[Haskell-cafe] Re: Numeric type classes
wnoise at ofb.net
Wed Sep 20 04:08:44 EDT 2006
On 2006-09-12, Brian Hulley <brianh at metamilk.com> wrote:
> Bryan Burgers wrote:
>> That being said, I'll have to play the other side of the coin: it
>> would probably be a little bit of a pain to have to define instances
>> of each data declaration (Integer, Int, Float, Matrix, Complex, etc.)
>> on each of these seperate classes--especially when being in a certain
>> class usually implies being in another (ie, the definition of a set
>> being a field requires that that set is a group, right?)
> Aaron Denney wrote:
>> On 2006-09-12, Bryan Burgers <bryan.burgers at gmail.com> wrote:
>>> And another problem I can see is that, for example, the Integers are
>>> a group over addition, and also a group over multiplication;
>> Not over multiplication, no, because there is no inverse.
>> I know of no good way to express that a given data type obeys the
>> same interface two (or more) ways. Some OO languages try to handle
>> the case of of an abstract base class being inherited twice through
>> two different intermediate classes, but none of them do it well.
> How about:
> data Multiply = Multiply
> data Add = Add
> class Group c e where
> group :: c -> e -> e -> e
> identity :: c -> e
> inverse :: c -> e -> e
> instance Group Multiply Rational where
> group Multiply x y = ...
> identity Multiply = 1
> inverse Multiply x = ...
> instance Group Add Rational where
> group Add x y = ...
> identity Add = 0
> inverse Add x = ...
> (+) :: Group Add a => a -> a -> a
> (+) = group Add
> (*) = group Multiply
> class (Group Multiply a, Group Add a) => Field a where ...
It's not horrible, but it's somewhat cumbersome, much like passing
around dictionaries explicitly is.
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