We study the π-calculus, enriched with pairing, and define a notion of type assignment that uses the type constructor →. We encode the terms of the calculus X into this variant of π, and show that all reduction (cut-elimination) and assignable types are preserved. Since X enjoys the Curry-Howard isomorphism for Gentzen’s calculu LK, this implies that all proofs in LK have a representation in π. We then enrich the logic with the connector ¬, and show that this also can be represented in π.

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, theX i-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. Key words: Curry-Howard, classical logic, generic unification, principal types, cut elimination 1.