Re: [Caml-list] What is an applicative functor?

[Jacques Garrigue <garrigue@math.nagoya-u.ac.jp>]

On 2011/04/08, at 17:44, Alain Frisch wrote:
> On 04/08/2011 10:20 AM, Jacques Garrigue wrote:
>> Applicative functors have other advantages, like the fact you can refer to a
>> type produced by a functor without having really applied it.
>> 
>> For instance think of the following functor definition
>> 
>>    module F(O : Set.OrderedType)(S : sig type t = Set.Make(O).t val union : t ->  t ->  t end) = ...
>> 
>> If you want to do the same thing with generative functors, I believe you have to
>> pass the result of Set.Make(O) around physically.
>> I do think this is a significant weakness.
> 
> I can imagine uses for:
> 
> module F(O : Set.OrderedType)(S : Set.S with type elt = O.t) =
> 
> but I don't see a real-life case where one would want functor F to know that the type S.t was really produced by applying Set.Make.  Do you have a specific example in mind?

Well, union was maybe not the right name for a new function, but imagine that you want
sets with an extra operation. With generative functors, your have to have pass around the
full implementation of sets. With applicative functors you just need to pass the extra
operation, using the standard implementation of sets for other operations.
I don't know whether this example is very useful.
My other example using a functor returning a signature is maybe more important.
To some extent one can do the same thing using destructive substitution, but before
them there was no easy way to define signatures modularly using generative functors.

Jacques Garrigue