Abstract

We study an extension of the second-order calculus of bounded quantification, System F , with bounded existential types. Surprisingly, the most natural formulation of this extension lacks the important minimal typing property of F , which ensures that the set of types possessed by a typeable term can be characterized by a single least element. We consider alternative formulations and give an algorithm computing minimal types for the slightly weaker Kernel Fun variant of F . 1 Introduction F is a typed lambda-calculus combining subtyping and second-order bounded quantification [4, 5, 7, 3]. Besides its utility as a vehicle for theoretical investigations, it has come to be seen as a good basis for the design of programming languages incorporating subtyping and polymorphism. The extension of F with bounded existential quantifiers to support programming with abstract data types is commonly regarded as a straightforward task; indeed, in a sense, pure F already contains bounded existentials...

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