[Haskell-cafe] Context for type parameters of type constructors

29 Mar 2004

      Sorry for sending this twice, but it seems to me that the newsgroup
fa.haskell only logs the discussion of haskell and haskell-cafe.

---------- Forwarded message ----------
Date: Mon, 29 Mar 2004 01:18:27 -0800
From: googlegroups@henning-thielemann.de (Henning Thielemann)
Newsgroups: fa.haskell
Subject: Context for type parameters of type constructors
NNTP-Posting-Host: 134.102.210.249
Message-ID: <a17fb6f7.0403290118.786ede0d@posting.google.com>

I have a problem with type classes that can be illustrated
with the following example:
I want to declare a class for vector like data.
'Vector' is not meant as a synonyme for 'array'
but a 'vector' shall be a mathematical object
that allows for some linear operations,
namely summing and scaling.

Thus I setup a type constructor VectorSpace
in the following way:
...
module VectorSpace
   where
class VectorSpace v where
   zero  :: v a
   add   :: v a -> v a -> v a
   scale :: a -> v a -> v a
I haven't added context requirements like (Num a)
to the signatures of 'zero', 'add', 'scale'
because I cannot catch all requirements
that instances may need.

The problematic part is the 'scale' operation
because it needs both a scalar value and a vector.
Without the 'scale' operation
'v' could be simply a type (*)
rather than a type constructor (* -> *).

Now let's try some instances:
...
data (Num a) => VList a = VList [a]
instance VectorSpace VList where
   zero                      = VList (repeat 0)
   add   (VList x) (VList y) = VList (zipWith (+) x y)
   scale s         (VList x) = VList (map (s*) x)
data (Num a) => VFunc b a = VFunc (b->a)
instance VectorSpace (VFunc b) where
   zero                      = VFunc (\_ -> 0)
   add   (VFunc f) (VFunc g) = VFunc (\x -> (f x) + (g x))
   scale s         (VFunc f) = VFunc (\x -> s*(f x))
But now GHC complains:

$ ghc -c VectorSpace.lhs

VectorSpace.lhs:37:
    Could not deduce (Num a) from the context (VectorSpace VList)
      arising from the literal `0' at VectorSpace.lhs:30
    Probable fix:
        Add (Num a) to the class or instance method `zero'
    In the first argument of `repeat', namely `0'
    In the first argument of `VList', namely `(repeat 0)'
    In the definition of `zero': zero = VList (repeat 0)

...

I hoped that when I declare VList within the context (Num a)
then it is always asserted
that a VList is built on a Num type.

If it is necessary to add (Num a) somewhere in the instance declaration -
then where?

Btw. I'm using

$ ghc --version
The Glorious Glasgow Haskell Compilation System, version 6.0