current implementation (broken)

main.pl

@@ -0,0 +1,66 @@
+% Two = [[0,10,9],[11,_,_],[10,_,_]], puzzle_solution(Two).
+% Three = [[0,14,10,35],[14,_,_,_],[15,_,_,_],[28,_,1,_]].
+
+:- use_module(library(clpfd)).
+:- use_module(library(apply)).
+
+
+%% puzzle_solution(+Puzzle)
+%
+puzzle_solution(Puzzle) :-
+  Puzzle = [_|Rows],
+  % unify_diagonal(Puzzle),
+  maplist(valid_row, Rows),
+  transpose(Puzzle, TransposedPuzzle),
+  TransposedPuzzle = [_|Columns],
+  maplist(valid_row, Columns).
+
+
+%% valid(+Row)
+%
+valid_row([Head|Tail]) :-
+  Tail ins 1..9, 
+  all_distinct(Tail),
+  valid_head(Head, Tail).
+
+
+%% valid_head(+Head, +Tail)
+%
+valid_head(Head, List) :-
+  sum(List, #=, Head)
+; foldl(mul, List, 1, Head).
+
+%% mul
+%
+mul(X, Acc, New) :-
+  New #= Acc * X.
+
+
+%% unify_diagonal(+Puzzle)
+%
+unify_diagonal(Puzzle) :-
+  main_diagonal(Puzzle, [_|Diag]),
+  all_same(Diag).
+
+
+%% main_diagonal(+Matrix, -Diag)
+%
+main_diagonal(Matrix, Diag) :-
+  main_diagonal(Matrix, 0, Diag).
+
+main_diagonal([], _, []).
+main_diagonal([M|Ms], I, [D|Ds]) :-
+  nth0(I, M, D),
+  I1 is I + 1,
+  main_diagonal(Ms, I1, Ds).
+
+
+%% all_same(List)
+% 
+all_same([Head|Tail]) :-
+  all_same(Head, Tail).
+
+all_same(Head, [X|Xs]) :-
+  Head = X,
+  all_same(Head, Xs).
+