[Haskell-beginners] help designing types for a gsl fit

[PICCA Frederic-Emmanuel]

Hello

I imagine that I have two types A and B

I want to create a ADT

data C = C A B


1) the toGsl class

class ToGsl a where
   toGsl :: a -> [Double]

this class allow to convert a type to a Vector of double in order to use gsl for a fit

so I can create instance for A and B (I do not write the instance but the result of the toGsl function)

A -> [a1, ... an]
B -> [b1, ... bm]

Now I want this to work also with C

C -> [a1..., an] ++ [b1, .... bm]

So the C instance is juste the (toGsl a) ++ (toGsl b)

Is there a way to write this generically for other type  construct like (data D = D C A) etc....

Functor, Applicative, Monoid ?

2) the fromGsl case

now the inverse method is

 cladd FromGsl a where
  fromGsl :: a -> [Double] -> a


so now the question is if I have a [Double], I need t osplit this list  for each composant of the ADT.

in the case of C

fromGSL (C a b) v = ...split the vector... and apply fromGsl to a and b

So my question is the symetic of the previous one.

Is it possible to create a generic function inorder to do this.

thanks for your help.


Frederic