[Haskell-cafe] Some questions on Atkey-style indexed monads

[Nicolas Trangez]

On Sun, 2022-12-04 at 21:08 +0000, Tom Ellis wrote:
> On Sun, Dec 04, 2022 at 06:05:28PM +0100, Nicolas Trangez wrote:
> > For some project, I'm considering (again) to use an indexed state
> > monad, which are now somewhat ergonomic to use with QualifiedDo.
> > 
> > When looking into existing packages exposing relevant
> > types/classes, I
> > had some questions:
> > 
> > 1. These packages provide something like
> > 
> > ```
> > class IxFunctor f where
> >     imap :: (a -> b) -> f i j a -> f i j b
> > 
> > class IxFunctor f => IxApplicative f where
> >     ...
> > ```
> > 
> > Is this `IxFunctor` actually required/useful? It seems to me the
> > implementation of `imap` for some `IxFunctor f` would be equal to
> > `fmap` in the `Functor` implementation for `forall i j. f i j`.
> > Hence,
> > can `IxFunctor` be dropped in lieu of
> > 
> > ```
> > class (forall i j. Functor (f i j)) => IxApplicative f where
> >     ...
> > ```
> 
> I suspect QualifiedConstraints didn't exist at the time that class
> was
> introduced.  I agree in modern GHC-flavoured Haskell the quantified
> constraint version is better.

Thanks, that confirms my intuition. Indeed, the aforementioned approach
requires some language extensions not available when the existing
packages were published.

Cheers,

Nicolas