I. On Sun, 2007-01-21 at 11:20 -0800, Stefan O'Rear wrote:
> On Sun, Jan 21, 2007 at 08:00:53PM +0100, Hans van Thiel wrote:
> > On Sun, 2007-01-21 at 09:42 -0800, Stefan O'Rear wrote:
> > > This is the closest you'll get with GHC extensions:
> > >
> > > > {-# OPTIONS_GHC -fallow-undecidable-instances #-}
> > > > instance Num a => Monoid a where
> > > > e = 0
> > > > add = (+)
>
> > Yes, thank you. The one with the gHC extension looks like what I wanted
> > to do, but then in reverse order, declare the numbers to be monoids.
> > Expanding on this, I've now got:
>
> In an instance definition, the => is implication; a number is a monoid if
> it is a number.
> (Yes, we know the class syntax is backward :( )
Thanks for pointing this out. :-)
>
> > class Monoid a => Group a where
> > inv :: a -> a
> > minus :: a-> a -> a
> > minus x y = add x (inv y)
> > inv x = minus e x
>
> > instance Group Int where
> > minus = flip subtract
> > -- inv x = -x
> >
> > This seems to work. What I like is that, like in EQ and Ord, functions
> > are defined in several ways by default. So, for Int, you can choose to
> > define either inv or minus, you don't have to do both.
>
> looks correct
>
> > But subtract and - are defined over all types of Num, so it would be
> > nice to have something like
> >
> > instance Group a => Num a where .....
> >
> > I understand this cannot be done in Haskell98, but it can with the GHC
> > extension? Does {-# OPTIONS_GHC -fallow-undecidable-instances #-} refer
> > to possibly infinite definitions? Thanks again!
>
> Almost - that instance definition says that every group is a number (~= ring),
> which probably isn't what you meant :)
As above, useful to know :-)
>
> instance Num a => Group a where .....
>
> Haskell instance definitions, unrestricted, effectively force the compiler
> to solve arbitrary logic problems, which can take up to and including forever.
> To keep type inference terminating, H98 imposes a number of severe
> restrictions.
> GHC has a number of options to relax the restrictions in ways that complicate
> typechecking but don't make it impossible (-fallow-overlapping-instances,
> etc);
> -fallow-undecidable-instances is the ultimate flag and basically says "Do
> what I
> say - I accept responsibility if the typechecker goes into an infinite loop".
>
> Keep SIGINT handy.
It's pretty clear now, thanks for the help!
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