[Haskell-cafe] Is it possible to represent such polymorphism?

[sdiyazg at sjtu.edu.cn]

Quoting Felipe Almeida Lessa <felipe.lessa at gmail.com>:

> On Sun, Oct 2, 2011 at 4:26 PM, Edward Z. Yang <ezyang at mit.edu> wrote:
>> What are you actually trying to do?  This seems like a rather
>> unusual function.
>
> If you're new to the language, most likely you're doing something
> wrong if you need this kind of function.  =)
>
> --
> Felipe.
>

{-# LANGUAGE TypeFamilies,FlexibleInstances #-}

module RicherListOp ( generalizedFilter,generalizedMap,generalizedFilterMap )
	where
import Data.List

generalizedFilter pred = impl.expand3 where
	impl (dL,dR,step) = generalizedFilterMap tf (dL+dR+1,step) where
		tf s = if pred s then [s !! dL] else []

generalizedMap tf = generalizedFilterMap $ \x->[tf x]

generalizedFilterMap tf ns ls = impl {-$ expand2-} ns where
	impl (len,step) = f ls where
		f xs | length xs >=len = (tf $ genericTake len xs) ++ (f $  
genericDrop step xs)
		f _ = []

class Expand3 t where
	type Result3 t
	expand3 :: t->Result3 t

instance (Integral a,Integral b)=>Expand3 (a,b) where
	type Result3 (a,b) = (a,b,Int)
	expand3 (l,r) = (l,r,1)

instance (Integral a,Integral b,Integral c)=>Expand3 (a,b,c) where
	type Result3 (a,b,c) = (a,b,c)
	expand3 = id

--instance (Integral a)=>Expand3 a where
--	type Result3 a = (a,a,a)
--	expand3 r = (0,r,1)

--class Expand2 t where
--	type Result2 t
--	expand2 :: t->Result2 t

--instance (Integral a)=>Expand2 (a,a) where
--	type Result2 (a,a) = (a,a)
--	expand2 = id

--instance (Integral a)=>Expand2 a where
--	type Result2 a = (a,a)
--	expand2 a = (a,1)

examples:
>> generalizedFilterMap (\[x,y,z]-> if(x==1&&z==1)then [y*10] else  
>> [0]) (3,1) [1,2,3,4,1,2,1,3,1,4,1,5,2]
[0,0,0,0,20,0,30,0,40,0,0]
it :: [Integer]
>> generalizedFilter (\[x,y,z] -> x==1&&z==1) (1,1) [1,2,3,4,1,2,1,3,1,4,1,5,2]
[2,3,4]
it :: [Integer]

The code commented out is what I still can't get working. (I'm no  
longer trying to finish them. They are included just to illustrate my  
idea). Of course, I could have simply used [Int] , (Num a)=>[a] or  
(Int,Int,Int), but I'm trying to write code as generic as possible.