monad writer factorial

let wReturn (x: 'a) : ('a * string) = (x, " got " + x.ToString() + ".")
let wReturnFrom (x: 'a * string) : 'a * string = x
let wBind (mx: ('a * string)) (f: 'a -> 'b * string) : 'b * string =
    let res = f (fst mx)
    (fst res, snd mx + snd res)

let (>>=) = wBind

type WriterMonad() =
    member x.Bind(p, f) = wBind p f
    member x.Return(y) = wReturn y
    member x.ReturnFrom(y) = wReturnFrom y


let rec f n = writer {
    if n = 1 then
        return 1
    else
        let! f_prev = f (n - 1)
        let! cur = mult n f_prev
        return cur
}


let rec fact n =
    if (n = 1) then
        wReturn 1
    else
        (fact (n - 1)) >>= (mult n) >>= wReturn