Michael Codish
Maurice Bruynooghe
Abstract
This article considers static analysis based on abstract interpretation of logic programs over combined domains. It is known that analyses over combined domains provide more information potentially than obtained by the independent analyses. However, the construction of a combined analysis often requires redefining the basic operations for the combined domain. A practical approach to maintain precision in combined analyses of logic programs which reuses the individual analyses and does not redefine the basic operations is illustrated. The advantages of the approach are that (1) proofs of correctness for the new domains are not required and (2) implementations can be reused. The approach is demonstrated by showing that a combined sharing analysis—constructed from “old” proposals—compares well with other “new” proposals suggested in recent literature both from the point of view of efficiency and accuracy.
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- Improving abstract interpretations by combining domains
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Improving abstract interpretations by combining domains
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Reviews
Francois Aribaud
In the abstract setting of domain theory, the meaning of a program P is expressed as the least fixed point of a monotonic operator f P on a domain E . In the development of the program, one leaves out the special features of the concrete data. This process can be seen as the definition of a new domain D linked to E by two monotonic operators, abstraction a :E?D and concretization g :D?E , for which a g d =d and e? g a e (? being the natural order on E ). Next, one must approximate f P by an operator g:D?D , which has a finitely computable least fixed point. D is not unique, however; intuitively, such a D gives greater emphasis to a particular type of information available from the concrete data. So it is natural to search for a way to merge two or more <__?__Pub Caret>abstraction domains. There is a direct product construct, but it corresponds to performing only independent analyses of each of the factors. The aim of this paper is to describe a new operation, the reduced product, which removes redundant information between the factors and thus increases efficiency. The authors give constructive definitions of reduced products for examples dealing with the sharing of variables in logic programs, and compare them with other recent analyses. The theory of logic programming has a reputation for being cryptic, a reputation from which this paper does not depart: written in a compact style, especially for the examples, it is hard to read, even for a research paper.
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