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Algebraic systems of equations define functions using recursion where parameter passing is permitted. This generalizes the notion of a rational system of equations where parameter passing is prohibited. It has been known for some time that algebraic systems in Greibach Normal Form have unique solutions. This paper presents a categorical approach to algebraic systems of equations which generalizes the traditional approach in two ways i) we define algebraic equations for locally finitely presentable categories rather than just Set; and ii) we define algebraic equations to allow right-hand sides which need not consist of finite terms. We show these generalized algebraic systems of equations have unique solutions by replacing the traditional metric-theoretic arguments with coalgebraic arguments.
Keywords: coalgebra, recursion, category theory
Marchi, Federico De ; Ghani, Neil ; Lüth, Christoph 1
@article{ITA_2003__37_4_301_0,
author = {Marchi, Federico De and Ghani, Neil and L\"uth, Christoph},
title = {Solving algebraic equations using coalgebra},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {301--314},
publisher = {EDP-Sciences},
volume = {37},
number = {4},
year = {2003},
doi = {10.1051/ita:2003021},
mrnumber = {2053029},
zbl = {1038.18005},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2003021/}
}
TY - JOUR AU - Marchi, Federico De AU - Ghani, Neil AU - Lüth, Christoph TI - Solving algebraic equations using coalgebra JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2003 SP - 301 EP - 314 VL - 37 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita:2003021/ DO - 10.1051/ita:2003021 LA - en ID - ITA_2003__37_4_301_0 ER -
%0 Journal Article %A Marchi, Federico De %A Ghani, Neil %A Lüth, Christoph %T Solving algebraic equations using coalgebra %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2003 %P 301-314 %V 37 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita:2003021/ %R 10.1051/ita:2003021 %G en %F ITA_2003__37_4_301_0
Marchi, Federico De; Ghani, Neil; Lüth, Christoph. Solving algebraic equations using coalgebra. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 37 (2003) no. 4, pp. 301-314. doi: 10.1051/ita:2003021
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