Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2018.18
URN: urn:nbn:de:0030-drops-91882
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9188/
Ikebuchi, Mirai ; Nakano, Keisuke
On Repetitive Right Application of B-Terms
| pdf-format: |
|
Abstract
B-terms are built from the B combinator alone defined by B == lambda f.lambda g.lambda x. f~(g~x), which is well-known as a function composition operator. This paper investigates an interesting property of B-terms, that is, whether repetitive right applications of a B-term cycles or not. We discuss conditions for B-terms to have and not to have the property through a sound and complete equational axiomatization. Specifically, we give examples of B-terms which have the property and show that there are infinitely many B-terms which do not have the property. Also, we introduce a canonical representation of B-terms that is useful to detect cycles, or equivalently, to prove the property, with an efficient algorithm.
BibTeX - Entry
@InProceedings{ikebuchi_et_al:LIPIcs:2018:9188,
author = {Mirai Ikebuchi and Keisuke Nakano},
title = {{On Repetitive Right Application of B-Terms}},
booktitle = {3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
pages = {18:1--18:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-077-4},
ISSN = {1868-8969},
year = {2018},
volume = {108},
editor = {H{\'e}l{\`e}ne Kirchner},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9188},
URN = {urn:nbn:de:0030-drops-91882},
doi = {10.4230/LIPIcs.FSCD.2018.18},
annote = {Keywords: Combinatory logic, B combinator, Lambda calculus}
}
| Keywords: | Combinatory logic, B combinator, Lambda calculus | |
| Seminar: | 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 04.07.2018 |
