On 29/03/2012, at 3:08 PM, Doug McIlroy wrote:
--------- without newtype
toSeries f = f : repeat 0 -- coerce scalar to series
instance Num a => Num [a] where (f:fs) + (g:gs) = f+g : fs+gs (f:fs') * gs@(g:gs') = f*g : fs'*gs + (toSeries f)*gs'
--------- with newtype
newtype Num a => PS a = PS [a] deriving (Show, Eq)
fromPS (PS fs) = fs -- extract list toPS f = PS (f : repeat 0) -- coerce scalar to series
instance Num a => Num (PS a) where (PS (f:fs)) + (PS (g:gs)) = PS (f+g : fs+gs) (PS (f:fs)) * gPS@(PS (g:gs)) = PS $ f*g : fromPS ((PS fs)*gPS + (toPS f)*(PS gs))
Try it again. newtype PS a = PS [a] deriving (Eq, Show) u f (PS x) = PS $ map f x b f (PS x) (PS y) = PS $ zipWith f x y to_ps x = PS (x : repeat 0) ps_product (f:fs) (g:gs) = whatever instance Num a => Num (PS a) where (+) = b (+) (-) = b (-) (*) = b ps_product negate = u negate abs = u abs signum = u signum fromInteger = to_ps . fromInteger I've avoided defining ps_product because I'm not sure what it is supposed to do: the definition doesn't look commutative.
The code suffers a pox of PS.
But it doesn't *need* to.