Positive Subtyping

Abstract

The statement S≤T in a λ-calculus with subtyping is traditionally interpreted by a semantic coercion function of type [[S]]→[[T]] that extracts the “T part” of an element of S. If the subtyping relation is restricted to covariant positions, this interpretation may be enriched to include both the implicit coercion and an overwriting function put[S,T] ∈ [[S]]→[[T]]→[[S]] that updates the T part of an element of S. We give a realizability model and a sound equational theory for a second-order calculus of positive subtyping.