[Haskell-cafe] technique to allow innocuous ambiguity in instance
declarations?
Nicolas Frisby
nicolas.frisby at gmail.com
Tue Jul 11 11:58:17 EDT 2006
Brief disclaimer: I'm using GHC 6.4.1 and haven't looked into Hugs; but I
don't suspect there's much difference on this issue. Could easily be
wrong there.
I've hit a bit of a road bump in ambiguity regarding type class
instances and transformer types (in the style of monad transformers).
The interesting point is that, in this case, I believe that the
ambiguity is harmless and that all possible derivations of instances
would be extensionally equivalent. But the typechecker won't let me
get far enough to test that hypothesis.
So, I have a relation C and intuition that the property can be carried
through transformations on either of its related types. I'm seeking
1) a suggested technique for formulating that intuition in such a way
that the type-checker could act on it
2) a suggestion claiming that such a harmless ambiguity is down right
impossible
Below is pseudo-code outlining the shape of my problem. Consider a 2
parameter (both are type constructors) class:
> class C f g where
> nest :: f a -> g a
I have instances for base types (analogous to the Identity monad).
> class C IdL IdR where
> nest = ...
I also have transformers that I can apply to these base types and
instances that correspond to "lifting" the C type class property
through the transformers.
> class C f g => C f (TransR g) where
> nest = ... code that involves the "nest" of the C f g instance ...
or
> class C f g => C (TransL f) g where
> nest = ... code that involves the "nest" of the C f g instance ...
The simple version of my issue is that, give the instances so far, the
compiler won't derive an instance for T.
> type T = C (TransL IdL) (TransR IdR)
The impasse is the ambiguity in the derivation from C IdL IdR to T.
One could apply first TransL or apply first TransR. The
"-fallow-overlapping-instances" type system extension fails to help
because there is no "most specific" instance.
The order of application of my transformers (i.e. transforming the
left or transforming the right parameter) does not seem to matter--I
have found no intuition that says the derivations ought to be
distinguishable in anyway.
My question: Is there a technique to allow such innocuous ambiguity in
instance declarations?
I experimented with introducing something akin to a trace in a third
parameter to the class which would disambiguate the derivation (by
specifying the order of the transformations; reminded me of "Strongly
typed heterogeneous collections"), but had no luck there (perhaps
someone else would). Because the ambiguity does not matter to me, I'd
be fine implementing a rule such as "always transform the left
parameter first", but I don't know how to/if I can formulate that in
Haskell.
I also tried to reduce the class to a single parameter, which
incorporated the the functors into a single type. The method of the
class needs those functor types available, so that approach sputtered
out.
Another issue is modularity: both of my attempts above would have
bloated the code using the class with the details needed to
disambiguate it. I certainly prefer the context "C f g" to one that
exposes the disambiguation. That is, I would highly prefer a solution
that allows h1 instead of h2.
> h1 :: C f g => a type
> h1 = ... some code with nest ...
> h2 :: (C f g, DisambiguationHelper f g ?) => a type
> h2 = ... some code with nest ...
My harrowing suspicion is that I will need to split the property into
two--something I can't readily see how to do.
Thanks for your time,
Nick
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