R. Bert, R. Echahed, and B.M. stvold. Abstract Rewriting. In Proc. Third Int'l Workshop on Static Analysis WSA'93, volume 724 of Lecture Notes in Computer Science, pages 178--192. Springer-Verlag, Berlin, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of unsatisfiability of equation sets or any analysis which is based on the program success set. We assume the framework of abstract interpretation for analysis of equational unsatisfiability as defined in [5] Another approach to constructing an abstract term rewriting system is followed in [16]. We think that another approximation of the fixpoint semantics given in the previous section which is di#erent from the one that we describe in this section can be characterized by following an approach similar to that in [16] We recall some previous principal definition about the abstract ....

.... to constructing an abstract term rewriting system is followed in [16] We think that another approximation of the fixpoint semantics given in the previous section which is di#erent from the one that we describe in this section can be characterized by following an approach similar to that in [16]. We recall some previous principal definition about the abstract domains and the associated abstract operators, see [2,5,8] for details. Then we describe the novel abstract immediate consequence , which approximates T , and the corresponding abstract fixpoint semantics, # (R) An ....

D. Bert, R. Echahed, and B.M. stvold. Abstract Rewriting. In Proc. of Third Int'l Workshop on Static Analysis, WSA'93, pages 178--192. Springer LNCS 724, 1993.

....of unsatisfiability of equation sets or any analysis which is based on the program success set. We assume the framework of abstract interpretation for analysis of equational unsatisfiability as defined in [4] Another approach to constructing an abstract term rewriting system is followed in [15]. We think that another approximation of the fixpoint semantics given in the previous section which is different from the one that we describe in this section can be characterized by following an approach similar to that in [15] We recall some previous principal definition about the abstract ....

.... to constructing an abstract term rewriting system is followed in [15] We think that another approximation of the fixpoint semantics given in the previous section which is different from the one that we describe in this section can be characterized by following an approach similar to that in [15]. We recall some previous principal definition about the abstract domains and the associated abstract operators, see [2,4,7] for details. Then we describe the novel abstract immediate conse quence operator Ti , which approximates T, and the corresponding abstract fixpoint semantics, Ci(T) and ....

D. Bert, R. Echahed, and B.M. Ostvold. Abstract Rewriting. In Proc. of Third Int'l Workshop on Static Analysis, WSA'93, pages 178-192. Springer LNCS 724, 1993.

....analysis of unsatis ability of equation sets or any analysis which is based on the program success set. We assume the framework of abstract interpretation for analysis of equational unsatis ability as de ned in [3] Another approach to constructing an abstract term rewriting system is followed in [9]. We think that another approximation of the xpoint semantics given in the previous section which is di erent from the one that we describe in this section can be characterized by following an approach similar to that in [9] We recall some previous principal de nition about the abstract domains ....

.... approach to constructing an abstract term rewriting system is followed in [9] We think that another approximation of the xpoint semantics given in the previous section which is di erent from the one that we describe in this section can be characterized by following an approach similar to that in [9]. We recall some previous principal de nition about the abstract domains and the associated abstract operators, see [1, 3, 4] for details. Then we describe the novel abstract immediate consequence operators T ] R which are able to approximate the operators T R , and the abstract xpoint ....

[Article contains additional citation context not shown here]

D. Bert, R. Echahed, and B.M. stvold. Abstract Rewriting. In Proc. of Third Int'l Workshop on Static Analysis, WSA'93, pages 178-192. Springer LNCS 724, 1993.

....logic programs is one of the most challenging problems in declarative programming. Many works have already addressed the analysis of certain run time properties of programs, e.g. mode inferencing [DW89, Han94b, HZ94, Lin88] demandedness patterns [MKMWH93, Zar97] equational unsatis ability [AFM95, AFRV93, AFV96, BE 93], detection of parallelism [HKL92, SR92] and a number of other properties which are also relevant for parallel execution [KMH92] Nevertheless, most of these approaches have been done in a rather ad hoc setting, gearing the analysis towards the application on hand. Up to now, there is no general ....

D. Bert, R. Echahed, and B.M. stvold. Abstract Rewriting. In P. Cousot, M. Falaschi, G. File, and A. Rauzy,, editors, Proc. of 3rd International Workshop on Static Analysis, WSA'93, LNCS 724:178-192, Springer-Verlag, Berlin, 1993.

....and is adequate for modular data ow analysis, such as the analysis of unsatis ability of equation sets. We assume the framework of abstract interpretation for analysis of equational unsatis ability as de ned in [2] Another approach to constructing an abstract term rewriting system is followed in [9]. We think that another approximation of the xpoint semantics given in the previous section which is di erent from the one that we describe in this section can be characterized by following an approach similar to that in [9] We rst recall the abstract domains and the associated abstract ....

.... approach to constructing an abstract term rewriting system is followed in [9] We think that another approximation of the xpoint semantics given in the previous section which is di erent from the one that we describe in this section can be characterized by following an approach similar to that in [9]. We rst recall the abstract domains and the associated abstract operators. Then we describe a novel abstract immediate consequence operator T ] R which is able to approximate the operator TR , and the abstract xpoint semantics F ] R) In the following, we denote the abstract analog of a ....

[Article contains additional citation context not shown here]

D. Bert, R. Echahed, and B.M. stvold. Abstract Rewriting. In Proc. of Third Int'l Workshop on Static Analysis, WSA'93, pages 178-192. Springer LNCS 724, 1993.

....is adequate for modular data flow analysis, such as the analysis of unsatisfiability of equation sets. We assume the framework of abstract interpretation for analysis of equational unsatisfiability as defined in [2] Another approach to construct an abstract term rewriting system is followed in [8]. We think that another approximation of the fixpoint semantics given in previous section different from the one that we describe in this section can be characterized by following an approach similar to that in [8] We first recall the abstract domains and the associated abstract operators. Then ....

.... [2] Another approach to construct an abstract term rewriting system is followed in [8] We think that another approximation of the fixpoint semantics given in previous section different from the one that we describe in this section can be characterized by following an approach similar to that in [8]. We first recall the abstract domains and the associated abstract operators. Then we describe a novel abstract immediate consequence operator T ] R able to approximate the operator TR , and the abstract fixpoint semantics F ] R) In the following we denote the abstract analog of a concrete ....

[Article contains additional citation context not shown here]

D. Bert, R. Echahed, and B.M. stvold. Abstract Rewriting. In Proc. of Third Int'l Workshop on Static Analysis, WSA'93, pages 178--192. Springer LNCS 724, 1993.

....logic programs is one of the most challenging problems in declarative programming. Many works have already addressed the analysis of certain run time properties of programs, e.g. mode inferencing [DW89, Han94b, HZ94, Lin88] demandedness patterns [MKMWH93, Zar97] equational unsatisfiability [AFM95, AFRV93, AFV96, BE93], detection of parallelism [HKL92, SR92] and a number of other properties which are also relevant for parallel execution [KMH92] Nevertheless, most of these approaches have been done in a rather ad hoc setting, gearing # Institut fur Informatik, Christian Albrechts Universitat Kiel, ....

D. Bert, R. Echahed, and B.M. stvold. Abstract Rewriting. In P. Cousot, M. Falaschi, G. File, and A. Rauzy,, editors, Proc. of 3rd International Workshop on Static Analysis, WSA'93, LNCS 724:178-192, Springer-Verlag, Berlin, 1993.

....because the search space is huge and contains infinite branches. In the last years, many authors have proposed optimizations (innermost [9] LSE [4] needed [2] lazy in the sense of [16, 15] or in the sense of [10, 14] outer [17] approximations [1] etc. or unsatisfiability tests [3]. Many of them need some restrictions on the rewrite system to keep completeness, like left linearity, non ambiguity, constructor discipline, strong sequentiality. Another idea consists in directing narrowing [8] This idea has led to the narrowing directed by a graph of terms [6] A graph of ....

D. Bert, R. Echahed, and B. Østvold. Abstract Rewriting. In P. Cousot, M. Falaschi, G. Fil`e, and A. Rauzy, editors, proceedings 3rd Internationnal Workshop on Static Analysis WSA'93, volume 724 of Lecture Notes in Computer Science, pages 178--192. Springer-Verlag, 1993.

....system computes WHNFs. We derive an efficient implementation on already efficient eager machinery from this model. Our method compares favourably to existing methods. Our notion of Lazy Normal Forms (LNFs) could also be helpful in an implementation of abstract rewriting, as described in [BE 93] or in the context of theorem proving. We would like to thank John Field for his very insightful comments on an earlier version of this paper, and Jan Heering for his meticulous reading of a later version. ....

Didier Bert, Rachid Echahed, and Bjarte M. Østvold. Abstract rewriting. In Third International Workshop on Static Analysis, Padova, Italy, volume 724 of Lecture Notes in Computer Science, pages 178--192. Springer-Verlag, 1993.

....system semantics for basic conditional narrowing that we have introduced in Definition 4. We first recall the abstract domains and the associated abstract operators together with some previous results concerning them. We note that a different analysis of unsatisfiability is introduced in [6] for constructor based programs where the computation is done by . This method is not comparable to ours, since there are examples which can be analyzed by only one of the two methods and our method is able to capture some computational properties related to the use of logical variables that ....

R. Bert, R. Echahed, and B.M. Østvold. Abstract Rewriting. In , volume 724 of , pages 178--192. Springer-Verlag, Berlin, 1993.

....we are limited to constructor based systems. Moreover their abstraction strategy depends not only on the CTRS but also on the goal. Much work must be done to determine more precisely the respective capabilities of each technique. Finally, the results presented in this paper generalize those of [3] in several respects. We have introduced a general framework for the construction of abstract domains of rewriting whereas the one presented in [3] is very limited and does not allow to capture the unsatisfiability or the validity of many trivial examples. The main advantage of these new abtract ....

....be done to determine more precisely the respective capabilities of each technique. Finally, the results presented in this paper generalize those of [3] in several respects. We have introduced a general framework for the construction of abstract domains of rewriting whereas the one presented in [3] is very limited and does not allow to capture the unsatisfiability or the validity of many trivial examples. The main advantage of these new abtract domains amounts to the possibility of tuning the approximation of rewriting as much as needed. We have also introduced a new definition of abstract ....

Didier Bert, Rachid Echahed, and Bjarte M. Østvold. Abstract rewriting. In Proceedings of the 3rd International Workshop on Static Analysis, WSA'93, number 724 in Lecture Notes in Computer Science, pages 178--192. SpringerVerlag, 1993.

....to denote such instantiated objects. Specially, a notation with explicit parameters is allowed; generic sorts are associated with sorts of the model, as in seq[nat] and operators or predicates are associated with effective operators and predicates of the parameter passing model, as in sort[ [3,2,4]) which is an occurrence of the operator declared in Sorting with the model of decreasing order on the natural numbers. In Figure 4, we present examples of definitions of generic predicates which can be used as higher order predicates. property Function sorts t1,t2 operators f: t1 t2 ....

....may be partial and TRS s are not even terminating, an extension of needed narrowing [1] to CTRS s will be a very good candidate. Another point is that narrowing strategies do not always avoid useless branches. Thus, other techniques can be used in order to detect wasted computations. In [4] we have started the investigation of a new method, based on abstract analysis techniques, which tries to avoid narrowing over some unsatisfiable equations or disequations. We plan to continue such investigations. ....

D. Bert, R. Echahed, and B. M. Østvold. Abstract rewriting. In Proc. of WSA'93, pages 178--192. LNCS 724, 1993.

....a model of the required property of D. In many cases, the models declared in the library are sufficient to determine what is the instance of an object. For example, if the library contains the declaration of the model : Nat Order: Total Order[nat operators , then a term like sort.Nat Order([2,4,1]) is the call of the operator to sort the sequence [2,4,1] using the order . A shorter form of this call is sort[ 2,4,1] because the type checking inference rules of lpg allow to determine the sort of the model from the sort of the argument (sequence of nat) At last, if the model ....

....models declared in the library are sufficient to determine what is the instance of an object. For example, if the library contains the declaration of the model : Nat Order: Total Order[nat operators , then a term like sort.Nat Order( 2,4,1] is the call of the operator to sort the sequence [2,4,1] using the order . A shorter form of this call is sort[ 2,4,1] because the type checking inference rules of lpg allow to determine the sort of the model from the sort of the argument (sequence of nat) At last, if the model Nat Order is the unique model of the property Total Order for the ....

[Article contains additional citation context not shown here]

Didier Bert, Rachid Echahed, and Bjarte M. Østvold. Abstract rewriting. In Proceedings of the 3rd International Workshop on Static Analysis, WSA'93, number 724 in Lecture Notes in Computer Science, pages 178--192. Springer-Verlag, 1993.

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R. Bert, R. Echahed, and B.M. stvold. Abstract Rewriting. In Proc. Third Int'l Workshop on Static Analysis WSA'93, volume 724 of Lecture Notes in Computer Science, pages 178--192. Springer-Verlag, Berlin, 1993.

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