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) sequent calculus for subtyping as logical entailment. This allows us 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.

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 are derived from elementary logical principles, which stresses the power of sequents and Gentzen-style proof methods. Indeed, proof techniques based on cut-elimination are at the core of our results.

The authors focus on how polymorphic functions, which may take types as inputs, depend on types. These functions are generally understood to have an essentially constant meaning, in all models, on input types. It is shown how the proof theory of the polymorphic lambda -calculus suggests a clear syntactic description of this phenomenon. Under a reasonable condition, it is shown that identity of two polymorphic functions on a single type implies identity of the functions (equivalently, every type is a generic input).>