Hi,
2010/9/15 Jan Christiansen
Hi,
On 15.09.2010, at 11:40, José Pedro Magalhães wrote:
I'm not sure I fully understand what you're trying to do. Could you
provide typical use cases of your function, to several arguments of different types?
Consider a polymorphic data type with one type variable like lists. I want to replace every value of the "polymorphic" type by a list of Booleans that corresponds to its position in the term (with respect to the :*: constructor). For example,
shape [1,2] = [[False],[True,False]]
because the generic representation (without the injections) of [1,2] is K 1 :*: (K 2 :*: U)) and in this term the path [False] corresponds to 1 while the path [True,False] corresponds to 2.
As another example consider the following data type for binary trees.
data Tree a = Node (Tree a) a (Tree a) | Leaf a
then we have
shape (Node (Leaf 'a') 'b' (Leaf 'c')) = Node (Leaf [False]) [True,False] (Leaf [True,True])
because the generic representation (without the injections) of the argument tree is K 'a' :*: (K 'b' :*: K 'c').
In fact, for the same reason I suspect that it is not possible to implement shape by means of regular I would expect that it is not possible to implement the standard fmap by means of regular. Is this correct?
Ah, I now see what you mean. Yes, you are right: regular does not abstract over type parameters, hence you can't do much to them. We have a similar library which does abstract over one parameter, though. It's called generic-deriving on Hackage, and used by the Utrecht Haskell Compiler [1, 2]. However, in your application of shape to Tree, I see that you want to replace not only the parameters but also the recursive occurrences. I think this function could still be expressed with generic-deriving, though. For curiosity: what do you want this shape function for? Cheers, Pedro [1] Hackage package: http://hackage.haskell.org/package/generic-deriving [2] Companion paper: http://dreixel.net/research/pdf/gdmh_draft.pdf