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

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 ωbifinite 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. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-89-37. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/788 Pseudo-Retract Functors For Local Lattices And Bifinite L-Domains MS-CIS-89-37 LOGIC & COMPUTATION 08