September Morn Update

Task/Pascals-triangle/Prolog/pascals-triangle-3.pro

@@ -0,0 +1,29 @@
+%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+% Produce a pascal's triangle of depth N
+%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+%  Prolog is declarative.  The predicate pascal/3 below says that to produce
+%  a row of depth N, we can do so by first producing the row at depth(N-1),
+%  and then adding the paired values in that row.  The triangle is produced
+%  by prepending the row at N-1 to the preceding rows as recursion unwinds.
+%  The triangle produced by pascal/3 is upside down and lacks the last row,
+%  so pascal/2 prepends the last row to the triangle and reverses it.
+%  Finally, pascal/1 produces the triangle, iterates each row and prints it.
+%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+pascal_row([V], [V]).                           % No more value pairs to add
+pascal_row([V0, V1|T], [V|Rest]) :-             % Add values from preceding row
+    V is V0 + V1, !, pascal_row([V1|T], Rest).  % Drops initial value (1).
+
+pascal(1, [1], []).    % at depth 1, this row is [1] and no preceding rows.
+pascal(N, [1|ThisRow], [Last|Preceding]) :- % Produce a row of depth N
+    succ(N0, N),                            % N is the successor to N0
+    pascal(N0, Last, Preceding),            % Get the previous row
+    !, pascal_row(Last, ThisRow).           % Calculate this row from the previous
+
+pascal(N, Triangle) :-
+   pascal(N, Last, Rows),             % Retrieve row at depth N and preceding rows
+   !, reverse([Last|Rows], Triangle). % Add last row to triangle and reverse order
+
+pascal(N) :-
+  pascal(N, Triangle), member(Row, Triangle), % Iterate and write each row
+  write(Row), nl, fail.
+pascal(_).

Task/Pascals-triangle/Prolog/pascals-triangle-4.pro

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+?- pascal(5).
+[1]
+[1,1]
+[1,2,1]
+[1,3,3,1]
+[1,4,6,4,1]