Prolog Constraints -> Solving Puzzle Grid - prolog

Question

So guys, I'm learning constraints with prolog, and trying to implement a little puzzle using this new knowledge.
The goal of the puzzle is simple: I have a square grid with some numbers on top/below each column and on the right/left of each row.
The domain of values goes from 0 to Gridsize -1, wich means, a grid 7x7 can have numbers from 0 to 6.
The constraints are as follow:
Each number can only apear once each row and once each column
The number on top/right are the sum of the First and Last digits on the column/row respectively
The number on bottom/left are the sum of the Second and SecondLast digits on the column/row respectively
Zeros don't count as digits, are only on the program to represent blank spaces
For an example:
TopConstraint = [7, 6, 4, 7, 3]
RightConstraint = [5, 5, 5, 5, 5]
BottomConstraint = [3, 4, 6, 3, 7]
LeftConstraint = [5, 5, 5, 5, 5]
This constraints can have a 0 too, wich make the program simple ignore (the sum can be any number, if it goes accordingly with the other restrictions).
One solution to the above lists would be the matrix:
3 | 4 | 1 | | 2
1 | 3 | 2 | 4 |
2 | | 4 | 1 | 3
| 1 | 3 | 2 | 4
4 | 2 | | 3 | 1
Now the problem is: my constraints somehow aren't applying, and the program isn't giving me the solution.
After puting the right domain and putting all column/row cells different(wich without any other restrictions it gives me the expected solution), I have this code to apply to each cell, the sum restrictions:
put_restrictions(Sol, Gridsize, SumT, SumR, SumB, SumL):-
put_restrictions_row(Sol, Gridsize, SumR, SumL, 1),
put_restrictions_col(Sol, Gridsize, SumT, SumB, 1).
Where Gridsize is the Gridsize to make iterations upon it, SumT, SumR, SumB, SumL, are the above constraint lists respectively, and 1 to start the iteration counter.
So this predicates are where my problem resides
put_restrictions_col(_, Gridsize, _, _, X):- X > Gridsize, write('end put_restrictions_col'),nl.
put_restrictions_col(Grid, Gridsize, [SumTH|SumTT], [SumBH|SumBT], X):-
get_cell(Grid, FirstInCol, X, 1, Gridsize),
get_cell(Grid, LastInCol, X, Gridsize, Gridsize),
get_cell(Grid, SecondInCol, X, 2, Gridsize),
SecondLastIndex is Gridsize-1,
get_cell(Grid, SecondLastInCol, X, SecondLastIndex, Gridsize),
get_cell(Grid, ThirdInCol, X, 3, Gridsize),
ThirdLastIndex is Gridsize-2,
get_cell(Grid, ThirdLastInCol, X, ThirdLastIndex, Gridsize),
(SumTH #> 0) #=>
(
(((FirstInCol #> 0) #/\ (LastInCol #> 0)) #=> (SumTH #= FirstInCol + LastInCol))
#\/
((FirstInCol #= 0) #=> (SumTH #= SecondInCol + LastInCol))
#\/
((LastInCol #= 0) #=> (SumTH #= FirstInCol + SecondLastInCol))
),
(SumBH #> 0) #=>
(
(((SecondInCol #> 0) #/\ (SecondLastInCol #> 0)) #=> (SumBH #= SecondInCol + SecondLastInCol))
#\/
((SecondInCol #= 0) #=> (SumBH #= ThirdInCol + SecondLastInCol))
#\/
((SecondLastInCol #= 0) #=> (SumBH #= SecondInCol + ThirdLastInCol))
),
X1 is X+1,
put_restrictions_col(Grid, Gridsize, SumTT, SumBT, X1).
put_restrictions_row([], _, _,_,_):- write('end put_restrictions_row'),nl.
put_restrictions_row([H|T], Gridsize, [SumRH|SumRT],[SumLH|SumLT], N):-
element(1, H, FirstInRow),
element(Gridsize, H, LastInRow),
element(2, H, SecondInRow),
SecondLastIndex is Gridsize -1,
element(SecondLastIndex, H, SecondLastInRow),
element(3, H, ThirdInRow),
ThirdLastIndex is Gridsize -2,
element(ThirdLastIndex, H, ThirdLastInRow),
(SumRH #> 0) #=>
(
(((FirstInRow #> 0) #/\ (LastInRow #> 0)) #/\ (FirstInRow + LastInRow #= SumRH))
#\/
((FirstInRow #= 0) #/\ (SecondInRow + LastInRow #= SumRH))
#\/
((LastInRow #= 0) #/\ (FirstInRow + SecondLastInRow #= SumRH))
),
(SumLH #> 0) #=>
(
(((SecondInRow #> 0) #/\ (SecondLastInRow #> 0)) #/\ (SumLH #= SecondInRow + SecondLastInRow))
#\/
((SecondInRow #= 0) #/\ (SumLH #= ThirdInRow + SecondLastInRow))
#\/
((SecondLastInRow #= 0) #/\ (SumLH #= SecondInRow + ThirdLastInRow))
),
N1 is N+1,
put_restrictions_row(T, Gridsize, SumRT, SumLT, N1).
I think the code is pretty self explanatory, if not, what I'm trying to do:
If there is a constraint on the right side:
If the 1st and last cells of the row aren't 0, then their sum is = to the restriction
If the 1st cell on the row is 0, then the sum of 2nd cell of the row and the last = to the restriction -> makes the left restriction being the sum of the 3rd cell from the left and the secondlast
And so on...
I'm not getting any solution on the problem.
What am I doing wrong associating the constraints?
Any help is welcome. Thanks in advance for helping the prologNoob here :P

Answer 1

I tried to solve, with simpler code...
restrictions :-
T = [7, 6, 4, 7, 3], % TopRestriction
R = [5, 5, 5, 5, 5], % RightRestriction
B = [3, 4, 6, 3, 7], % BottomRestriction
L = [5, 5, 5, 5, 5], % LeftRestriction
restrictions(T, R, B, L, Sol),
maplist(writeln, Sol).
restrictions(T, R, B, L, Rows) :-
% check all restrictions are properly sized
maplist(length_(N), [T, R, B, L]),
% solution is a square
length_(N, Rows),
maplist(length_(N), Rows),
transpose(Rows, Cols),
% main constraints
append(Rows, Vs),
N1 is N-1,
Vs ins 0..N1,
maplist(all_different, Rows),
%maplist(all_different, Cols),
% apply restrictions
maplist(restriction, Rows, L, R),
maplist(restriction, Cols, T, B),
% if constraints are not enough strong for an unique solution
label(Vs).
restriction(Tile, S1, S2) :-
append([A,B], R, Tile),
append(_, [C,D], R),
S1 #= 0 #\/ A #= 0 #\/ D #= 0 #\/ S1 #= A + D,
S2 #= 0 #\/ B #= 0 #\/ C #= 0 #\/ S2 #= B + C.
length_(N, L) :- length(L, N).
Note the second all_different constraint is commented out, since when I post it, no solution is found. Removing constraints (so, 'weakening' solutions), it's the only 'real' debugging tool that I've been able to find so far by myself.
Solutions sample:
?- restrictions.
[3,0,1,4,2]
[1,0,2,3,4]
[0,1,2,4,3]
[2,1,4,0,3]
[4,2,0,3,1]
true ;
[3,0,1,4,2]
[1,0,2,3,4]
[0,1,2,4,3]
[2,1,4,0,3]
[4,2,3,0,1]
...