The converse principal type-scheme theorem in lambda calculus

Studia Logica 51 (1):83 - 95 (1992)
Abstract
A principal type-scheme of a -term is the most general type-scheme for the term. The converse principal type-scheme theorem (J.R. Hindley, The principal typescheme of an object in combinatory logic, Trans. Amer. Math. Soc. 146 (1969) 29–60) states that every type-scheme of a combinatory term is a principal type-scheme of some combinatory term.This paper shows a simple proof for the theorem in -calculus, by constructing an algorithm which transforms a type assignment to a -term into a principal type assignment to another -term that has the type as its principal type-scheme. The clearness of the algorithm is due to the characterization theorem of principal type-assignment figures. The algorithm is applicable to BCIW--terms as well. Thus a uniform proof is presented for the converse principal type-scheme theorem for general -terms and BCIW--terms.
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