Tail recursion - FP in Erlang 2.5

tail.erl

%% @doc Tail recursion - FP in Erlang 2.5

-module(tail).
-export([sum/2, maximum/2, fib/1, perfect/1, test/0]).

%% @doc Given a function (Fun: int -> int) and an integer N,
%% find the value of Fun(N) + Fun(N - 1) + ... + Fun(0).
%%
%% sum_aux is auxiliary function keeping a current Sum value

sum_aux(0, _, Total) ->
    Total;
sum_aux(N, Fun, Sum) when N > 0 ->
    sum_aux(N - 1, Fun, Sum + Fun(N)).

sum(N, F) ->
    sum_aux(N, F, 0).

test_sum() ->
    6 = tail:sum(3, fun (X) -> X end),
    14 = tail:sum(3, fun (X) -> X * X end),
    ok.

%% @doc Given a function (Fun: int -> int) and an integer N,
%% find the largest value Fun(N), Fun(N - 1) ,... ,Fun(0).
%%
%% maximum_aux is auxiliary function keeping a current Max value

maximum_aux(0, Fun, Max) ->
    max(Max, Fun(0));
maximum_aux(N, Fun, Max) when N > 0 ->
   maximum_aux(N - 1, Fun, max(Max, Fun(N - 1))).

maximum(N, F) ->
    maximum_aux(N, F, F(N)).

test_maximum() ->
    10 = tail:maximum(10, fun (X) -> X end),
    0 = tail:maximum(10, fun (X) -> - X end),
    ok.

%% @doc Tail recursive version of fib function
%%
%% fib_aux accumulates value in Current variable

fib_aux(1, _, Value) ->
    Value;
fib_aux(N, Previous, Current) when N > 1 ->
    fib_aux(N - 1, Current, Previous + Current).

fib(N) ->
    fib_aux(N, 0, 1).

test_fib() ->
    1 = tail:fib(2),
    3 = tail:fib(4),
    8 = tail:fib(6),
    987 = tail:fib(16),
    1100087778366101931 = tail:fib(88), % direct version of fib function would hang here
    ok.

%% @doc Step-by-step evaluation of fib(4)
%% fib(4)
%% = fib_aux(4, 0, 1)
%% = fib_aux(3, 1, 1)
%% = fib_aux(2, 1, 2)
%% = fib_aux(1, 2, 3)
%% = 3

%% @doc Convert integer to boolean

to_bool(0) ->
    true;
to_bool(_) ->
    false.

%% @doc Conditional add

add(true, Number, Sum) ->
    Sum + Number;
add(false, _, Sum) ->
    Sum.

%% @doc Check if Number is perfect

perfect_aux(Number, Divisor, Sum) when Divisor > 0 ->
    Rem = Number rem Divisor, % if Rem == 0 then we have a divisor
    CurrentSum = add(to_bool(Rem), Divisor, Sum),
    perfect_aux(Number, Divisor - 1, CurrentSum);
perfect_aux(Number, 0, Sum) ->
    Number == Sum.

perfect(N) ->
    perfect_aux(N, N - 1, 0).

test_perfect() ->
    true = tail:perfect(6),
    false = tail:perfect(10),
    true = tail:perfect(28),
    false = tail:perfect(100),
    true = tail:perfect(496),
    true = tail:perfect(8128),
    ok.

test() ->
    ok = test_sum(),
    ok = test_maximum(),
    ok = test_fib(),
    ok = test_perfect(),
    ok.

Great job!
A few more idiomatic/stylistic comments:

1. Auxiliary functions, when available, tend to be called just like the main function (i.e. perfect_aux/3 -> perfect/3). The distinction is clear, due to the different arities.
2. In the same way we generally use snake_case for atoms, we generally use PascalCase for variables (i.e. Current_sum -> CurrentSum)

Thanks.

1. Auxiliary functions, when available, tend to be called just like the main function (i.e. perfect_aux/3 -> perfect/3). The distinction is clear, due to the different arities.

I know a bit of OCaml and here it gets in the way. In Erlang perfect/3 and perfect/2 are different functions. In OCaml the latter would be a "curried" version of the former and that's why another (auxiliary) function is needed.

2. In the same way we generally use snake_case for atoms, we generally use PascalCase for variables (i.e. Current_sum -> CurrentSum)

OK.