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, --Grady Lemoine