% --------------------------------------------------------------------- %
% DIRECTORY: CPO							%
%									%
% DESCRIPTION: basic theory of CPO's and fixed-points 			%
%									%
% AUTHOR: Albert J Camilleri						%
%									%
% ADDRESS: Hewlet Packard Laboratories					%
%	   Filton road							%
%	   Stoke Gifford						%
%	   Bristol, BS12 6QZ						%
%	   England.							%
%									%
%	   email: ac@uucp.hplb						%
%									%
% DATE: 90.06.01							%
% --------------------------------------------------------------------- %

I have found the [contributed] theory very useful for defining non primitive
recursive operators. I use it to define the recursive operators in my latest
model for CSP and I intend to install it in the library in some future release
of HOL. In the mean time, however, it might come in handy to other HOL users.

The [contributed] HOL theory is simply intended to lead to the fixed point
theorem which will allow the definitions of recursive operators.  It is not
intended as an exhaustive theory on domains, etc.  Users may need to prove
further theorems as required, but I think that [it] gives a good start for
defining recursions. For example, in CSP an ordering on processes (<= say) is
defined and proved to be a CPO, a `bottom' process is defined and proved to be
so, and then for all functions f:process->process, recursion can be defined as
(CONTINUOUS f) ==> (MU f = FIX f $<=) and the definition of FIX can be
expanded to the value of the least upper bound.

Hope it comes in useful.

Albert
