A Universal Domain Technique for Profinite Posets

CMU-CS-85-142

Carl A. Gunter

July 1985 oot A preliminary version of this paper appeared in the proceedings of ICALP 1985.

We introduce a category of what we call profinite domains . This category of domains differs from most of the familiar ones in having a categorical coproduct as well as being cartesian closed. Study of these domains is carried out through the use of an equivalent category of pre-orders in a manner similar to the information systems approach advocated by Dana Scott and others. A class of universal profinite domains is defined and used to derive sufficient conditions for the profinite solution of domain equations involving continuous operators. Necessary conditions for the existence of such solutions are also given and used to derive results about solutions of some important equations. A new universal bounded complete domain is also demonstrated using an operator which has bounded complete domains as its fixed points.

28 pages

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