Abstract interpretation with specialized definitions

Resumen

The relationship between abstract interpretation and partial deduction has received considerable attention and (partial) integrations have
been proposed starting from both the partial deduction and abstract interpretation perspectives. In this work we present what we argue is the first fully
described generic algorithm for efficient and precise integration of abstract interpretation and partial deduction. Taking as starting point state-of-the-art
algorithms for context-sensitive, polyvariant abstract interpretation and (abstract) partial deduction, 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.
Our framework is parametric w.r.t. different control strategies and abstract domains. Different combinations of such parameters correspond to existing algorithms for program analysis and specialization. Simultaneously, our approach
opens the door to the efficient computation of strictly more precise results than
those achievable by each of the individual techniques. The algorithm is now
one of the key components of the CiaoPP analysis and specialization system.