Re: mutually recursive types and modules

From: Francisco Valverde Albacete (
Date: Fri May 14 1999 - 13:11:19 MET DST

Date: Fri, 14 May 1999 13:11:19 +0200
From: "Francisco Valverde Albacete" <>
Subject: Re: mutually recursive types and modules

Andrew Kay wrote:

> Dear OCaml users,
> We have a problem with mutually recursive types.

> In our project we use a graph representation which could be reduced to:
> # type node = {
> # node_id : int;
> # mutable edges : node list;
> # ... (other fields)
> # }
> Node_ids are generated at node creation time, and are unique, so we defined:
> # type compare_nodes n1 n2 = n1.node_id n2.node_id
> Then we built sets of nodes:
> # module NodeSet = Set.Make(struct type t=node let compare=compare_nodes end)
> So far so good. Next we realised that we don't care about the order of
> edges in the edge list, and we are always converting edge lists into sets
> to do union operations and so on, so we decided to recode the node type
> with edges as sets for efficiency (which is very important here).
> * type node = {
> * node_id : int;
> * mutable edges : NodeSet.t;
> * ... (other fields)
> * }
> At this point the world seemed to spin and make me dizzy, because we can't
> defined NodeSet without node, and we can't define node without NodeSet.
> I can't see any way to express this in OCaml.
> Am I missing something obvious here? How should I proceed? Is this kind
> of recursion unreasonable, or just syntactically hard to express in OCaml?
> Or am I merely incapable of understanding the manual?

I have come across this problem as well in trying to implement heuristic
As recursive modules are, for the time being, dangerous to type and thus
disallowed, you'll have to make do with:

a) defining both structures at the same time, with the obvious work of
sets, etc.

b) pass a *polymorphic* set structure to your nodes:

module Node
    ( Set : (* set signature *) )
        type 'a set = 'a Set.t (* whatever its name in the Set module *)
        type node = {
             node_id : int;
             mutable edges : node set; (* <- Here's the trick *)
             ... (other fields)


But BEWARE, this is going to cost you almost always an extra parameter to any
constructor in the Set module, a "compare" function to guarantee a linear
that makes the Set implementation efficient, so balance very well this with
previous alternative...

Hope this helps,


PS: I have a polymorphic n-ary tree using the same structure you are trying to
build here in case you want to have a look at it. But I warn you that it is
quite gory. F.

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