Experience report on automated procedure construction for deductive synthesis

Deductive program synthesis systems based on automated theorem proving offer the promise of "correct by construction" software. However, the difficulty encountered in constructing usable deductive synthesis systems has prevented their widespread use. Amphion is a real-world, domain-independent program synthesis system. It is specialized to specific applications through the creation of an operational domain theory and a specialized deductive engine. This paper describes an experiment aimed at making the construction of usable Amphion applications easier. The software system Theory Operationalization for Program Synthesis (TOPS) has a library of decision procedures with a theory template for each procedure. TOPS identifies axioms in the domain theory that are an instance of a library of procedure and uses partial deduction to augment the procedure with the capability to construct ground terms for deductive synthesis. Synthesized procedures are interfaced to a resolution theorem prover. Axioms in the original domain theory that are implied by the synthesized procedures are removed. During deductive synthesis, each procedure is invoked to test conjunctions of literals in the language of the theory of that procedure. When possible, the procedure generates ground terms and binds them to variables in a problem specification. These terms are program fragments. Experiments show that the procedures synthesized by TOPS can reduce theorem proving search at least as much as hand tuning of the deductive synthesis system.