[Haskell-beginners] Ratio data constructor

[Bob Ippolito]

That sounds about right. numerator and denominator are deconstructors,
which you need to use to access the fields because you can’t pattern match
without access to the :% constructor. If you look at their implementation,
they are deconstructing with a pattern match rather than constructing like
the % function.

On Tue, Jul 20, 2021 at 15:10 Galaxy Being <borgauf at gmail.com> wrote:

> Yes, I see here
> <http://support.hfm.io/1.0/api/haskell2010-1.1.2.0/Data-Ratio.html> that
> the module Data.Ratio exports this
>
> module  Data.Ratio (
>     Ratio, Rational, (%), numerator, denominator, approxRational ) where
>
> which doesn't include :%.  But then I see numerator and denominator which
> do have :%. But then to use them, this, e.g., won't work
>
> numerator (60 20)
>
> It needs the %
>
> numerator (60 % 20)
>
> So internally, :% is used, but users can never use :%, only %, which
> sends things through reduce first. I could write my own version of Ratio
> that didn't hide :<some symbol> and that would be okay. Have I got this
> right?
>
>
>
> On Tue, Jul 20, 2021 at 4:37 PM Bob Ippolito <bob at redivi.com> wrote:
>
>> Yes, the (%) function is a smart constructor for Data.Ratio because the
>> (:%) constructor is not exported. Other examples of this smart constructor
>> technique would be modules like Data.Set or Data.Map.
>>
>> A smart constructor means that the module that defines the type does not
>> export its data constructor(s), making the implementation details
>> opaque, generally because the author wanted to be able to make assumptions
>> about the implementation that are not enforced by the type system. In this
>> case, they wanted all Ratio to be in reduced form. This makes many
>> operations faster or trivial, e.g. implementing Eq only requires comparing
>> the numerators and denominators. More information about the technique is
>> here: https://wiki.haskell.org/Smart_constructors
>>
>>
>>
>> On Tue, Jul 20, 2021 at 2:17 PM Galaxy Being <borgauf at gmail.com> wrote:
>>
>>> ... does the last question have to do with a "smart constructor" by
>>> chance? If so, how?
>>>
>>> On Tue, Jul 20, 2021 at 3:42 PM Galaxy Being <borgauf at gmail.com> wrote:
>>>
>>>> I'm investigating rational numbers with Haskell. This is the source
>>>> I've found
>>>>
>>>> data Ratio a = !a :% !a deriving (Eq)
>>>>
>>>> reduce ::  (Integral a) => a -> a -> Ratio a
>>>> {-# SPECIALISE reduce :: Integer -> Integer -> Rational #-}
>>>> reduce _ 0              =  ratioZeroDenominatorError
>>>> reduce x y              =  (x `quot` d) :% (y `quot` d)
>>>>                            where d = gcd x y
>>>> (%) :: (Integral a) => a -> a -> Ratio a
>>>> x % y =  reduce (x * signum y) (abs y)
>>>>
>>>> The Ratio data type would seem to be a parameterized type with two
>>>> parameters of the same type that must be "settled" in that they're not to
>>>> be lazily dealt with. Then the :% is the data constructor, the :
>>>> meaning it's a data constructor and not just an operation function. So this
>>>> could have been
>>>>
>>>> data Ratio a = :% !a !a deriving (Eq)
>>>>
>>>> correct? But then what confuses me is in reduce, why
>>>>
>>>> reduce x y  =  (x `quot` d) :% (y `quot` d)
>>>>
>>>> and not just %? We have :% defined in the data type and then (%)
>>>> defined as a function. What is going on here?
>>>>
>>>> --
>>>> ⨽
>>>> Lawrence Bottorff
>>>> Grand Marais, MN, USA
>>>> borgauf at gmail.com
>>>>
>>>
>>>
>>> --
>>> ⨽
>>> Lawrence Bottorff
>>> Grand Marais, MN, USA
>>> borgauf at gmail.com
>>> _______________________________________________
>>> Beginners mailing list
>>> Beginners at haskell.org
>>> http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
>>>
>> _______________________________________________
>> Beginners mailing list
>> Beginners at haskell.org
>> http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
>>
>
>
> --
> ⨽
> Lawrence Bottorff
> Grand Marais, MN, USA
> borgauf at gmail.com
> _______________________________________________
> Beginners mailing list
> Beginners at haskell.org
> http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.haskell.org/pipermail/beginners/attachments/20210720/8fb718ec/attachment-0001.html>