language ESSENCE' 1.b.a
$ Killer Sudoku puzzle solver, by Andras Salamon
$ see http://en.wikipedia.org/wiki/Killer_sudoku
$ the instance is specified in the parameter file

letting   SIZE   be 9
letting   NUMQD  be domain int( 0..lastdx )
letting   RANGE  be domain int( 1..SIZE )
letting   VALUES be domain int( 0..SIZE )
$ index of last lt entry
given     lastdx : int( 1..((2*SIZE*(SIZE-1)-1)) )
$ list of cage constraints in the problem
given     cage   : matrix indexed by [NUMQD, int(0..8)] of VALUES

find      field  : matrix indexed by [RANGE, RANGE] of RANGE

such that
$ all rows have to be different
    forall row : RANGE .
	alldifferent(field[row,..]),

$ all columns have to be different
    forall col : RANGE .
	alldifferent(field[..,col]),	 

$ all blocks have to be different
    forall i,j : int(0..2) . 
	forall col1,col2,row1,row2 : int(1..3) .
	    ((col1 != col2) /\ (row1 != row2)) => 
		(field[row1+(i*3), col1+(j*3)] 
		    != field[row2+(i*3), col2+(j*3)]),

$ all cage constraints are satisfied
$ handle each arity separately due to lack of variable length lists
    forall i : NUMQD .
	( ( cage[i,7] != 0 ) /\
	    ( cage[i,0] = field[ cage[i,1], cage[i,2] ]
		+ field[ cage[i,3], cage[i,4] ]
		+ field[ cage[i,5], cage[i,6] ]
		+ field[ cage[i,7], cage[i,8] ]
	    )
	) \/
	( ( cage[i,7] = 0 ) /\ ( cage[i,5] != 0 ) /\
	    ( cage[i,0] = field[ cage[i,1], cage[i,2] ]
		+ field[ cage[i,3], cage[i,4] ]
		+ field[ cage[i,5], cage[i,6] ]
	    )
	) \/
	( ( cage[i,5] = 0 ) /\ ( cage[i,3] != 0 ) /\
	    ( cage[i,0] = field[ cage[i,1], cage[i,2] ]
		+ field[ cage[i,3], cage[i,4] ]
	    )
	) \/
	( ( cage[i,3] = 0 ) /\
	    ( cage[i,0] = field[ cage[i,1], cage[i,2] ] )
	)