[Haskell-cafe] type classes

[Cotton Seed]

Hi Henning,

The numeric prelude was inspiration for a lot of my design.  Part of
the reason I didn't use it was because one of my goals is to learn
Haskell better, and I wanted to grapple with these design decisions
myself.

I decided, like IsZeroTestable in the numeric prelude, to make
zero/one separate type classes.  Thus, I have

class AbelianGroup a where
  (+) :: a -> a -> a
  negate :: a -> a

class HasZero a where
  zero :: a

so ZModN is an instance of AbelianGroup but not HasZero.  Most
functions that "want" a zero have two forms, for example,

sum :: (HasZero a, AbelianGroup a) => [a] -> a
sumWithZero :: (AbelianGroup a) => a -> [a] -> a

although I may eventually require all types to have a corresponding Ty
class and change this to

sumWithTy :: (AbelianGroup a) => AblieanGroupTy a -> [a] -> a

Matrices are another example that fits this model.  Numeric prelude
defines zero/one to be 1x1 matrices, but asserts dimensions match in
various operations, so they don't actually seem usable.

Cotton

On Thu, Jul 3, 2008 at 1:22 AM, Henning Thielemann
<lemming at henning-thielemann.de> wrote:
>
> On Wed, 2 Jul 2008, Cotton Seed wrote:
>
>> Hi everyone,
>>
>> I'm working on a computational algebra program and I've run into a
>> problem.
>> In my program, I have types for instances of algebraic objects, e.g. ZModN
>> for modular integers, and types for the objects themselves, e.g. ZModNTy
>> for
>> the ring of modular integers.
>
> Maybe you are also interested in:
>  http://darcs.haskell.org/numericprelude/src/Number/ResidueClass.hs
>  http://darcs.haskell.org/numericprelude/src/Number/ResidueClass/
>
>