Compact bracket abstraction in combinatory logic

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

Authors

Broda, S (Author) FCUP; Damas, L (Author) FCUP

Journal

Title: Journal of Symbolic Logic

Vol. 62

Pages: 729-740

ISSN: 0022-4812

Publisher: Cambridge University Press

Indexing

ISI Web of Knowledge - 6 Citations

Scopus - 7 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-001-AT4

DOI: 10.2307/2275570

Abstract (EN): Translations from Lambda calculi into combinatory logics can be used to avoid some implementational problems of the former systems. However, this scheme can only be efficient if the translation produces short output with a small number of combinators, in order to reduce the time and;transient storage space spent during reduction of combinatory terms. In this paper we present a combinatory system and an abstraction algorithm, based on the original bracket abstraction operator of Schonfinkel [9]. The algorithm introduces at most one combinator for each abstraction in the initial Lambda term. This avoids explosive term growth during successive abstractions and makes the system suitable for practical applications. We prove the correctness of the algorithm and establish some relations between the combinatory system and the Lambda calculus.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 12