# [Haskell-cafe] Strange type behavior in GHCi 6.4.2

Sat Dec 2 12:53:14 EST 2006

```Hello,

I've been playing around with Dan Piponi's work on automatic
differentiation (from
http://sigfpe.blogspot.com/2005/07/automatic-differentiation.html and
http://sigfpe.blogspot.com/2006/09/practical-synthetic-differential.html)
and I'm getting some odd behavior with the inferred types of functions
in GHCi 6.4.2.  My test case is as follows:

> data Dual a = D a a deriving (Show,Eq)

> instance Num a => Num (Dual a) where
>   fromInteger i = D (fromInteger i) 0
>   (D a a')+(D b b') = D (a+b) (a'+b')
>   (D a a')-(D b b') = D (a-b) (a'-b')
>   (D a a')*(D b b') = D (a*b) (a*b'+a'*b)

> evalDeriv f x = (v, v')
>     where D v v' = f (D x 1)

> f x = x^3

> f' = snd . (evalDeriv f)

When I load this in GHCi, I get:

*Main> :t f
f :: (Num a) => a -> a
*Main> :t snd . (evalDeriv f)
snd . (evalDeriv f) :: (Num a, Num (Dual a)) => a -> a
*Main> :t f'
f' :: Integer -> Integer

Why is the type of f' Integer -> Integer, especially when the type of
the expression it's defined as is more general?  Is this something I'm
not understanding about Haskell, or is it more to do with GHC 6.4.2
specifically?

Any help appreciated,