Abstract

Iteration grove theories are iteration theories equipped with an additive structure satisfying certain one-sided distributivity laws. In any iteration grove theory, the fixed point operation determines and is determined by a generalized star operation that takes familiar form in many applications. We relate properties of the dagger operation to properties of the generalized star operation and present some applications to continuous functions over complete lattices, continuous monoids, and to tree languages.KeywordsComplete LatticeParameter IdentityTree LanguagePairing IdentityIteration TheoryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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