Pruning Terms for Principal Type Assignment

Abstract

Affine terms are lambda terms in which no variable occurs twice, and linear terms are affine terms in which each bound variable occurs exactly once. The principal type of a term is the most general type which is assignable to the term. Hirokawa gave characterisations of the principal types of linear terms and of beta-normal affine terms. Shouji gave a characterisation of the principal types of beta-eta-normal linear terms. The proofs of these three theorems are parallel, but independent to each other. This paper points out that by using Berardi's pruning, the theorem on beta-normal affine terms is obtained from the theorem on linear terms. This is the first result. And also this paper shows a characterisation of principal types of beta-eta-normal affine terms. Its proof is obtained from the theorem on beta-eta-normal linear terms by Berardi's pruning. This is the second result. Besides, this paper gives other proofs of the the theorems on eta-normal terms. This is the third result.