A Theoretical Foundation of Program Synthesis by Equivalent Transformation

Abstract

Equivalent transformation (ET) is useful for synthesis and transformation of programs. However, it is not so clear what semantics should be preserved in synthesis and transformation of programs in logic and functional programming, which come from the disagreement of computation models (inference or evaluation) and equivalent transformation. To overcome the difficulty, we adopt a new computation model, called equivalent transformation model, where equivalent transformation is used not only for program synthesis, but also for computation. We develop a simple and general foundation for computation and program synthesis, and prove the correctness ofET-based program synthesis.