composition.erl

-module(composition).
-export([twice/2,compose/2,iterate/1]).
-export([test/0]).

%% Composition

compose(F, G) ->
  fun (X) -> F(G(X)) end.

%% Iteration

iterate(N) ->
  Iterate = fun Iterate(0, F) -> F; Iterate(M, F) -> Iterate(M - 1, compose(F, F)) end,
  fun (F) -> Iterate(N, F) end.

iterate_test() ->
  4 = ((iterate(0))(fun (X) -> 2*X end))(2),
  8 = ((iterate(1))(fun (X) -> 2*X end))(2),
  passed.

%% Twice

twice(F, X) ->
  (compose(F, F))(X).

twice_test() ->
  18 = twice(fun(X) -> 3 * X end, 2),
  32 = twice(fun (X) -> twice(fun (Y) -> 2*Y end, X) end, 2),
  passed.

test() ->
  twice_test(),
  iterate_test(),
  passed.