metapredicate unique

Colin Barker, an occasional poster here at comp.lang.prolog, recently
posted an interesting problem to alt.math.recreational.

[Dominoes on a chessboard]
http://groups.google.com/group/alt....ee3e53f8bebb15f

The problem is whether it's always possible to remove N squares from
an N by N chessboard (checkerboard) in such a way that it can be
tiled with dominoes in one and only one way.

This suggested to me the implementation in Prolog of a metapredicate
unique/1 which takes as an argument Goal and succeeds precisely if
Goal succeeds in exactly one way.

Determinism:
Even if backtrack points are left by "Goal" after its first success,
provided
there are no additional solutions found by backtracking, unique(Goal)
is
supposed to succeed.  unique(Goal) itself would be deterministic, ie.
it can succeed in at most one way.

Binding:
It would be desirable for the success of unique(Goal) to preserve the
bindings of the successful solution of Goal.  This is not an issue for
the metapredicate not, because not(Goal) never binds variables that
appear in Goal.

Efficiency:
It would be efficient if the search tree invoked to find the first
solution
to Goal was effectively continued from that point to assure no further
solutions exist.

regards, chip