Equational properties of iteration in algebraically complete categories

Z. Ésik, A. Labella

Research output: Contribution to journal › Article

19 Citations (Scopus)

Abstract

We prove the following completeness theorem: If the fixed point operation over a category is defined by initiality, then the equations satisfied by the fixed point operation are exactly those of iteration theories. Thus, in such categories, the equational axioms of iteration theories provide a sound and complete axiomatization of the equational properties of the fixed point operation.

Original languageEnglish
Pages (from-to)61-69
Number of pages9
JournalTheoretical Computer Science
Volume195
Issue number1
Publication statusPublished - Mar 20 1998

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Fixed point
Acoustic waves
Iteration
Axiomatization
Axioms
Completeness
Theorem
Sound

Keywords

  • Algebraically complete categories
  • Fixed points
  • Iteration theories

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

Equational properties of iteration in algebraically complete categories. / Ésik, Z.; Labella, A.

In: Theoretical Computer Science, Vol. 195, No. 1, 20.03.1998, p. 61-69.

Research output: Contribution to journal › Article

Ésik, Z & Labella, A 1998, 'Equational properties of iteration in algebraically complete categories', Theoretical Computer Science, vol. 195, no. 1, pp. 61-69.
Ésik Z, Labella A. Equational properties of iteration in algebraically complete categories. Theoretical Computer Science. 1998 Mar 20;195(1):61-69.
Ésik, Z. ; Labella, A. / Equational properties of iteration in algebraically complete categories. In: Theoretical Computer Science. 1998 ; Vol. 195, No. 1. pp. 61-69.
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