InstanceSigs -- rationale for the "must be more polymorphic than"

[David Feuer]

To the best of my knowledge, `InstanceSigs` are never strictly necessary.
They can, however, be useful for at least four purposes:

1. To provide a compiler-checked reminder of the type.
2. To bind type variables with `ScopedTypeVariables`.
3. To generalize the type so you can use polymorphic recursion.
4. To enhance parametricitry/polymorphism for internal documentation
purposes.

The third reason is probably the main technical one to allow a more general
signature, but the fourth is likely helpful too.

On Sun, Aug 8, 2021, 3:04 AM Anthony Clayden <anthony.d.clayden at gmail.com>
wrote:

> I can't help but feel InstanceSigs are either superfluous or upside-down.
> It's this bit in the User Guide:
>
> > The type signature in the instance declaration must be
> > more polymorphic than (or the same as) the one in the class declaration,
> > instantiated with the instance type.
>
> Usually if you give a signature, it must be _less_ polymorphic (or the
> same as) the type inferred from the term:
>
> >    lessPolyPlus :: Integral a => a -> a -> a
> >    lessPolyPlus x y = x + y
>
> Or
>
> >    lessPolyPlus (x :: a) y = x + y :: Integral a => a
>
> The examples in the User Guide aren't helping: you could just drop the
> InstanceSigs, and all is well-typed. (Even the example alleging to use
> -XScopedTypeVariables in a where sub-decl: you could just put random `xs ::
> [b]` without scoping `b`.)
>
> Dropping the Sigs altogether works because the type from the class decl,
> suitably instantiated, is less polymorphic than inferred from the term. IOW
> the suitably instantiated type restricts what would otherwise be inferred.
> Situation normal.
>
> I suppose it might be helpful to give an explicit InstanceSig as 'belt and
> braces' for the instantiated -- possibly because the instantiation is hard
> to figure out; possibly because you want to use -XScopedTypeVariables
> within a where-bound sub-decl, as an extra piece of string.
>
> I can see you mustn't make the InstanceSig _less_ polymorphic than the
> suitably instantiated.
>
> But the docos don't give any example where it's essential to provide an
> InstanceSig _and_  make it strictly more polymorphic. Here all the sigs and
> annotations are just superfluous:
>
> >    maxPolyPlus :: Num a => a -> a -> a
> >    maxPolyPlus = (+)
> >
> >    class C a  where foo :: a -> T a
> >    instance Integral a => C a  where
> >      foo :: Num a => a -> T a
> >      foo (x :: a) = MkT (maxPolyPlus x x :: Num a => a)
>
> Is there a persuasive example (to put in the User Guide)?
>
> AntC
>
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