Minimal typings in atomic subtyping
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A framework for type inference with subtyping
ICFP '98 Proceedings of the third ACM SIGPLAN international conference on Functional programming
Simplifying subtyping constraints: a theory
Information and Computation
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Many type inference and program analysis systems include notions of subtyping and parametric polymorphism. When used together, these two features induce equivalences that allow types to be simplified by eliminating quantified variables. Eliminating variables both improves the readability of types and the performance of algorithms whose complexity depends on the number of type variables. We present an algorithm for simplifying quantified types in the presence of subtyping and prove it is sound and complete for non-recursive and recursive types. We also show that an extension of the algorithm is sound but not complete for a type language with intersection and union types, as well as for a language of constrained types.