Centrum voor Wiskunde en Informatica REPORT RAPPORT A structural co - induction theorem
نویسنده
چکیده
The Structural Induction Theorem (Lehmann and Smyth, 1981; Plotkin, 1981) characterizes initial F-algebras of locally continuous functors F on the category of cpo's with strict and continuous maps. Here a dual of that theorem is presented, giving a number of equivalent characterizations of nal coalgebras of such functors. In particular, nal coalgebras are order strongly-extensional (sometimes called internal full abstractness): the order is the union of all (ordered) F-bisimulations. (Since the initial xed point for locally continuous functors is also nal, both theorems apply.) Further a similar co-induction theorem is given for a category of complete metric spaces and locally contracting functors.
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Robert van Liere Centrum voor Wiskunde en Informatica P.O. Box 94079, 1090 GB Amsterdam The Netherlands E-mail: [email protected] Jurriaan D. Mulder Centrum voor Wiskunde en Informatica P.O. Box 94079, 1090 GB Amsterdam The Netherlands E-mail: [email protected] Jarke J. van Wijk Netherlands Energy Research Foundation ECN P.O. Box 1, 1755 ZG Petten The Netherlands Centrum voor Wiskunde en Informatica P...
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1 Laboratoire A2X, Université Bordeaux I, 351, cours de la Libération, 33405 Talence, France [email protected] 2 CWI and Department of Mathematics, Leiden University; Centrum voor Wiskunde en Informatica (CWI), Sciencepark 123, 1098 XG Amsterdam, The Netherlands [email protected] 3 CWI and Department of Mathematics, University of Amsterdam; Centrum voor Wiskunde en Informatica (C...
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