Structural subtyping for inductive types with functorial equality rules

Abstract

In this paper we study subtyping for inductive types in dependent type theories in the framework of coercive subtyping. General structural subtyping rules for parameterised inductive types are formulated based on the notion of inductive schemata. Certain extensional equality rules play an important role in proving some of the crucial properties of the type system with these subtyping rules. In particular, it is shown that the structural subtyping rules are coherent and that transitivity is admissible in the presence of the functorial rules of computational equality.