binary sudoku in swi prolog

Question

As a prolog newbie, I wanted to try to implement a binary sudoku solver.(Code is below, swi-prolog). Binary sudoku is explained here : https://cstheory.stackexchange.com/questions/16982/how-hard-is-binary-sudoku-puzzle

However, when performing the following query :

binarySudoku([[1,0],[0,1]]). I get "true."
binarySudoku([[1,_],[_,_]]). I get "false."

Now obviously it shouldn't return false as there is a solution... Why is this happening/how can I fix this?

:-use_module(library(clpfd)).

validRow(Row) :-
    Row ins 0..1,
    length(Row,L),
    sum(Row,#=,L/2).

matrixNth(Matr,X,Y,El) :-
    nth1(Y,Matr,CurRow),
    nth1(X,CurRow,El).

allDifferent([]).
allDifferent([X|Y]) :-
    not(member(X,Y)),
    allDifferent(Y).


invalid(Rows,X,Y) :-
    AboveY is Y-1,
    BelowY is Y+1,
    matrixNth(Rows,X,Y,1),
    matrixNth(Rows,X,AboveY,1),
    matrixNth(Rows,X,BelowY,1).
invalid(Rows,X,Y) :-
    LeftX is X-1,
    RightX is X+1,
    matrixNth(Rows,X,Y,1),
    matrixNth(Rows,LeftX,Y,1),
    matrixNth(Rows,RightX,Y,1).

binarySudoku(Rows) :-
    length(Rows,Height),
    transpose(Rows,Cols),
    length(Cols,Height),
    maplist(validRow,Rows),
    foreach(between(1,Height,X),foreach(between(1,Height,Y),not(invalid(Rows,X,Y)))),
    allDifferent(Rows).

Answer 1

Instead of (\+)/1, which is not logically sound in this case, use the pure constraint dif/2: Your code works as expected of you change the line not(member(X,Y)) to:

maplist(dif(X), Y)

Example query (notice that I also use a_more_readable_naming_convention insteadOfMixingTheCases):

?- binary_sudoku([[1,A],[B,C]]), label([A,B,C]).
A = B, B = 0,
C = 1 ;
false.

+1 for using CLP(FD), which is a good fit for this task.