Re: [Haskell-beginners] Num instnace for [Double]

2 Oct 2013

      Nathan Hüsken  writes:
...
Hey,
I am working a lot with timeseries (with instances at discrete moments) 
of doubles.
So I use [Double].
You may want to consider using a more efficient type than [Double] if
your data is at all large. Unless you really want the laziness that
lists offer you might be better off using vectors.
...
Now I want to be able to do stuff like
timeSeries3 = timeSeries1 + timeSeries2
So I was thinking, I create a newtype
newtype TimeSeries a  = TimeSeries [a]
Now, can I somehow autoderive List, Monad, MonadPlus for TimeSeries?
As far as I'm aware, List is not a typeclass. You can conveniently derive
newtype instances with GeneralizedNewtypeDeriving[1] in most cases. That
being said you need to decide what sort of semantics you want your type
to have. In the case of Appplicative, you have a choice between ZipList
(which would make point-wise operations straightforward) and standard
list (making non-determinism straightforward).

Applicative is tricky in the case of vector-like types as you
don't know what length you want your timeseries to be. In the
list case you can simply produce a non-terminating series. One way
around this (although perhaps not the best way) would be to introduce a
constructor to represent a homogenous timeseries. This might look
something like,

    import qualified Data.Vector as V
    import Control.Applicative

    data TimeSeries a = Pure a
                      | Moments (V.Vector a)
                      deriving (Show)

    instance Functor TimeSeries where
        fmap f (Pure a)     = Pure (f a)
        fmap f (Moments as) = Moments (fmap f as)

    instance Applicative TimeSeries where
        pure = Pure
        Pure a <*> Pure b      = Pure (a b)
        Pure a <*> Moments bs  = Moments $ fmap a bs 
        Moments as <*> Pure b  = Moments $ fmap ($ b) as
        Moments as <*> Moments bs = Moments $ V.zipWith ($) as bs

    fromList :: [a] -> TimeSeries a
    fromList = Moments . V.fromList

    times :: TimeSeries Int
    times = fromList [1,5,9,2,5]

    main = do
        print $ (+) <$> pure 4 <*> times

Of course, this presents the possibility of trying to perform a
point-wise operation on differently sizes series. Zip-like functions
will typically truncate their output to the shortest of their arguments,
opening the possibility for silent data loss. One (hacky) way around
this would be to accept a partial Applicative instance, returning bottom
in the event of incompatible series.

Another approach would be to parametrize the type on the length of the
series with type-level naturals[3]. This still leaves open the
possibility of performing actions on series of incompatible stride or
offset, but at least you can be certain your series are of compatible
shapes.
...
Also I would like to derive from Num. Most of the things can be done 
pointwise!
What about fromInteger??? Should that just be a list with one element? 
Or does it simple not make sense?
I probably wouldn't use the Num typeclass here for this reason, among
others. If you give you type the right Applicative instance the
operations you are after should be easily performed. 

Cheers,

- Ben

[1] http://www.haskell.org/ghc/docs/7.4.1/html/users_guide/deriving.html
[2] http://hackage.haskell.org/package/linear

Re: [Haskell-beginners] Num instnace for [Double]

Ben Gamari