Prolog math puzzle solver

About

Prolog program solving a specific n x n math puzzle, in which the puzzle consists of a header row, a header column, and the body (the body is n x n). The headers represent either the sum or product of that column / row. Every cell in each column / row must be distinct from one another. The diagonal of the puzzle's body must hold the same value as well.

If either of these specifications are not met, the program will simply return false (the puzzle isn't square, the diagonal values are specified to not match, there is no viable solution, etc.). Here's an example of a puzzle:

Puzzle = [[0,14,10,35],[14,_,_,_],[15,_,_,_],[28,_,1,_]]

which is equivalent to:

    | 14 | 10 | 35 |
----+----+----+----+
 14 |    |    |    |
----+----+----+----+
 15 |    |    |    |
----+----+----+----+
 28 |    |  1 |    |
----+----+----+----+

where 14, 10, 35 is the header row, and 14, 15, 28 is the header column. The solution to this puzzle would be:

Puzzle = [[0, 14, 10, 35], [14, 7, 2, 1], [15, 3, 7, 5], [28, 4, 1, 7]]

which is equivalent to:

    | 14 | 10 | 35 |
----+----+----+----+
 14 |  7 |  2 |  1 |
----+----+----+----+
 15 |  3 |  7 |  5 |
----+----+----+----+
 28 |  4 |  1 |  7 |
----+----+----+----+

We can see that, say, for the third row, 28 is the sum - in fact for all rows in this puzzle actually - while the for the first and second columns, 14 and 10 are their respective sums instead. Also, the diagonal cells all hold the same value 7.

Usage

To run the program, go into the correct directory in terminal, and enter command swipl, and then run the file solve:

?- [solve].
true.

After successfully loading up solve.pl, simply input the Puzzle with the same format as specified above (a list of sublists, with first sublist being the header row, and the head of the other sublists being the components of header column).

And run it through the puzzle_solution predicate:

1 ?-  Puzzle = [[0,14,16,18],[189,_,_,_],[17,_,_,_],[60,_,_,_]],
  |   puzzle_solution(Puzzle).
     | 14 | 16 | 18 |
-----+----+----+----+
 189 |  3 |  9 |  7 |
-----+----+----+----+
  17 |  6 |  3 |  8 |
-----+----+----+----+
  60 |  5 |  4 |  3 |
-----+----+----+----+
Puzzle = [[0, 14, 16, 18], [189, 3, 9, 7], [17, 6, 3, 8], [60, 5, 4, 3]] ;
false.