[Haskell-cafe] Confused about types

[Lanny Ripple]

Well ick.  It makes sense (not that I can do it yet but I 
understand what you are saying).

I'll try both approaches since this is all about learning the 
language.  I can throw in the "closeness" concept to norm as 
well.  Without symbolic computation hitting an irrational value 
will take more time to get a numeric answer than I'm willing to 
spend.

Thanks for pointing the way,
   -ljr

Cale Gibbard wrote:
> Note that you can't pattern match to make special cases for handling
> particular types, only against data constructors in the specific type
> which your function accepts as input.
> 
> You need a typeclass if you want to have a function which acts
> differently at different types. As you might have realised abs is
> somewhat ineffective for comparing the magnitudes of numbers which
> aren't already in Ord, as it will produce a value of the same type.
> 
> The main trouble here is that
>   abs :: (Num a) => a -> a
> and doesn't help to order the complex numbers. On the other hand, there is
>   magnitude :: (RealFloat a) => Complex a -> a
> which will take your Complex Double and give you back a Double, for
> instance, and Double will be ordered, which is exactly what you want.
> 
> The quickest way to solve this problem is to just make a typeclass for
> the Newton's method functions, and put them in it, and change the
> implementation for the Complex instance. You might also consider
> making a class for a general norm operation, but this would pretty
> much necessarily be a multiparameter typeclass, and you'd likely want
> to use functional dependencies, so that the result type would be
> determined by the input type.
> 
> hope this helps,
>  - Cale

-- 
Lanny Ripple <lanny at cisco.com>
CC Tools / Cisco Systems, Inc.