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Abstract: Fixed point calculus is about the solution of recursive equations de ned by a monotonic endofunction on a partially ordered set. This tutorial discusses applications of xed point calculus in the construction of computer programs, beginning with standard applications and progressing to recent research. The basic properties of least and greatest xed points are presented. Wellfoundedness and inductive properties of relations are expressed in terms of xed points. A class of xed point equations, ... (Update)
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...assumption. Our proof is conducted entirely in Tarski s axiomatic calculus of binary relations [8] and the fixed point calculus [1]. This formal approach has two benefits. On the practical side, the proof is constructive and yields an algorith1 Since kernel theory is...
...3.3. Let (X, be an ordered set. The relation on the set of functions on X is defined by f # #(x X : f(x) g(x) Theorem 3.4. See, e.g. [3]) The following properties hold: a) f (g) monotonic) b) Let g be continuous and strict. Then f (f) g( h) fusion law) c) f...
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2: Relational algebraic semantics of deterministic and nondeterministic programs (context) - Berghammer, Zierer - 1986
2: A lattice-theoretical fixpoint theorem and its applications (context) - Tarski - 1955
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BibTeX entry: (Update)
Backhouse R. et al.: Fixed-point calculus, Inf. Proc. Letters 53, 131-136 (1995) http://citeseer.ist.psu.edu/backhouse00fixed.html More
@unpublished{ backhouse00fixed,
author = "Ronald Backhouse",
title = "Fixed Point Calculus",
year = "2000",
url = "citeseer.ist.psu.edu/backhouse00fixed.html" }
Citations (may not include all citations):275 The Science of Programming (context) - Gries - 1981
141 Predicate Calculus and Program Semantics (context) - Dijkstra, Scholten - 1990
104 Science of Computer Programming (context) - Malcolm, program - 1990
97 North-Holland (context) - Freyd, cedrov et al. - 1990
84 Law and Order in Algorithmics (context) - Fokkinga - 1992
84 A completeness theorem for Kleene algebras and the algebra o.. - Kozen - 1994
69 Revised report on the algorithmic language ALGOL (context) - Ed - 1963
67 Formal Aspects of Computing (context) - Meertens - 1992
63 Algebraic data types and program transformation (context) - Malcolm - 1990
49 van der Woude (context) - Backhouse, de Bruin et al. - 1991
49 van der Woude (context) - Backhouse, de Bruin et al. - 1992
29 Representation of events in nerve nets and nite automata (context) - Kleene - 1956
24 Virtual data structures - Swierstra, de Moor - 1993
16 Induction and recursion on datatypes - Doornbos, Backhouse - 1995
12 Prentice-Hall International (context) - Backhouse, Verication - 1986
10 Science of Computer Programming (context) - Doornbos, Backhouse - 1996
7 Mathematical Structures in Computer Science (context) - Backhouse, van der Woude et al. - 1993
7 Regular algebra applied to path-nding problems (context) - Backhouse, Carr - 1975
6 Department of Mathematics and Computing Science (context) - Doornbos, program et al. - 1996
6 A calculation approach to mathematical induction (context) - Doornbos, Backhouse et al. - 1997
6 Department of Mathematics and Computing Science (context) - Hoogendijk, Theory et al. - 1997
6 A xpoint theorem for complete categories (context) - Lambek - 1968
1 What is a container type (context) - Hoogendijk, de Moor - 2000
The graph only includes citing articles where the year of publication is known.
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