Definedness and Strictness in Generator Inductive Definitions

We consider a generalized form of inductive definitions as first suggested by Guttag. Partial functions may be defined by introducing error values in the right hand sides. For such definitions the intuitive semantics is not consistent with that of unrestricted rewriting. In general, the addition of rewrite rules capturing the intuitively motivated error propagation will destroy confluence of the rewrite system. We show how to mechanically modify the rewrite system in order to obtain a confluent system consistent with the intuitive semantics.