Abstract interpretation of algebraic polynomial systems (Extended abstract)

Cousot, Patrick; Cousot, Radhia

doi:10.1007/bfb0000468

Cited by 9 publications

(2 citation statements)

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“…In static program analysis, decidability issues commonly force to sacrifice completeness for achieving termination and/or efficiency; examples of complete abstract interpretations more frequently occur in other fields of application. For instance, several complete abstractions of algebraic polynomial systems have been studied by Cousot and Cousot [1997], and many complete abstract interpretations can be found in comparative program semantics [Cousot 1997;Cousot and Cousot 1992;Giacobazzi 1996] and in model checking by abstract interpretation [Cousot and Cousot 2000;Ranzato 2001].…”

Section: The Main Resultsmentioning

confidence: 99%

Making abstract domains condensing

Giacobazzi

Ranzato

Scozzari

2005

ACM Trans. Comput. Logic

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In this paper we show that reversible analysis of logic languages by abstract interpretation can be performed without loss of precision by systematically refining abstract domains. The idea is to include semantic structures into abstract domains in such a way that the refined abstract domain becomes rich enough to allow approximate bottom-up and top-down semantics to agree. These domains are known as condensing abstract domains. Substantially, an abstract domain is condensing if goal-driven and goal-independent analyses agree, namely no loss of precision is introduced by approximating queries in a goal-independent analysis. We prove that condensation is an abstract domain property and that the problem of making an abstract domain condensing boils down to the problem of making the domain complete with respect to unification. In a general abstract interpretation setting we show that when concrete domains and operations give rise to quantales, i.e. models of propositional linear logic, objects in a complete refined abstract domain can be explicitly characterized by linear logic-based formulations. This is the case for abstract domains for logic program analysis approximating computed answer substitutions where unification plays the role of multiplicative conjunction in a quantale of idempotent substitutions. Condensing abstract domains can therefore be systematically derived by minimally extending any, generally non-condensing domain, by a simple domain refinement operator.

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Section: The Main Resultsmentioning

confidence: 99%

Making abstract domains condensing

Giacobazzi

Ranzato

Scozzari

2005

ACM Trans. Comput. Logic

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“…A relation can be isomorphically encoded as a set-valued function by a Galois connection: Subset Abstraction [17]:. Given a set C and a strict subset A ⊂ C hereof, the restriction to the subset induces a Galois connection: A(n upper) closure operator ρ is map ρ : S → S on a poset S; ⊑ , that is (a) monotone: (for all s, s ′ ∈ S : s ⊑ s ′ =⇒ ρ(s) ⊑ ρ(s ′ )), (b) extensive (for all s ∈ S : s ⊑ ρ(s)), and (c) idempotent, (for all s ∈ S : ρ(s) = ρ(ρ(s))).…”

Section: Introductionmentioning

confidence: 99%

Control-flow analysis of function calls and returns by abstract interpretation

Midtgaard

Jensen

2009

Proceedings of the 14th ACM SIGPLAN International Conference on Functional Programming

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interpretation techniques are used to derive a control-flow analysis for a simple higher-order functional language. The analysis approximates the interprocedural control-flow of both function calls and returns in the presence of first-class functions and tail-call optimization. In addition to an abstract environment, the analysis computes for each expression an abstract call-stack, effectively approximating where function calls return. The analysis is systematically derived by abstract interpretation of the stack-based C a EK abstract machine of Flanagan et al. using a series of Galois connections. We prove that the analysis is equivalent to an analysis obtained by first transforming the program into continuation-passing style and then performing control flow analysis of the transfored program. We then show how the analysis induces an equivalent constraint-based formulation, thereby providing a rational reconstruction of a constraint-based CFA from abstract interpretation principles.

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