formatting

main.pl

@@ -27,10 +27,11 @@
 :- use_module(library(clpfd)).
 
 
-%% puzzle_solution(+Puzzle)
+%% puzzle_solution(+Puzzle: list)
 %
 %  Holds when `Puzzle` is a solved math puzzle.
 %  See the top of this file for more information.
+
 puzzle_solution(Puzzle) :-
   Puzzle = [_|Rows],
   unify_diagonal(Puzzle),
@@ -40,17 +41,19 @@ puzzle_solution(Puzzle) :-
   maplist(valid_row, Columns).
 
 
-%% unify_diagonal(+Puzzle)
+%% unify_diagonal(+Puzzle: list)
 %
 %  Holds when every variable in the main diagonal of `Puzzle` is the same.
+
 unify_diagonal(Puzzle) :-
   main_diagonal(Puzzle, [_|Diag]),
   all_same(Diag).
 
 
-%% main_diagonal(+Matrix, -Diag)
+%% main_diagonal(+Matrix: list, -Diag: list)
 % 
-% Holds when the list `Diag` is the main diagonal of the 2d list `Matrix`.
+%  Holds when `Diag` is the main diagonal of the 2d list `Matrix`.
+
 main_diagonal(Matrix, Diag) :-
   main_diagonal(Matrix, 0, Diag).
 
@@ -61,50 +64,52 @@ main_diagonal([Row|Rows], Column, [D|Ds]) :-
   main_diagonal(Rows, Next_column, Ds).
 
 
-%% all_same(+Vars)
+%% all_same(+Vars: list)
 % 
-% Holds when the variables in the list `Vars` can be unified 
-all_same([Var|Vars]) :-
-  all_same(Var, Vars).
+%  Holds when the variables in `Vars` can be unified.
 
-all_same(Var, [Var]).
-all_same(Var, [Var|Vars]) :-
-  all_same(Var, Vars).
+all_same([]).
+all_same([_]).
+all_same([Head,Head|Tail]) :-
+  all_same([Head|Tail]).
 
 
-%% valid(+Row)
+%% valid_row(+Row: list)
 %
 %  Holds when `Row` is valid.
 %  A row is valid when:
 %    1. All elements except the head are integers from 1 to 9 (inclusive)
 %    2. All elements except the head are distinct 
 %    3. The head of the row is either the sum or the product of the tail of `Row`
+
 valid_row([Total|Vars]) :-
   Vars ins 1..9, 
   all_distinct(Vars),
-  valid_total(Total, Vars),
+  valid_total(Vars, Total),
   labeling([ff], Vars).
 
 
-%% valid_total(+Total, +Vars)
+%% valid_total(+Vars: list, +Total: integer)
 %
-% Holds when the integer `Total` is either the sum or the product of the list 
-% `Vars`.
-valid_total(Total, Vars) :-
+%  Holds when `Total` is either the sum or the product of `Vars`.
+
+valid_total(Vars, Total) :-
   sum(Vars, #=, Total)
 ; product(Vars, Total).
 
 
-%% product(+Vars, -Product)
+%% product(+Vars: list, -Product: integer)
 %
-% Holds when the integer `Product` is the product of the list `Vars`.
+%  Holds when `Product` is the product of `Vars`.
+
 product(Vars, Product) :-
   foldl(times, Vars, 1, Product).
 
 
-%% times(?Int1, ?Int2, ?Int3)
+%% times(?Int1: integer, ?Int2: integer, ?Int3: integer)
 %
 %  Holds when Int3 #= Int1 * Int2.
+
 times(Int1, Int2, Int3) :-
   Int3 #= Int1 * Int2.