Towards High-Assurance High-Performance Program Synthesis
Domain-specific automatic program synthesis tools, also called application generators, are playing an ever-increasing role in software development. However, high-performance application generators require difficult manual construction, and are very difficult to verify correct. This paper describes research and an implemented system that transforms program synthesis tools based on deductive synthesis into high-performance application generators. Deductive synthesis uses theorem-proving to construct solutions when given problem specifications. The verification condition for a deductive synthesis tool is essentially the soundness of the implemented inference rules. Theory Operationalization for Program Synthesis (TOPS) synergistically combines reformulation, automated mathematical classification, and compilation through partial deduction to decision procedures. It transforms general-purpose deductive synthesis, with exponential performance, into efficient special-purpose deductive synthesis, with near-linear performance. This paper describes our experience with and empirical results of PD(TH) theory-based partial deduction - in which partial deduction of a set of first-order formulae is performed within the context of a background theory. The implemented TOPS system currently performs a special variant of PD(TH) in which the compilation process results in the transformation of a set of first order formulae into the theory of an instantiated library decision procedure augmented by a compiled unit theory.