Treffer: Strategies for combining decision procedures
Strategic CAD Labs, Intel Corporation, Hillsboro, Oregon, United States
CC BY 4.0
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Mathematics
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Implementing efficient algorithms for combining decision procedures has been a challenge and their correctness precarious. In this paper we describe an inference system that has the classical Nelson-Oppen procedure at its core and includes several optimizations: variable abstraction with sharing, canonization of terms at the theory level, and Shostak's streamlined generation of new equalities for theories with solvers. The transitions of our system are fine-grained enough to model most of the mechanisms currently used in designing combination procedures. In particular, with a simple language of regular expressions we are able to describe several combination algorithms as strategies for our inference system, from the basic Nelson-Oppen to the very highly optimized one recently given by Shankar and Rueß. Presenting the basic system at a high level of generality and non-determinism allows transparent correctness proofs that can be extended in a modular fashion when new features are introduced in the system.