Implementation of factorial with primitive recursive function in Erlang

factorial.erl

#!/usr/bin/env escript

-module(factorial).
-export([fac/1]).

%% Successor
succ(X) -> X + 1.

%% Addition
add(0, Y) -> Y;
add(X, Y) -> succ(add(X - 1, Y)).  % add(X + 1, Y) -> succ(add(X, Y))

%% Multiplication
mult(0, _) -> 0;
mult(X, Y) -> add(mult(X - 1, Y), Y). % mult(X + 1, Y) -> add(mult(X, Y), Y)

%% Factorial
fac(0) -> 1;
fac(X) -> mult(X, fac(X - 1)). % fac(X + 1) -> mult(fac(X), X)

main(_) ->
    io:fwrite("!0 = ~w~n", [fac(0)]),
    io:fwrite("!3 = ~w~n", [fac(3)]),
    io:fwrite("!5 = ~w~n", [fac(5)]).