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18 CHAPTER 1. The TOY(FD) System

• Type declaration:

indomain :: int → bool

• Deﬁnition: ‘indomain X’ assigns a value, from the minimum to the maximum

in its domain, to X.

• Example at the TOY(FD) command level:

Next goal assigns (by backtracking and from minimum to maximum in its range)

each value to a variable.

TOY(FD)> domain [X] 1 2, indomain X

yes

X == 1

Elapsed time: 0 ms.

more solutions (y/n/d) [y]?

yes

X == 2

Elapsed time: 0 ms

labeling/2

• Type declaration:

labeling :: [labelType] → [int] → bool

• Deﬁnition: ‘labeling O ptions L’ is true if an assignment of the variables in L

can be found such that all of the constraints already presented in the constraint

store are satisﬁed. Options is a list of at most four elements that allow to specify

the nature of the search.

Each element in this list may have a value in one of the following groups:

1. The ﬁrst group controls the order in which variables are chosen for assign-

ment (i.e., variable ordering) and allows to select the leftmost variable in L

(leftmost), the variable with the smallest lower bound (mini), the variable

the greatest upper bound (maxi) or the variable with the smallest domain

(ﬀ). The value ﬀc extends the option ﬀ by selecting the variable involved

in the higher number of constraints.

2. The second group controls the value ordering, that is to say, the order in

which values are chosen for assignment. For instance, from the minimum

to the maximum (enum), by selecting the minimum or maximum (step)

or by dividing the domain in two choices by the mid point (bisect). Also

the domain of a variable can be explored in ascending order (up) or in

descending order (down).

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Ascend FD-23R Manual de usuario Pagina 30