--Apple-Mail-2--73796428
Content-Type: text/plain;
	charset=ISO-8859-1;
	format=flowed;
	delsp=yes
Content-Transfer-Encoding: quoted-printable

I've encountered a complicated issue that I'm wondering if anyone can =20=

shed some light on here. It relates to polymorphic types what I like =20
to call Schr=F6dinger types (sorry, I don't know the real name for =20
these, but they're the dreaded polymorphic variables with underscores =20=

that, like Schr=F6dinger's cat, are undefined until you use them for the =
=20
first time). I'll try to distill it down to its simplest form here, =20
but the issue arises from desiring to implement something based on =20
"type-indexed values" such as described here: =
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=3D10.1.1.53.1977

In its simplest form, I have a writer type and a dispatching handler =20
like this:

type ('a, 'b) writer =3D ((unit -> 'a) -> 'b)
type ('a, 'b) handler =3D { handle : 'a -> (string -> 'a -> 'b, 'b) =20
writer }

Then I wish to define a family of handlers that ultimately call the =20
writer's continuation. In the very simplest form, a handler might be =20
expressed as:

let f =3D { handle =3D fun a k -> write_int_field "f" a k }

which would have type "(int, 'a) handler" as desired. (In the real =20
implementation, there will be more than one handler, hence the need =20
for the record.) However, I wish to define a family of handlers that =20
all share common implementation, so I define a helper function (again, =20=

vastly simplified):

let helper name wf =3D { handle =3D fun a k -> wf name a k }
let f =3D helper "f" write_int_field

However, here the type of "f" is now "('int, '_a) handler" and fails =20
to unify with the desired type expressed in the interface.

Now, I could get around this by making "f" be a function that when =20
evaluated returns the result of the helper. However, I'm trying to =20
avoid that because in the real implementation, the work of the helper =20=

is somewhat expensive and should only be performed once. An alternate =20=

solution can be achieved by pushing the universal qualifier for the =20
result type down into the handler:

type 'a handler =3D { handle : 'b . 'a -> (string -> 'a -> 'b, 'b) =20
writer }

However, this doesn't allow me to define the helper function as before:

   let helper name wf =3D { handle =3D fun a k -> wf name a k };;
                                   ^^^^^^^^^^^^^^^^^^^^^^
This field value has type 'a -> (string -> 'a -> 'b, 'b) writer
which is less general than 'c. 'd -> (string -> 'd -> 'c, 'c) writer

I am forced into reworking the helper parameter function, wf, to also =20=

become a record in order for it to be universally qualified:

type 'a field_handler =3D { write_field : 'b . string -> 'a -> (unit -> =20=

string -> 'a -> 'b) -> 'b }

This works:

let helper name wf =3D { handle =3D fun a k -> wf.write_field name a k }
let f =3D helper "f" write_int_field

Here "f" has type "int handler" as desired, although this solution =20
seems somewhat round-about, and was difficult to arrive at. Can anyone =20=

suggest another approach that prevents the dreaded underscores? (Note =20=

that using objects instead of records exhibits the exact same behavior.)

Warren Harris
Metaweb Technologies




--Apple-Mail-2--73796428
Content-Disposition: attachment;
	filename=smime.p7s
Content-Type: application/pkcs7-signature;
	name=smime.p7s
Content-Transfer-Encoding: base64
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--Apple-Mail-2--73796428--