Polarized Subtyping for Sized Types

Abstract

AbstractWe present an algorithm for deciding polarized 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 normalization theorem. Inductive and coinductive types are enriched with a notion of size and the subtyping calculus is extended to account for the arising inclusions between the sized types.KeywordsOperational SemanticLogical FrameworkGalois ConnectionType ConstructorWeak NormalizationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.