comment file and functions, reorder for niceness

main.pl

@@ -1,74 +1,111 @@
-% Three = [[0,14,10,35],[14,_,_,_],[15,_,_,_],[28,_,1,_]], puzzle_solution(Three)
+%% Will Holdsworth 1353032
-% Three = [[0, 14, 10, 35], [14, 7, 2, 1], [15, 3, 7, 5], [28, 4, 1, 7]].
+%
+% Implements puzzle_solution/1 which solves incomplete proper math puzzles and 
+% validates complete proper math puzzles.
+% 
+% 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
+% 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 
+% complete, or complete. An incomplete/partially complete puzzle should have 
+% "_" 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 
+% the puzzle in order of restrictiveness. 
+%
+% 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 
+% 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.
+% Finally, we take the transpose of the puzzle and apply the row validation 
+% predicate to the puzzle again, this time effectively validting the columns.
+%
+% The resulting puzzle is labelled using the "first fail" strategy outlined in 
+% the clpfd docs.
+
 
 :- use_module(library(clpfd)).
 
+
 %% puzzle_solution(+Puzzle)
 %
+% 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),
   maplist(valid_row, Rows),
-  transpose(Puzzle, TransposedPuzzle),
+  transpose(Puzzle, Transposed_puzzle),
-  TransposedPuzzle = [_|Columns],
+  Transposed_puzzle = [_|Columns],
   maplist(valid_row, Columns).
 
 
-%% valid(+Row)
-%
-valid_row([Head|Row]) :-
-  Row ins 1..9, 
-  all_distinct(Row),
-  valid_head(Head, Row),
-  label(Row).
-
-
-%% valid_head(+Head, +Tail)
-%
-valid_head(Head, List) :-
-  sum(List, #=, Head)
-; product(List, Head).
-
-
-%% product(+List, -Product)
-%
-product(List, Product) :-
-  foldl(times, List, 1, Product).
-
-
-%% times(?Int1, ?Int2, ?Int3)
-%
-% true if Int3 #= Int1 * Int2
-times(Int1, Int2, Int3) :-
-  Int3 #= Int1 * Int2.
-
-
 %% unify_diagonal(+Puzzle)
 %
+% 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)
-%
+% 
+% Holds when the list `Diag` is the main diagonal of the 2d list `Matrix`.
 main_diagonal(Matrix, Diag) :-
   main_diagonal(Matrix, 0, Diag).
 
 main_diagonal([], _, []).
-main_diagonal([M|Ms], I, [D|Ds]) :-
+main_diagonal([Row|Rows], Column, [D|Ds]) :-
-  nth0(I, M, D),
+  nth0(Column, Row, D),
-  I1 is I + 1,
+  Next_column is Column + 1,
-  main_diagonal(Ms, I1, Ds).
+  main_diagonal(Rows, Next_column, Ds).
 
 
-%% all_same(+List)
+%% all_same(+Vars)
 % 
-all_same([Head|Tail]) :-
+% Holds when the variables in the list `Vars` can be unified 
-  all_same(Head, Tail).
+all_same([Var|Vars]) :-
+ all_same(Var, Vars).
+
+all_same(Var, [Var]).
+all_same(Var, [Var|Vars]) :-
+ all_same(Var, Vars).
+
+
+%% valid(+Row)
+%
+% 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),
+  labeling([ff], Vars).
+
+
+%% valid_total(+Total, +Vars)
+%
+% Holds when the integer `Total` is either the sum or the product of the list 
+% `Vars`.
+valid_total(Total, Vars) :-
+  sum(Vars, #=, Total)
+; product(Vars, Total).
+
+
+%% product(+Vars, -Product)
+%
+% Holds when the integer `Product` is the product of the list `Vars`.
+product(Vars, Product) :-
+  foldl(times, Vars, 1, Product).
+
+
+%% times(?Int1, ?Int2, ?Int3)
+%
+% Holds when Int3 #= Int1 * Int2.
+times(Int1, Int2, Int3) :-
+  Int3 #= Int1 * Int2.
+
 
-all_same(X, [X]).
-all_same(Head, [X|Xs]) :-
-  Head #= X,
-  all_same(Head, Xs).
-