Abstract Interpretation with Specialized Definitions

The relationship between abstract interpretation and partial evaluation has received considerable attention and (partial) integrations have been proposed starting from both the partial evaluation and abstract interpretation perspectives. In this work we present what we argue is the first generic algorithm for efficient and precise integration of abstract interpretation and partial evaluation from an abstract interpretation perspective. Taking as starting point state-of-the-art algorithms for context-sensitive, polyvariant abstract interpretation and (abstract) partial evaluation of logic programs, we present an algorithm which combines the best of both worlds. Key ingredients include the accurate success propagation inherent to abstract interpretation and the powerful program transformations achievable by partial deduction. In our algorithm, the calls which appear in the analysis graph are not analyzed w.r.t. the original definition of the procedure but w.r.t. specialized definitions of these procedures. Such specialized definitions are obtained by applying both unfolding and abstract executability. Also, our framework is parametric w.r.t. different control strategies and abstract domains. Different combinations of these parameters correspond to existing algorithms for program analysis and specialization. Our approach efficiently computes strictly more precise results than those achievable by each of the individual techniques. The algorithm is one of the key components of CiaoPP, the analysis and specialization system of the Ciao compiler.

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