Re: [Caml-list] Naming polymorphic variant types

[Jacques Garrigue <garrigue@kurims.kyoto-u.ac.jp>]

From: "Nick Alexander" <nalexander@amavi.com>

> module type TEST =
>   sig
>     type outer = [ `A | `B]
>     and inner = [ `B]
>     val x : outer -> outer
>     val y : inner
>   end
> module Test : TEST
> # let p = Test.y;;
> val p : Test.inner = `B
> # let q = Test.x p;;
>                  ^
> This expression has type Test.inner = [ `B] but is here used with type
>   Test.outer = [ `A | `B]
> The first variant type does not allow tag(s) `A
>
> I'm confused.  Can I get an explanation for why the parameter to a
> function with a sum variant type needs all summands to be possible
> arguments? 

Inner is a subtype of outer, but they cannot be unified (unification
requires equality, not subtyping).
 
You can get subtyping by writing explicit coercions:

# let q = Test.x (p :> Test.outer);;
val q : Test.outer = `A

You can also give polymorphic types to your values in the interface:
  val x : [< outer] -> outer
and
  val y : [> inner]
are both valid, and one of them is enough to allow (Test.x p) without
coercion. I.e., [< outer] can be unified with inner, and [> inner] can
be unified with outer.

        Jacques Garrigue
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