Re: type recursifs et abreviations cyclique and Co

From: Jason Hickey (
Date: Tue Nov 25 1997 - 05:40:54 MET

Date: Mon, 24 Nov 1997 23:40:54 -0500 (EST)
Message-Id: <>
From: Jason Hickey <>
Subject: Re: type recursifs et abreviations cyclique and Co

Although my French is not what I would like, I gather that the feature
of general recursive types in OCaml has been drawn back because it is
prone to error. For instance, the type I originally proposed

    type x = x option

is not allowed because types of that form are prone to error. The
solution would be to apply an explicit boxing:

    type x = X of x option.

I would like to make an argument against this policy.

1. The interpretation of the general recursive type has a
    well-defined type theoretic meaning. For instance, the type

        type x = x option

    is isomorphic to the natural numbers. The _type_theory_ does not
    justify removing it from the language. Why not issue a warning rather
    than forbidding the construction? For instance, the following code is
    not forbidden:

        let flag = (match List.length [] with 0 -> true)

    even though constructions of this form are "prone to error,"
    and generate warning messages.

2. The policy imposes a needless efficiency penalty on type
    abstraction. For instance, suppose we have an abstract type

        type 'a t

    then we can't form the recursive type

        type x = x t

    without a boxing. Although the type

        type x = X of x t

    is equivalent, it requires threading a lot of superfluous X's through
    the code, and ocaml will insert an extraneous boxing for each
    occurrence of an item of type x in t. Consider an unlabeled
    abstract binary tree:

        type 'a t = ('a option) * ('a option) (* abstract *)
        type node = X of node t

    Every node is boxed, with a space penalty that is
    linear in the number of nodes.

3. If the type system can be bypassed with an extraneous boxing,

        type x = x t -----> type x = X of x t

    then what is the point?

4. (Joke) All significant programs are "prone to error." Perhaps the
    OCaml compiler should forbid them all!

    I use this construction extensively in Nuprl (theorem proving)
    and Ensemble (communications) applications; do I really need
    to change my code?


This archive was generated by hypermail 2b29 : Sun Jan 02 2000 - 11:58:13 MET