Global Constraint Catalog

2.2.4. Declaring a global constraint

Declaring a global constraint consists of providing the following information:

A term $𝚌𝚘𝚗𝚜𝚝𝚛𝚊𝚒𝚗𝚝 (A_{1}, A_{2}, \dots, A_{n})$ , where $𝚌𝚘𝚗𝚜𝚝𝚛𝚊𝚒𝚗𝚝$ corresponds to the name of the global constraint and $A_{1}, A_{2}, \dots, A_{n}$ to its arguments.
A possibly empty list of type declarations, where each declaration has the form $𝚝𝚢𝚙𝚎$ : $𝚝𝚢𝚙𝚎_𝚍𝚎𝚌𝚕𝚊𝚛𝚊𝚝𝚒𝚘𝚗$ ; $𝚝𝚢𝚙𝚎$ is the name of the new type we define and $𝚝𝚢𝚙𝚎_𝚍𝚎𝚌𝚕𝚊𝚛𝚊𝚝𝚒𝚘𝚗$ is a basic data type, a compound data type or a type previously defined.
An argument declaration $A_{1}$ : $T_{1}, A_{2}$ : $T_{2}, \dots, A_{n}$ : $T_{n}$ giving for each argument $A_{1}, A_{2},$ $\dots, A_{n}$ of the global constraint $𝚌𝚘𝚗𝚜𝚝𝚛𝚊𝚒𝚗𝚝$ its type. Each type is a basic data type, a compound data type, or a type that was declared in the list of type declarations.
A possibly empty list of restrictions, where each restriction is one of the restrictions described in Section 2.2.3 on page 2.2.3.

EXAMPLE: The arguments of the $𝚊𝚕𝚕_𝚍𝚒𝚏𝚏𝚎𝚛_𝚏𝚛𝚘𝚖_𝚊𝚝_𝚕𝚎𝚊𝚜𝚝_𝚔_𝚙𝚘𝚜$ constraint are described by:

Constraint

$𝚊𝚕𝚕_𝚍𝚒𝚏𝚏𝚎𝚛_𝚏𝚛𝚘𝚖_𝚊𝚝_𝚕𝚎𝚊𝚜𝚝_𝚔_𝚙𝚘𝚜$ $(𝙺, 𝚅𝙴𝙲𝚃𝙾𝚁𝚂)$

Type(s)

$𝚅𝙴𝙲𝚃𝙾𝚁 - 𝚌𝚘𝚕𝚕𝚎𝚌𝚝𝚒𝚘𝚗 (𝚟𝚊𝚛 - 𝚍𝚟𝚊𝚛)$

Argument(s)

$𝙺 - 𝚒𝚗𝚝$

$𝚅𝙴𝙲𝚃𝙾𝚁𝚂 - 𝚌𝚘𝚕𝚕𝚎𝚌𝚝𝚒𝚘𝚗 (𝚟𝚎𝚌 - 𝚅𝙴𝙲𝚃𝙾𝚁)$

Restriction(s)

$𝚛𝚎𝚚𝚞𝚒𝚛𝚎𝚍 (𝚅𝙴𝙲𝚃𝙾𝚁, 𝚟𝚊𝚛)$

$𝙺 \geq 0$

$𝚛𝚎𝚚𝚞𝚒𝚛𝚎𝚍 (𝚅𝙴𝙲𝚃𝙾𝚁𝚂, 𝚟𝚎𝚌)$

$𝚜𝚊𝚖𝚎_𝚜𝚒𝚣𝚎 (𝚅𝙴𝙲𝚃𝙾𝚁𝚂, 𝚟𝚎𝚌)$

The first line indicates that the $𝚊𝚕𝚕_𝚍𝚒𝚏𝚏𝚎𝚛_𝚏𝚛𝚘𝚖_𝚊𝚝_𝚕𝚎𝚊𝚜𝚝_𝚔_𝚙𝚘𝚜$ constraint has two arguments: $𝙺$ and $𝚅𝙴𝙲𝚃𝙾𝚁𝚂$ . The second line declares a new type $𝚅𝙴𝙲𝚃𝙾𝚁$ , which corresponds to a collection of variables. The third line indicates that the first argument $𝙺$ is an integer, while the fourth line tells that the second argument $𝚅𝙴𝙲𝚃𝙾𝚁𝚂$ corresponds to a collection of vectors of type $𝚅𝙴𝙲𝚃𝙾𝚁$ . Finally the four restrictions respectively enforce that:

All the items of the $𝚅𝙴𝙲𝚃𝙾𝚁$ collection mention the $𝚟𝚊𝚛$ attribute,
$𝙺$ be greater than or equal to 0,
All the items of the $𝚅𝙴𝙲𝚃𝙾𝚁𝚂$ collection mention the $𝚟𝚎𝚌$ attribute,
All the vectors have the same number of components.

Global Constraint Catalog

2. Describing Global Constraints

2.2.4. Declaring a global constraint