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Re: [Caml-list] let rec and polymorphic functions
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Date: 2007-06-27 (10:24)
From: David Allsopp <dra-news@m...>
Subject: Re: [Caml-list] let rec and polymorphic functions
> There are many problems with this. Google for ad-hoc polymorphism,
> polymorphic recursion and generic printing.
> On Wednesday 27 June 2007 09:40:31 David Allsopp wrote:
> >   out "TEST";
> val out : string -> unit
> >   out "%d" 0;
> val out : format -> int -> unit

The type-checker doesn't see that surely? Surely on that expression it sees
out : string -> int -> unit?? Note that changing the sequence to

out "%b" true;
out "%d" 0;

and removing the out "TEST" still causes problems - although O'Caml manages
to infer the [format4] first argument for [out], it fixes the first
parameter of the [format4] as being [bool -> unit] and so prevents [out]
from being used with anything other than a single "%b" argument and hence
gives a type error on the next application.

> As printf is ad-hoc polymorphic, you must supply the format specifier 
> immediately and OCaml will generate a custom printer for you. OCaml does
> not use run-time types so you cannot have a generic print function: you
> must specific print functions for each of your (possibly higher-order)
> types.

Yes, except that what's odd to me is that the type-checker doesn't behave as
the manual says it ought to with [let rec]. BUT... 

> Also, recursive calls ossify the function to a monomorphic type, so you 
> cannot do polymorphic recursion in OCaml. There are workaround using 
> recursive modules or objects but I don't think this is what you want here.

That does explain it - which I didn't know. Consider this which is also
broken (and simpler because it has nothing to do with the ad-hoc
polymorphism of printf)

let rec id x = x
and _ = id 0
  id (); (* *** *)
  id 1;;

Gives a type error for *** because id is already inferred as int -> int
because of the monomorphic nature of the recursive definition. This is
over-guarded but I never got an answer on a previous post as to why. The
equivalent SML does type polymorphically:

let fun id x = x
val _ = id 0
  id ();
  id 1

Incidentally, it's lucky that this is polymorphic in SML because all
function definitions are recursive IIRC.

But no-one posted an explanation as to why there's this difference in the
let construct between the two flavours of ML :(