# Lifting to the limit

**Saswat Anand
**
iscp9157@nus.edu.sg

*Fri, 16 Feb 2001 21:45:32 +0800*

Dear All,
I have this following simplified problem. Please help.
type Formula a b = a -> b
type Env = (Integer,Char)
fun :: Formula Integer Integer
fun n = n+1
sun :: Formula Char Integer
sun c = toInteger.ord c
I want to be able to write
(sun + fun) (2,'a')
(fun + sun) (2,'a')
both of which should be equal to (sun 'a' + fun 2)
So I did this:
lift2 :: (a -> b -> c) -> Formula d a -> Formula e b -> Formula Env c
lift2 f a1 a2 = \env -> f ( (lift a1) n ) ( (lift a2) n )
-- Here hugs gives error
class Lift a where
lift :: Formula a b -> Formula Env b
instance Lift Char where
lift f = \(i,c) -> f c
instance Lift Integer where
lift f =\(i,c) -> f i
With this, hugs (with extensions enabled) gives following error:
Cannot justify constraints in explicitly typed binding
***Expression : lift2
***Type : (a -> b -> c) -> Formula d a -> Formula e b ->
Formula Env c
***Given Constraint: ()
***Constraints : (Lift d, Lift e)
Any help is very much appreciated.
Thanks,
Saswat