Dependent type system with subtyping (I) type level transitivity elimination

Abstract

Dependent type systems are the basis of many proof development environments. In Aspinall and Compagnoni's paper, a system λP≤ is proposed as a subtyping extension of the first order dependent type system λP (also called λΠ). λP≤, has nice meta-theoretic properties including subject reduction and decidability. In this article, we give a reformulation of λP≤, called λΠ≤. The advantages of λΠ≤ include: type level transitivity elimination property and pretype-based subtyping system. These features considerably facilitate the meta-theoretical study and further extensions of this system.