$ Langford's number problem (CSP lib problem 24)
$
$ Arrange l sets of positive integers 1..k to a sequence,
$ such that, following the first occurence of an integer i, 
$ each subsequent occurrence of i, appears i+1 indices later
$ than the last. 
$ For example, for l=2, k=4, a solution would be 41312432
$
$ by Peter Gregory

language ESSENCE' 1.b.a

given k : int
given l : int
letting positionDomain be domain int(1..l*k)
find position : matrix indexed by [positionDomain] of positionDomain

such that 
        
    forall i : int(1..k) .  $for each number
        forall j : int(1..(l-1)) .   $for each instance of that number
            position[j*k+i] = position[(j-1)*k+i] + i + 1,
    (l = 2) =>
      forall i : int(1..k) .  $for each number
          position[k+i] = position[i] + i + 1,

    allDifferent(position)