[Haskell-cafe] Backpack: polymorphic instantation?

Jaro Reinders jaro.reinders at gmail.com
Sat Sep 11 09:58:26 UTC 2021

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 

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.



[1] https://blog.shaynefletcher.org/2017/05/more-type-classes-in-ocaml.html

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