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10 CHAPTER 1. The TOY(FD) System

In the following, we describe one by one all the FD constraints supported by

TOY(FD). Table 1.2 shows the whole set of FD constraints currently supported by

the system.

Table 1.2: The Predeﬁned Set of FD Constraints

RELATIONAL CONSTRAINTS

(#>), (#<), (#>=), (#<=), (# =), (#\=) :: int → int → bool

ARITHMETICAL CONSTRAINTS

(#∗), (#/), (#+), (#−) :: int → int → int

sum :: [int] → (int → int → bool) → int → bool

scalar product :: [int] → [int] → (int → int → bool) → int → bool

COMBINATORIAL CONSTRAINTS

assignment, circuit’, serialized :: [int] → [int] → bool

all different, all distinct, circuit :: [int] → bool

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

serialized’ :: [int] → [int] → [newOptions] → bool

count :: int → [int] → (int → int → bool) → int → bool

element, exactly :: int → [int] → int → bool

cumulative :: [int] → [int] → [int] → int → bool

cumulative’ :: [int] → [int] → [int]→ int → [newOptions] → bool

STATISTICS CONSTRAINTS

fd statistics :: statistics → int → bool

fd statistics’ :: bool

ENUMERATION CONSTRAINTS

indomain :: int → bool

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

MEMBERSHIP CONSTRAINTS

domain :: [int] → int → int → bool

PROPOSITIONAL CONSTRAINTS

#<=> :: bool → bool → bool

1.4.2 Membership Constraint

It restricts a list of FD variables to have values in an integer interval.

domain/3

• Type declaration:

domain :: [int] → int → int → bool

• Deﬁnition: ’domain L A B’ returns true if each element in the list L (with inte-

gers and/or FD variables) belongs to the closed interval [A,B] and also constrains

each FD variable in L to have values in the integer interval [A,B].

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