all_different/1

all_different(List) enforces pairwise distinctness of all variables in List.

Propagation

The propagator prunes values using value elimination and Hall‑interval reasoning. This often fixes variables early when domains are tight.

Examples

?- X in 1..2, Y in 1..2, Z in 1..3, all_different([X,Y,Z]).
true.
?- fd_dom(Z, DZ).
DZ = 3..3.

Pigeonhole principle

If you have more variables than available values, failure is detected without search.

?- X in 1..2, Y in 1..2, Z in 1..2, all_different([X,Y,Z]).
false.

Tips

• Combine with sum/ordering constraints for stronger propagation.
• Avoid redundant #\= pairs when all_different/1 is present; let the global constraint propagate.