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From: Michael Vanier <mvanier@cs.caltech.edu>
To: caml-list@inria.fr
Subject: [Caml-list] yet another question on lazy lists
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First off, thanks very much to all of you who have helped me understand
lazy evaluation in ocaml.  Now for another question: I get a strange type
error from the following code:

(* "stream" means lazy lists for my purposes. *)
type 'a stream =
    Nil
  | Cons of 'a * 'a stream Lazy.t

let stream_cons x y = Cons (x, lazy y)

let stream_hd s =
  match s with
    Nil -> invalid_arg "stream_hd"
  | Cons (x, y) -> x

let stream_tl s =
  match s with
    Nil -> invalid_arg "stream_tl"
  | Cons (x, y) -> Lazy.force y

let rec stream_map2 proc s1 s2 =
  match (s1, s2) with
    (Cons (x1, y1), Cons (x2, y2)) ->
      Cons ((proc x1 x2), lazy (stream_map2 proc 
                                  (Lazy.force y1) 
                                  (Lazy.force y2)))
  | _ -> invalid_arg "stream_map2"
    
let add_streams s1 s2 =
  stream_map2 (+) s1 s2

(* Generating fibonacci numbers. *)

let rec fibs =
  Cons (0,
        lazy (Cons (1,
                    lazy (add_streams
                            (stream_tl fibs)
                            fibs))))


Thus far, everything works properly.  But when I try to convert the "Cons"
expressions into "stream_cons" function calls, I get a weird type error:


let rec fibs2 =
  stream_cons 0 (stream_cons 1 (add_streams (stream_tl fibs2) fibs2))

# let rec fibs2 =
    stream_cons 0 (stream_cons 1 (add_streams (stream_tl fibs2) fibs2))
    -------------------------------------------------------------------
  ;;
This kind of expression is not allowed as right-hand side of `let rec'


What does this mean?  My best guess is that ocaml sees that you're defining
a value in terms of itself (like e.g. "let rec a = 2 * a") and won't allow
it, but that doesn't explain why the lazy version works.  Does this mean
that my "stream_cons" function is useless?

Thanks in advance,

Mike

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