Varieties of iteration theories

Stephen L. Bloom, Z. Ésik

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

The equational properties of iteration, when combined with composition and pairing, are captured by the notion of 'iteration theory'. We believe that every iterative construction satisfies at least the properties of iteration theories. Axiomatizations are given for several varieties of iteration theories which occur naturally in the semantics of programming languages, i.e., those generated by theories of trees, theories of sequacious functions, theories of partial functions, and theories of both sequacious and partial functions with distinguished predicates. We show which additional equations must be added to the axioms for iteration theories in order to obtain a set of axioms for these subvarieties. Concrete descriptions of the free theories in each variety are given.

Original languageEnglish
Pages (from-to)939-966
Number of pages28
JournalSIAM Journal on Computing
Volume17
Issue number5
Publication statusPublished - Oct 1988

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Iteration
Computer programming languages
Semantics
Axioms
Chemical analysis
Partial
Axiomatization
Pairing
Predicate
Programming Languages

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics
  • Theoretical Computer Science

Cite this

Varieties of iteration theories. / Bloom, Stephen L.; Ésik, Z.

In: SIAM Journal on Computing, Vol. 17, No. 5, 10.1988, p. 939-966.

Research output: Contribution to journalArticle

Bloom, SL & Ésik, Z 1988, 'Varieties of iteration theories', SIAM Journal on Computing, vol. 17, no. 5, pp. 939-966.
Bloom, Stephen L. ; Ésik, Z. / Varieties of iteration theories. In: SIAM Journal on Computing. 1988 ; Vol. 17, No. 5. pp. 939-966.
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