Principal Types as Lambda Nets

Abstract

We show that there are connections between principal type schemata, cut-free ?-nets, and normal forms of the ?-calculus, and hence there are correspondences between the normalisation algorithms of the above structures, i.e. unification of principal types, cut-elimination of ?-nets, and normalisation of ?-terms. Once the above correspondences have been established, properties of the typing system, such as typability, subject reduction, and inhabitation, can be derived from properties of ?-nets, and vice-versa. We illustrate the above pattern on a specific type assignment system, we study principal types for this system, and we show that they correspond to ?-nets with a non-standard notion of cut-elimination. Properties of the type system are then derived from results on ?-nets