## 9087Re: "ocaml_beginners"::[] Circular dependencies between modules

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• Dec 1, 2007
> > Please Jon, could you develop a bit more on this ?
> > I'm unable to see what you mean here.
>
> Sure.
Thanks a lot !

> Consider a pair of mutually recursive functions:
>
> # let rec even ?(xs=[]) ?(ys=[]) = function
> | [] -> xs, ys
> | h::t -> odd ~xs:(h::xs) ~ys t
> and odd ?(xs=[]) ?(ys=[]) = function
> | [] -> xs, ys
> | h::t -> even ~xs ~ys:(h::ys) t;;
> # even [0;1;2;3;4;5];;
> - : int list * int list = ([4; 2; 0], [5; 3; 1])
>
> We want to keep them in separate modules and, consequently, we must break
> their cyclic dependency. To do this, you just parameterize "even" over "odd"
> and vice-versa:
>
> # let rec even odd xs ys = function
> | [] -> xs, ys
> | h::t -> odd (h::xs) ys t;;
> val even :
> ('a list -> 'b -> 'a list -> 'a list * 'b) ->
> 'a list -> 'b -> 'a list -> 'a list * 'b = <fun>
> # let odd even xs ys = function
> | [] -> xs, ys
> | h::t -> even xs (h::ys) t;;
> val odd :
> ('a -> 'b list -> 'b list -> 'a * 'b list) ->
> 'a -> 'b list -> 'b list -> 'a * 'b list = <fun>
>
> Some people refer to this as "untying the recursive knot". Now, how do we use
> these? Well, we just tie the knot again in a module that depends upon both:
That is absolutely cool !

>
> # let rec even' xs = even odd' xs and odd' xs = odd even' xs in
> even' [] [] [0;1;2;3;4;5];;
> - : int list * int list = ([4; 2; 0], [5; 3; 1])
>
> You can do exactly the same thing with types:
>
> type a = A of b
> and b = B of a;;
>
> becomes:
>
> type 'b a = A of 'b;;
> type 'a b = B of 'a;;
>
> and so on.

Thanks for this interesting method I just discover here.

Regards,

Fabrice
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