[Haskell-cafe] Quantification in Instance Contexts

[adam vogt]

Hi Julian,

Does each child have only one parent? In other words, is a larger
"tree" still accepted if you use:

class Child1 a b bool | a b -> bool, b -> a

instead of your Child.

Regards,
Adam


On Wed, Jun 25, 2014 at 5:46 AM, Julian K. Arni <jkarni at gmail.com> wrote:
> Hi Cafe,
>
> I'm playing around with simple logic-programming at the type level. For
> instance, encoding trees:
>
>>> {-# LANGUAGE MultiParamTypeClasses
>>> , FunctionalDependencies
>>> , FlexibleInstances
>>> , UndecidableInstances
>>> , FlexibleContexts
>>> , OverlappingInstances #-}
>>> {-# OPTIONS_GHC -fcontext-stack=100 #-}
>>>
>>>
>>> --     *A
>>> --    / \
>>> --  B*   *C
>>> --   |
>>> --  D*
>>>
>>>
>>> data A
>>> data B
>>> data C
>>> data D
>>> class Child a b bool | a b -> bool
>>> instance Child A B TrueT
>>> instance Child B D TrueT
>>> instance Child B C TrueT
>>> class Path a b bool | a b -> bool
>
> Now the following obviously doesn't work (never mind for now that 'Path' needs
> a recursive definition, and that this is really just 'Grandchild'):
>
>>> instance (Child a b TrueT, Child b c TrueT) => Path a c TrueT
>
> Because 'b' is ambiguous. Fair enough. But I can't directly use a fundep,
> because 'b' *is* in fact ambiguous. What I want to tell the compiler is that
> it's really okay, since the RHS side (and any possible 'where' expressions)
> doesn't depend on what is instantiated for 'b'.
>
> I know I could switch to a class 'Children a bs bool' and encode all children
> of as a type-level list, and then have a fundep between 'a' and 'bs'. That's
> not a *bad* solution: it does give a good sense of the intention. But it's not
> very extensible; really I'd rather be using something like 'forall'
> - something, I would guess, along the lines of:
>
>>> instance forall a c. (forall b. (Child a b TrueT, Child b c TrueT)) => Path
>>> a c TrueT
>
> That, however, fails with:
>
>     Malformed instance head: (forall b.
>                               (Child a b TrueT, Child b c TrueT))
>                              -> Path a c TrueT
>     In the instance declaration for ‘Path a c TrueT’
>
>
> So: is there a way (presumably with 'forall') of telling the compiler that the
> ambiguous type 'b' actually won't "leak through" to the RHS, so stop bugging me
> about ambiguity?
>
> Thanks,
>   Julian
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