A Logic of Subtyping (Extended Abstract)

The relation of inclusion between types has been suggested by the practice of programming, as it enriches the polymorphism of functional languages. We propose a simple (and linear) calculus of sequents for subtyping as logical entailment. This allows to derive a complete and coherent approach to subtyping from a few, logically meaningful, sequents. In particular, transitivity and anti-symmetry will be derived from elementary logical principles, which stresses the power of sequents and Gentzen-style proof methods. Indeed, proof techniques based on cut-elimination will be at the core of our results.