Improving Programs Which Recurse over Multiple Inductive Structures

This paper considers generic recursion schemes for programs which recurse over multiple inductive structures simultane ously such as equality zip and the nth element of a list function Such schemes have been notably absent from pre vious work This paper de nes a uniform mechanism for de ning such programs and shows that these programs sat isfy generic theorems These theorems are the basis for an automatic improvement algorithm This algorithm is an im provement over the algorithm presented earlier because in addition to inducting over multiple structures it can be incorporated into any algebraic language and is no longer restricted to a safe subset