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

[Mario Blažević]

On 14-11-11 04:35 AM, Herbert Valerio Riedel 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...)

+1 from me.

	Regarding the partial vs. saturated negation, I'm in favour of the 
former. However, there is another option nobody mentioned so far: NaN. I.e.,

1 - 2 = NaN
3 + 1 - 2 = 2
3 + (1 - 2) = NaN

	Could a GMP-based implementation provide such semantics without too 
much performance loss? If so, this would be my preference.

>
> 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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