formatting

main.pl

@@ -1,36 +1,37 @@
 %% Will Holdsworth 1353032
 %
-% Implements puzzle_solution/1 which solves incomplete proper math puzzles and 
+%  Implements puzzle_solution/1 which solves incomplete proper math puzzles and 
-% validates complete proper math puzzles.
+%  validates complete proper math puzzles.
-% 
+%  
-% A math puzzle is a matrix with a size between 2 and 4. The first row and first
+%  A math puzzle is a matrix with a size between 2 and 4. The first row and first
-% column of the puzzle are reserved for totals, which should always be ground. A
+%  column of the puzzle are reserved for totals, which should always be ground. A
-% total is either the sum or the product of its respective row/column. The top 
+%  total is either the sum or the product of its respective row/column. The top 
-% and left corner can be ignored. A puzzle can be incomplete, partially 
+%  and left corner can be ignored. A puzzle can be incomplete, partially 
-% complete, or complete. An incomplete/partially complete puzzle should have 
+%  complete, or complete. An incomplete/partially complete puzzle should have 
-% "_" where the cell is empty. A proper math puzzle has at most one solution.
+%  "_" where the cell is empty. A proper math puzzle has at most one solution.
-% 
+%  
-% We approach puzzle validation via the clpfd library. We apply constraints to 
+%  We approach puzzle validation via the clpfd library. We apply constraints to 
-% the puzzle in order of restrictiveness. 
+%  the puzzle in order of restrictiveness. 
 %
-% First, we unify the main diagonal by ensuring all cells are the same.
+%  First, we unify the main diagonal by ensuring all cells are the same.
-% Second, we verify that the rows are valid. A valid row's cells should all be 
+%  Second, we verify that the rows are valid. A valid row's cells should all be 
-% digits from 1 to 9 (inclusive), contain only distinct digits. Also, a valid 
+%  digits from 1 to 9 (inclusive), contain only distinct digits. Also, a valid 
-% row's head should be the sum or the product of the cells in the row.
+%  row's head should be the sum or the product of the cells in the row.
-% Finally, we take the transpose of the puzzle and apply the row validation 
+%  Finally, we take the transpose of the puzzle and apply the row validation 
-% predicate to the puzzle again, this time effectively validting the columns.
+%  predicate to the puzzle again, this time effectively validting the columns.
 %
-% The resulting puzzle is labelled using the "first fail" strategy outlined in 
+%  The resulting puzzle is labelled using the "first fail" strategy outlined in 
-% the clpfd docs.
+%  the clpfd docs.
 
 
 :- use_module(library(clpfd)).
 
 
-%% puzzle_solution(+Puzzle)
+%% puzzle_solution(+Puzzle: list)
 %
-% Holds when `Puzzle` is a solved math puzzle.
+%  Holds when `Puzzle` is a solved math puzzle.
-% See the top of this file for more information.
+%  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.
+%  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 
+%  Holds when the variables in `Vars` can be unified.
-all_same([Var|Vars]) :-
-  all_same(Var, Vars).
 
-all_same(Var, [Var]).
+all_same([]).
-all_same(Var, [Var|Vars]) :-
+all_same([_]).
-  all_same(Var, Vars).
+all_same([Head,Head|Tail]) :-
+  all_same([Head|Tail]).
 
 
-%% valid(+Row)
+%% valid_row(+Row: list)
 %
-% Holds when `Row` is valid.
+%  Holds when `Row` is valid.
-% A row is valid when:
+%  A row is valid when:
-%   1. All elements except the head are integers from 1 to 9 (inclusive)
+%    1. All elements except the head are integers from 1 to 9 (inclusive)
-%   2. All elements except the head are distinct 
+%    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`
+%    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 
+%  Holds when `Total` is either the sum or the product of `Vars`.
-% `Vars`.
+
-valid_total(Total, 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.
+%  Holds when Int3 #= Int1 * Int2.
+
 times(Int1, Int2, Int3) :-
   Int3 #= Int1 * Int2.