Re: iteration vs. recursion

Re: iteration vs. recursion

[HASEGAWA Masahito]

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

iteration vs. recursion

[Stephen Bloom]

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.