PROPOSAL: Add 'Natural' type to base:Data.Word

[Richard Eisenberg]

What would the semantics of subtraction be for this? I'm assuming there would be a `Num` instance for `Natural`.

Richard

On Nov 11, 2014, at 4:35 AM, Herbert Valerio Riedel <hvr at gnu.org> wrote:

> Hello CLC et al.,
> 
> I hereby suggest to add a type for encoding term-level naturals
> 
>  data Natural = <opaque/hidden>
>       deriving (...the usual standard classes...)
> 
> to `base:Data.Word` module
> 
> Motivation
> ==========
> 
> - GHC 7.10 is planned to ship with integer-gmp2[2] as its default
>   `Integer` lib, whose low-level primitives are based on *unsigned*
>   BigNums. And 'Natural' type for integer-gmp2 can be implemented
>   directly w/o the overhead of wrapping an `Integer` via
> 
>     data Natural = NatS# Word# | NatJ# !PrimBigNat#
> 
>   as well as having a twice as large domain handled via the small-word
>   constructor and thus avoiding FFI calls into GMP.
> 
> - GHC/`base` already provides type-level naturals, but no term-level
>   naturals
> 
> - Remove the asymmetry of having an unbounded signed `Integer` but no
>   unbounded /unsigned/ integral type.
> 
>   Also, `Data.Word` has been carrying the following note[1] for some
>   time now:
> 
>> It would be very natural to add a type Natural providing an
>> unbounded size unsigned integer, just as Integer provides unbounded
>> size signed integers. We do not do that yet since there is no
>> demand for it.
> 
> 
> 
> Discussion period: ~10 days (GHC 7.10 RC freeze is scheduled for Nov 21st)
> 
> Cheers,
>  hvr
> 
> [1]: http://hackage.haskell.org/package/base-4.7.0.1/docs/Data-Word.html#g:3
> 
> [2]: https://phabricator.haskell.org/D82 
>      https://ghc.haskell.org/trac/ghc/wiki/Design/IntegerGmp2 
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