Deductive and Inductive Synthesis of Equational Programs |Draft|

An equational approach to the synthesis of functional and logic program is taken. Typically, the synthesis task involves nding equations which make the given speci cation an inductive theorem. To synthesize such programs, induction is necessary. We formulate e cient procedures for inductive proof as well as 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 not adequate to come with a program.