[Haskell-cafe] Mixed Fraction data type

[Bob Ippolito]

I don't think there's any deep lore, it doesn't really make much sense to
specialize the mixedBit but not the numerator and denominator. I think it
was just an example to show that the cardinality is 256 * |a| * |a|.

With that representation, constraints can only be enforced with a smart
constructor. https://wiki.haskell.org/Smart_constructors

On Wed, Sep 15, 2021 at 7:35 AM Galaxy Being <borgauf at gmail.com> wrote:

> Guess I was just wondering what deep lore was behind choosing Word8 for
> the whole number instead of an Integer. Right, Fraction 5 1 2, but what's
> up with "mixedBit" and Word8? BTW, how might that constraint numerator <
> denominator be handled if setting up MIxedFraction for real use?
>
> On Tue, Sep 14, 2021 at 11:13 PM Bob Ippolito <bob at redivi.com> wrote:
>
>> From context it's only used as a more concrete example of a product type
>> to show how cardinality analysis works. I would infer that the idea is that
>> this type would use mixedBit for the whole number and there would be a
>> constraint that numerator < denominator. Fraction 5 1 2 would be the
>> canonical way to represent 5 1/2 in that scheme. Practically speaking
>> there's no reason to have the mixedBit field because a pair is enough to
>> represent any fraction, but if it was simplified this way then the example
>> would be redundant since there's already an example of a pair type on the
>> same page.
>>
>>
>> On Tue, Sep 14, 2021 at 8:51 PM Galaxy Being <borgauf at gmail.com> wrote:
>>
>>> I'm looking at Sandy Maguire's _Thinking With Types_ and he's talking
>>> about the cardinality of types. He introduces the product type
>>>
>>> data MixedFraction a = Fraction
>>> { mixedBit :: Word8
>>> , numerator :: a
>>> , denominator :: a
>>> }
>>>
>>> How is this a type for holding mixed fractions such as 5-1/2?
>>>
>>> ⨽
>>> Lawrence Bottorff
>>> Grand Marais, MN, USA
>>> borgauf at gmail.com
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>>
>>
>
> --
> ⨽
> Lawrence Bottorff
> Grand Marais, MN, USA
> borgauf at gmail.com
>
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