Recursive program optimization through inductive synthesis proof transformation

The research described in this paper involved developing transformation techniques which increase the efficiency of the original program, the {\em source}, by transforming its synthesis proof into one, the {\em target}, which yields a computationally more efficient algorithm. We describe a working proof transformation system which, by exploiting the duality between mathematical induction and recursion, employs the novel strategy of optimizing recursive programs by transforming inductive proofs. We compare and contrast this approach with the more traditional approaches to program transformation, and highlight the benefits of proof transformation with regards to search, correctness, automatability and generality