Abstract
We prove the following completeness theorem: If the fixed point operation over a category is defined by initiality, then the equations satisfied by the fixed point operation are exactly those of iteration theories. Thus, in such categories, the equational axioms of iteration theories provide a sound and complete axiomatization of the equational properties of the fixed point operation.
Original language | English |
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Pages (from-to) | 61-69 |
Number of pages | 9 |
Journal | Theoretical Computer Science |
Volume | 195 |
Issue number | 1 |
Publication status | Published - Mar 20 1998 |
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Keywords
- Algebraically complete categories
- Fixed points
- Iteration theories
ASJC Scopus subject areas
- Computational Theory and Mathematics
Cite this
Equational properties of iteration in algebraically complete categories. / Ésik, Z.; Labella, A.
In: Theoretical Computer Science, Vol. 195, No. 1, 20.03.1998, p. 61-69.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Equational properties of iteration in algebraically complete categories
AU - Ésik, Z.
AU - Labella, A.
PY - 1998/3/20
Y1 - 1998/3/20
N2 - We prove the following completeness theorem: If the fixed point operation over a category is defined by initiality, then the equations satisfied by the fixed point operation are exactly those of iteration theories. Thus, in such categories, the equational axioms of iteration theories provide a sound and complete axiomatization of the equational properties of the fixed point operation.
AB - We prove the following completeness theorem: If the fixed point operation over a category is defined by initiality, then the equations satisfied by the fixed point operation are exactly those of iteration theories. Thus, in such categories, the equational axioms of iteration theories provide a sound and complete axiomatization of the equational properties of the fixed point operation.
KW - Algebraically complete categories
KW - Fixed points
KW - Iteration theories
UR - http://www.scopus.com/inward/record.url?scp=0346703020&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0346703020&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0346703020
VL - 195
SP - 61
EP - 69
JO - Theoretical Computer Science
JF - Theoretical Computer Science
SN - 0304-3975
IS - 1
ER -