* iteration vs. recursion
@ 2001-06-07 14:55 Stephen Bloom
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From: Stephen Bloom @ 2001-06-07 14:55 UTC (permalink / raw)
To: categories
Both iteration and recursion are operations
yielding fixed points. They have the same
equational properties in standard models.
See the following articles:
S. Bloom and Z. Esik,``Fixed point operations in ccc's'', Theoretical
Computer Science,
155:1996, 1--38,
S. Bloom and Z. Esik,``The equational logic of fixed points'' ,
Theoretical Computer Science, 179(1997), 1--60,
and
Z. Esik and A. Labella:
Equational properties of iteration in
algebraically complete categories.
Mathematical foundations of computer
science (Cracow, 1996).
Theoret. Comput. Sci. 195 (1998), no. 1, 61--89.
and the book:
Iteration Theories: The Equational Logic of Iterative Processes,
EATCS Monograph Series on Theoretical Computer Science,
Springer-Verlag, 1993
ISBN 0-387-56378-4, by Bloom and Esik.
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* Re: iteration vs. recursion
@ 2001-06-08 15:07 HASEGAWA Masahito
0 siblings, 0 replies; 2+ messages in thread
From: HASEGAWA Masahito @ 2001-06-08 15:07 UTC (permalink / raw)
To: categories
On fixed-point operators and their axiomatizations including
the iteration theories of Bloom and Esik, one of the latest
(and concise) accounts is found in
Alex Simpson and Gordon Plotkin:
Complete Axioms for Categorical Fixed-point Operators.
Fifteenth Annual IEEE Symposium on Logic in Computer Science,
pp.30-41, 2000
available from Simpson's page
http://www.dcs.ed.ac.uk/home/als/Research/ .
- Masahito Hasegawa
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