Sudoku solver in Prolog

sudoku.pl

:- use_module(library(clpfd)).

/*
	Show a sublist of <Pos> in <Sublist>.
	<Offset>    Offset into <Pos>
	<Step>      Step size used in iterating through <Pos>
	<Length>    Length of the sublist.
*/
getSublist(_,_,_,0,[]). % base case

getSublist(Pos,Offset,Step,Length,Sublist) :-
	Idx is Offset + Step*(Length-1),
	nth0(Idx,Pos,Elem),
	Length_n is Length-1,
	getSublist(Pos,Offset,Step,Length_n,Sublist_n),
	Sublist = [Elem|Sublist_n].

getBlock(Blockidx,Grid,Block) :-
	A is (Blockidx mod 3)*3 + (Blockidx - Blockidx mod 3)*9,
	B is A + 9,
	C is B + 9,
	getSublist(Grid,A,1,3,RowA),
	getSublist(Grid,B,1,3,RowB),
	getSublist(Grid,C,1,3,RowC),
	append(RowC,RowB,RowsBC),
	append(RowsBC,RowA,Block).

postConstraints(9,_).
postConstraints(Idx,Grid) :-
	Firstinrow is 9*Idx,
	getSublist(Grid,Firstinrow,1,9,Row),
	all_different(Row),
	getSublist(Grid,Idx,9,9,Column),
	all_different(Column),
	getBlock(Idx,Grid,Block),
	all_different(Block),
	Idx_n is Idx + 1,
	postConstraints(Idx_n,Grid).

postCellConstraints(81,_).
postCellConstraints(Idx,Grid) :-
	nth0(Idx,Grid,A),
	( integer(A) ->
		A #= A
	;
		true
	),
	Idx_n is Idx + 1,
	postCellConstraints(Idx_n,Grid).

pprint(Grid) :-
	\+ (
		between(0,8,Idx),
		Firstinrow is 9*Idx,
		getSublist(Grid,Firstinrow,1,9,Row),
		format('~w~n',[Row]),
		fail
	).
	
/*
 * 	To have this predicate solve a Sudoku, pass it the puzzle as an 81 element
 * 	list, which is a concatenation of all rows of the puzzle. Fixed, predefined
 * 	numbers shall be at their respective places, fields still to be populated
 * 	shall be left unbound.
 */
sudoku(Grid) :-
	length(Grid,81),
	Grid ins 1..9,
	postCellConstraints(0,Grid),
	postConstraints(0,Grid),
	label(Grid),
	pprint(Grid).