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.
Equational Properties of Iteration in Algebraically Complete Categories / Z., Esik; Labella, Anna. - In: THEORETICAL COMPUTER SCIENCE. - ISSN 0304-3975. - STAMPA. - 195:(1998), pp. 61-89. [10.1016/S0304-3975(97)00158-8]
Equational Properties of Iteration in Algebraically Complete Categories
LABELLA, Anna
1998
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.File allegati a questo prodotto
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