Strong Typed Böhm Theorem and Functional Completeness on the Linear Lambda Calculus
In this paper, we prove a version of the typed Böhm theorem on the linear lambda calculus, which says, for any given types A and B, when two different closed terms s1 and s2 of A and any closed terms u1 and u2 of B are given, there is a term t such that t s1 is convertible to u1 and t s2 is converti...
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Online Access: | http://arxiv.org/pdf/1505.01326v2 |
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doaj-8038102bc1c34afea6803f6e22b3888c2020-11-24T21:06:51ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802016-04-01207Proc. MSFP 201612210.4204/EPTCS.207.1:7Strong Typed Böhm Theorem and Functional Completeness on the Linear Lambda CalculusSatoshi Matsuoka0 National Institute of Advanced Industrial Science and Technology In this paper, we prove a version of the typed Böhm theorem on the linear lambda calculus, which says, for any given types A and B, when two different closed terms s1 and s2 of A and any closed terms u1 and u2 of B are given, there is a term t such that t s1 is convertible to u1 and t s2 is convertible to u2. Several years ago, a weaker version of this theorem was proved, but the stronger version was open. As a corollary of this theorem, we prove that if A has two different closed terms s1 and s2, then A is functionally complete with regard to s1 and s2. So far, it was only known that a few types are functionally complete.http://arxiv.org/pdf/1505.01326v2 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Satoshi Matsuoka |
spellingShingle |
Satoshi Matsuoka Strong Typed Böhm Theorem and Functional Completeness on the Linear Lambda Calculus Electronic Proceedings in Theoretical Computer Science |
author_facet |
Satoshi Matsuoka |
author_sort |
Satoshi Matsuoka |
title |
Strong Typed Böhm Theorem and Functional Completeness on the Linear Lambda Calculus |
title_short |
Strong Typed Böhm Theorem and Functional Completeness on the Linear Lambda Calculus |
title_full |
Strong Typed Böhm Theorem and Functional Completeness on the Linear Lambda Calculus |
title_fullStr |
Strong Typed Böhm Theorem and Functional Completeness on the Linear Lambda Calculus |
title_full_unstemmed |
Strong Typed Böhm Theorem and Functional Completeness on the Linear Lambda Calculus |
title_sort |
strong typed böhm theorem and functional completeness on the linear lambda calculus |
publisher |
Open Publishing Association |
series |
Electronic Proceedings in Theoretical Computer Science |
issn |
2075-2180 |
publishDate |
2016-04-01 |
description |
In this paper, we prove a version of the typed Böhm theorem on the linear lambda calculus, which says, for any given types A and B, when two different closed terms s1 and s2 of A and any closed terms u1 and u2 of B are given, there is a term t such that t s1 is convertible to u1 and t s2 is convertible to u2. Several years ago, a weaker version of this theorem was proved, but the stronger version was open. As a corollary of this theorem, we prove that if A has two different closed terms s1 and s2, then A is functionally complete with regard to s1 and s2. So far, it was only known that a few types are functionally complete. |
url |
http://arxiv.org/pdf/1505.01326v2 |
work_keys_str_mv |
AT satoshimatsuoka strongtypedbohmtheoremandfunctionalcompletenessonthelinearlambdacalculus |
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1716764531036782592 |