ILOG OPL Development Studio Language Reference Manual

{forall(i in 1..8)forall(j in 1..8: i < j)a[i][j] >= 0;}the constraint a[i][j] >= 0 is modeled for all i and j such that 1 i < j 8.Several parameters can often be combined together to produce more compact statements. Forinstance, the declarationint s = sum(i,j in 1..n: i < j) i*j;is equivalent toint s = sum(i in 1..n) sum(j in 1..n: i < j) i*j;which is less readable.The declarationint s = sum(i in 1..n, j in 1..m) i*j;is equivalent toint s = sum(i in 1..n) sum(j in 1..m) i*j;These parameters can, of course, be subject to filtering conditions. The excerptforall(i,j in 1..n : i < j)a[i][j] >= 0;is equivalent toforall(i in 1..n, j in 1..n : i= 0;Here is an even more compact form:forall(ordered i,j in 1..n)a[i][j] >= 0;Indeed, in many applications one is interested, given a set S, in stating filters or conditionsover all pairs (i, j) of elements of S satisfying i < j in the ordering associated with S. In thisexcerptI L O G O P L D E V E L O P M E N T S T U D I O L A N G U A G ER E F E R E N C E M A N U A L135