SN combinators and partial combinatory algebras

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

We introduce an intersection typing system for combinatory logic. We prove the soundness and completeness for the class of partial combinatory algebras. We derive that a term of combinatory logic is typeable iff it is SN. Let F be the class of non-empty filters which consist of types. Then F is an extensional non-total partial combinatory algebra. Furthermore, it is a fully abstract model with respect to the set of SN terms of combinatory logic. By F, we can solve Bethke-Klop’s question; “find a suitable representation of the finally collapsed partial combinatory algebra of P”’. Here, P is a partial combinatory algebra, and is the set of closed SN terms of combinatory logic modulo the inherent equality. Our solution is the following: the finally collapsed partial combinatory algebra of P is representable in F. To be more precise, it is isomorphically embeddable into F.

Original languageEnglish
Title of host publicationRewriting Techniques and Applications - 9th International Conference, RTA 1998, Proceedings
EditorsTobias Nipkow
PublisherSpringer-Verlag
Pages302-316
Number of pages15
ISBN (Print)354064301X, 9783540643012
DOIs
Publication statusPublished - 1998 Jan 1
Externally publishedYes
Event9th International Conference on Rewriting Techniques and Applications, RTA 1998 - Tsukuba, Japan
Duration: 1998 Mar 301998 Apr 1

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1379
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other9th International Conference on Rewriting Techniques and Applications, RTA 1998
CountryJapan
CityTsukuba
Period98/3/3098/4/1

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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