Week 3 - Functions as Results

returning_funs.erl

-module(returning_funs).

-compile(export_all).

-type unary() :: fun((Term) -> Term).

% composes a function onto another F(G(X))
-spec compose(unary(), unary()) -> unary().
compose(F, G) ->
  fun (X) -> F(G(X)) end.

% composes a list of functions onto each other F(G(...N(X)))
-spec compose_many([unary()]) -> unary().
compose_many(Fs) ->
  lists:foldl(fun compose/2, fun identity/1, Fs).

% applies the function twice F(F(X))
-spec twice(unary(), Term) -> Term.
twice(F, X) ->
  F2 = compose_many([F, F]),
  F2(X).

% returns a function
-spec iterate(pos_integer()) -> unary().
iterate(0) ->
  fun identity/1;
iterate(N) ->
  fun (F) -> compose_many([F || _ <- lists:seq(1, N)]) end.

% applies a function N times to a value
-spec apply_many(unary(), Term, pos_integer()) -> Term.
apply_many(F, X, N) ->
  RepeatedFn = iterate(N),
  G = RepeatedFn(F),
  G(X).

% identity fn for arity 1
-spec identity(Term) -> Term.
identity(X) -> X.