Foundations for the Implementation of Higher-Order Subtyping

10 years 1 months ago
Foundations for the Implementation of Higher-Order Subtyping
We show how to implement a calculus with higher-order subtyping and subkinding by replacing uses of implicit subsumption with explicit coercions. To ensure this can be done, a polymorphic function is adjusted to take, as an additional argument, a proof that its type constructor argument has the desired kind. Such a proof is extracted from the derivation of a kinding judgement and may in turn require proof coercions, which are extracted from subkinding judgements. This technique is formalized as a type-directed translation from a calculus of higher-order subtyping to a subtyping-free calculus. This translation generalizes an existing result for second-order subtyping calculi (such as F ). We also discuss two interpretations of subtyping, one that views it as type inclusion and another that views it as the existence of a well-behaved coercion, and we show, by a type-theoretic construction, that our translation is the minimum consequence of shifting from the inclusion interpretation to t...
Karl Crary
Added 06 Aug 2010
Updated 06 Aug 2010
Type Conference
Year 1997
Where ICFP
Authors Karl Crary
Comments (0)