Subtyping with Power Types

Authors:
David Aspinall
Affiliations:
-
Venue:
Proceedings of the 14th Annual Conference of the EACSL on Computer Science Logic
Year:
2000

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Abstract

This paper introduces a typed λ-calculus called λPOWER, 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 difficulty in the meta-theory and semantics which has impeded the application of power types so far. Basic properties of λPOWER 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 λPOWER. 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.