Rippling: A Heuristic for Guiding Inductive Proofs

We describe rippling: a tactic for the heuristic control of the key part of proofs by mathematical induction. This tactic signiicantly reduces the search for a proof of a wide variety of inductive theorems. We rst present a basic version of rippling, followed by various extensions which are necessary to capture larger classes of inductive proofs. Finally, we present a general-ised form of rippling which embodies these extensions as special cases. We prove that generalised rippling always terminates, and we discuss the implementation of the tactic and its relation with other inductive proof search heuristics.