Closures on CPOs Form Complete Lattices |
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| Authors: | Francesco Ranzato |
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| Affiliation: | Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Belzoni 7, 35131, Padova, Italyf1 |
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| Abstract: | It is well known that closure operators on a complete lattice, ordered pointwise, give rise to a complete lattice, and this basic fact plays an important rôle in many fields of the semantics area, notably in domain theory and abstract interpretation. We strengthen that result by showing that closure operators on any directed-complete partial order (CPO) still form a complete lattice. An example of application in abstract interpretation theory is given. |
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| Keywords: | closure operator complete lattice CPO domain theory abstract interpretation |
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