In this paper, abstract interpretation algorithms are described for computing the sharmg as well as the freeness information about the run-time instantiations of program variables. An abstract domain is proposed which accurately and concisely represents combined freeness and sharing information for program variables. Abstract unification and all other domain-specific functions for an abstract i...

Linear relation analysis (polyhedral analysis), devoted to discovering linear invariant relations among variables of a program, remains one of the most powerful abstract interpretations but is subject to convexity limitations. Absolute value enjoys piecewise linear expressiveness and thus natively fits to encode certain non-convex properties. Based on this insight, we propose to use linear abso...

Interpretation Abstract Interpretation: General theory of sound approximations of semantics [Cousot78]. Numerical Abstract Domain: • computer-representable set D of abstract values, together with: • a concretisation: γ: D → P(V → I), • a partial order: ⊑, ⊥, ⊤, • sound, effective abstract transfer functions {| I |}: ({| I |} ◦ γ)(X ) ⊆ (γ ◦ {| I |})(X ), a sound, effective abstract union ∪: γ(X...

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In this paper, we show that it is possible to abstract program fragments using real variables using formulas in the theory of real closed fields. This abstraction is compositional and modular. We first propose an exact abstraction for programs without loops. Given an abstract domain (in a wide class including intervals and octagons), we then show how to obtain an optimal abstraction of program ...

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Extended Abstract ABSTRACT We recast Milner's work on nite delay in synchronous CCS by giving a denota-tional semantics for admissibility of innnite computations on a biinite domain K. Using Abramsky's SFP domain D for bisimulation we obtain a fully abstract model D K for an operational preorder which generalizes Milner's fortiica-tion and whose restriction to nite behavior corresponds to Abram...