Abstract

Dependent type systems have been the basis of many proof development enviroments. In [AC96], a system P is proposed as a subtyping extension of the dependent type system P[Bar92] (also called \Pi[Dow95]). P has nice meta-theoretic properties including subject reduction and decidability, but transitivity elimination is restricted to the fi 2 normalized types. In this report, we propose a system \Pi , which is equivalent to P , but it has type level transitivity eliminatioin property. This feature distinguishes our approach from the existing subtyping systems with reduction relations in types. e.g. P[AC96], F ! [SP94], F ! [Com94], where transitivity elimination only holds for normalized types. Meta-theoretic properties including subject reduction and decidability are established. The system is shown to be equivalent with P in typing, kinding and context formation. The type checking algorithm is more clear and efficient than P . The technique is suitable for future extensions and...

Citations