Synthesis from Assume-Guarantee Contracts using Skolemized Proofs of Realizability

The realizability problem in requirements engineering is to determine the existence of an implementation that meets the given formal requirements. A step forward after realizability is proven, is to construct such an implementation automatically, and thus solve the problem of program synthesis. In this paper, we propose a novel approach to program synthesis guided by k-inductive proofs of realizability of assumeguarantee contracts constructed from safety properties. The proof of realizability is performed over a set of ∀∃-formulas, and synthesis is performed by extracting Skolem functions witnessing the existential quantification. These Skolem functions can then be combined into an implementation. Our approach is implemented in the JSyn tool which constructs Skolem functions from a contract written in a variant of the Lustre programming language and then compiles the Skolem functions into a C language implementation. For a variety of benchmark models that already contained hand-written implementations, we are able to identify the usability and effectiveness of the synthesized counterparts, assuming a component-based verification framework.