How do you check the elements of a submatrix in Prolog

Question

I am trying to write a Shikaku solver in EclipsE Prolog. My contraints are defined as follow:

solve(Problemname):-
writeln("Start shikaku."),
problem(Problemname, Width, Height, Hints),
shikaku(Width, Height, Hints).

shikaku(Width, Height, Hints):- 
length(Hints, HintCount),
array_list(HintsArray, Hints),

% Prepare the matrix and assign an ID to every Hint (from 1 to HintCount)
dim(Matrix, [Width, Height]),
Matrix[1..Width,1..Height] :: 1..HintCount,

%flatten_array(Matrix,FlattenedMatrix),
(for(ID,1,HintCount), foreach((HintX, HintY, HintNumber), Hints), param(Width, Height, Matrix, HintsArray) do
    (   
        occurrences(ID, Matrix, HintNumber),
        L :: 1..Width, R :: 1..Width,
        T :: 1..Height, B :: 1..Height,

        % Hint coordinates are inside the rectangle.
        L #=< HintX,
        R #>= HintX,
        T #=< HintY,
        B #>= HintY,
        DeltaX #= R-L+1,
        DeltaY #= B-T+1,
        HintNumber #= DeltaX * DeltaY,

        Matrix[L..R,T..B] :: ID..ID
        %writematrix(Submatrix, DeltaX, DeltaY, HintsArray),

        %flatten(Submatrix, FlatSubmatrix), 
        %array_list(FlatSubmatrixArray, FlatSubmatrix),

        % Cell count in rectangle must equal HintNumber
        %length(FlatSubmatrix, HintNumber),

        % All cells in rectangle must have ID as value
        %FlatSubmatrixArray[1..HintNumber] :: ID    

    )
),

% Start searching
labeling(Matrix),

writematrix(Matrix, Width, Height, HintsArray). 

writematrix(Matrix, Width, Height, HintsArray):-
writeln("Writing as classic view:"),
(for(I, 1, Height), param(Matrix, Width, HintsArray) do
    write("["),
    Row is Matrix[I],
    (for(J, 1, Width), param(Row, HintsArray) do
        ID is Row[J],
        (_,_,Val) is HintsArray[ID],
        write(" "),
        write(Val),
        write(" ")
    ),

    writeln("]")
).

The line in comments should check if the submatrix going from L..R - T..B only contains elements that are equal to ID. How can this be done?

Running this gives an "instantiation fault in _3264{1 .. 3} =< 3"

edit1: full code

edit2 It seems that eclipse is not able to reduce the domain of the LR/TB variables to apply an instantiation. Is this a correct assumption? If so, how would this be solvable?

Answer 1

I haven't run your code, but looking at the documentation of the :: operator for instantiating domains, we see that it expects a lower and upper bound of the domain range. For your example, if you just want every number in a subset of an array to be equal to let's say 4, you could simply write the following:

Matrix[A..B,C..D] :: 4..4

EDIT

The error you are receiving is not triggered by that line of code. It gives an instantiation fault while comparing a domain variable with an integer. My guess is that you accidentally wrote =< instead of #=< somewhere in code that isn't included in this question, since the domain of {1..3} is in fact =< 3 and shouldn't give any error were constraint operators correctly used.

If you can't seem to figure out which line of code is producing the error, try performing a trace - it (almost) always reveals the cause. If you are using tkeclipse, a built-in tracer tool is available.