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Re: polymorphic references [was: unsound typechecker]
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Date: -- (:)
From: Xavier Leroy <xavier@T...>
Subject: Re: polymorphic references [was: unsound typechecker]
The Caml Light typechecker has never been advertised as type-safe.
To quote the manual page:

          Polymorphic references, and more generally mutable concrete
          types, are not safe: it is possible to create polymorphic refer-
          ences through a functional encoding.

Martin Elsman's example is an instance of these functional encoding.

In addition to the problem with functional encodings of mutable data
structures, there are also various sources of unsoundness in the
module system: since .zi files are not timestamped/fingerprinted, the
user can perfectly break the type system by renaming or modifying .zi
files, or even just forgetting to recompile .mli files that have
changed. Strange things can also happen if the program exceeds some of
the unchecked limitations of the Caml Light compiler.

As for the problem with polymorphic mutable structures, the approach
followed in Caml Light relies on two mechanisms: dangerous type
variables and closure typing (for more details, see the paper in POPL
91, or my PhD thesis). Dangerous type variables catch 99% of the
offending programs, do not modify the ML type algebra, and are easy to
implement. Closure typing catches the remaining 1% (that is, the
functional encodings of mutable structures), complicates the type
algebra tremendously, and is not that easy to implement.

At the time the Caml Light typechecker was written, the details of
closure typing hadn't been worked out completely, and I chose to
implement only the dangerous variables and see how this works in
practice. I claimed at that time that no real programs would run into
the hole in the type system, just like no normal user would run into
the holes in the module system: only specially-designed examples would
expose the problems. This is engineering, folks -- that's the same
reason why .zi files are still unsafe as well: sure, we could make
them safe by using cryptographically secure authentication techniques
or whatever, but it wouldn't make sense to devote so much effort to a
problem that never occurs in practice.

Actually, no "normal" user complained about the polymorphic mutable
structures for more than two years (one or two persons with strong
background in type systems did notice, but again they were not
programming, they were just playing with the type checker), and then
we got several bug reports since the beginning of the year. (Maybe
there's something in the position of the planets or something that
suddenly urges Caml Light users to exercice the bug...)

As for adding closure typing to the Caml Light type checker, I have
decided against it. I did a quick and dirty implementation of closure
typing a long time ago, as a proof of concept. The conclusions were
that it works beautifully -- except when the user writes module
interfaces by hand, which becomes almost impossible with closure
typing, due to the excessive richness of type expressions. (See my
thesis for discussion.)

My conclusion (after having worked on the problem for quite a long
time) is that there are no perfect solutions to the problem of
polymorphic mutable structures. By "perfect", I mean
        (1) sound,
        (2) providing good support for imperative programming,
        (3) with a sensible type algebra (where type expressions are
            usable as partial specifications; in other terms, they
            do not reflect purely operational properties of the functions),
        (4) compatible with the purely applicative subset of ML.

Imperative variables as in SML satisfy (1) and (4) but not (2) nor (3).
Dangerous variables + closure typing satisfy (1), (2), (4) but not (3).
The hack currently used in Caml Light satisfy (2), (3), (4) but not (1).

Finally, an amazingly simple solution recently put forward by Andrew
Wright satisfies (1), (2), (3) but not (4). The idea is to restrict
type generalization to definitions that are syntactically values, that
is, functions (fun x -> e), constants and identifiers. So, for

        let id x = x;;          is polymorphic (f: forall 'a. 'a -> 'a)
                                since fun x -> x is a value

        let x = [];;            is polymorphic, since [] is a constant

        let f = map id;;        is *not* polymorphic ('a list -> 'a list
                                for some 'a, not for all 'a), since
                                map id is not syntactically a value.
                                The definition will probably be rejected,
                                as 'a is free but not generalizable in
                                the type of f.

Notice that there are some perfectly correct purely applicative
programs (e.g. f above) that will get rejected. Wright's claim is that
these program are uncommon in practice.

The current trend is to adopt the latter solution, but again it's not
a perfect solution, it's just the "less bad" solution, and it's bound
to generate lots of complaints from baffled users 
(``why can't I do "let f = map list_length;;" any longer?'').

- Xavier Leroy