Locally abstract types scope over the definition body where they can
be used as type names or to refine GADTs by pattern-matching.

module type Ty = sig type t end

(* we need the scoping of the locally abstract type in this example;
   note that (type a) would work as well *)
let mkTy : type a . unit -> (module Ty with type t = a) =
  fun () ->
    let module T = struct type t = a end in
    (module T)

> val mkTy : unit -> (module Ty with type t = 'a) = <fun>

(* a type variable 'a only scopes over the type annotation *)
let mkTy : 'a . unit -> (module Ty with type t = 'a) =
  fun () ->
    let module T = struct type t = 'a end in
    (module T)

>  let module T = struct type t = 'a end in
>                                 ^^
> Error: Unbound type parameter 'a


type _ tag = Int : int tag | Prod : 'a tag * 'b tag -> ('a * 'b) tag

(* we need the ability to be refined by GADT matching here *)
let rec default : type a . a tag -> a =
  function
  | Int -> 0
  | Prod (ta, tb) -> (default ta, default tb)

> val default : 'a tag -> 'a = <fun>

(* a type variable just unifies with the first case and fails on the second *)
let rec default : 'a . 'a tag -> 'a =
  function
  | Int -> 0
  | Prod (ta, tb) -> (default ta, default tb)
>   ^^^^^^^^^^^^^
> Error: This pattern matches values of type ($0 * $1) tag
>        but a pattern was expected which matches values of type int tag
>        Type $0 * $1 is not compatible with type int

(* the difference by "(type a) ..." and "type a . ..." is that the latter
   allows polymorphic recursion (just as "'a . ..."), so this example fails
   with just (type a) *)
let rec default (type a) : a tag -> a =
  function
  | Int -> 0
  | Prod (ta, tb) -> (default ta, default tb)
>                             ^^
> Error: This expression has type $0 tag but an expression
> was expected of type 'a
> The type constructor $0 would escape its scope

On Mon, Mar 28, 2016 at 6:20 AM, Gregory Malecha <gmalecha@gmail.com> wrote:
> Thanks. I'm not sure I understand the difference between the two though. Is
> there an example showing when they produce different results?
>
> On Sun, Mar 27, 2016 at 6:12 PM, Jacques Garrigue
> <garrigue@math.nagoya-u.ac.jp> wrote:
>>
>> On 2016/03/28 03:52, Gregory Malecha wrote:
>> >
>> > Thanks, Leo --
>> >
>> > This is exactly what I needed to know. I thought that the (type a)
>> > annotation was forcing the function to be polymorphic. For future reference,
>> > is there any way to write the annotation (that forces the function to be
>> > polymorphic) without having to write explicit ‘fun's?
>>
>> You should either write
>>
>>   let generic_search_stream : ‘b. int option -> (internal_result, ‘b)
>> result_stream = …
>>
>> or
>>
>>   let generic_search_stream : type b. int option -> (internal_result, b)
>> result_stream = …
>>
>> where the latter one both requires polymorphism and defines a locally
>> abstract type,
>> i.e. probably the behavior you expect with (type b).
>>
>> Jacques
>>
>
>
>
> --
> gregory malecha