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Abstract: . A special final coalgebra theorem, in the style of Aczel's [2], is proved within standard Zermelo-Fraenkel set theory. Aczel's AntiFoundation 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 [12]. The approach is less general than Aczel's, but the... (Update)
Context of citations to this paper: More
.... theorems of various types may be found in the works cite above, and also in Barr [Bar93, Bar94] Moss and Danner[MD] and in Paulson [P]. The results of this paper also give a final coalgebra: the maximal formulas of L F in the semantic preorder. This connects coalgebraic...
...of the Knaster Tarski Theorem. Another form of the Theorem constructs a greatest fixedpoint; this justifies coinductive definitions [23], but will not concern us here. 2.2. The Bounding Set When justifying some instance of lfp(D,h) showing that h is monotone is generally...
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9: Non-Well-Founded Sets (context) - Aczel - 1987
8: from foundations to functions (context) - Paulson, for - 1993
8: The lazy lambda calculus - Abramsky - 1990
BibTeX entry: (Update)
Paulson, L. C., A concrete final coalgebra theorem for ZF set theory, Tech. rep., Comp. Lab., Univ. Cambridge, 1994 http://citeseer.ist.psu.edu/paulson94concrete.html More
@inproceedings{ paulson94concrete,
author = "Lawrence C. Paulson",
title = "A Concrete Final Coalgebra Theorem for {ZF} Set Theory",
booktitle = "{TYPES}",
pages = "120-139",
year = "1994",
url = "citeseer.ist.psu.edu/paulson94concrete.html" }
Citations (may not include all citations):1933 Communication and Concurrency (context) - Milner - 1989
179 The lazy lambda calculus - Abramsky - 1977
159 Non-Well-Founded Sets (context) - Aczel - 1988
91 A final coalgebra theorem (context) - Aczel, Mendler - 1989
77 Co-induction in relational semantics (context) - Milner, Tofte - 1991
67 Terminal coalgebras in well-founded set theory (context) - Barr - 1993
47 A fixedpoint approach to implementing (context) - Paulson - 1994
39 From foundations to functions (context) - Paulson, Set - 1993
35 Set Theory: An Introduction to Independence Proofs (context) - Kunen - 1980
26 Set theory for verification: II (context) - Paulson - 1993
The graph only includes citing articles where the year of publication is known.
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