Program synthesis by analogy

By extending a given analogy, a known program which solves a given problem is converted to a program which solves a different but analogous problem. The domains of the two problems need not be the same but they must be related by an initial specified analogy. There are three features which distinguish the approach. First the analogy formation evolves gradually with the synthesis of the new program. Secondly the formation of the analogy is directed by the correctness proof of the known program. Finally the output of the synthesis process produces a correctness proof for the synthesized program.