THIS WEEK'S
=================== Concurrency / Real-Time Seminar =================
Chu(Set,K) as a Theory O.E. and Chu(Set,K)^op as a Model O.E.
Work in progress by
Michael Barr
Vineet Gupta
Vaughan Pratt (speaker)
Stanford University
Margaret Jacks Hall 301
4PM, Wednesday, April 14th
Chu(Set,K), defined by Barr and studied by Chu in 1979, is a universal
complete self-dual symmetric closed category whose objects are matrices
over a *set* K dualized by transposition. Its morphisms may be understood
as any of linear transformations, continuous functions, Boolean theory
morphisms, or a certain 2D "genetic splicing" process, but not as
hypergraph morphisms. Most or all Pontrjagin-Stone dualities in
Johnstone's "Stone Spaces" embed in Chu(Set,K). We interpret Prolog, Petri
nets, Kripke structures, and object-oriented (self-sufficient) programs,
but not PRAM's, as Chu matrices whose rows are attributes and columns
states, taking time to be linear and discrete and dually information
rotational and dense, with each satisfying a local triangle inequality.
Each matrix has its own Planck constant h-bar = 1/width x 1/height as
an entropic abstraction of Heisenberg's constructive refinement of the
Cantor-Russell paradox.