ScholarlyCommons

Title

Pseudo-Retract Functors for Local Lattices and Bifinite L-Domains

Author(s)

Elsa L. Gunter, University of Pennsylvania

Document Type

Technical Report

Date of this Version

June 1989

Comments

University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-89-37.

Abstract

Recently, a new category of domains used for the mathematical foundations of denotational semantics, that of L-domains, have been under study. In this paper we consider a related category of posets, that of local lattices. First, a completion operator taking posets to local lattices is developed, and then this operator is extended to a functor from posets with embedding-projection pairs to local lattices with embedding-projection pairs. The result of applying this functor to a local lattice yields a local lattice isomorphic to the first; this functor is a pseudo-retract.

Using the functor into local lattices, a continuous pseudo-retraction functor from ω-bifinite posets to ω-bifinite L-domains can be constructed. Such a functor takes a universal domain for the ω-bifinite posets to a universal domain for the ω-bifinite L-domains. Moreover, the existence of such a functor implies that, from the existence of a saturated universal domain for the ω-algebraic bifinites, we can conclude the existence of a saturated universal domain for the ω-bifinite L-domains.

Recommended Citation

Elsa L. Gunter, "Pseudo-Retract Functors for Local Lattices and Bifinite L-Domains", . June 1989.