Reasoning on a complex system in the abstract interpretation theory starts with a formal description of the system behavior specified by a collecting semantics. We take the common point of view that a collecting semantics is a very precise semantics from which other abstractions may be derived. We elaborate on both the concepts of precision and derivability, and introduce a notion of adequacy which tell us when a collecting semantics is a good choice for a given family of abstractions. We instantiate this approach to the case of first-order functional programs by considering three common collecting semantics and some abstract properties of functions. We study their relative precision and give a constructive characterization of the classes of abstractions which are adequate for the collecting semantics.

On collecting semantics for program analysis

Amato G.
;
Meo M. C.
;
Scozzari F.
2020

Abstract

Reasoning on a complex system in the abstract interpretation theory starts with a formal description of the system behavior specified by a collecting semantics. We take the common point of view that a collecting semantics is a very precise semantics from which other abstractions may be derived. We elaborate on both the concepts of precision and derivability, and introduce a notion of adequacy which tell us when a collecting semantics is a good choice for a given family of abstractions. We instantiate this approach to the case of first-order functional programs by considering three common collecting semantics and some abstract properties of functions. We study their relative precision and give a constructive characterization of the classes of abstractions which are adequate for the collecting semantics.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11564/733991
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