On the foundations of corecursion (1997) [12 citations — 1 self]
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by Lawrence S. Moss
Logic Journal of the IGPL
http://www3.oup.co.uk/igpl/Volume_05/Issue_02/ps/moss.ps.gz
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Abstract:
We consider foundational questions related to the definition of functions by corecursion. This method is especially suited to functions into the greatest fixed point of some monotone operator, and it is most applicable in the context of non-wellfounded sets. We review the work on the Special Final Coalgebra Theorem of Aczel [1] and the Corecursion Theorem of Barwise and Moss [4]. We offer a condition weaker than Aczel's condition of uniformity on maps, and then we prove a result relating the operators satisfying the new condition to the smooth operators of [4].
Citations
| 163 | Non-Well-Founded Sets – Aczel - 1988 |
| 146 | P.: A Final Coalgebra Theorem. in – Aczel, Mendler - 1989 |
| 102 | Terminal coalgebras in well-founded set theory – Barr - 1993 |
| 72 | Vicious Circles – Bairwise, Moss - 1996 |
| 50 | Initial algebra and final co-algebra semantics for concurrency – Rutten, Turi - 1994 |
| 44 | Set theory with free construction principles – Forti, Honsell - 1983 |
| 44 | On the Foundations of Final Semantics: non-standard sets, metric spaces, partial orders – Rutten, Turi - 1993 |
| 21 | Processes as terms: non-well-founded models for bisimulation – Rutten - 1992 |
| 20 | A calculus of transition systems (towards universal co-algebra – Rutten - 1995 |
| 16 | Final Semantics for a Higher Order Concurrent Language – Lenisa - 1996 |
| 10 | Final semantics for untyped -calculus – Honsell, Lenisa - 1995 |
| 7 | Non-Well-Founded Sets Modeled as Ideal Fixed Points – Mislove, Moss, et al. - 1991 |
