Hylo again

The previous blogpost implements a hylomorphism in Erlang.

Following is again the same in F#: but this is part of my exercices to learn F#, and I just begin to learn … so the code is … ergh, whatever.

And I have no idea how to implement default values. Any advice?

#light
open Microsoft.FSharp.Collections.List;

let rec hylo step till col inj v s =
    if till s
    then
        v
    else
        let ns = step s in
        let nv = inj v (col s) in
        hylo step till col inj nv ns;

let fact =
    let step = fun x -> x - 1 in
    let till = fun x -> x <= 1 in
    let col = fun x -> x in
    let inj = fun a x -> a * x in
    hylo step till col inj 1;

let evens n =
    let step = fun x -> x + 2 in
    let till = fun x -> x >= n in
    let col = fun x -> x in
    let inj = fun a x -> x :: a in
    rev (hylo step till col inj [] 0);

let to_bin n =
    let step = fun x -> x / 2 in
    let till = fun x -> x <= 0 in
    let col = fun x -> x % 2 in
    let inj = fun a x -> x :: a in
    hylo step till col inj [] n;

let expand l =
    let rec duplicate c n a =
        if n > 0
        then duplicate c (n - 1) (c::a)
        else a
        in
    let step = fun li -> tl li in
    let till = fun li -> match li with |[] -> true |_ -> false in
    let col = fun li -> match hd(li) with |(c,n) -> duplicate c n [] in
    let inj = fun a x -> (x :: a) in
    rev (hylo step till col inj [] l);

do printf "fact(5)=%a\n" output_any (fact 5);
do printf "evens(10)=%a\n" output_any (evens 10);
do printf "to_bin(10)=%a\n" output_any (to_bin 10);
do printf "expand([(1,2); (4,7)])=%a\n" output_any (expand [(1, 2); (4,7)]);