Closure functions and general iterates as reflectors
type: Item
instance of: scholarly article
title: Closure functions and general iterates as reflectors
zbMATH Open document ID: 0731.68073
DOI: 10.1016/0304-3975(91)90223-O
published in: Theoretical Computer Science
publication date: 1991-01-01T00:00:00Z
review text: In a previous paper [Ann. Pure Appl. Logic 40, No.3, 217-256 (1988; Zbl 0664.68047)] the authors have studied primitive iterates, corresponding to for-until-do statements; in the present paper they deal with general iterates, corresponding to while-do statements. An analogy between closure functions and general iterates leads the authors to investigate their common algebraic structure. To this aim they develop a closure theory for categories from which both the classical closure theory and the closure theory for iteration can be obtained as particular cases. Both the closure functions and the general iterates are the (object part of) reflector, i.e. left adjoints for the inclusion functor. This result supports the asserted importance of adjoints in computer science. Furthermore, the offered semantics of the while-do statement is independent from the semantics of recursive procedures and closer to the usual iterative implementation of the construct.
Mathematics Subject Classification ID: 68Q60
Mathematics Subject Classification ID: 68Q55
Mathematics Subject Classification ID: 18A40
zbMATH DE Number: 4209622
zbMATH Keywords: semantics of programs
zbMATH Keywords: general iterates
zbMATH Keywords: while-do statements
zbMATH Keywords: closure functions
zbMATH Keywords: closure theory for categories
author: G. M. Germano
author: S. Mazzanti
reviewed by: Andrea Maggiolo-Schettini
MaRDI profile type: Publication
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