include "var_perm_sym.mzn";

predicate
var_sqr_sym(array[int,int] of var int: x) =
  let { int: n = card(index_set_1of2(x));
        int: n2 = card(index_set_2of2(x));
        constraint assert(n = n2,"square symmetry applied to non-square array");
        int: l = n * n;
        array[1..l] of var int:
          y = [ x[i,j] | i in index_set_1of2(x),
                         j in index_set_2of2(x) ];
        array[1..8,1..l] of 1..l:
          p = array2d(1..8,1..l,
            [ if k == 1 then i*n + j - n 
              elseif k == 2 then (n - j)*n + i           % r270
              elseif k == 3 then (n - i)*n + (n - j)+1   % r180
              elseif k == 4 then (j*n - n) + (n - i + 1) % r90
              elseif k == 5 then (n - i)*n + j           % x flip
              elseif k == 6 then (i*n - n) + (n - j + 1) % y flip
              elseif k == 7 then (n - j)*n + (n - i + 1) % d2 flip
              else               (j*n - n) + i           % d1 flip
              endif
            | k in 1..8, i,j in 1..n]) }
  in
  var_perm_sym(y,p);