R. Giacobazzi and F. Scozzari. A logical model for relational abstract domains. ACM Trans. Program. Lang. Syst., 20(5), 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....into the induced magic framework by using an explicit redo list storing those call and answer patterns which have changed, thereby de ning the clauses which need to be reevaluated. The goal independent analyser is based on semi na ve iteration. Neither of these analysers has exploited condensing [16, 21]. 6 Experimental Evaluation To assess the feasibility of multiheaded clauses as a representation of positive Boolean functions, the Pos based groundness analysers were tested on a large benchmark suite. BDD representations of Boolean functions have been popular for the implementation of ....

R. Giacobazzi and F. Scozzari. A Logical Model for Relational Abstract Domains. ACM Transactions on Programming Languages and Systems, 20(5):1067{ 1109, 1998.

....deriving the most general call pattern # for which i is satisfied and thus the optimisation is safe. Every call pattern # for which # automatically satisfies (1) In the context of Pos this means computing the pseudo complement of # i w.r.t. i which corresponds to the logical implication [2]: # m def = # i i . Def does not have a pseudo complement in general, so in that case approximation may be needed. In general these pseudocomplements involve any variable of the predicate, while we are only interested in information regarding the variables occurring in the head of the ....

....which illustrates how the precision of the domain can influence the obtained results. We limit this currently to complete lattices. This is a generalisation of the definition of a pseudo complement, which is specifically defined in terms of the greatest lower bound of the domain [2]. 4 Conclusion Collecting information about possible optimisations within a program before actually generating code supporting the optimisations is, in our view, an essential step for a better understanding of which versions need to be generated to obtain better global optimisation results. Here ....

R. Giacobazzi and F. Scozzari. A logical model for relational abstract domains. ACM Transactions on Programming Languages and Systems, 20(5):1067--1109, 1998.

....the clause from right to left has already propagated a condition e b at the point b . Then, to insure that e b will hold after the success of q, it suces to require at a the conjunction of q with the weakest condition such that ( q ) e b . This is precisely the pseudo complement [10] of q with respect to e b which for Pos is obtained as q e b . So propagating one step to the left gives the condition e a = q ( q b ) Now consider a clause h( x) b 1 ; b n with an assertion 2 Pos. Denote the current approximation of the precondition for b i by i ....

R. Giacobazzi and F. Scozzari. A logical model for relational abstract domains. ACM Transactions on Programming Languages and Systems, 20(5):1067-1109, 1998.

....the clause from right to left has already propagated a condition b at the point b . Then, to insure that b will hold after the success of q, it suces to require at a the conjunction of q with the weakest condition such that ( q ) b . This is precisely the pseudo complement [10] of q with respect to b , obtained as q b . So propagating one step to the left gives the condition a = q ( q b ) Now consider a clause h( x) b 1 ; b n with an assertion 2 Pos at the left of the body. Assume that the current approximation for the precondition of ....

R. Giacobazzi and F. Scozzari. A logical model for relational abstract domains. ACM Transactions on Programming Languages and Systems, 20(5):1067-1109, 1998.

....to be bound to some variable in a given program point. Freeness analysis is useful for optimising uni cation, for goal reordering and for avoiding type checking. It is well known that performing sharing and freeness analysis in conjunction improves the precision of both [14; 19] Linear re nement [11] is a technique for systematically constructing abstract domains for program analysis. Given a basic abstract domain representing just the property of interest and a concrete operation (which, as we are analysing logic programs, is usually uni cation) the new more re ned domain is constructed. The ....

R. Giacobazzi and F. Scozzari. A Logical Model for Relational Abstract Domains. ACM Transactions on Programming Languages and Systems, 20(5):1067-1109, 1998.

....safe with respect to the concrete operations. We illustrate how the domain may be used in a practical analysis by means of a small example. Keywords: Abstract interpretation, abstract domain, linear re nement, static analysis, freeness analysis, logic programming. 1 Introduction Linear re nement [13] is a technique for systematically constructing abstract domains for program analysis. Given a basic abstract domain representing just the property of interest together with an appropriate concrete operation (which, as we are analysing logic programs, is usually uni cation) the new more re ned ....

R. Giacobazzi and F. Scozzari. A Logical Model for Relational Abstract Domains. ACM Transactions on Programming Languages and Systems, 20(5):1067-1109, 1998.

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R. Giacobazzi and F. Scozzari. A logical model for relational abstract domains. ACM Trans. Program. Lang. Syst., 20(5):1067-1109, 1998.

....the reduced power operation [9] for abstract domain refinement as the basic operation able to include input output relations in domains. The reduced power operation has been proved to give the necessary structure of abstract domains in order to model relational properties of program behavior [10, 21, 24, 28]. A similar structure can be included in semantics as well. If [ P 1 ] and [ P 2 ] are the semantics of program components P1 and P2 , and # is a syntactic operator for program composition, then the semantics [ is compositional if there exists an operation # such that: P 1 # P2 ] ....

....(HPR) can be formulated in terms of intuitionistic implication on the complete Heyting algebra constructed on dependency graphs. On the other side the reduced relative power operation exploits linear implications on a given quantale [20] which is a generalization of complete Heyting algebras [21, 27]. The analogy and the relation between these two constructions deserves further research. 10. ....

Giacobazzi, R., and Scozzari, F. A logical model for relational abstract domains. ACM Trans. Program. Lang. Syst. 20, 5 (1998), 1067--1109.

....2 3. 3 Heyting completion Heyting completion [17] is a refinement operator which has been recently introduced to logically interpret the Cousot and Cousot s reduced cardinal power refinement [7] In this section we recall the definition and some basic results on Heyting completion refinement from [17,18]. The aim of this refinement is to enhance domains to represent relational information. The idea is to enrich an abstract domain by adding all the relative pseudo complements (intuitionistic implications) built from every pair of elements in the given domain. From a logical point of view, the new ....

.... Psi Gamma A v A. We recall some basic algebraic properties of Heyting completion with respect to other domain operations. In particular, we consider reduced product (u) and disjunctive completion ( b ) of abstract domains. In the following of the paper, A; B; C 2 Moore(L) Proposition 3 ([18]) Let L be a cHa. 1) A Psi Gamma (B u C) A Psi Gamma B) u (A Psi Gamma C) 2) A u B) Psi Gamma C = A Psi Gamma (B Psi Gamma C) 3) b (A) Psi Gamma B = A Psi Gamma B if A is finite. The main feature of Heyting completion is the reduction of the ....

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R. Giacobazzi and F. Scozzari. A logical model for relational abstract domains. ACM Transactions on Programming Languages and Systems, 20(5):1067--1109, 1998.

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R. Giacobazzi and F. Scozzari. A logical model for relational abstract domains. ACM Trans. Program. Lang. Syst., 20(5), 1998.

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R. Giacobazzi and F. Scozzari. A Logical Model for Relational Abstract Domains. ACM Transactions on Programming Languages and Systems, 20(5):1067-1109, 1998.

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R. Giacobazzi and F. Scozzari. A logical model for relational abstract domains. ACM Transactions on Programming Languages and Systems, 20(5):1067--1109, 1998.

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R. Giacobazzi and F. Scozzari. A logical model for relational abstract domains. ACM Transactions on Programming Languages and Systems, 20(5):1067-1109, 1998.

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