Why is hmatrix Matrix not an instance of 'functor'?

[odcameron]

To quote LYAH: “Functors are things that can be mapped over”.
So when I tried to fmap over a matrix, I was surprised to discover that Matrix is not an instance.

   m = (2><3)[3,5,4,6,5,7]
   x =  fmap (1+) m 
-- "No instance for (Functor Matrix) arising from a use of ‘fmap’"

Why ever not?

[f-a]

Because hmatrix is a container only for certains elements.

Makes sense since the package is about linear systems, hence Matrix String would carry little meaning.

[sullyj3]

Possibly Container/cmap will do what you want?

Numeric.LinearAlgebra.Data

[odcameron]

Ahh I think I understand… The constructor Matrix in the definition is hidden (so we can’t pattern match ). Instead members of Matrix class are produced by functions like matrix, (><), fromColumns, etc. - functions whose type definitions restrict the type of matrix elements to Double (type alias R), Element or Storable type. If Matrix could be a member of Functor then fmap :: (a -> b) -> Matrix a -> Matrix b would need to apply for arbitrary a and b. But it would only make sense for the type signature fmap :: (Storable a, Storable b) => (a -> b) -> Matrix a -> Matrix b. Essentially this is what cmap does, but where Container takes the role of Functor, and cmap takes the role of fmap. (Aside - it seems to me that this limited fmap-like functionality - call it SemiFunctor - should be totally generic, whereas the Container implementation limits what can be ‘contained’ to Elements. Has this been done? Would it be a worthwhile addition to the Haskell ecosystem?)

I wonder - if Matrix is to be limited to Storable (or in practice, Element) types, why not embed this in the data declaration using GADTs?

data Matrix t where
    Matrix :: Storable t => Int -> Int -> Int -> Int -> (Vector t) -> Matrix t
                      --   irows  icols   xRow   xCol     xdat

[f-a]

I wonder - if Matrix is to be limited to Storable (or in practice, Element) types, why not embed this in the data declaration using GADTs?

Not library author but: I suspect because typeclasses are open to new instances — even instances created by library users —, while GADTs are not.

[vmchale]

part of the answer is “Functors are things that can be mapped over” is not quite right!

An oversimplification maybe.

[theobat]

A relevant discussion is here:

Why Data.Set (containers) doesn't have Functor and Monad instance?

You could do it like this: {-# LANGUAGE ConstraintKinds, TypeFamilies, FlexibleInstances #-} import qualified Data.Set as Set import Data.Set (Set) import qualified Data.List as List import Data.Kind class Mappable m where type C m a :: Constraint type C m a = () -- no constraint by default mmap :: (C m a, C m b) => (a -> b) -> m a -> m b instance Mappable Set where type C Set a = Ord a -- overwrite default with the Ord constraint mmap = Set.map instance Mappable [] where mmap …

In particular this solution (Why Data.Set (containers) doesn't have Functor and Monad instance? - #19 by jaror) is, I believe, something that could be in base but … who knows

[sclv]

The problem with embedding with GADTs is you now have no way of guaranteeing to the compiler that two Matrix t share the same Storable dictionary. Also, you don’t get any benefit out of it – it just makes things more complicated. Try coding up some simple examples in that style and you’ll see the limitations soon enough for yourself!

[ocramz]

A functor is a function between functions ^___^