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Abstract: We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operator is defined, embodying the equational properties of iteration theories. We prove a general completeness theorem for iteration operators, relying on a new, purely syntactic characterisation of the free iteration theory. (Update)
Context of citations to this paper: More
.... and the author independently observed a bijective correspondence between Conway (Bekic, or dinatural diagonal) fixpoint operators [3,12] and traces on categories with finite products [6,7] Thus, in this setting, the notion of trace precisely captures the well behaved...
.... some canonical axiomatizations including iteration theories [1] and Conway theories, equivalently traced cartesian categories [3] see [12] for recent results) Because the # calculus is an extension of the simply typed call by name # calculus, it looks straightforward to...
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BibTeX entry: (Update)
A.K. Simpson and G.D. Plotkin. Complete axioms for categorical fixed-point operators. In Proceedings of 15th Annual Symposium on Logic in Computer Science. To appear, 2000. http://citeseer.ist.psu.edu/simpson00complete.html More
@incollection{ simpson00complete,
author = "Alex Simpson and Gordon Plotkin",
title = "Complete Axioms for Categorical Fixed-Point Operators",
booktitle = "Proceedings 15th Annual {IEEE} Symp.\ on Logic in Computer Science, {LICS}'00, Sta Barbara, {CA}, {USA}, 26--29 June 2000",
publisher = "IEEE Computer Society Press",
address = "Los Alamitos, CA",
pages = "30--44",
year = "2000",
url = "citeseer.ist.psu.edu/simpson00complete.html" }
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359 Introduction to Higher Order Categorical Logic (context) - Lambek, Scott - 1986
291 Computational lambda-calculus and monads - Moggi - 1989
210 its Syntax and Semantics (context) - Barendregt, Calculus - 1984
194 The Formal Semantics of Programming Languages (context) - Winskel - 1993
152 Semantics of Programming Languages (context) - Gunter - 1992
69 Triples and Theories (context) - Barr, Wells - 1985
59 Axiomatic Domain Theory in Categories of Partial Maps (context) - Fiore - 1996
58 Algebraically complete categories (context) - Freyd - 1990
55 Available from httpwww (context) - The, Available et al. - 1983
54 Games and Full Abstraction for a Functional Metalanguage wit.. (context) - McCusker - 1998
45 New foundations for fixpoint computations: FIX-hyperdoctrine.. (context) - Crole, Pitts - 1992
36 Remarks on algebraically compact categories (context) - Freyd - 1992
26 Mathematical Proceedings of the Cambridge Philosophical Soci.. (context) - Joyal, Street et al. - 1996
25 Recursive types in Kleisli categories - Simpson - 1992
21 Models of Sharing Graphs: A Categorical Semantics of let and.. (context) - Hasegawa - 1999
19 General synthetic domain theory --- a logical approach - Reus, Streicher - 1999
17 The equivalence problem for deterministic pushdown automata .. (context) - Senizergues - 1997
16 Complete cuboidal sets in axiomatic domain theory - Fiore, Plotkin et al. - 1997
16 EATCS Monographs on Theoretical Computer Science (context) - Bloom, Esik - 1993
13 An extension of models of axiomatic domain theory to models .. - Fiore, Plotkin - 1997
12 Computational adequacy in an elementary topos - Simpson - 1999
10 algebras and fixed points (context) - Mulry - 1992
9 Independence of the equational axioms of iteration theories (context) - Esik - 1988
9 A uniform account of domain theory in realizability models (context) - Longley, Simpson - 1997
8 The logic of recursive equations - Hurkens, McArthur et al. - 1998
8 Unpublished manuscript (context) - Eilenberg
7 A characterisation of the least-fixed-point operator by dina.. - Simpson - 1993
6 Induction and recursion on the partial real line with applic.. - Escardo, Streicher - 1999
5 Information and Computation (context) - Esik, for - 1999
4 Archiv fur Math (context) - Statman, functionals et al. - 1983
2 Equational lifting monads - Bucalo, Fuhrmann et al. - 1999
2 To appear in Theoretical Computer Science (context) - Stirling, DPDA - 2000
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