DouKaku?

#light
open LazyList

type LListBuilder() =
    member l.Bind(v,f) = LazyList.concat (LazyList.map f v)
    member l.Return x = LazyList.consf x LazyList.empty
    member l.Let(v,f) = f v

let doLList = new LListBuilder()

let replicate n x = LazyList.take n (LazyList.repeat x)
let rec fact (n:int) = if n = 0 then 1 else n * fact (n-1)
let combination n m =
    if n < m then 0 else (fact n)/((fact m) * (fact (n-m)))

let rec make_perm n m =
    match n,m with
    | n,0 -> doLList { return (replicate n 0) }
    | n,m when n = m -> doLList { return (replicate n 1)}
    | n,m when n < m -> doLList { return (empty()) }
    | n,m -> let c = combination n m
             let d = combination (n-1) (m-1)
             append
                 (map2 append (replicate d (consf 1 empty))
                     (make_perm (n-1) (m-1)))
                 (map2 append (replicate (c-d) (consf 0 empty))
                     (make_perm (n-1) m))

let inv_hash (n,m) num =
    let nth lls i = take i lls |> hd
    let c = (combination n m)
    nth (make_perm n m) (c-num)