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The Converse Principal Type-Scheme Theorem in Lambda Calculus

Sachio Hirokawa
Studia Logica: An International Journal for Symbolic Logic
Vol. 51, No. 1 (1992), pp. 83-95
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015610
Page Count: 13
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The Converse Principal Type-Scheme Theorem in Lambda Calculus
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Abstract

A principal type-scheme of a λ-term is the most general type-scheme for the term. The converse principal type-scheme theorem (J. R. Hindley, "The principal type-scheme 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 λ-calculus, by constructing an algorithm which transforms a type assignment to a λ-term into a principal type assignment to another λ-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-λ-terms as well. Thus a uniform proof is presented for the converse principal type-scheme theorem for general λ-terms and BCIW-λ-terms.

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