R. Giacobazzi and F. Ranzato. Functional dependencies and Moore-set completions of abstract interpretations and semantics. In Proc. ILPS '95 , pp. 321-335, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....intention is to use the existing (abstract interpretation based) analyses for pure functional and logic programming in our integrated framework. The explicit semantic connections between the basic paradigms allow us to combine those analyses by using the existing tools to combine abstract domains [GR95]. Particularly interesting, as a subject of future work, is the possibility of giving a logic interpretation to these domain combinations [GS97, GS98] 37 ....

R. Giacobazzi and F. Ranzato. Functional Dependencies and Moore-Set Completions of Abstract Interpretations and Semantics. In J.W. Lloyd, editor, Proc. of the 1995 International Symposium on Logic Programming, pages 321-335, The MIT Press, Cambridge, MA, 1995.

....6 and 7 contain, respectively, the applications in logic program analysis and semantics. Finally, Section 8 discusses related work, while Section 9 concludes. The Appendix contains the technical proofs of some results of Section 7. A preliminary account of parts of this paper has been presented in [35]. 2 Preliminaries Throughout the paper we will assume familiarity with the standard notions of lattice theory (see e.g. 7, 39] abstract interpretation ( 19, 20] and logic programming (see e.g. 3, 45] In this section, we briefly introduce some notation and recall some well known notions. ....

R. Giacobazzi and F. Ranzato. Functional dependencies and Moore-set completions of abstract interpretations and semantics. In J. Lloyd, editor, Proc. of the 1995 Internat. Logic Programming Symp. (ILPS '95 ), pages 321--335. The MIT Press, Cambridge, Mass., 1995.

....of the underlying abstract domain, although they claim that abstract interpretation does not offer a systematic approach to accomplish this task. We believe that all the works on systematic domain refinement in abstract interpretation, e.g. Cousot and Cousot 1979b, 1992a, 1994; Fil e et al. 1996; Giacobazzi and Ranzato 1995, 1997, 1998; Giacobazzi and Scozzari 1997] and in particular the present work on refinements for achieving completeness, can be extremely helpful to both specify optimal abstract models strongly preserving a given property of interest and to tune the accuracy and cost in abstract interpretation ....

Giacobazzi, R. and Ranzato, F. 1995. Functional dependencies and Moore-set completions of abstract interpretations and semantics. In Proc. of the 1995 Internat. Logic Programming Symp. (ILPS '95 ), J. Lloyd, Ed. The MIT Press, Cambridge, Mass., 321--335.

....intention is to use the existing (abstract interpretation based) analyses for pure functional and logic programming in our integrated framework. The explicit semantic connections between the basic paradigms allow us to combine those analyses by using the existing tools to combine abstract domains [GR95]. Particularly interesting, as a subject of future work, is the possibility of giving a logic interpretation to these domain combinations [GS97, GS98] ....

R. Giacobazzi and F. Ranzato. Functional Dependencies and Moore-Set Completions of Abstract Interpretations and Semantics. In J.W. Lloyd, editor, Proc. of the 1995 International Symposium on Logic Programming, ILPS'95, pages 321-335, The MIT Press, Cambridge, MA, 1995.

....work up to isomorphism. Our idea is to concentrate exclusively on the property of groundness. We reconstruct the domain Pos in a systematic way and show that it is possible to avoid ad hoc characterizations in the construction process of domains. A first example in this direction is shown in [14], where the abstract domain Def has been reconstructed as the space of monotone functions between elements in G. Our work is based on the Heyting completion refinement operator [17] The first use of this operator has been presented in [17] where Heyting completion is used to construct the ....

....space of monotone functions between elements in G. Our work is based on the Heyting completion refinement operator [17] The first use of this operator has been presented in [17] where Heyting completion is used to construct the abstract domain Def , by exploiting the characterization given in [14]. An attempt of building the domain Pos starting from the disjunctive completion of G is shown in [17] Even in this case, the construction does not directly come from the basic property of groundness, but from a domain more complex than G. Moreover, no property of optimality has been taken into ....

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R. Giacobazzi and F. Ranzato. Functional dependencies and Moore-set completions of abstract interpretations and semantics. In J. Lloyd, editor, Proc. 1995 Int'l Symposium on Logic Programming (ILPS'95), pages 321--335. The MIT Press, 1995.

....of more concrete observables, i.e. refinement operators (see [23] for a recent survey) Examples of refinement operators are reduced product, disjunctive completion, functional dependencies and Heyting completion. The above mentioned examples can be handled by these techniques. In particular [31] shows that the resultants semantics can be obtained by refining the domain of the s semantics by functional dependencies, while [32, 39] reconstruct POS from the groundness observable by Heyting completion. Within our framework, one can handle the problem of establishing general results about ....

R. Giacobazzi and F. Ranzato. Functional dependencies and Moore-set completions of abstract interpretations and semantics. In J. Lloyd, editor, Proceedings of the 1995 Interantional Symposium on Logic Programming (ILPS'95), pages 321--335. The MIT Press, 1995.

....domains. Designing an analysis by abstract interpretation is a complex process. The quest for simplifying this process has resulted in systematic methods for constructing abstract domains and program analyses [8, 1, 11] These methods construct abstract domains and program analyses by composition [4, 8, 12, 14, 17] and decomposition [6, 13] One important way to compose abstract domains is the reduced product approach [8] The reduced product of two abstract domains captures information represented by the two component abstract domains without redundancy. The reduced product approach has been used to design ....

R. Giacobazzi and F. Ranzato. Functional dependencies and Moore-set completions of abstract interpretations and semantics. In J. Lloyd, editor, Proceedings of the 1995 International Symposium on Logic Programming, pages 321--335. The MIT Press, 1995.

....Designing an analysis by abstract interpretation is a complex process. The quest for simplifying this process has resulted in systematic methods for constructing abstract domains and program analyses [6, 2, 8] These methods construct abstract domains and program analyses by composition [1, 6, 9, 11, 12] and decomposition [5, 10] One important way to compose abstract domains is the reduced product approach [6] The reduced product of two abstract domains captures information represented by the two component abstract domains without redundancy. The reduced product approach has been used to design ....

R. Giacobazzi and F. Ranzato. Functional dependencies and moore-set completions of abstract interpretations and semantics. In J. Lloyd, editor, Proceedings of the 1995 International Symposium on Logic Programming, pages 321--335. The MIT Press, 1995.

....independent analysis, the operator of functional dependencies provides a systematic approach to build new abstract domains, which has been first exploited in [8] as domain for attribute dependent analyses. In [8] it was essentially the domain of monotonic functions between two abstract domains. In [15] this definition was extended by introducing a concrete binary operator which encodes the data dependencies between two different abstract interpretations and some applications to logic programs as been shown. Let us first recall the definition of functional dependencies operator [15] adapted to ....

....domains. In [15] this definition was extended by introducing a concrete binary operator which encodes the data dependencies between two different abstract interpretations and some applications to logic programs as been shown. Let us first recall the definition of functional dependencies operator [15], adapted to our formalization by means of upper closure operators. Definition 2.5 (Functional dependencies operator) Let ae 1 and ae 2 be two uco s over the complete lattice C and fi be a left additive binary operator over C. Then, we define (ae 1 fi ae 2 ) x) G fx 0 2 C j 8y 2 ae 1 ....

[Article contains additional citation context not shown here]

R. Giacobazzi and F. Ranzato. Functional dependencies and moore-set completions of abstract interpretations and semantics. In J. Lloyd, editor, Proc. 1995 Int'l Symposium on Logic Programming (ILPS'95), pages 321--335, Portland, OR, 1995. The MIT Press.

....concrete ones by abstraction. As observed in [14] among these methods, the operations for abstract domain refinement and their inverses, like reduced product ( 7] complementation ( 5] disjunctive completion ( 7] least disjunctive basis ( 20] and reduced power for functional dependencies ([7, 19]) may play a central role in semantics design, as well as in analysis, in order to provide formal algebraic methods to manipulate and compare semantics. In this work, we show how reduced product , and its inverse operation which is complementation, can be used to study the semantics of ....

....programming language enjoying a simple semantic definition. Due to its semantic simplicity, logic programming is probably the programming language where the abstract interpretation based approach to semantics design was mostly successful, as shown by the increasing literature in this field (cf. [3, 4, 17, 19]) Our approach gives rise to a hierarchy of declarative semantics for logic programs where semantics, and the corresponding observable properties, can be manipulated algebraically by complementation and reduced product. After some results in Section 4 on complementation and reduced product in ....

R. Giacobazzi and F. Ranzato. Functional dependencies and Moore-set completions of abstract interpretations and semantics. In Proc. ILPS '95 , pp. 321-335, 1995.

....Different frameworks for abductive analysis can be defined by modifying abductive logic programming (e.g. 27] to cope with abstract interpretation. This may provide an interesting alternative approach for abductive analysis by abstract compilation ( 24] In a recent work, Giacobazzi and Ranzato [22] proved that most well known compositional semantics for logic programs, like the semantics in [5] can be obtained systematically by abstraction from a given operational semantics of logic programs. The idea is that any semantics of logc programs (and more in general of a programming language, ....

....that any semantics of logc programs (and more in general of a programming language, see [13] can be viewed as an abstraction of a fixed, more concrete, operational semantics which is basically SLD resolution (e.g. see [20] Therefore, composing abstractions corresponds to compose semantics. In [22] the authors proved that compositionality for logic program semantics can be systematically achieved by composing, by a suitable functional combination operator, the abstractions corresponding to more abstract, possibly non compositional semantics. The resulting framework is powerful enough to ....

R. Giacobazzi and F. Ranzato. Functional dependencies and Moore-set completions of abstract interpretations and semantics. In J. Lloyd, editor, Proceedings of the 1995.

....logic: for example, Chen s treatment of modules [5] is based on secondorder logic, while Miller s [29] uses implication goals in clause bodies. In [12] Comini et al. define 11 a taxonomy of semantics that can be derived by abstracting SLD trees, and preserve properties like compositionality. In [23], the authors introduce an operation for functional combination of semantics, providing a systematic way to derive compositional semantics for logic programs. In these works, the semantics appear to be somewhat more complicated than that considered in [3] and we conjecture that a formal treatment ....

R. Giacobazzi and F. Ranzato. Functional dependencies and Moore-set completions of abstract interpretations and semantics. In J. Lloyd, editor, Proceedings of the 1995 International Logic Programming Symposium (ILPS '95), pages 321--335. The MIT Press, 1995. 13

....Different frameworks for abductive analysis can be defined by modifying abductive logic programming (e.g. 26] to cope with abstract interpretation. This may provide an interesting alternative approach for abductive analysis by abstract compilation ( 23] In a recent work, Giacobazzi and Ranzato [21] proved that most abstract domains for analysis and most compositional semantics for logic programs can be obtained by functional composition of more simple domains or semantics. The resulting framework is powerful enough to encode well known compositional semantics for logic programming as ....

R. Giacobazzi, and F. Ranzato. Functional dependencies and Moore-set completions of abstract interpretations and semantics. To appear in J. Lloyd, editor, Proc. of the 12nd International Logic Programming Symposium, ILPS '95. The MIT Press, Cambridge, Mass., 1995. URL http://www.di.unipi.it/giaco/papers.html.

....Different frameworks for abductive analysis can be defined by modifying abductive logic programming (e.g. 27] to cope with abstract interpretation. This may provide an interesting alternative approach for abductive analysis by abstract compilation ( 24] In a recent work, Giacobazzi and Ranzato [22] proved that most well known compositional semantics for logic programs, like the semantics in [5] can be obtained systematically by abstraction from a given operational semantics of logic programs. The idea is that any semantics of logc programs (and more in general of a programming language, ....

....that any semantics of logc programs (and more in general of a programming language, see [13] can be viewed as an abstraction of a fixed, more concrete, operational semantics which is basically SLD resolution (e.g. see [20] Therefore, composing abstractions corresponds to compose semantics. In [22] the authors proved that compositionality for logic program semantics can be systematically achieved by composing, by a suitable functional combination operator, the abstractions corresponding to more abstract, possibly non compositional semantics. The resulting framework is powerful enough to ....

R. Giacobazzi and F. Ranzato. Functional dependencies and Moore-set completions of abstract interpretations and semantics. In J. Lloyd, editor, Proceedings of the 1995 International Logic Programming Symposium (ILPS '95), pages 321--335. The MIT Press, 1995.

.... programming is probably the programming paradigm where abstract interpretation ideas have been mostly successful in the study of semantics, as the growing literature on this topic shows (e.g. see [Amato and Levi 1997; Comini and Levi 1994; Comini et al. 1995; Fages and Gori 1996; Giacobazzi 1996; Giacobazzi and Ranzato 1995, 1996] and therefore our results well fit along this trend. Order Theoretic Foundations of Abstract Domain Refinements. The idea of domain refinement is recurrent in abstract interpretation. Relevant examples include the disjunctive completion [Cousot and Cousot 1979, 1994; Fil e and Ranzato ....

Giacobazzi, R. and Ranzato, F. 1995. Functional dependencies and Moore-set completions of abstract interpretations and semantics. In Proceedings of the 1995 International Symposium on Logic Programming (ILPS '95 ), J. Lloyd, Ed. The MIT Press, Cambridge, Mass., 321--335.

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