The sum function really only needs the argument list to be a monoid.
And the same is true for the product function, but with 1 and * as
the monoid operators. Sum and product are really the same function. :)
I don't think Haskell really has the mechanisms for setting up an
algebraic class hierarchy the right way. Consider some classes we
might want to build:
SemiGroup
Monoid
AbelianMonoid
Group
AbelianGroup
SemiRing
Ring
...
The problem is that going from, say, AbelianMonoid to SemiRing you
want to add a new Monoid (the multiplicative) to the class. So
SemiRing is a subclass of Monoid in two different way, both for + and
for *.
I don't know of any nice way to express this is Haskell.
-- Lennart
On Sep 13, 2006, at 03:26 , [EMAIL PROTECTED] wrote:
G'day all.
Quoting Jason Dagit <[EMAIL PROTECTED]>:
I was making an embedded domain specific language for excel
spreadsheet formulas recently and found that making my formula
datatype an instance of Num had huge pay offs.
Just so you know, what we're talking about here is a way to make that
even _more_ useful by dicing up Num.
I can even use things like Prelude.sum to
add up cells.
Ah, but the sum function only needs 0 and (+), so it doesn't need
the full power of Num. It'd be even _more_ useful if it worked on
all data types which supported 0 and (+), but not necessarily (*):
sum :: (AdditiveAbelianMonoid a) => [a] -> a
product :: (MultiplicativeAbelianMonoid a) => [a] -> a
Those are bad typeclass names, but you get the idea.
Right now, to reuse sum, people have to come up with fake
implementations for Num operations that simply don't make sense on
their data type, like signum on Complex numbers.
All I really needed was to define Show and Num
correctly, neither of which took much mental effort or coding
tricks.
You also needed to derive Eq, which gives you, in your case,
structural
equality rather than semantic equality (which is probably
undecidable for
your DSL).
Cheers,
Andrew Bromage
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