hof.erl

-module(hof).
-export([compose/1, twice/1, add/1, times/1, compose/2, id/1, iterate/1]).
-include_lib("eunit/include/eunit.hrl").

%%
%% compose
%% 
-spec compose([function()]) -> function().
compose(Fs) ->
    lists:foldr(fun compose/2, fun id/1, Fs).

compose_test() ->
    ?assert((compose(add(3), times(4)))(2) == (compose([add(3), times(4)]))(2)).

%%
%% twice
%%
-spec twice(function()) -> function().
twice(F) ->
    compose(F,F).

twice_test() ->
    ?assert((twice(add(3)))(5) == 11).
twice_twice_test() ->
    ?assert((twice(twice(add(3))))(5) == 17).

%%
%% iterate


%%
-spec iterate(non_neg_integer()) -> function().
iterate(0) ->
    fun(_, X) ->
        id(X) end;
iterate(N) ->
    fun(F, X) ->
        F( (iterate(N-1))(F,X) ) end.

iterate_zero_test() ->
    ?assert((iterate(0))(times(3), 2) == 2).
iterate_other_test() ->
    ?assert((iterate(3))(times(3), 2) == 54).

%%
%% auxiliary functions
%%
add(X) ->
    fun(Y) -> X+Y end.

times(X) ->
    fun(Y) ->
	     X*Y end.

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

id(X) ->
    X.