Section: New Results

Semantic Subtyping

In a programming language, subtyping represents a notion of safe substitutability (it is always safe to replace a value of some type with a value of a subtype). There are several ways such a relation can be formally defined. Semantic subtyping consists of giving a set-theoretic denotation to types and using set inclusion to define subtyping. Works by Benzaken, Castagna, Frisch and Xu have described how to define such relations for complex type algebras comprising recursive, product, function, intersection, union, and complement types together with type variables. In [17] , we showed how to formalise such a relation in logic and decide it in EXPTIME, answering an open question, and discussed experiments made with the full implementation of the system in our solver ( 6.3 ).