%% Testing detection of singleton variables.

p( V, 'V' ).                  % singleton V

a( _, _X ) :-  b( _Y, Z ).    % only Z is a singleton

% Note that Y is truly a singleton on the second branch in the first clause, but
% not in the second!
a(X) :- b(X, Y), c( Y ); d( Y ).
a(X) :- b(X, Y), (c( Y ); d( Y )).


% Here Y should be a singleton.
a( 1 ) :- \+ b( Y ), c( Y ).

% Here Y should be a singleton in the first branch
a( 2 ) :- (\+ b( Y ); c( Y )), d( Y ).

% Here Y should be a singleton in the first branch
a(X) :-(b( Y ), fail ; c( X )), d( Y ).

% Here X should be a singleton, and Y should be a singleton in the first branch
a(X) :-(b( Y ), fail ; c( Y )), d( Y ).

% Here d( Y ) should be dead code, X and Y singletons.
a(X) :-(b( Y ), fail ; c( Y ), fail), d( Y ).


a( 3 ) :-
        ( b( Y ), c( X )
        ; b( Y ), fail        % Y is singleton here
        ; \+ b( Z )           % Z is singleton here
        ),
        d( X, Y, Z ).


% Suppress uninteresting warnings:
b(a).
b(a,a).
c(a).
d(a).
d(a,a,a).
:- topl a/1, a/2, p/2.