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
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/