[Haskell-cafe] Beautiful Differentiation using VectorSpace

[Christopher Witte]

Hi all,

I'm trying to go through the paper Beautiful Differentiation by Conal
Elliott and got a bit stuck.  So I decided to download the VectorSpace
package, which as far as I know implements the paper, and just try and play
around with it.  Unfortunately when I tried the simple examples at the
beginning of the paper I got an error:

Prelude Data.VectorSpace> :m Data.Derivative
Prelude Data.Derivative> let f1 z = sqrt(3*sin z)
Prelude Data.Derivative> f1 (D 2 1)

Top level:
    Couldn't match expected type `Data.VectorSpace.Scalar a'
           against inferred type `Data.VectorSpace.Scalar
                                    (Data.VectorSpace.Scalar a)'
      NB: `Data.VectorSpace.Scalar' is a type function, and may not be
injective

<interactive>:1:0:
    No instances for (Data.MemoTrie.HasTrie (Data.Basis.Basis a),
                      Floating (Data.VectorSpace.Scalar a),
                      Data.VectorSpace.VectorSpace (Data.VectorSpace.Scalar
a))
      arising from a use of `f1' at <interactive>:1:0-9
    Possible fix:
      add an instance declaration for
      (Data.MemoTrie.HasTrie (Data.Basis.Basis a),
       Floating (Data.VectorSpace.Scalar a),
       Data.VectorSpace.VectorSpace (Data.VectorSpace.Scalar a))
    In the expression: f1 (D 2 1)
    In the definition of `it': it = f1 (D 2 1)

<interactive>:1:8:
    No instance for (Num
                       (a Data.LinearMap.:-* (a :> Data.VectorSpace.Scalar
a)))
      arising from the literal `1' at <interactive>:1:8
    Possible fix:
      add an instance declaration for
      (Num (a Data.LinearMap.:-* (a :> Data.VectorSpace.Scalar a)))
    In the second argument of `D', namely `1'
    In the first argument of `f1', namely `(D 2 1)'
    In the expression: f1 (D 2 1)

Which was completely incomprehensible to me.  I tried looking at the
documentation but I couldn't find anything about actually using the
library.  Does anyone have any experience using this library and maybe have
some examples of it's use?

Thanks

Chris Witte
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