[Haskell-cafe] Backpack: polymorphic instantation?

[Daniel Díaz]

Perhaps this is not what you had in mind, but we could write a signature
like

    {-# LANGUAGE KindSignatures #-}
>     signature Mystery where
>     import Data.Kind
>     import Control.Monad
>     data MysteryMonad :: Type -> Type
>     instance Functor MysteryMonad
>     instance Applicative MysteryMonad
>     instance Monad MysteryMonad
>     instance PrimMonad MysteryMonad


that reused the existing PrimMonad class. Code could depend on that
signature without being tied to a concrete monad (this would make the
package that has the code "indefinite"). Once we compiled the indefinite
code against an actual implementation, it would be optimized as if we had
used concrete types from the beginning.

One problem with this solution is that it leaves out ST. If we wanted to
make it work with ST, one possible hack would be to define the signature
like this

    data MysteryMonad :: Type -> Type -> Type
>     instance Functor (MysteryMonad s)
>     instance Applicative (MysteryMonad s)
>     instance Monad (MysteryMonad s)
>     instance PrimMonad (MysteryMonad s)


And then use some kind of newtype adapter with a phantom type for non-ST
monads:

module Mystery where

type MysteryMonad = W IO
> newtype W m a b = W (m b) deriving newtype (Functor, Applicative, Monad)


But perhaps it would complicate things too much.

On Sat, Sep 11, 2021 at 2:08 PM <haskell-cafe-request at haskell.org> wrote:

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> Today's Topics:
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>    1. Backpack: polymorphic instantation? (Jaro Reinders)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Sat, 11 Sep 2021 11:58:26 +0200
> From: Jaro Reinders <jaro.reinders at gmail.com>
> To: Haskell Cafe <haskell-cafe at haskell.org>
> Subject: [Haskell-cafe] Backpack: polymorphic instantation?
> Message-ID: <3fb19986-f998-61c7-8c56-482b1647e2eb at gmail.com>
> Content-Type: text/plain; charset=utf-8; format=flowed
>
> I'm playing around with backpack, trying to rewrite existing libraries. My
> end
> goal is to see if Backpack could improve the primitive library. Right now,
> the
> primitive library (in my opinion) relies too heavily on specialization of
> its
> type classes, so I think Backpack could help. However, I seem to be
> running
> into a limitation. I am wondering if it is a fundamental limitation, if
> perhaps
> there is a workaround, or if Backpack could be improved to support this
> use-case.
>
> Instead of primitive, I will take the simpler example: semigroup, which
> also
> shows this limitation. Let's convert the Semigroup class to a backpack
> signature:
>
>      unit indef where
>        signature Semigroup where
>          import Prelude hiding ((<>))
>          data T
>          (<>) :: T -> T -> T
>
> The problem is how to implement this signature with the type of
> polymorphic
> lists. It is easy to implement it for concrete lists like strings:
>
>      unit string where
>       module Semigroup where
>        import Prelude hiding ((<>))
>        type T = String
>        (<>) :: T -> T -> T
>        (<>) = (++)
>
> It is also possible to implement it in terms of another signature:
>
>      unit list where
>        signature Elem where
>          data A
>
>        module Semigroup where
>          import Prelude hiding ((<>))
>          import Elem
>          type T = [A]
>          (<>) :: T -> T -> T
>          (<>) = (++)
>
> This is still problematic, because it is annoying that this new type A
> needs to
> be instantiated each time you want to use it. However, even more
> importantly,
> if I want to translate the 'PrimMonad' class to a Backpack signature then
> the
> 'ST s' instance needs a polymorphic type variable 's', which cannot be
> made
> concrete.
>
> And do note that I want the monad to be concrete for performance reasons,
> but
> the 's' parameter doesn't have to be concrete, because it is a phantom
> parameter anyway. And for lists making the 'a' parameter concrete also
> would
> not improve performance as far as I know.
>
> One possible way to fix this is to add a type variable in the 'Semigroup'
> signature, but then I think it becomes impossible to write the 'String'
> instance and sometimes you need more than one new type variable such as
> with
> the 'ReaderT r (ST s)' instance of 'PrimMonad'.
>
> In OCaml you can still kind of work around this problem by creating local
> instances inside functions. That trick still allows you to write a
> polymorphic
> concatenation function using a monoid signature (taken from [1]):
>
>      let concat (type a) xs =
>        let module MU = MonoidUtils (ListMonoid(struct type t = a end)) in
>        MU.concat xs;;
>
> So, I'm wondering if it would be possible to "generalise" over indefinite
> Backpack types such as 'A' in the 'Elem' signature above or if we can at
> least
> implement something which enables the same trick that you can use in OCaml.
>
> Thanks,
>
> Jaro
>
> [1]
> https://blog.shaynefletcher.org/2017/05/more-type-classes-in-ocaml.html
>
>
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