Carnegie Mellon University

Semilattices
and Domains

Abstract:

As everyone knows,
one popular notion of Scott domain is defined as a bounded complete
algebraic cpo. These are closely related to algebraic lattices:
(i) A Scott domain becomes an algebraic lattice with the adjunction of
an (isolated) top element. (ii) Every non-empty Scott-closed
subset of an algebraic lattice is a Scott domain. Moreover, the
isolated (= compact) elements of an algebraic lattice form a
semilattice (under join). This semilattice has a zero element,
and, provided the top element is isolated, it also has a unit
element. The algebraic lattice itself may be regarded as the
ideal completion of the semilattice of isolated elements. This is
all well known. What is not so clear that is that there is an
easy-to-construct domain of countable semilattices giving isomorphic
copies of all countably based domains. This approach seems to have
advantages over "information systems" and makes definitions of
solutions to domain equations very elementary to justify.

Friday, March 20, 2009

3:30 p.m.

Wean Hall 4615A

Principles
of Programming Seminars