[Haskell-cafe] Re: Polyvariadic functions operating with a monoid

[Kevin Jardine]

For example, the notation can be reduced to:

poly([String],True () (Just (5::Int)))

using:

#define poly(TYPE,VALUES) ((polyToMonoid (mempty :: TYPE) VALUES) ::
TYPE)

which I think is as concise as it can get.

Kevin

On Oct 10, 1:47 pm, Kevin Jardine <kevinjard... at gmail.com> wrote:
> It is interesting to see that the dummy parameters can actually be
> replaced by:
>
> mempty :: [String]
> mempty :: String
> mempty: Int
>
> in my three examples and the code still compiles and gives the
> expected results.
>
> This suggests that a further simplification might be possible (ideally
> in straight Haskell, but if not then with CPP or Template Haskell).
>
> Kevin
>
> On Oct 10, 1:28 pm, Kevin Jardine <kevinjard... at gmail.com> wrote:
>
> > For anyone who's interested, the code I have now is:
>
> > {-# LANGUAGE TypeSynonymInstances, FlexibleInstances,
> > MultiParamTypeClasses #-}
> > module PolyTest where
>
> > import Data.Monoid
>
> > class Monoid m => Monoidable a m where
> >     toMonoid :: a -> m
>
> > squish :: Monoidable a m => m -> a -> m
> > squish m a = (m `mappend` (toMonoid a))
>
> > class Monoid m => PolyVariadic m r where
> >     polyToMonoid :: m -> r
>
> > instance Monoid m => PolyVariadic m m where
> >     polyToMonoid acc = acc
>
> > instance (Monoidable a m, PolyVariadic m r) => PolyVariadic m (a->r)
> > where
> >     polyToMonoid acc = \a -> polyToMonoid (squish acc a)
>
> > and three example uses are:
>
> > -- [String] example
> > instance Show a => Monoidable a [String] where
> >     toMonoid a = [show a]
>
> > testStringList = putStrLn $ show $ ((polyToMonoid [""] True () (Just
> > (5::Int))) :: [String])
>
> > -- String example
> > instance Show a => Monoidable a String where
> >     toMonoid a = show a
>
> > testString = putStrLn $ ((polyToMonoid "" True () (Just (5::Int))) ::
> > String)
>
> > -- sum example
>
> > instance Monoid Int where
> >     mappend = (+)
> >     mempty = 0
>
> > instance Monoidable Int Int where
> >     toMonoid = id
>
> > testSum = putStrLn $ show $ ((polyToMonoid (0::Int) (1::Int) (2::Int)
> > (3::Int)) :: Int)
>
> > main = do
> >     testStringList
> >     testString
> >     testSum
>
> > $ runhaskell PolyTest.hs
> > ["","True","()","Just 5"]
> > True()Just 5
> > 6
>
> > This removes the unwrap and I don't mind the need for the outer type
> > cast.
>
> > I do wonder if there is a need for the first (dummy) parameter to
> > communicate the type as well as this seems redundant given the outer
> > type cast but I can't find a way to remove it.
>
> > It appears that GHC needs to be told the type both coming and going so
> > to speak for this to work consistently.
>
> > Any suggestions for improvement welcome!
>
> > Kevin
>
> > On Oct 10, 11:12 am, Kevin Jardine <kevinjard... at gmail.com> wrote:
>
> > > OK, upon further investigation, the problem is that GHC cannot in
> > > general infer the return type of polyToMonoid despite the hint it is
> > > given (the type signature of the first parameter).
>
> > > If I write:
>
> > > main = putStrLn $ show $ unwrap $ ((polyToMonoid [""] True (Just
> > > (5::Int))) :: WMonoid [String])
>
> > > or
>
> > > main = putStrLn $ show $ unwrap $ ((polyToMonoid (0::Int) (1::Int)
> > > (2::Int) (3::Int)) :: WMonoid Int)
>
> > > the code compiles and returns the expected result.
>
> > > Kevin
>
> > > On Oct 10, 8:58 am, Kevin Jardine <kevinjard... at gmail.com> wrote:
>
> > > > And in fact in both cases, it appears that GHC is trying to derive the
> > > > *wrong* instances of PolyVariadic.
>
> > > > It should be deriving:
>
> > > > PolyVariadic Int (WMonoid Int)
>
> > > > not
>
> > > > PolyVariadic Int (WMonoid m)
>
> > > > and
>
> > > > PolyVariadic [String] (WMonoid [String])
>
> > > > not
>
> > > > PolyVariadic [String] (WMonoid String)
>
> > > > specifically, GHC is attempting to derive PolyVariadic with the wrong
> > > > version of WMonoid in each case.
>
> > > > I'm using GHC 6.12.3
>
> > > > Perhaps the new GHC 7 type system would work better?
>
> > > > Kevin
>
> > > > On Oct 10, 8:26 am, Kevin Jardine <kevinjard... at gmail.com> wrote:
>
> > > > > Hi Brandon,
>
> > > > > True, when I replace [] with [""], I get a different error message:
>
> > > > >  No instance for (PolyVariadic [[Char]] (WMonoid String))
>
> > > > > which now looks a bit like the Int example. In both cases, GHC appears
> > > > > to be unable to derive the appropriate instance of PolyVariadic. Why
> > > > > this is so, but worked for Oleg's specific example. is still not clear
> > > > > to me.
>
> > > > > Kevin
>
> > > > > On Oct 9, 11:51 pm, Brandon S Allbery KF8NH <allb... at ece.cmu.edu>
> > > > > wrote:
>
> > > > > > -----BEGIN PGP SIGNED MESSAGE-----
> > > > > > Hash: SHA1
>
> > > > > > On 10/9/10 10:25 , Kevin Jardine wrote:
>
> > > > > > > instance Show a => Monoidable a [String] where
> > > > > > >     toMonoid a = [show a]
>
> > > > > > > main = putStrLn $ unwrap $ polyToMonoid [] True () (Just (5::Int))
>
> > > > > > > fails to compile.
>
> > > > > > > Why would that be? My understanding is that all lists are
> > > > > > > automatically monoids.
>
> > > > > > I *think* the problem here is that Oleg specifically pointed out that the
> > > > > > first parameter to polyToMonoid must specify the type of the monoid.  []
> > > > > > tells you it's a list, therefore a monoid, but it doesn't say enough to
> > > > > > allow the [String] instance to be chosen.  (No, the fact that you only
> > > > > > declared an instance for [String] isn't really enough.)
>
> > > > > > - --
> > > > > > brandon s. allbery     [linux,solaris,freebsd,perl]      allb... at kf8nh.com
> > > > > > system administrator  [openafs,heimdal,too many hats]  allb... at ece.cmu.edu
> > > > > > electrical and computer engineering, carnegie mellon university      KF8NH
> > > > > > -----BEGIN PGP SIGNATURE-----
> > > > > > Version: GnuPG v2.0.10 (Darwin)
> > > > > > Comment: Using GnuPG with Mozilla -http://enigmail.mozdev.org/
>
> > > > > > iEYEARECAAYFAkyw49wACgkQIn7hlCsL25VZygCfVETk+3AZ3gKoBy4pZ7j8g4Km
> > > > > > WXgAnjrbO9rEl2HnQtGQ31EyRuhWzI4r
> > > > > > =YMDw
> > > > > > -----END PGP SIGNATURE-----
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