Proposal for removing separate `Nat` in favour of promoted `Natural` type.

[Oleg Grenrus]

There is an old GHC issue
https://gitlab.haskell.org/ghc/ghc/-/issues/10776 which got recently a
PR https://gitlab.haskell.org/ghc/ghc/-/merge_requests/3583

- Oleg

On 9.7.2020 12.59, Rinat Stryungis wrote:
> Hello, libraries!
>
> I want to present a proposal for changes in the `Base` library.
> The changes in my proposal partially solve the following issue:
>     https://gitlab.haskell.org/ghc/ghc/-/issues/10776
> and remove the separate built-in kind `Nat` in favor of promoted type
> `Natural`.
>
> It means that previously one can't directly promote a data type with
> Natural fields:
>
>     data MyPointN = PointN Natural Natural -- could not be promoted
>     data MyPointP = PointP Nat Nat         -- could be promoted, but
> uninhabited in terms
>
>     type M = PointP 1 10  
>
> but now one could promote the `Natural` data type:
>
>     data MyPoint = Point Natural Natural
>     type MyTLPoint1 = Point 1 10
>
> The proposed changes both simplify the internals of the GHC by removing
> separate kind and related things and make using of the type-level
> naturals more convenient for users.
>
> Also new type synonym
>
>     type Nat = Natural
>
> appeared in the Data.Type.TypeNats in the name of backward compatibility.
>
> I've opened a new MR with the patch. In the patch with the already
> implemented promotion of Naturals, one could find new and updated
> tests and docs.
>
> Also, I want to say about the breakages:  
>
> 1. One must enable `TypeSynonymInstances` in order to define instances
> for `Nat`.
> 2. Different instances for `Nat` and `Natural` won't type check anymore.
> 3. Type checker plugins that work with the natural numbers now
>    should use `naturalTy` kind instead of removed `typeNatKind`
>
> Anyone interested is welcome to look at the MR and discuss the
> proposal and its implementation.
>
> https://gitlab.haskell.org/ghc/ghc/-/merge_requests/3583
>
> The latter is very short and easy, thanks to the recently merged patch
> with a new `ghc-bignum` library. It greatly simplified my work.
>
> Thanks and best regards.
> Rinat Stryungis. 
>
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