Global Constraint Catalog: Kfunctional

3.7.107. Functional dependency

$𝚊𝚋𝚜_𝚟𝚊𝚕𝚞𝚎$ (intension, first argument),
$𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝_𝚜𝚊𝚖𝚎_𝚟𝚊𝚕𝚞𝚎$ (intension, first argument),
$𝚊𝚖𝚘𝚗𝚐$ (intension, first argument),
$𝚊𝚖𝚘𝚗𝚐_𝚍𝚒𝚏𝚏_0$ (intension, first argument),
$𝚊𝚖𝚘𝚗𝚐_𝚒𝚗𝚝𝚎𝚛𝚟𝚊𝚕$ (intension, first argument),
$𝚊𝚖𝚘𝚗𝚐_𝚖𝚘𝚍𝚞𝚕𝚘$ (intension, first argument),
$𝚊𝚖𝚘𝚗𝚐_𝚟𝚊𝚛$ (intension, first argument),
$𝚊𝚗𝚍$ (intension, first argument),
$𝚋𝚊𝚕𝚊𝚗𝚌𝚎$ (intension, first argument),
$𝚋𝚊𝚕𝚊𝚗𝚌𝚎_𝚌𝚢𝚌𝚕𝚎$ (intension, first argument),
$𝚋𝚊𝚕𝚊𝚗𝚌𝚎_𝚒𝚗𝚝𝚎𝚛𝚟𝚊𝚕$ (intension, first argument),
$𝚋𝚊𝚕𝚊𝚗𝚌𝚎_𝚖𝚘𝚍𝚞𝚕𝚘$ (intension, first argument),
$𝚋𝚊𝚕𝚊𝚗𝚌𝚎_𝚙𝚊𝚛𝚝𝚒𝚝𝚒𝚘𝚗$ (intension, first argument),
$𝚋𝚊𝚕𝚊𝚗𝚌𝚎_𝚙𝚊𝚝𝚑$ (intension, first argument),
$𝚋𝚊𝚕𝚊𝚗𝚌𝚎_𝚝𝚛𝚎𝚎$ (intension, first argument),
$𝚋𝚒𝚐_𝚙𝚎𝚊𝚔$ (intension, first argument),
$𝚋𝚒𝚐_𝚟𝚊𝚕𝚕𝚎𝚢$ (intension, first argument),
$𝚋𝚒𝚗𝚊𝚛𝚢_𝚝𝚛𝚎𝚎$ (intension, first argument),
$𝚌𝚊𝚛𝚍𝚒𝚗𝚊𝚕𝚒𝚝𝚢_𝚊𝚝𝚕𝚎𝚊𝚜𝚝$ (intension, first argument),
$𝚌𝚊𝚛𝚍𝚒𝚗𝚊𝚕𝚒𝚝𝚢_𝚊𝚝𝚖𝚘𝚜𝚝$ (intension, first argument),
$𝚌𝚊𝚛𝚍𝚒𝚗𝚊𝚕𝚒𝚝𝚢_𝚊𝚝𝚖𝚘𝚜𝚝_𝚙𝚊𝚛𝚝𝚒𝚝𝚒𝚘𝚗$ (intension, first argument),
$𝚌𝚊𝚜𝚎$ (extension),
$𝚌𝚑𝚊𝚗𝚐𝚎$ (intension, first argument),
$𝚌𝚑𝚊𝚗𝚐𝚎_𝚌𝚘𝚗𝚝𝚒𝚗𝚞𝚒𝚝𝚢$ (intension, first,second,...,eighth argument),
$𝚌𝚑𝚊𝚗𝚐𝚎_𝚙𝚊𝚒𝚛$ (intension, first argument),
$𝚌𝚑𝚊𝚗𝚐𝚎_𝚙𝚊𝚛𝚝𝚒𝚝𝚒𝚘𝚗$ (intension, first argument),
$𝚌𝚑𝚊𝚗𝚐𝚎_𝚟𝚎𝚌𝚝𝚘𝚛𝚜$ (intension, first argument),
$𝚌𝚒𝚛𝚌𝚞𝚕𝚊𝚛_𝚌𝚑𝚊𝚗𝚐𝚎$ (intension, first argument),
$𝚌𝚕𝚒𝚚𝚞𝚎$ (intension, first argument),
$𝚌𝚘𝚕𝚘𝚛𝚎𝚍_𝚖𝚊𝚝𝚛𝚒𝚡$ (intension, third attribute of fifth argument, third attribute of sixth argument),
$𝚌𝚘𝚖𝚖𝚘𝚗$ (intension, first, second argument),
$𝚌𝚘𝚖𝚖𝚘𝚗_𝚒𝚗𝚝𝚎𝚛𝚟𝚊𝚕$ (intension, first, second argument),
$𝚌𝚘𝚖𝚖𝚘𝚗_𝚖𝚘𝚍𝚞𝚕𝚘$ (intension, first, second argument),
$𝚌𝚘𝚖𝚖𝚘𝚗_𝚙𝚊𝚛𝚝𝚒𝚝𝚒𝚘𝚗$ (intension, first, second argument),
$𝚌𝚘𝚗𝚗𝚎𝚌𝚝_𝚙𝚘𝚒𝚗𝚝𝚜$ (intension, fourth argument),
$𝚌𝚛𝚘𝚜𝚜𝚒𝚗𝚐$ (intension, first argument),
$𝚌𝚢𝚌𝚕𝚎$ (intension, first argument),
$𝚌𝚢𝚌𝚕𝚎_𝚘𝚛_𝚊𝚌𝚌𝚎𝚜𝚜𝚒𝚋𝚒𝚕𝚒𝚝𝚢$ (intension, second argument),
$𝚌𝚢𝚌𝚕𝚒𝚌_𝚌𝚑𝚊𝚗𝚐𝚎$ (intension, first argument),
$𝚌𝚢𝚌𝚕𝚒𝚌_𝚌𝚑𝚊𝚗𝚐𝚎_𝚓𝚘𝚔𝚎𝚛$ (intension, first argument),
$𝚍𝚎𝚎𝚙𝚎𝚜𝚝_𝚟𝚊𝚕𝚕𝚎𝚢$ (intension, first argument),
$𝚍𝚒𝚏𝚏𝚎𝚛_𝚏𝚛𝚘𝚖_𝚎𝚡𝚊𝚌𝚝𝚕𝚢_𝚔_𝚙𝚘𝚜$ (intension, first argument),
$𝚍𝚒𝚜𝚌𝚛𝚎𝚙𝚊𝚗𝚌𝚢$ (intension, second argument),
$𝚍𝚒𝚜𝚝𝚊𝚗𝚌𝚎$ (intension, third argument),
$𝚍𝚒𝚜𝚝𝚊𝚗𝚌𝚎_𝚋𝚎𝚝𝚠𝚎𝚎𝚗$ (intension, first argument),
$𝚍𝚒𝚜𝚝𝚊𝚗𝚌𝚎_𝚌𝚑𝚊𝚗𝚐𝚎$ (intension, first argument),
$𝚎𝚕𝚎𝚖$ (extension, second attribute of first argument),
$𝚎𝚕𝚎𝚖𝚎𝚗𝚝$ (extension, third argument),
$𝚎𝚕𝚎𝚖𝚎𝚗𝚝_𝚙𝚛𝚘𝚍𝚞𝚌𝚝$ (extension, fourth argument),
$𝚎𝚕𝚎𝚖𝚎𝚗𝚝𝚜$ (extension, second attribute of first argument),
$𝚎𝚕𝚎𝚖𝚎𝚗𝚝𝚜_𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝$ (extension, second attribute of first argument),
$𝚎𝚚$ (intension, first, second argument),
$𝚎𝚚_𝚌𝚜𝚝$ (intension, first, second, and third argument),
$𝚎𝚚𝚞𝚒𝚟𝚊𝚕𝚎𝚗𝚝$ (intension, first argument),
$𝚎𝚡𝚊𝚌𝚝𝚕𝚢$ (intension, first argument),
$𝚏𝚒𝚛𝚜𝚝_𝚟𝚊𝚕𝚞𝚎_𝚍𝚒𝚏𝚏_0$ (intension, first argument),
$𝚐𝚌𝚍$ (intension, third argument),
$𝚐𝚕𝚘𝚋𝚊𝚕_𝚌𝚊𝚛𝚍𝚒𝚗𝚊𝚕𝚒𝚝𝚢$ (intension, second attribute of second argument),
$𝚐𝚕𝚘𝚋𝚊𝚕_𝚌𝚊𝚛𝚍𝚒𝚗𝚊𝚕𝚒𝚝𝚢_𝚗𝚘_𝚕𝚘𝚘𝚙$ (intension, first argument as well as second attribute of third argument),
$𝚐𝚕𝚘𝚋𝚊𝚕_𝚌𝚊𝚛𝚍𝚒𝚗𝚊𝚕𝚒𝚝𝚢_𝚠𝚒𝚝𝚑_𝚌𝚘𝚜𝚝𝚜$ (intension, second attribute of second argument and fourth argument),
$𝚐𝚛𝚊𝚙𝚑_𝚌𝚛𝚘𝚜𝚜𝚒𝚗𝚐$ (intension, first argument),
$𝚐𝚛𝚘𝚞𝚙$ (intension, first, second,...,sixth argument),
$𝚐𝚛𝚘𝚞𝚙_𝚜𝚔𝚒𝚙_𝚒𝚜𝚘𝚕𝚊𝚝𝚎𝚍_𝚒𝚝𝚎𝚖$ (intension, first, second,...,fourth argument),
$𝚑𝚒𝚐𝚑𝚎𝚜𝚝_𝚙𝚎𝚊𝚔$ (intension, first argument),
$𝚒𝚖𝚙𝚕𝚢$ (intension, first argument),
$𝚒𝚗𝚌𝚛𝚎𝚊𝚜𝚒𝚗𝚐_𝚗𝚟𝚊𝚕𝚞𝚎$ (intension, second argument),
$𝚒𝚗𝚌𝚛𝚎𝚊𝚜𝚒𝚗𝚐_𝚜𝚞𝚖$ (intension, first argument),
$𝚒𝚗𝚏𝚕𝚎𝚡𝚒𝚘𝚗$ (intension, first argument),
$𝚒𝚗𝚟𝚎𝚛𝚜𝚎$ (intension, second and third attributes of first argument),
$𝚒𝚗𝚟𝚎𝚛𝚜𝚎_𝚘𝚏𝚏𝚜𝚎𝚝$ (intension, second and third attributes of third argument),
$𝚕𝚎𝚗𝚐𝚝𝚑_𝚏𝚒𝚛𝚜𝚝_𝚜𝚎𝚚𝚞𝚎𝚗𝚌𝚎$ (intension, first argument),
$𝚕𝚎𝚗𝚐𝚝𝚑_𝚕𝚊𝚜𝚝_𝚜𝚎𝚚𝚞𝚎𝚗𝚌𝚎$ (intension, first argument),
$𝚕𝚘𝚗𝚐𝚎𝚜𝚝_𝚌𝚑𝚊𝚗𝚐𝚎$ (intension, first argument),
$𝚕𝚘𝚗𝚐𝚎𝚜𝚝_𝚍𝚎𝚌𝚛𝚎𝚊𝚜𝚒𝚗𝚐_𝚜𝚎𝚚𝚞𝚎𝚗𝚌𝚎$ (intension, first argument),
$𝚕𝚘𝚗𝚐𝚎𝚜𝚝_𝚒𝚗𝚌𝚛𝚎𝚊𝚜𝚒𝚗𝚐_𝚜𝚎𝚚𝚞𝚎𝚗𝚌𝚎$ (intension, first argument),
$𝚖𝚊𝚙$ (intension, first, second argument),
$𝚖𝚊𝚡_𝚍𝚎𝚌𝚛𝚎𝚊𝚜𝚒𝚗𝚐_𝚜𝚕𝚘𝚙𝚎$ (intension, first argument),
$𝚖𝚊𝚡_𝚒𝚗𝚌𝚛𝚎𝚊𝚜𝚒𝚗𝚐_𝚜𝚕𝚘𝚙𝚎$ (intension, first argument),
$𝚖𝚊𝚡_𝚗$ (intension, first argument),
$𝚖𝚊𝚡_𝚗𝚟𝚊𝚕𝚞𝚎$ (intension, first argument),
$𝚖𝚊𝚡_𝚜𝚒𝚣𝚎_𝚜𝚎𝚝_𝚘𝚏_𝚌𝚘𝚗𝚜𝚎𝚌𝚞𝚝𝚒𝚟𝚎_𝚟𝚊𝚛$ (intension, first argument),
$𝚖𝚊𝚡_𝚘𝚌𝚌_𝚘𝚏_𝚌𝚘𝚗𝚜𝚎𝚌𝚞𝚝𝚒𝚟𝚎_𝚝𝚞𝚙𝚕𝚎𝚜_𝚘𝚏_𝚟𝚊𝚕𝚞𝚎𝚜$ (intension, first argument),
$𝚖𝚊𝚡_𝚘𝚌𝚌_𝚘𝚏_𝚜𝚘𝚛𝚝𝚎𝚍_𝚝𝚞𝚙𝚕𝚎𝚜_𝚘𝚏_𝚟𝚊𝚕𝚞𝚎𝚜$ (intension, first argument),
$𝚖𝚊𝚡_𝚘𝚌𝚌_𝚘𝚏_𝚝𝚞𝚙𝚕𝚎𝚜_𝚘𝚏_𝚟𝚊𝚕𝚞𝚎𝚜$ (intension, first argument),
$𝚖𝚊𝚡𝚒𝚖𝚞𝚖$ (intension, first argument),
$𝚖𝚊𝚡𝚒𝚖𝚞𝚖_𝚖𝚘𝚍𝚞𝚕𝚘$ (intension, first argument),
$𝚖𝚒𝚗_𝚍𝚎𝚌𝚛𝚎𝚊𝚜𝚒𝚗𝚐_𝚜𝚕𝚘𝚙𝚎$ (intension, first argument),
$𝚖𝚒𝚗_𝚒𝚗𝚌𝚛𝚎𝚊𝚜𝚒𝚗𝚐_𝚜𝚕𝚘𝚙𝚎$ (intension, first argument),
$𝚖𝚒𝚗_𝚗$ (intension, first argument),
$𝚖𝚒𝚗_𝚗𝚟𝚊𝚕𝚞𝚎$ (intension, first argument),
$𝚖𝚒𝚗_𝚜𝚒𝚣𝚎_𝚜𝚎𝚝_𝚘𝚏_𝚌𝚘𝚗𝚜𝚎𝚌𝚞𝚝𝚒𝚟𝚎_𝚟𝚊𝚛$ (intension, first argument),
$𝚖𝚒𝚗_𝚠𝚒𝚍𝚝𝚑_𝚙𝚎𝚊𝚔$ , (intension, first argument),
$𝚖𝚒𝚗_𝚠𝚒𝚍𝚝𝚑_𝚟𝚊𝚕𝚕𝚎𝚢$ , (intension, first argument),
$𝚖𝚒𝚗𝚒𝚖𝚞𝚖$ (intension, first argument),
$𝚖𝚒𝚗𝚒𝚖𝚞𝚖_𝚎𝚡𝚌𝚎𝚙𝚝_0$ (intension, first argument),
$𝚖𝚒𝚗𝚒𝚖𝚞𝚖_𝚖𝚘𝚍𝚞𝚕𝚘$ (intension, first argument),
$𝚖𝚒𝚗𝚒𝚖𝚞𝚖_𝚠𝚎𝚒𝚐𝚑𝚝_𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝$ (intension, third argument),
$𝚖𝚞𝚕𝚝𝚒𝚙𝚕𝚎$ (intension, third argument),
$𝚗𝚊𝚗𝚍$ (intension, first argument),
$𝚗𝚌𝚕𝚊𝚜𝚜$ (intension, first argument),
$𝚗𝚎𝚚𝚞𝚒𝚟𝚊𝚕𝚎𝚗𝚌𝚎$ (intension, first argument),
$𝚗𝚒𝚗𝚝𝚎𝚛𝚟𝚊𝚕$ (intension, first argument),
$𝚗𝚘𝚛$ (intension, first argument),
$𝚗𝚙𝚊𝚒𝚛$ (intension, first argument),
$𝚗𝚜𝚎𝚝_𝚘𝚏_𝚌𝚘𝚗𝚜𝚎𝚌𝚞𝚝𝚒𝚟𝚎_𝚟𝚊𝚕𝚞𝚎𝚜$ (intension, first argument),
$𝚗𝚟𝚊𝚕𝚞𝚎$ (intension, first argument),
$𝚗𝚟𝚊𝚕𝚞𝚎_𝚘𝚗_𝚒𝚗𝚝𝚎𝚛𝚜𝚎𝚌𝚝𝚒𝚘𝚗$ (intension, first argument),
$𝚗𝚟𝚎𝚌𝚝𝚘𝚛$ (intension, first argument),
$𝚗𝚟𝚒𝚜𝚒𝚋𝚕𝚎_𝚏𝚛𝚘𝚖_𝚎𝚗𝚍$ (intension, first argument),
$𝚗𝚟𝚒𝚜𝚒𝚋𝚕𝚎_𝚏𝚛𝚘𝚖_𝚜𝚝𝚊𝚛𝚝$ (intension, first argument),
$𝚘𝚙𝚎𝚗_𝚊𝚖𝚘𝚗𝚐$ (intension, second argument),
$𝚘𝚛$ (intension, first argument),
$𝚘𝚛𝚌𝚑𝚊𝚛𝚍$ (intension, first argument),
$𝚘𝚛𝚍𝚎𝚛𝚎𝚍_𝚗𝚟𝚎𝚌𝚝𝚘𝚛$ (intension, first argument),
$𝚘𝚛𝚝𝚑_𝚕𝚒𝚗𝚔_𝚘𝚛𝚒_𝚜𝚒𝚣_𝚎𝚗𝚍$ (intension, first, second and third attributes of first argument),
$𝚙𝚊𝚝𝚑$ (intension, first argument),
$𝚙𝚎𝚊𝚔$ (intension, first argument),
$𝚙𝚎𝚛𝚒𝚘𝚍$ (intension, first argument),
$𝚙𝚎𝚛𝚒𝚘𝚍_𝚎𝚡𝚌𝚎𝚙𝚝_0$ (intension, first argument),
$𝚙𝚎𝚛𝚒𝚘𝚍_𝚟𝚎𝚌𝚝𝚘𝚛𝚜$ (intension, first argument),
$𝚙𝚘𝚠𝚎𝚛$ (intension, third argument),
$𝚙𝚛𝚘𝚙𝚎𝚛_𝚏𝚘𝚛𝚎𝚜𝚝$ (intension, first argument),
$𝚛𝚎𝚖𝚊𝚒𝚗𝚍𝚎𝚛$ (intension, third argument),
$𝚜𝚒𝚐𝚗_𝚘𝚏$ (intension, first argument),
$𝚜𝚒𝚣𝚎_𝚖𝚊𝚡_𝚜𝚎𝚚_𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝$ (intension, first argument),
$𝚜𝚒𝚣𝚎_𝚖𝚊𝚡_𝚜𝚝𝚊𝚛𝚝𝚒𝚗𝚐_𝚜𝚎𝚚_𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝$ (intension, first argument),
$𝚜𝚖𝚘𝚘𝚝𝚑$ (intension, first argument),
$𝚜𝚝𝚊𝚐𝚎_𝚎𝚕𝚎𝚖𝚎𝚗𝚝$ (extension, second attribute of first argument),
$𝚜𝚘𝚛𝚝$ (intension, second argument),
$𝚜𝚘𝚛𝚝_𝚙𝚎𝚛𝚖𝚞𝚝𝚊𝚝𝚒𝚘𝚗$ (intension, second, third argument),
$𝚜𝚞𝚖$ (intension, fourth argument),
$𝚜𝚞𝚖_𝚘𝚏_𝚠𝚎𝚒𝚐𝚑𝚝𝚜_𝚘𝚏_𝚍𝚒𝚜𝚝𝚒𝚗𝚌𝚝_𝚟𝚊𝚕𝚞𝚎𝚜$ (intension, third argument),
$𝚝𝚎𝚖𝚙𝚘𝚛𝚊𝚕_𝚙𝚊𝚝𝚑$ (intension, first argument),
$𝚝𝚛𝚎𝚎$ (intension, first argument),
$𝚝𝚛𝚎𝚎_𝚛𝚊𝚗𝚐𝚎$ (intension, first, second argument),
$𝚝𝚠𝚘_𝚕𝚊𝚢𝚎𝚛_𝚎𝚍𝚐𝚎_𝚌𝚛𝚘𝚜𝚜𝚒𝚗𝚐$ (intension, first argument),
$𝚟𝚊𝚕𝚕𝚎𝚢$ (intension, first argument),
$𝚠𝚎𝚒𝚐𝚑𝚝𝚎𝚍_𝚙𝚊𝚛𝚝𝚒𝚊𝚕_𝚊𝚕𝚕𝚍𝚒𝚏𝚏$ (intension, fourth argument),
$𝚡𝚘𝚛$ (intension, first argument).

A constraint that allows for representing a functional dependency between possibly several domain variables and a single domain variable. A sequence of variables $X_{1}, X_{2}, \dots, X_{n}$ is said to functionally determine another variable $Y$ if and only if each potential tuple of values of $X_{1}, X_{2}, \dots, X_{n}$ is associated with exactly one potential value of $Y$ (i.e., $Y$ is a function of $X_{1}, X_{2}, \dots, X_{n}$ ). For each constraint we indicate whether its functional dependency is defined in intention or in extension. We also indicate which variable $var$ is determined by the functional dependency. Within the Arg. properties slot of a constraint that mentions the functional dependency keyword, we also mention which variables determine $var$ .

Finally, the keyword Pure functional dependency provides the list of constraints that are only defined by one or several functional dependencies. For instance the $𝚗𝚟𝚊𝚕𝚞𝚎$ $(n, 〈 v_{1}, v_{2}, \dots, v_{m})$ constraint is only defined in term of a functional dependency (i.e., $n$ is equal to the number of distinct values in $v_{1}, v_{2}, \dots, v_{m}$ ), while the $𝚝𝚛𝚎𝚎$ $(n, 〈 {𝑛𝑜𝑑𝑒}_{1}, {𝑛𝑜𝑑𝑒}_{2}, \dots, {𝑛𝑜𝑑𝑒}_{m})$ constraint is not only defined in term of a functional dependency since, in addition of counting trees, it also enforces no cycle in the corresponding graph.

Global Constraint Catalog

3. Description of the Catalogue

3.7.107. Functional dependency