On 23.10.2010 05:11, wren ng thornton wrote:
On 10/22/10 8:46 AM, Alexey Khudyakov wrote:
Hello everyone!
It's well known that Num & Co type classes are not adequate for vectors
(I don't mean arrays). I have an idea how to address this problem.
Conal Elliott wrote very nice set of type classes for vectors.
(Definition below). I used them for some time and quite pleased. Code is
concise and readable.
> class AdditiveGroup v where
> zeroV :: v
> (^+^) :: v -> v -> v
> negateV :: v -> v
[...]
I'd like to know opinion of haskellers on this and specifically opinion
of Conal Eliott as author and maintainer (I CC'ed him)
Just my standard complaint: lack of support for semirings, modules, and
other simple/general structures. How come everyone's in such a hurry to
run off towards Euclidean spaces et al.?
They give familiar warm fuzzy feeling. It's same as monads and
applicative functors (-:
I'd rather see,
class Additive v where -- or AdditiveMonoid, if preferred
zeroV :: v
(^+^) :: v -> v -> v
class Additive v => AdditiveGroup v where
negateV :: v -> v
Seems good for me. One more instance declaration to write and no changes
in usage.
However when written this way it becomes obvious that
`zeroV' == `mempty' and ^+^ = mappend. Is Additive really needed then?
type family Scalar :: * -> *
class Additive v => LeftModule v where
(*^) :: Scalar v -> v -> v
class Additive v => RightModule v where
(^*) :: v -> Scalar v -> v
Could you give some example of data type for which (*^) ≠ flip (^*)?
I couldn't imagine one.
...
Though I don't know how much that'd affect the niceness properties you
mentioned.
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