A Higher-Order Unification Algorithm for Inductive Types and Dependent Types

This paper presents a method to define a set of mutuaJly recursive inductive types, and develops a higherorder unilication algorithm for Anz extended with inductive types. The algorithm is an extension of Eiliott’s algoritbJn for λ∑.The notation of normal forms plays a vital role in higher-order unification.The weak head normal forms in the extended troe theory is defined to reveal the ultimate "top level structures" of the fully normalized terms and types. Unification transformation rules are designed to deal with inductive types, a recursive operator and its reduction rule. The algoritlun can construct recuxsive functions automatically.