Topological completeness in an ideal model for polymorphic types
We have a look at the topological structure underlying the ideal model of recursive polymorphic types proposed by MacQueen, Plotkin and Sethi. We show that their central argument in establishing a well defined semantical function, viz., completeness with respect to a metric obtained from the construction of their domain, is a special case of complete uniformities which arise in a natural way from the study of closeness of ideals on domains. These uniformities are constructed and studied, and a general fixed — point theorem is derived for maps defined on these ideals.
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