-module(apcl).

-export([identity/1, constant/1, compose/2, apply/1, flip/1, left/2, right/2, recombine/3,
         under/2]).

%% @doc Returns its argument.
identity(X) ->
        X.

%% @doc Returns a function which returns `x' no matter what it is passed.
constant(X) ->
        fun(_Y) -> X end.

%% @doc Performs function composition.
compose(F, G) ->
        fun(X) -> F(G(X)) end.

%% @doc Returns a function which applies `F' to `Xs'.
apply(F) ->
        fun(Xs) -> apply(F, Xs) end.

%% @doc Returns a function which permutes its arguments and applies `F' to them.
flip(F) ->
        fun(X, Y) -> F(Y, X) end.

%% @doc Given two arguments, returns the left one.
left(X, _Y) ->
        X.

%% @doc Given two arguments, returns the right one.
right(_X, Y) ->
        Y.

%% @doc Returns a function that applies `G' and `H' to its arguments, taking the resulting values as the arguments to `F'.
recombine(F, G, H) ->
        fun(X) -> F(G(X), H(X)) end.

%% @doc Returns a function that applies `G' to each of its arguments, taking the resulting values as the arguments to `F'.
under(F, G) ->
        fun(X, Y) -> F(G(X), G(Y)) end.