Global Constraint Catalog

2.6.12. Implies (items to collection)

Given two constraints $C_{𝑒𝑛𝑡𝑟𝑦}$ and $C_{𝑎𝑙𝑠𝑜}$ where:

$C_{𝑒𝑛𝑡𝑟𝑦}$ has a single argument ${𝚊𝚛𝚐}_{1}$ corresponding to a collection of $k$ items, each attribute of type $𝚒𝚗𝚝$ or $𝚍𝚟𝚊𝚛$ .
$C_{𝑎𝑙𝑠𝑜}$ has a single argument ${𝚊𝚛𝚐}_{2}$ corresponding to a collection of collections of $𝚍𝚟𝚊𝚛$ , each of them having the same number of items $k$ .

If constraint $C_{𝑒𝑛𝑡𝑟𝑦} ({𝚊𝚛𝚐}_{1})$ holds then constraint $C_{𝑎𝑙𝑠𝑜} ({𝚊𝚛𝚐}_{2})$ also holds.

EXAMPLE: As an example, we can go from constraint $C_{𝑒𝑛𝑡𝑟𝑦} =$ $𝚌𝚒𝚛𝚌𝚞𝚒𝚝$ to constraint $𝚕𝚎𝚡_𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝$ if we create for each item “ $𝚒𝚗𝚍𝚎𝚡 - i 𝚜𝚞𝚌𝚌 - s$ ” of the $𝚌𝚒𝚛𝚌𝚞𝚒𝚝$ constraint a collection $〈 𝚟𝚊𝚛 - i, 𝚟𝚊𝚛 - s 〉$ .