Closures on CPOs form complete lattices
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 role 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. (C) 1999 Academic Press.
cpo complete lattice closure operator domain theory abstract interpretation