B. Le Charlier, K. Musumbu, P. Van Hentenryck, A generic abstract interpretation algorithm and its complexity analysis (extended abstract). 8th Internat. Conf. on Logic Programming (ICLP-91), Paris (France), June 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....[14] An abstract unification algorithm is defined which, in turn, describes an abstract analog of unify. Once an abstract unify operator is specified and proved safe, a complete and correct abstract interpreter is practically defined by virtue of existing abstract interpretation frameworks [2, 18, 24]. Correctness is also proved. For reasons of brevity and continuity, however, the proofs are relegated to an appendix, section 7. Finally, sections 5 and 6 present the related work and the concluding discussion. 2 Notation and preliminaries To introduce the analysis some notation and preliminary ....

....3.1. is a poset. The poset has a top element = hffl ; cod(ffl ) i and a bottom element = hfail; i since fl ) Sub and fl ) The bottom element is meaningful and, in fact, represents goal failure. Specifically, in a top down abstract interpretation framework [2, 18, 24], it is possible for a goal to fail if it is called with some abstract substitutions. Returning for the success abstract substitution indicates that the goal can never be satisfied under any calling substitution which the calling abstract substitution abstracts. For the purposes of abstract ....

B. Le Charlier, K. Musumbu, and P. Van Hentenryck. A generic abstract interpretation algorithm and its complexity. In ICLP'91, pages 64--78. MIT Press, 1991.

....algorithm is precisely and succinctly defined which, in turn, describes an abstract analog of unify. Once an abstract unify operator is specified and proved safe, a complete and correct abstract interpreter is practically defined by virtue of existing abstract interpretation frameworks [1, 17, 21]. Finally, sections 5 and 6 present the related work and the concluding discussion. For reasons of brevity and continuity, proofs are not included in the paper, but can be found in [15] 2 Notation and preliminaries To introduce the analysis some notation and preliminary definitions are ....

B. Le Charlier, K. Musumbu, and P. Van Hentenryck. A generic abstract interpretation algorithm and its complexity. In ICLP'91, pages 64--78. MIT Press, 1991.

.... a variant of Cousot and Cousot s chaotic iteration [2] and uses neededness (or dependency) information to guide the fixpoint iteration, as for instance in Kildall s early algorithm [11] The neededness analysis is as in the algorithms proposed by Muthukumar and Hermenegildo [6] and Le Charlier [9], with the main difference being that our neededness analysis is of a more shallow nature, and that our approach is more iterative and less recursive. The complexity result implies that the worst case number of iterations per equation is independent of the total number of equations in the ....

.... analysis (with the aim of reducing the number of times that each element in the relevant sub domain is evaluated) In the context of analysis of logic programs, algorithms along these lines have been proposed by Muthukumar and Hermenegildo [6] and Le Charlier, Musumbu, and Van Hentenryck [9], the latter algorithm having been shown to be optimal for certain classes of programs and perform very well in practice [10] The algorithm presented in this paper originates from an algorithm described in [5] for analysis of Prolog programs. The algorithm is similar to the one proposed in [9] in ....

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B. Le Charlier, K. Musumbu, P. Van Hentenryck. A generic abstract interpretation algorithm and its complexity analysis. , 1991, pp. 64--78.

....Tabulation allows abstracting the AND OR tree, representing the concrete collecting semantics, by an AND OR graph. In practice, however, abstract interpretation systems such as PLAI [Muthukumar and Hermenegildo 1990; 1992] and GAIA [Englebert et al. 1992; Le Charlier and Van Hentenryck 1994; Le Charlier et al. 1991] are based on a variant of the above tabulation technique, where the stored key is not hb 1 ; b n ; c 1 i. Instead, with ha; G ; ci as the preceding state, ha; 9 Gammavars(a) ci is stored as key and 9 Gammavars(a) a = h c out ) as answer for an atom a if h2 ae ; c out i has occurred ....

....1996. 580 Delta M. Garc ia de la Banda et al. The relevant information about the analysis (the atoms with their abstract entry and exit constraint) are all collected in Table. Abstract interpretation systems such as PLAI [Muthukumar and Hermenegildo 1990; 1992] GAIA [Englebert et al. 1992; Le Charlier et al. 1991] and AMAI [Janssens et al. 1995] do not construct the AND OR graph explicitly. The systems use a more compact dependency structure which is sufficient to control the order of the transitions to be performed on the implicit AND OR graph. Major difference among the systems is in the way they ....

Le Charlier, B., Musumbu, K., and Van Hentenryck, P. 1991. A generic abstract interpretation algorithm and its complexity analysis (extended abstract). In Proceedings of the 8th International Conference on Logic Programming, K. Furukawa, Ed. MIT Press, Cambridge, Mass., 64--78.

....even though the changes that triggered a new iteration do not a#ect it. One solution to remedy this situation consists of maintaining dependencies so that when a change occurs, only those abstract functions a#ected by the change are reanalyzed. Another problem discussed in the literature (e.g. [Charlier, Musumbu, and Hentenryck 1991]) has to do with the way the control flow of the analyzed program is traversed by the analysis. Some traversal strategies cause abstract functions to be analyzed more times than necessary. For example, traversing a control flow graph depth first as opposed to breadth first can a#ect the rate at ....

....then use this information to accelerate the convergence of the fixpoint process. For example, subsets of abstract functions derived from strongly connected components of the control flow graph can be solved individually. Strategies for first order programs are presented in the literature (e.g. [Charlier, Musumbu, and Hentenryck 1991]) However, when the analyzed program is higher order, only an approximation of the call graph can be computed. More importantly, the call graph analysis itself requires a fixpoint process. Consequently, exploiting call graph information to accelerate the fixpoint process requires an analysis for ....

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Charlier, B. L., Musumbu, K., and Hentenryck, P. V. 1991. A generic abstract interpretation algorithm and its complexity analysis. In K. Furukawa (Ed.), Proceedings of the Eighth International Conference on Logic Programming, Paris, France, pp. 64--78. MIT Press, Cambridge, Massachusetts.

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B. Le Charlier, K. Musumbu, P. Van Hentenryck, A generic abstract interpretation algorithm and its complexity analysis (extended abstract). 8th Internat. Conf. on Logic Programming (ICLP-91), Paris (France), June 1991.

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B. Le Charlier, K. Musumbu and P. Van Hentenryck, `A generic abstract interpretation algorithm and its complexity analysis (extended abstract)', Eighth International Conference on Logic Programming (ICLP-91), Paris, France, June 1991.

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