%============================================================================%
%    DIRECTORY: reduct                                                       %
%                                                                            %
%  DESCRIPTION: General theorems about reflexive/symmetric/transitive        %
%               closure of binary relations ("rstc.ml" / "rstc.sml").        %
%                                                                            %
%               Some basic theorems about confluence and termination of      %
%               abstract reduction relations ("reduct.ml" / "reduct.sml").   %
%                                                                            %
%       AUTHOR: John Harrison                                                %
%               University of Cambridge Computer Laboratory                  %
%               New Museums Site                                             %
%               Pembroke Street                                              %
%               Cambridge CB2 3QG                                            %
%               England.                                                     %
%               jrh@cl.cam.ac.uk                                             %
%                                                                            %
%         DATE: 31st May 1993                                                %
%============================================================================%

The file "rstc.[s]ml" is a general theory of reflexive, symmetric and transitive
closures of arbitrary binary relations (represented as curried functions of type
":*->*->bool"). All distinct combinations of these closures are defined, and a
fairly extensive set of theorems proved about each. Although only a few of these
are defined using the inductive definitions package (and some of those
gratuitously), induction and cases theorems of the standard form are derived, to
allow use of the standard rule induction tactics.

The file "reduct.[s]ml" is a basic theory of abstract reduction relations (again
the nature of the relations is arbitrary). This is far from complete, but provides
some potentially useful theorems, e.g. Newman's Lemma (weak confluence /\ strong
normalization ==> confluence).

The files have been tested in HOL88 v2.01 and hol90.5 as appropriate, and appear
to work.

Any bug reports or suggestions for improvements should be sent by email to me
at jrh@cl.cam.ac.uk.

John Harrison, 31st May 1993.
