F#: Cartesian product of Collections.I want to write pure sequence version of it.

cartesian.fs

(* Result
[[1; 3]; [1; 4]; [2; 3]; [2; 4]]
[[3; 1]; [4; 1]; [3; 2]; [4; 2]]
seq [[1; 3]; [1; 4]; [2; 3]; [2; 4]]
seq [[1; 3]; [1; 4]; [2; 3]; [2; 4]]
*)
(*
 let rec cartesian5 (ls: seq<seq<'a>>) : seq<seq<'a>> = seq{..}
 I couldn't make cartesian from sequence of sequence
 below 4 examples are similar to my purpose but little different
 *)
 
open System
let rec cartesian = function
  | l::ls -> 
    let accs = cartesian ls
    let rec f=function
      | e::es -> List.map(fun acc->e::acc) accs @ f es
      | [] -> []
    f l
  | [] -> [[]]

let cartesian2 = List.fold(fun accs l->List.collect(fun acc->List.map(fun e->e::acc)l)accs) [[]] 

let rec cartesian3 ls=
  seq{
    match ls with
    | [] -> yield []
    | hd::tl -> 
      for h in hd do
        for t in cartesian3 tl do
          yield h::t
  }

let rec cartesian4 (ls: seq<'a>list) : seq<'a list> = seq{
  match ls with
  | [] -> yield []
  | hd::tl -> yield! Seq.collect(fun h-> Seq.map(fun t-> h::t)<|cartesian4 tl)hd }

  
cartesian  [[1;2];[3;4]] |> printfn"%A"
cartesian2 [[1;2];[3;4]] |> printfn"%A"
cartesian3 [[1;2];[3;4]] |> printfn"%A"
cartesian4 [[1;2];[3;4]] |> printfn"%A"

Console.ReadKey()|>ignore