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Interpreting abstract interpretations in membership equational logic. (English) Zbl 1268.68066
van den Brand, Mark (ed.) et al., RULE 2001. Proceedings of the 2nd international workshop on rule-based programming (Satellite Event of PLI 2001), Florence, Italy, September 4, 2001. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 59, No. 4, 271-285 (2001).
Summary: We present a logical framework in which abstract interpretations can be naturally specified and then verified. Our approach is based on membership equational logic which extends equational logics by membership axioms, asserting that a term has a certain sort. We represent an abstract interpretation as a membership equational logic specification, usually as an overloaded order-sorted signature with membership axioms. It turns out that, for any term, its least sort over this specification corresponds to its most concrete abstract value. Maude implements membership equational logic and provides mechanisms to calculate the least sort of a term efficiently. We first show how Maude can be used to get prototyping of abstract interpretations “for free”. Building on the meta-logic facilities of Maude, we further develop a tool that automatically checks an abstract interpretation against a set of user-defined properties. This can be used to select an appropriate abstract interpretation, to characterize the specific loss of information during abstraction, and to compare different abstractions with each other.
For the entire collection see [Zbl 1266.68020].

MSC:
68N30 Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
03B70 Logic in computer science
Software:
Maude; OBJ3
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