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1.4. FD Constraints 17

all different/1

all different’/2

all distinct/1

all distinct’/2

• Type declaration:

all different :: [int] → bool

all different’ :: [int] → [options] → bool

all distinct :: [int] → bool

all distinct’ :: [int] → [options] → bool

• Deﬁnition:

• ‘all diﬀerent L’ and ‘all distinct L’ are true if each variable in L is constrained to

have a value that is unique in the list L and there are no duplicate integers in the

list L, i.e., this is equivalent to say that for all X, Y ∈ L, X 6= Y . The diﬀerence

between both constraints is that all diﬀerent/1 uses a complete algorithm that

maintains the domain consistency R´egin, 1994 whereas all distinct/1 uses an

incomplete one.

There are extended versions that allow one more argument which is a list of

options, where each option may have one of the following values

1. ‘on value’, ‘on domains’ or ‘on range’ to specify that the constraint has to be

woken up, respectively, when a variable becomes ground, when the domain

associated to a variable changes, or when a bound of the domain (in interval

form) associated to a variable changes.

2. ‘complete true’ or ‘complete false’ to specify if the propagation algorithm to

apply is complete or incomplete.

• Example at the TOY(FD) command level:

TOY(FD)> L== [X,1,Z], domain L 1 3,

all_different’ L [complete true, on range]

yes

L == [ X, 1, Z ]

Z in 2..3

X in 2..3

Elapsed time: 0 ms.

1.4.6 Enumeration Constraints

Enumeration constraints reactivate the search process when no more constraint prop-

agation is possible. TOY(FD) provides two enumeration constraints:

indomain/1

1 2 ... 24 25 26 27 28 29 30 31 32 33 34 ... 80 81

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