Program synthesis from examples by theory formation

This paper presents a logic-based framework which integrates an incremental generic method for learning from examples into program synthesis with generic theories. It allows to incorporate constraints, strategic and domain specific knowledge in an additive way. We derive a knowledge-based synthesis method which is based on the computational paradigm of “divide-and-conquer” as a meta-level proof method. The generic method provides a basis to construct case solutions of more general requirement specifications with efficiency constraints. Based on the abstracted results of example computations an automatic extension of problem descriptions may be performed. The emphasis is elucidating that learning techniques may support construction of definitions required for the derivation of efficient programs. The system has been used to synthesize a previously unknown mathematical algorithm.