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Date: Mon, 14 Jul 2008 20:37:47 +0100
From: Jeremy Yallop <jeremy.yallop@ed.ac.uk>
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To: Dario Teixeira <darioteixeira@yahoo.com>
Cc: caml-list@yquem.inria.fr
Subject: Re: [Caml-list] Troublesome nodes
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X-Spam: no; 0.00; nodes:01 node:01 generative:01 denotes:01 module-level:01 bindings:01 denoting:01 ocaml:01 bindings:01 node:01 polymorphic:01 wrote:01 abstract:01 abstract:01 syntactic:01 

Dario Teixeira wrote:
>     type ('a, 'b) t = private 'a constraint 'a = [< super_node_t ]

I don't think this is quite what you want yet, although it's getting
close!

The first problem is that phantom types must be implemented in terms
of abstract (or at least generative) types.  A simple example to
illustrate the problem: the types

     int t

and

     float t

denote the same type given the alias declaration

     type 'a t = unit

but different types given the abstract type declaration

     type 'a t

The clause "= private 'a" in your declaration above indicates that `t'
denotes an alias, not an abstract type.

The second problem is indicated by the error message you reported:

    "The type of this expression contains type variables that cannot be
     generalized"

Weak (ungeneralised) type variables are not allowed at module-level
bindings.  You'll see a similar error message if you try to compile a
module containing the following binding, for example

    let x = ref None

The solution to this problem is usually to change the form of the
offending expression, for example by eta-expanding a term denoting a
function.  In your case, though, the solution is to change the
declaration of the abstract type `t' to indicate that the type
parameters do not occur negatively in the right-hand side.  This takes
advantage of a novel feature of OCaml -- the "relaxed value
restriction" -- which uses a subtype-based analysis rather than a
simple syntactic check to determine whether bindings can be made
polymorphic.

The final type declaration, then, is

     type (+'a, +'b) t
           constraint 'a = [< super_node_t ]

in the signature and

     type (+'a, +'b) t = 'a
           constraint 'a = [< super_node_t ]

in the implementation.

Jeremy.