Abstract: "A special final coalgebra theorem, in the sytle of Aczel's [2], is proved within standard Zermelo-Fraenkel set theory. Aczel's Anti-Foundation Axiom is replaced by a variant definition of function that admits non-well-founded constructions. Variant ordered pairs and tuples,...

Ausführliche Beschreibung

Bibliographische Detailangaben

1. Verfasser:	Paulson, Lawrence C. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Cambridge 1994
Schriftenreihe:	Computer Laboratory <Cambridge>: Technical report 334
Schlagworte:	Applied statistics, operational research Computer software Mathematics Mathematik Set theory
Zusammenfassung:	Abstract: "A special final coalgebra theorem, in the sytle of Aczel's [2], is proved within standard Zermelo-Fraenkel set theory. Aczel's Anti-Foundation Axiom is replaced by a variant definition of function that admits non-well-founded constructions. Variant ordered pairs and tuples, of possibly infinite length, are special cases of variant functions. Analogues of Aczel's Solution and Substitution Lemmas are proved in the style of Rutten and Turi [11]. The approach is less general than Aczel's; non-well-founded objects can be modelled only using the variant tuples and functions. But the treatment of non-well-founded objects is simple and concrete. The final coalgebra of a functor is its greatest fixedpoint. The theory is intended for machine implementation and a simple case of it is already implemented using the theorem prover Isabelle [7]. The theorem, like Aczel's, applies only to functors that are uniform on maps. This property is discussed and it is noted that the identity functor is not uniform on maps, a point omitted from previous literature."
Beschreibung:	21 Bl.