Andrea Corradini and Fabio Gadducci. CPO models for infinite term rewriting. In V. S. Alagar and M. Nivat, editors, Algebraic Methodology and Software Technology, 4th International Conference, AMAST'95, Montreal, Canada, July 3--7,  Home/Search   Document Details and Download   Summary   Related Articles   Check

....on the case of infinite computations for actor systems specified in rewriting logic, to obtain a precise semantic account of their fair computations. Her ideas and results are very elegant; they are discussed in [99] Yet another, quite interesting approach has been taken by Corradini and Gadducci [24]. They consider rewrite theories with empty set of equations and interpret them in continuos cpo algebra models in such a way that not only the terms, but also the proof terms, become endowed with an approximation ordering. They then propose a natural infinitary extension of rewriting logic that ....

A. Corradini and F. Gadducci. CPO models for infinite term rewriting. In Proc. AMAST'95, pages 368--384. Springer LNCS 936, 1995.

....di Informatica of Pisa and the Technical University of Berlin. a very interesting subclass of infinite terms, because they have a finitary representation; usually, however, this is not unique. Infinitary extensions of Term Rewriting have been considered by various authors during the last decade [12, 11, 15, 16, 7, 20, 21, 22, 9, 8]. Most of those contributions are concerned with the study of the rewriting relation induced by a set of finite term rules on infinite terms, presenting results about the existence of normal forms (possibly reachable after steps) confluence and so on. Only a few of them, namely [20, 21, 8] ....

.... term reductions with a pre iteration structure, and by imposing on them exactly the same axioms of Definition 6. Space constraints forbid us to introduce the deduction rules for sequential composition, which allow to derive sequents which model many step reductions (as done for example in [25, 9]) This will be included in the full version of the paper: we just discuss in the concluding section the relevance of this extension. Definition 22 (rewriting sequents) Let R = h Sigma ; L; Ri be an orthogonal trs over X . Let = n n be the signature containing all the rules d : l r 2 R with ....

A. Corradini and F. Gadducci. CPO Models for infinite term rewriting. In Algebraic Methodology and Software Technology, volume 936 of LNCS, pages 368--384. Springer Verlag, 1995.

....(yet suggestive, in our case) representation of terms as trees. The complete agreement between the classical definition of derivability among terms and the one above using Rewriting Logic was already stated in [Mes92] and it has been formally established and generalized to infinite rewriting in [CG94]) More precisely, it is not difficult to show that there exists a derivation from t to s in a trs R iff R entails a sequent (flat or full) ff : t s. The same kind of agreement holds between full and flat entailment: a rewriting system R entails a full sequent ff : t s, iff there exists a ....

A. Corradini, F. Gadducci, CPO Models for Infinite Term Rewriting, draft.

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A. Corradini, F. Gadducci, CPO Models for Infinite Term Rewriting, in Proc. AMAST'95, LNCS 936, 1995, pp. 368--384.

....theory R ccs with the proved transition system of Tab. 2. We first give the definition and a characterization of the class of active proof terms (and associated sequents) roughly denoted as those closed proof terms of sort SAP such that the sequential composition operator never occurs (see [4,5]) Definition 3.3 Let ff be a closed proof term. Then ff is ffl one step, if it does not contain the composition operator Delta ; ffl active, if it is one step and contains just one occurrence of an operator , for any 2 A; ffl initial, if it is active and does not contain any occurrence ....

....exchange axiom are applicable to a proof term only when some of its sub components are enabled to perform a rewrite step, which is impossible, according to Lemma 3.4, because they have sort SP . 2 The statement above is equivalent to the usual decomposition property stated in [19] but see also [4,5]) the main difference is its uniqueness, due to the structure of the proof terms entailed by R ccs . It is not a trivial property, and it is not in general valid for any generic rewriting theory. On the contrary, it will be the basis for the proof of our correspondence result. Proof of Theorem ....

A. Corradini and F. Gadducci. CPO Models for infinite term rewriting. In Algebraic Methodology and Software Technology, volume 936 of LNCS, pages 368--384. Springer Verlag, 1995.

No context found.

A. Corradini, F. Gadducci, CPO Models for Infinite Term Rewriting, in Proc. AMAST'95, LNCS 936, 1995, pp. 368--384.

.... the Context Systems introduced by Larsen and Xinxin [LX90] A partial answer can be found in [GM95] With regard instead to term rewriting, the methodology has been successfully applied to term graph rewriting and infinitary term rewriting: we refer the curious reader respectively to [CGM95b] and [CG95]. Finally, our hope is that [Gad95] will provide a comprehensive overview of the whole subject. ....

A. Corradini, F. Gadducci, CPO Models for Infinite Term Rewriting, in Proc. AMAST'95, LNCS 936, 1995, pp. 368-384.

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Andrea Corradini and Fabio Gadducci. CPO models for infinite term rewriting. In V. S. Alagar and M. Nivat, editors, Algebraic Methodology and Software Technology, 4th International Conference, AMAST'95, Montreal, Canada, July 3--7,

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