Richard O'Keefe ok at cs.otago.ac.nz
Thu Mar 29 05:34:46 CEST 2012

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.