Soundness and principal contexts for a shallow polymorphic type system based on classical logic

In this paper we investigate how to adapt the well-known notion of ML-style polymorphism (shallow polymorphism) to a term calculus based on a Curry-Howard correspondence with classical sequent calculus, namely, the χⁱ-calculus. We show that the intuitive approach is unsound, and pinpoint the precise nature of the problem. We define a suitably refined type system, and prove its soundness. We then define a notion of principal contexts for the type system, and provide an algorithm to compute these, which is proved to be sound and complete with respect to the type system. In the process, we formalise and prove correctness of generic unification, which generalises Robinson’s unification to shallow-polymorphic types.