Abstract

This paper introduces a typed #-calculus called # Power , a predicative reformulation of part of Cardelli's power type system. Power types integrate subtyping into the typing judgement, allowing bounded abstraction and bounded quantification over both types and terms. This gives a powerful and concise system of dependent types, but leads to di#culty in the meta-theory and semantics which has impeded the application of power types so far. Basic properties of # Power are proved here, and it is given a model definition using a form of applicative structures. A particular novelty is the auxiliary system for rough typing, which assigns simple types to terms in # Power . These "rough" types are used to prove strong normalization of the calculus and to structure models, allowing a novel form of containment semantics without a universal domain.

Citations