[Haskell-cafe] Ambiguous reified dictionaries

[Lennart Augustsson]

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
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