[Haskell-cafe] Type level functions (type of decreasing list)

[Greg Buchholz]

    I'm wondering about creating a data structure that has the type of
decreasing numbers.  If I want an increasing list, it is easy...

> {-# OPTIONS -fglasgow-exts #-}  
> 
> data Succ a = S a deriving Show 
> data Zero   = Z   deriving Show
> 
> data Seq' a = Cons' a (Seq' (Succ a)) | Nil' deriving Show

...which can be used like...

> 
> zero  = Z
> one   = S zero
> two   = S one
> three = S two
> 
> increasing = Cons' zero (Cons' one (Cons' two (Cons' three Nil')))

...on the other hand, if I want the decreasing list, I can try...

> 
> class Pre a b | a -> b 
> instance Pre (Succ a) a
> instance Pre Zero Zero
> 
> data (Pre a b) => Seq a = Cons a (Seq b) | Nil
> 
> decreasing = Cons three (Cons two (Cons one Nil))

...but that complains about "Not in scope: type variable `b'".  Of
course that makes perfect sense, but I'd like to know if there is a
Haskell idiom that I'm missing in order to get this to work.


Thanks,

Greg Buchholz