[Haskell-cafe] Ambiguous reified dictionaries
Edward Kmett
ekmett at gmail.com
Thu Apr 9 18:42:54 EDT 2009
On Thu, Apr 9, 2009 at 5:14 AM, Simon Peyton-Jones <simonpj at microsoft.com>
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 at haskell.org [mailto:
> haskell-cafe-bounces at 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
> | <martijn at van.steenbergen.nl> 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 at haskell.org
> | > http://www.haskell.org/mailman/listinfo/haskell-cafe
> | >
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