[Hs-Generics] type constructor genericity with regular

[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?

Cheers, Jan