Results 1  10
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45
Systematic design of program analysis frameworks
 In 6th POPL
, 1979
"... Semantic analysis of programs is essential in optimizing compilers and program verification systems. It encompasses data flow analysis, data type determination, generation of approximate invariant ..."
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Cited by 765 (50 self)
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Semantic analysis of programs is essential in optimizing compilers and program verification systems. It encompasses data flow analysis, data type determination, generation of approximate invariant
Constructive Design of a Hierarchy of Semantics of a Transition System by Abstract Interpretation
, 2002
"... We construct a hierarchy of semantics by successive abstract interpretations. Starting from the maximal trace semantics of a transition system, we derive the bigstep semantics, termination and nontermination semantics, Plotkin’s natural, Smyth’s demoniac and Hoare’s angelic relational semantics and ..."
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Cited by 124 (19 self)
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We construct a hierarchy of semantics by successive abstract interpretations. Starting from the maximal trace semantics of a transition system, we derive the bigstep semantics, termination and nontermination semantics, Plotkin’s natural, Smyth’s demoniac and Hoare’s angelic relational semantics and equivalent nondeterministic denotational semantics (with alternative powerdomains to the EgliMilner and Smyth constructions), D. Scott’s deterministic denotational semantics, the generalized and Dijkstra’s conservative/liberal predicate transformer semantics, the generalized/total and Hoare’s partial correctness axiomatic semantics and the corresponding proof methods. All the semantics are presented in a uniform fixpoint form and the correspondences between these semantics are established through composable Galois connections, each semantics being formally calculated by abstract interpretation of a more concrete one using Kleene and/or Tarski
Constructive Versions Of Tarski's Fixed Point Theorems
 Pacific Journal of Mathematics
, 1979
"... this paper is to give a constructive proof of Tarski's theorem without using the continuity hypothesis. The set of fixed points of F is shown to be the image of L by preclosure operations defined by means of limits of stationary transfinite iteration sequences. Then the set of common fixed poin ..."
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Cited by 54 (8 self)
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this paper is to give a constructive proof of Tarski's theorem without using the continuity hypothesis. The set of fixed points of F is shown to be the image of L by preclosure operations defined by means of limits of stationary transfinite iteration sequences. Then the set of common fixed points of a family of commuting monotone operators on a complete lattice into itself is characterized in the same way. The advantage of characterizing fixed points by iterative schemes is that they lead to practical computation or approximation procedures. Also the definition of fixed points as limits of stationary iteration sequences allows the use of transfinite induction for proving properties of these fixed points
Complementation in abstract interpretation
, 1997
"... Reduced product of abstract domains is a rather wellknown operation for domain composition in abstract interpretation. In this article, we study its inverse operation, introducing a notion of domain complementation in abstract interpretation. Complementation provides a systematic way to design new ..."
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Cited by 42 (23 self)
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Reduced product of abstract domains is a rather wellknown operation for domain composition in abstract interpretation. In this article, we study its inverse operation, introducing a notion of domain complementation in abstract interpretation. Complementation provides a systematic way to design new abstract domains, and it allows to systematically decompose domains. Also, such an operation allows to simplify domain verification problems, and it yields spacesaving representations for complex domains. We show that the complement exists in most cases, and we apply complementation to three wellknown abstract domains, notably to Cousot and Cousot’s interval domain for integer variable analysis, to Cousot and Cousot’s domain for comportment
Generalized Semantics and Abstract Interpretation for Constraint Logic Programs
, 1995
"... We present a simple and powerful generalized algebraic semantics for constraint logic programs that is parameterized with respect to the underlying constraint system. The idea is to abstract away from standard semantic objects by focusing on the general properties of any possibly nonstandard ..."
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Cited by 41 (5 self)
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We present a simple and powerful generalized algebraic semantics for constraint logic programs that is parameterized with respect to the underlying constraint system. The idea is to abstract away from standard semantic objects by focusing on the general properties of any possibly nonstandard  semantic definition. In constraint logic programming, this corresponds to a suitable definition of the constraint system supporting the semantic definition. An algebraic structure is introduced to formalize the notion of a constraint system, thus making classical mathematical results applicable. Both topdown and bottomup semantics are considered. Nonstandard semantics for constraint logic programs can then be formally specified using the same techniques used to define standard semantics. Different nonstandard semantics for constraint logic languages can be specified in this ...
Optimal domains for disjunctive abstract interpretation
 Sci. Comput. Program
, 1998
"... In the context of standard abstract interpretation theory, we define the inverse operation to the disjunctive completion of abstract domains, introducing the notion of least disjunctive basis of an abstract domain D. This is the most abstract domain inducing the same disjunctive completion as D. We ..."
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Cited by 33 (21 self)
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In the context of standard abstract interpretation theory, we define the inverse operation to the disjunctive completion of abstract domains, introducing the notion of least disjunctive basis of an abstract domain D. This is the most abstract domain inducing the same disjunctive completion as D. We show that the least disjunctive basis exists in most cases, and study its properties, also in relation with reduced product and complementation of abstract domains. The resulting framework provides advanced algebraic methodologies for abstract domain manipulation and optimization. These notions are applied to wellknown abstract domains for static analysis of functional and logic programming languages.
SetSharing is Redundant for PairSharing
 Theoretical Computer Science
, 1997
"... . Although the usual goal of sharing analysis is to detect which pairs of variables share, the standard choice for sharing analysis is a domain that characterizes setsharing. In this paper, we question, apparently for the first time, whether this domain is overcomplex for pairsharing analysis. We ..."
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Cited by 29 (12 self)
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. Although the usual goal of sharing analysis is to detect which pairs of variables share, the standard choice for sharing analysis is a domain that characterizes setsharing. In this paper, we question, apparently for the first time, whether this domain is overcomplex for pairsharing analysis. We show that the answer is yes. By defining an equivalence relation over the setsharing domain we obtain a simpler domain, reducing the complexity of the abstract unification procedure. We present preliminary experimental results, showing that, in practice, our domain compares favorably with the setsharing one over a wide range of benchmark programs. 1 Introduction In logic programming, a knowledge of sharing between variables is important for optimizations such as the exploitation of parallelism. Today, talking about sharing analysis for logic programs is almost the same as talking about the setsharing domain Sharing of Jacobs and Langen [11,12]. The adequacy of this domain is not norma...
The Reduced Relative Power Operation on Abstract Domains
 Theor. Comput. Sci
, 1999
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Functional Dependencies and MooreSet Completions of Abstract . . .
 Proc. of the 1995 Internat. Logic Programming Symp. (ILPS '95
, 1995
"... Interpretations and Semantics Roberto Giacobazzi Dipartimento di Informatica Universit`a di Pisa Corso Italia 40, 56125 Pisa, Italy giaco@di.unipi.it Francesco Ranzato Dipartimento di Matematica Pura ed Applicata Universit`a di Padova Via Belzoni 7, 35131 Padova, Italy franz@hilbert.math.unipd. ..."
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Cited by 19 (10 self)
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Interpretations and Semantics Roberto Giacobazzi Dipartimento di Informatica Universit`a di Pisa Corso Italia 40, 56125 Pisa, Italy giaco@di.unipi.it Francesco Ranzato Dipartimento di Matematica Pura ed Applicata Universit`a di Padova Via Belzoni 7, 35131 Padova, Italy franz@hilbert.math.unipd.it Abstract We introduce the notion of functional dependencies of abstract interpretations relatively to a binary operator of composition. Functional dependencies are obtained by a functional composition of abstract domains, and provide a systematic approach to construct new abstract domains. In particular, we study the case of autodependencies, namely monotone operators on a given abstract domain. Under suitable hypotheses, this corresponds to a Mooreset completion of the abstract domain, providing a compact latticetheoretic representation for dependencies. We prove that the abstract domain Def for grounddependency analysis of logic programs can be systematically derived by autodepende...
Completeness in Abstract Interpretation: A Domain Perspective. Pages 231–245 of: M. Johnson (ed
 Proc. 6th International Conference on Algebraic Methodology and Software Technology (AMAST’97). Lecture Notes in Computer Science
, 1997
"... Abstract. Completeness in abstract interpretation is an ideal and rare situation where the abstract semantics is able to take full advantage of the power of representation of the underlying abstract domain. In this paper, we develop an algebraic theory of completeness in abstract interpretation. We ..."
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Cited by 16 (4 self)
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Abstract. Completeness in abstract interpretation is an ideal and rare situation where the abstract semantics is able to take full advantage of the power of representation of the underlying abstract domain. In this paper, we develop an algebraic theory of completeness in abstract interpretation. We show that completeness is an abstract domain property and we prove that there always exist both the greatest complete restriction and the least complete extension of any abstract domain, with respect to continuous semantic functions. Under certain hypotheses, a constructive procedure for computing these complete domains is given. These methodologies provide advanced algebraic tools for manipulating abstract interpretations, which can be fruitfully used both in program analysis and in semantics design. 1