Polarised subtyping for sized types

Abstract

We present an algorithm for deciding polarised higher-order subtyping without bounded quantification. Constructors are identified not only modulo β, but also η. We give a direct proof of completeness, without constructing a model or establishing a strong normalisation theorem. Inductive and coinductive types are enriched with a notion of size and the subtyping calculus is extended to account for the inclusions arising between the sized types.