism 8 Related work Our rewriting semantics are related to other (algebraic) approaches to semantics of recursive program schemes [Cou90] and TRSs [Bou85]. For instance, a computational semantics, Comp hR;Ai (t) of a ground term t in a TRS R = Sigma; R) is given in [Bou85] as the collection of lub s of increasing partial information obtained along maximal computations starting from t (see [Bou85] page 212) The partial information associated ....

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G. Boudol. Computational semantics of term rewriting systems. In M. Nivat and J. Reynolds, editors, Algebraic Methods in Semantics, pages 169-236, Cambridge University Press, Cambridge, 1985.

....sequences in the computation of terms. Huet and L evy took an important step towards standardization theorem for orthogonal term rewriting systems in 1979 [6] and they demonstrated standardization theorem holds for orthogonal rewrite systems. Their result was extended to left linear TRSs by Boudol[2]. Although, their proof involves in some unfamiliar notions like initial redex, external positions, or external redex positions, and is complicated. Just after Huet and Levy s work, Klop proposed a nice looking way to view standardization. He introduced a (meta) reduction on a set of reduction ....

G. Boudol. Computational semantics of terms rewriting systems. Technical report, Rapport de recherche INRIA, Feb. 1983.

....blessing in disguise. The theorem (claim 3) justi es giving up a narrowing attempt as soon as the failure to nd a rule occurs without further attempts to narrow t at other positions with the hope that a di erent rule might be found after other narrowing steps or that the position might be deleted [7] by another narrowing step. If (p; 2 (t; T ) no equation having (t) as one side can be solved. Any amount of work applied toward nding a solution would be wasted. This is an opportunity for optimization. In fact (t) may be narrowable at other positions di erent from p and an equation ....

....(1) the concept of need as the foundation of laziness, 2) strategies for using narrowing in programming, and (3) implementations of narrowing in Prolog. 6. 1 Narrowing and need Seminal studies on the concept of need in rewriting appear in [24, 39] Subsequent variations and extensions, e.g. [7, 21, 27, 30, 33, 40, 41, 45, 48], do not address narrowing, but limit the discussion to rewriting. We have introduced a concept of need for narrowing that extends a similar concept for rewriting. We have shown that the concept of need for narrowing is inherently more complicated than that for rewriting. In orthogonal systems, a ....

G. Boudol. Computational semantics of term rewriting systems. In M. Nivat and J. C. Reynolds, editors, Algebraic methods in semantics, chapter 5. Cambridge University Press, Cambridge, UK, 1985.

....in the calculus. The proof makes a signi cant use of the standardisation theorem. In this paper, we extend L evy s result to the calculus. The task is not easy for three reasons at least: The calculus is not orthogonal (11 critical pairs, see gure 2) Despite the work of Boudol [4] in the mid eighties and more recently of Clark and Kennaway [7] our current understanding of non orthogonal dynamics is limited. We take the opportunity here to develop a general theory of neededness in rewriting systems with critical pairs, much broader in scope than calculi with explicit ....

....## aa (Ia)a v 0 1 ## = x:xx I = x:x v; u 0 u; v 1 ; v 0 2 v 1 ; v 0 2 v 2 ; v 0 1 v 2 ; v 0 1 v 1 ; v 0 2 Figure 5: A standardisation procedure in (G ; Property 1. and 2. correspond to what is called existence and uniqueness of standardisation in [16, 4, 9, 20]. By property 2, there exists a unique standard path (unique modulo ) in each L evy equivalence class . By property 1, this path d is characterised by the equivalence d d . We illustrate this in gure 5, where the rewriting path v; u 0 : Ia) aa enjoys two standard paths u; v 1 ; v 0 ....

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G. Boudol, \Computational semantics of term rewriting systems". Algebraic methods in Semantics, Maurice Nivat and John C. Reynolds (eds), Cambridge University Press, 1985.

....relative to T . We assume that: 1. there is no infinite reduction relative to T , 2. all developments of T end on the same term, 3. if u is any redex in M , the residuals of u do not depend upon the development of F . This ensures Church Rosser, but we do not stress this property here. See [3, 5, 1, 6, 7, 8] for a careful study. Finite Developments will just be useful technically. The first important axiom, which allows us to define standard reductions, is Axiom 1 (Linearity) u 6 t = 9 t 0 : t[ u] t 0 Thus redexes may disappear, or may be duplicated, only if they are inside contracted redexes. ....

....1 ] and u 2 : un are shorter equivalent standard derivations. By induction on n they are square permutation equivalent, hence d and e are too. 2 6 Abstract systems with incompatibility. Permutations of reductions have been considered even in the presence of conflicts (critical pairs) in [5]. These TRS are incredibly more difficult to treat. The main reason is that the Church Rosser property no longer holds. Take fA B; A Cg. This system has two trivial overlapping rules, and is not ChurchRosser. However, finite developments are still correct, if one considers a set of non ....

G. Boudol, "Computational semantics of term rewriting systems," in Algebraic methods in semantics (M. Nivat and J. Reynolds, eds.), Cambridge Univ. Press, 1985.

....program is referred to by an associated statement number. Similarly, a subterm in a higher order program will be referred to by an associated label. Given a parse tree of a program, an initial assignment of labels to subexpressions subtrees can be done with the use of occurrences, as described in [15]. Definition: For every natural number k, let s k be a function that maps any tree, op(t 1 ; t k ; t n ) to t k . An occurrence is defined as any function obtained by composing an arbitrary number of such functions s i . All programs considered, hence, will be assumed to have ....

G. Boudol. Computational semantics of term rewriting systems. In M. Nivat and J. C. Reynolds, editors, Algebraic Methods in Semantics. Cambridge University Press, 1985.

....rewriting must be well defined, and should be related in some way to the result obtained by applying the redexes in any order. This is easily achieved by allowing only for the parallel application of non overlapping, left linear redexes: the definitions below summarize those in [6, 5] see also [2]) Intuitively, finite parallel rewriting can be defined easily by exploiting the confluence of orthogonal term rewriting. In fact, the parallel reduction of a finite number of redexes is defined simply as any complete development of them: any such development ends with the same term, so the ....

G. Boudol, Computational Semantics of Term Rewriting Systems, chapter 8 of Algebraic Methods in Semantics, eds. M.Nivat and J. Reynolds, CUP, 1985.

....may clarify these concepts. Consider the operation le of display (4) and the problem of normalizing a term t equal to le(add(0; 0) add(0; 0) where add is the usual addition of natural numbers. We previously argued that the first argument of le, say x, is needed. In this trivial case 2 Boudol [7] similarly suggests to mark occurrences with colors and credits J. Vuillemin for this idea. Lazy Rewriting in Logic Programming 19 one can easily verify this claim by computing every reduction sequence normalizing t. Thus, let us reduce instead the second argument of le after underlining in t the ....

....is not an overly restrictive property. Seminal studies on normalizing reduction strategies appear in [25, 42] The problem is further analyzed and or summarized in [8, 25, 30, 43] The difficulty of the normalization problem led to a number of variations of the concept of sequentiality [7, 21, 30, 44, 51]. We deal with a particular class of sequential rewrite systems, which seem to be of practical interest. Our solution has two Lazy Rewriting in Logic Programming 38 distinctive characteristics: 1) sufficient conditions for the application of our method are provided at design time or can be easily ....

G. Boudol. Computational semantics of term rewriting systems. In Maurice Nivat and John C. Reynolds, editors, Algebraic methods in semantics, chapter 5. Cambridge University Press, Cambridge, UK, 1985.

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G. Boudol. Computational semantics of term rewriting systems. Algebraic methods in Semantics, Maurice Nivat and John C. Reynolds (eds). Cambridge University Press, 1985.

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G. Boudol, "Computational semantics of term rewriting systems," in Algebraic methods in semantics (M. Nivat and J. Reynolds, eds.), Cambridge Univ. Press, 1985.

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G. Boudol, "Computational semantics of term rewriting systems". Algebraic methods in Semantics, Maurice Nivat and John C. Reynolds (eds), Cambridge University Press, 1985.

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G. Boudol, "Computational semantics of term rewriting systems". Algebraic methods in Semantics, Maurice Nivat and John C. Reynolds (eds), Cambridge University Press, 1985.

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G. Boudol, \Computational semantics of term rewriting systems". Algebraic methods in Semantics, Maurice Nivat and John C. Reynolds (eds), Cambridge University Press, 1985.

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G. Boudol. Computational semantics of term rewriting systems. In Maurice Nivat and John C. Reynolds (eds), Algebraic methods in Semantics. Cambridge University Press, 1985.

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G. Boudol. Computational semantics of term rewriting systems. Algebraic methods in Semantics, Maurice Nivat and John C. Reynolds (eds). Cambridge University Press, 1985.

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G. Boudol. Computational semantics of term rewriting systems. In Algebraic Methods in Semantics, pages 169--236. Cambridge University Press, 1985.

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G. Boudol. Computational semantics of term rewriting systems. In Maurice Nivat and John C. Reynolds, editors, Algebraic methods in semantics (Fontainebleau, 1982), pages 169--236. Cambridge Univ. Press, Cambridge, 1985.

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G. Boudol, "Computational semantics of term rewriting systems" in Algebraic Methods in Semantics, M. Nivat, J. Reynolds (eds.), 1986.

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G. Boudol. Computational semantics of term rewriting systems. In M. Nivat and J. C. Reynolds, editors, Algebraic methods in semantics, chapter 5. Cambridge University Press, Cambridge, UK, 1985.

No context found.

G. Boudol. Computational semantics of term rewriting systems. In M. Nivat and J. C. Reynolds, editors, Algebraic methods in semantics, chapter 5. Cambridge University Press, Cambridge, UK, 1985.

No context found.

G. Boudol. Computational semantics of term rewriting systems. In M. Nivat and J. C. Reynolds, editors, Algebraic Methods in Semantics, chapter 5, pages 169--236. Cambridge University Press, 1985.

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