On combinatory complete sets of proper combinators

• Type: Article in International Scientific Journal
• Date: 1997

Authors

Broda, S (Author) FCUP; DAMAS, L (Author) Other

Journal

Title: Journal of Functional Programming

Vol. 7

Pages: 593-612

ISSN: 0956-7968

Publisher: Cambridge University Press

Other information

Authenticus ID: P-00R-Y19

DOI: 10.1017/s0956796897002888

Abstract (EN): <jats:p>A combinatory system (or equivalently the set of its basic combinators) is called combinatorially complete for a functional system, if any member of the latter can be defined by an entity of the former system. In this paper the decision problem of combinatory completeness for finite sets of proper combinators is studied for three subsystems of the pure lambda calculus. Precise characterizations of proper combinator bases for the linear and the affine ¿-calculus are given, and the respective decision problems are shown to be decidable. Furthermore, it is determined which extensions with proper combinators of bases for the linear ¿-calculus are combinatorially complete for the ¿<jats:italic>I</jats:italic>-calculus.</jats:p>

Language: English

Type (Professor's evaluation): Scientific