Martijn van Steenbergen wrote:

Two simultaneous instances are okay as long as you don't use any of those instances, right? Just like two imported symbols with the same name are okay as long as you don't use them.

This makes little sense. Sorry, my bad. I was thinking about instances available in the complete module instead of also those made available by pattern matching on constructors. Martijn.

On Thu, Apr 9, 2009 at 5:14 AM, Simon Peyton-Jones wrote:

| > 3) Is it possible to implement the following function? | > | >> mkMonoidInst :: a -> (a -> a -> a) -> MonoidInst a | >> mkMonoidInst mempty mappend = ...

No it's not possible. And now you know why!

Simon

Simon, While we can't give him exactly what he asked for, we can approximate the construction using Oleg and CC Shan's Implicit Configurations and fulfill the spirit of the request.

{-# LANGUAGE ScopedTypeVariables, TypeOperators, MultiParamTypeClasses, FlexibleContexts, UndecidableInstances, Rank2Types, GeneralizedNewtypeDeriving #-}

Please, pardon the gratuitous use of extensions.

import Data.Bits import Data.Monoid import Data.Reflection -- from package 'reflection'

First define the concept of a dictionary for a monoid.

type M a = (a, a -> a -> a)

Then provide a type level brand that indicates which dictionary you are going to use.

data (a `WithMonoid` s) = Mon { getWithMonoid :: a } deriving (Eq,Ord,Show)

Use reflection to access the dictionary

instance (s `Reflects` M a) => Monoid (a `WithMonoid` s) where mempty = Mon (fst (reflect (undefined :: s))) Mon a `mappend` Mon b = Mon ((snd (reflect (undefined :: s))) a b)

Reify a monoid dictionary for use within a universally quantified world, ala ST.

reifyMonoid :: a -> (a -> a -> a) -> (forall s. (s `Reflects` M a) => s -> w) -> w reifyMonoid = curry reify

Change the type of the above to avoid the spurious argument, and to automatically unwrap the result.

withMonoid :: a -> (a -> a -> a) -> (forall s. (s `Reflects` M a) => w `WithMonoid` s) -> w withMonoid = withMonoid' undefined where withMonoid' :: w -> a -> (a -> a -> a) -> (forall s. (s `Reflects` M a) => w `WithMonoid` s) -> w withMonoid' (_::w) (i::a) f k = reifyMonoid i f (\(_::t) -> getWithMonoid (k :: w `WithMonoid` t))

And now we have some likely candidates to test:

test :: Int test = withMonoid 0 (+) (mconcat [Mon 2,mempty,Mon 0])

test2 :: Int test2 = withMonoid 1 (*) (mconcat [Mon 3,mempty,Mon 2])

test3 :: Integer test3 = withMonoid 0 xor (mconcat [Mon 4,mempty,Mon 4])

*Main> test Loading package reflection-0.1.1 ... linking ... done. 2 *Main> test2 6 *Main> test3 0 There you have it, everything works out. Amusingly, I have a similar set of constructions for reifying other kinds of constructs in my 'monoids' library on Hackage, but I don't currently provide a reified Monoid type, mainly because the signature isn't enough to enforce its associativity. However, I do allow you to reify an arbitrary function into a 'Reducer' using this trick to enable you to uniformly inject values into a particular monoid. -Edward Kmett

| -----Original Message----- | From: haskell-cafe-bounces@haskell.org [mailto: haskell-cafe-bounces@haskell.org] On | Behalf Of Lennart Augustsson | Sent: 09 April 2009 09:54 | To: Martijn van Steenbergen | Cc: Haskell Cafe | Subject: Re: [Haskell-cafe] Ambiguous reified dictionaries | | That program is incorrect, it contains two instances for Monoid Int, | and the compiler should flag it as illegal. | | -- Lennart | | On Thu, Apr 9, 2009 at 10:35 AM, Martijn van Steenbergen | wrote: | > Good morning, | > | > The [1]GHC user's guide, section 8.4.5 says: | > | > "The new feature is that pattern-matching on MkSet (as in the definition of | > insert) makes available an (Eq a) context. In implementation terms, the | > MkSet constructor has a hidden field that stores the (Eq a) dictionary that | > is passed to MkSet; so when pattern-matching that dictionary becomes | > available for the right-hand side of the match." | > | > But what happens if there are several dictionaries available? | > | > Consider these three modules: | > | > ReifyMonoid.hs: | > | >> {-# LANGUAGE GADTs #-} | >> | >> module ReifyMonoid where | >> | >> import Data.Monoid | >> | >> data MonoidInst a where | >> MkMonoidInst :: Monoid a => MonoidInst a | > | > ReifySum.hs: | > | >> module ReifySum where | >> | >> import ReifyMonoid | >> import Data.Monoid | >> | >> instance Monoid Int where | >> mempty = 0 | >> mappend = (+) | >> | >> intSum :: MonoidInst Int | >> intSum = MkMonoidInst | > | > ReifyProd.hs: | > | >> module ReifyProd where | >> | >> import ReifyMonoid | >> import Data.Monoid | >> | >> instance Monoid Int where | >> mempty = 1 | >> mappend = (*) | >> | >> intProd :: MonoidInst Int | >> intProd = MkMonoidInst | > | > Now a function | > | >> emp :: MonoidInst a -> a | >> emp MkMonoidInst = mempty | > | > works as you'd expect: | > | > *ReifySum ReifyProd> emp intSum | > 0 | > *ReifySum ReifyProd> emp intProd | > 1 | > | > But what about this function? | > | >> empAmb :: MonoidInst a -> MonoidInst a -> a | >> empAmb MkMonoidInst MkMonoidInst = mempty | > | > Now there are two dictionaries available. GHC consistently picks the one | > from the second argument: | > | > *ReifySum ReifyProd> empAmb intProd intSum | > 1 | > *ReifySum ReifyProd> empAmb intSum intProd | > 0 | > | > My questions are: | > | > 1) Shouldn't GHC reject this as being ambiguous? | > 2) Should class constraints only be available on existentially qualified | > type variables to prevent this from happening at all? | > 3) Is it possible to implement the following function? | > | >> mkMonoidInst :: a -> (a -> a -> a) -> MonoidInst a | >> mkMonoidInst mempty mappend = ... | > | > Thank you, | > | > Martijn. | > | > | > | > [1] | > http://www.haskell.org/ghc/docs/latest/html/users_guide/data-type- | extensions.html#gadt-style | > _______________________________________________ | > Haskell-Cafe mailing list | > Haskell-Cafe@haskell.org | > http://www.haskell.org/mailman/listinfo/haskell-cafe | > | _______________________________________________ | Haskell-Cafe mailing list | Haskell-Cafe@haskell.org | http://www.haskell.org/mailman/listinfo/haskell-cafe

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