Paper Abstract and Keywords |
Presentation |
2007-12-17 10:45
On the Acyclicity of Combinators Munehiro Iwami (Shimane Univ.) SS2007-41 |
Abstract |
(in Japanese) |
(See Japanese page) |
(in English) |
Sumllyan proposed that combinator L with rewrite rule
L x y -> x (y y) and combinator O with rewrite rule
O x y -> y (x y).
In this paper, we give the sufficient condition for acyclicity
of combinators.
First, we give the sufficient condition for acyclicity of
combinators using the generalized method of Bergstra et al.
We show that acyclicity of combinators L and O using
this condition. Furthermore, we show that combinator O
is not terminating on terms consisted of only O.
Next, we show that non-ground loopingness of combinator
O by similar method of Waldmann.
Finally, we show that reverse relation ->^-1 of
rewrite step -> by rewrite rule L x y -> x (y y)
is terminating and we give the simple proof of acyclicity
of combinator L. Furthermore, we show that combinator L
has the ground loop. |
Keyword |
(in Japanese) |
(See Japanese page) |
(in English) |
term rewriting system / combinator / combinatory logic / acyclicity / lambda calculus / / / |
Reference Info. |
IEICE Tech. Rep., vol. 107, no. 392, SS2007-41, pp. 19-24, Dec. 2007. |
Paper # |
SS2007-41 |
Date of Issue |
2007-12-10 (SS) |
ISSN |
Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 |
Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) |
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SS2007-41 |
Conference Information |
Committee |
SS |
Conference Date |
2007-12-17 - 2007-12-18 |
Place (in Japanese) |
(See Japanese page) |
Place (in English) |
Shimane Univ. |
Topics (in Japanese) |
(See Japanese page) |
Topics (in English) |
general |
Paper Information |
Registration To |
SS |
Conference Code |
2007-12-SS |
Language |
Japanese |
Title (in Japanese) |
(See Japanese page) |
Sub Title (in Japanese) |
(See Japanese page) |
Title (in English) |
On the Acyclicity of Combinators |
Sub Title (in English) |
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Keyword(1) |
term rewriting system |
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combinator |
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combinatory logic |
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acyclicity |
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lambda calculus |
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Munehiro Iwami |
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Shimane University (Shimane Univ.) |
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Speaker |
Author-1 |
Date Time |
2007-12-17 10:45:00 |
Presentation Time |
30 minutes |
Registration for |
SS |
Paper # |
SS2007-41 |
Volume (vol) |
vol.107 |
Number (no) |
no.392 |
Page |
pp.19-24 |
#Pages |
6 |
Date of Issue |
2007-12-10 (SS) |
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