M. Alpuente, M. Falaschi, and G. Vidal. A Compositional Semantic Basis for the Analysis of Equational Horn Programs. Theoretical Computer Science, 165(1):97-- 131, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....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, ....

M. Alpuente, M. Falaschi, and G. Vidal. A Compositional Semantic Basis for the Analysis of Equational Horn Programs. Theoretical Computer Science, 165(1):97131, 1996.

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M. Alpuente, M. Falaschi, and G. Vidal. A Compositional Semantic Basis for the Analysis of Equational Horn Programs. Theoretical Computer Science, 165(1):97-- 131, 1996.

.... 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 abstract success set semantics can also be systematically derived from the concrete one, by replacing the considered narrowing ....

.... consequence , which approximates T , and the corresponding abstract fixpoint semantics, # (R) An abstract success set semantics can also be systematically derived from the concrete one, by replacing the considered narrowing calculus by a corresponding abstract version, see e.g. [8]. In the following, we denote the abstract analog of a concrete object O by O . The abstract methodology in this section generalizes the results in [2] by making them parametric w.r.t. # = inn, out. 5.1 Abstract Programs and Operators A description is the association of an abstract domain ....

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M. Alpuente, M. Falaschi, and G. Vidal. A Compositional Semantic Basis for the Analysis of Equational Horn Programs. Theoretical Computer Science, 165(1):97--131, 1996. 28

.... 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 ca(T) An abstract success set semantics (D can also be systematically derived from the concrete one, by replacing the ....

.... quence operator Ti , which approximates T, and the corresponding abstract fixpoint semantics, Ci(T) and ca(T) An abstract success set semantics (D can also be systematically derived from the concrete one, by replacing the considered narrowing calculus by a corresponding abstract version, see e.g. [7]. In the following, we denote the abstract analog of a concrete object O by O. The abstract methodology in this section generalizes the results in [2] by making them parametric w.r.t. inn, out. 5.1 Abstract Programs and Operators A description is the association of an abstract domain (D, ....

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M. Alpuente, M. Falaschi, and G. Vidal. A Compositional Semantic Basis for the Analysis of Equational Horn Programs. Theoretical Computer Science, 165(1):97-131, 1996.

....It transforms the rules of the program and the speci cation of the equa( equa(s 1 ; t 1 ) equa(s n ; t n ) to one internal predicate. It determines the list of equations. astrae.pl: It generates a correct approximation of the program speci cation in the style described in [3]. narrowing.pl: Implementation of the narrower, it de nes both the concrete and the abstract immediate consequences operators. 8 fix.pl: It computes the xpoint of the immediate consequences operators and it visualizes the overapproximation and underapproximation. correttore.pl: It nds ....

M. Alpuente, M. Falaschi, and G. Vidal. A Compositional Semantic Basis for the Analysis of Equational Horn Programs. Theoretical Computer Science, 165(1):97-131, 1996.

.... 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 semantics F ] R) and F ca] R) In the following, we denote the abstract analog of a concrete object O by O ] 5.1 ....

....are introduced for the purpose of describing the computed answer substitutions for a given goal. The domains for equations and substitutions are based in a notion of the abstract Herbrand universe H ] V = V [ f]g) which introduces an irreducible symbol ] such that ] 62 (see [1, 3, 4]. Our analysis is based on a form of simpli ed (abstract) program which always terminates and in which the query can be executed eciently. Our notion of abstract program is parametric with respect to a loop check. Two di erent instances can be found in [3, 4] De nition 10. A loop check is a ....

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M. Alpuente, M. Falaschi, and G. Vidal. A Compositional Semantic Basis for the Analysis of Equational Horn Programs. Theoretical Computer Science, 165(1):97-131, 1996.

....uni cation algorithm has been proven in [2] Our analysis is based on a form of simpli ed (abstract) program which always terminates and in which the query can be executed eciently. Our notion of abstract program is parametric with respect to a loop check. Two di erent instances can be found in [2, 3]. De nition 14. A loop check is a graph GR associated with a program R, i.e. a relation consisting of a set of pairs of terms, such that: 1) the transitive closure G R is decidable and (2) Let t = t 0 be a function which assigns to a term t some node t 0 in GR . If there is an in nite ....

M. Alpuente, M. Falaschi, and G. Vidal. A Compositional Semantic Basis for the Analysis of Equational Horn Programs. Theoretical Computer Science, 165(1):97-131, 1996.

....from the answers computed independently by its flat constituents, i.e. f(x) a and g(y) x. This essentially corresponds to a kind of formulation of the compositionality property of the semantics. Unfortunately, this property does not hold in general for unrestricted (conditional) narrowing [AFV96, Vid96] as opposed to the case of SLD resolution, which is compositional with respect to the AND operator. As a consequence, the (generalized) closedness does not suffice for completeness under the conditions required for the completeness of unrestricted conditional narrowing, as illustrated by ....

....closedness condition. The following results show that there exists a close connection between the completeness of basic narrowing and the completeness of the PE transformation based on unrestricted narrowing. Basic conditional narrowing was proven to be AND compositional whenever it is complete [AFV96] This suggests to us the requirements that ensure the completeness of the PE transformation. Note that here we give a direct proof which does not require the compositionality results in Alpuente et al. AFV96] Basic (conditional) narrowing is a restricted form of (conditional) narrowing where ....

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M. Alpuente, M. Falaschi, and G. Vidal. A compositional semantic basis for the analysis of equational Horn programs. Theoretical Computer Science, 165(1):97--131, 1996.

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M. Alpuente, M. Falaschi, and G. Vidal. A Compositional Semantic Basis for the Analysis of Equational Horn Programs. Theoretical Computer Science, 165(1):97-131, 1996.

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