Abstract
A method is presented for incrementally computing success patterns of logic programs. The set of success patterns of a logic program with respect to an abstraction is formulated as the success set of an equational logic program modulo an equality theory that is induced by the abstraction. The method is exemplified via depth and stump abstractions. Also presented are algorithms for computing most general unifiers modulo equality theories induced by depth and stump
Highlights
In abstract interpretation, program analyses are viewed as program execution over non-standard data domains
The set of success patterns of a logic program with respect to an abstraction is formulated as the success set of an equational logic program modulo an equality theory that is induced by the abstraction
For a class of abstractions, that the set of success patterns of a logic program P with respect to an abstraction α is tantamount to the success set of the equational logic program P Eα where Eα is an equality theory induced by α
Summary
Program analyses are viewed as program execution over non-standard data domains. Cousot and Cousot first laid solid logical foundations for abstract interpretations [1,2] Their idea is to define a collecting semantics for a program which associates each program point with the set of all storage states that are possibly obtained when the execution reaches the point. The safeness of the analysis is verified by formalizing a correspondence between the concrete domain and the abstract domain and proving that the abstract operations safely simulate the concrete operations with respect to the correspondence.
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