Grady Lemoine wrote: > 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
You have two different things making this error possible. First there is the default(Integer,Int) that Haskell implicitly provides. Second, there is the monomorphism restriction. Try this: > default () > > 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) > abs _ = error "no abs" > signum _ = error "no signum" > > evalDeriv f x = (v, v') > where D v v' = f (D x 1) > > f x = x^(3::Int) > > f' :: (Num a) => a -> a > f' = snd . (evalDeriv f) I played with such things, as seen on the old wiki: http://haskell.org/hawiki/ShortExamples_2fSymbolDifferentiation -- Chris _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
