Typed compilation of inclusive subtyping

Abstract

I present a type-preserving translation that eliminates subtyping and bounded quantification without introducing any run-time costs. This translation is based on Mitchell and Pierce's encoding of bounded quantification using intersection types. I show that, previous negative observations notwithstanding, the encoding is adequate given a sufficiently rich target type theory. The necessary target type theory is made easily typecheckable by including a collection of explicit coercion combinators, which are already desired for eliminating subtyping. However, no form of coercion abstraction is necessary (even to support bounded quantification), leading to a simple target language.