On the power of higher-order algebraic specification methods

Soundness and adequacy theorems are presented for the expressive power of higher-order initial algebra specifications with respect to the arithmetical and analytical hierarchies. These results demonstrate that higher-order initial algebra semantics substantially extends the power of both first-order initial and first-order final algebra semantics. It thus provides a unifying framework for all three different approaches to the semantics of algebraic specifications. (C) 1996 Academic Press, Inc.