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Dagger extension theorem†

Published online by Cambridge University Press:  22 August 2011

Z. ÉSIK  and
T. HAJGATÓ
Z. ÉSIK
Affiliation:
Department of Computer Science, University of Szeged, Hungary Email: ze@inf.u-szeged.hu; hajgato@inf.u-szeged.hu
T. HAJGATÓ
Affiliation:
Department of Computer Science, University of Szeged, Hungary Email: ze@inf.u-szeged.hu; hajgato@inf.u-szeged.hu
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Abstract

Partial iterative theories are algebraic theories such that for certain morphisms f the equation ξ = f ⋅ 〈ξ, 1p〉 has a unique solution. Iteration theories are algebraic theories satisfying a certain set of identities. We investigate some similarities between partial iterative theories and iteration theories.

In our main result, we give a sufficient condition ensuring that the partially defined dagger operation of a partial iterative theory can be extended to a totally defined operation so that the resulting theory becomes an iteration theory. We show that this general extension theorem can be instantiated to prove that every Elgot iterative theory with at least one constant morphism 1 → 0 can be extended to an iteration theory. We also apply our main result to theories equipped with an additive structure.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 21 , Issue 5 , October 2011 , pp. 1035 - 1066
Copyright
Copyright © Cambridge University Press 2011

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