Factorial, Twice

Implement the functions

val fact_dir : int -> int
val fact_tr : int -> int

so that fact_dir n and fact_tr n are \(n!\), but fact_dir is implemented directly, i.e., using the definition

\[ n ! = \begin{cases} 1 & n = 0 \\ n \times (n - 1)! & \text{n > 0} \end{cases} \]

and fact_tr is implemented tail recursively.

let _ = assert (fact_dir 5 = 120)
let _ = assert (fact_tr 5 = 120)