Deductive and inductive synthesis of equational programs

An equational approach to the synthesis of functional and logic program is taken. In this context, the synthesis task involves finding executable equations such that the given specification holds in their standard model. Hence, to synthesize such programs, induction is necessary. We formulate procedures for inductive proof, as well as for program synthesis, using the framework of “ordered rewriting”. We also propose heuristics for generalizing from a sequence of equational consequences. These heuristics handle cases where the deductive process alone is inadequate for coming up with a program.