mutually recursive types and modules

From: Andrew Kay (
Date: Tue May 11 1999 - 18:32:17 MET DST

Date: Tue, 11 May 1999 17:32:17 +0100 (BST)
From: Andrew Kay <>
Message-Id: <>
Subject: mutually recursive types and modules

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?

Thanks for any help you can give.

Andrew Kay
Sharp Labs Europe Ltd, Oxford Science Park, Oxford, UK, OX4 4GB Tel:+44 1865 747711 FAX:+44 1865 747717

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