A Structural Co-Induction Theorem (1993)
| Venue: | PROC. MFPS '93, SPRINGER LNCS 802 |
| Citations: | 7 - 1 self |
BibTeX
@INPROCEEDINGS{Rutten93astructural,
author = {J. J. M. M. Rutten},
title = {A Structural Co-Induction Theorem},
booktitle = {PROC. MFPS '93, SPRINGER LNCS 802},
year = {1993},
pages = {83--102},
publisher = {Springer-Verlag}
}
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Abstract
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 final coalgebras of such functors. In particular, final coalgebras are order strongly-extensional (sometimes called internal full abstractness): the order is the union of all (ordered) F-bisimulations. (Since the initial fixed point for locally continuous functors is also final, both theorems apply.) Further a similar co-induction theorem is given for a category of complete metric spaces and locally contracting functors.
