Fixed-point operations on ccc's. Part I

Stephen L. Bloom, Z. Ésik

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

Most studies of fixed points involve their existence or construction. Our interest is in their equational properties. We study certain equational properties of the fixed-point operation in computationally interesting cartesian closed categories. We prove that in most of the poset categories that have been used in semantics, the least fixed-point operation satisfies four identities we call the Conway identities. We show that if script C sign0 is a sub-ccc of any ccc script C sign with a fixed-point operation satisfying these identities, then there is a simple normal form for the morphisms in the least sub-ccc of script C sign containing script C sign0 closed under the fixed-point operation. In addition, the standard functional completeness theorem is extended to Conway ccc's.

Original languageEnglish
Pages (from-to)1-38
Number of pages38
JournalTheoretical Computer Science
Volume155
Issue number1
DOIs
Publication statusPublished - Feb 26 1996

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Fixed point
Semantics
Cartesian Closed Category
Morphisms
Poset
Normal Form
Completeness
Closed
Theorem

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

Fixed-point operations on ccc's. Part I. / Bloom, Stephen L.; Ésik, Z.

In: Theoretical Computer Science, Vol. 155, No. 1, 26.02.1996, p. 1-38.

Research output: Contribution to journalArticle

Bloom, Stephen L. ; Ésik, Z. / Fixed-point operations on ccc's. Part I. In: Theoretical Computer Science. 1996 ; Vol. 155, No. 1. pp. 1-38.
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