[Haskell-cafe] More liberal than liberal type synonyms

Brent Yorgey byorgey at seas.upenn.edu
Thu Dec 8 19:50:20 CET 2011 

On Wed, Dec 07, 2011 at 04:47:47PM +0100, Gábor Lehel wrote:
> On Wed, Dec 7, 2011 at 1:07 PM, Dmitry Kulagin <dmitry.kulagin at gmail.com> wrote:
> >> For short, type synonyms work for mere aliases, but not for full-fledged> type-level non-inductive functions.> And sometimes we intuitively want to use them as such.
> > Thank you, Yves! It is now more clear for me.
> >
> > Still, it seems that ability to use partially applied type synonyms would be
> > very natural (and useful) extension to the language. It would allow to avoid
> > boilerplate code associated with creating "really new" types instead of just
> > using synonims for existing ones.
> 
> The problem as I understand it is that partially-applied type synonyms
> are in effect type level lambdas, and type checking in the presence of
> type level lambdas requires higher-order unification, which is
> undecidable in general. Restricted cases might be possible, I'm not an
> expert in the field. GHC hackers could probably elaborate.
> 
> [1] http://stackoverflow.com/questions/8248217/are-there-type-level-combinators-will-they-exist-in-some-future
> [2]
> http://en.wikipedia.org/wiki/Unification_(computer_science)#Higher-order_unification

It's actually type *inference* that requires higher-order unification
in the presence of type-level lambdas, not type checking.  This might
not be a huge deal: we just have to clearly state that enabling
-XPartialTypeFunApps means that you may have to provide some explicit
type annotations in places where type inference cannot figure things
out.  We already have extensions like this (e.g. RankNTypes).

The bigger problem for the moment is that for various technical
reasons, enabling partial applications of type functions can lead to
unsoundness (i.e. typechecked programs which nonetheless crash at
runtime) in the way that type equality is handled.  For more details
see 

  http://stackoverflow.com/questions/7866375/why-does-ghc-think-that-this-type-variable-is-not-injective/7950614#7950614

I agree that the ability to use partially applied type
synonyms/functions would be natural and useful.  I hope we will
eventually see a version of GHC which supports it but there are some
nontrivial technical issues to be worked out first.

-Brent

> 
> >
> > On Wed, Dec 7, 2011 at 3:51 PM, Yves Parès <limestrael at gmail.com> wrote:
> >> Ah, maybe Dan could tell us if it works only with GHC 7.
> >>
> >> Dmitry, I had your problem many times. The last time was when I saw you
> >> could define the ContT monad in terms of Cont (the opposite is done in the
> >> mtl).
> >> It leads to a simpler code, but you are stucked when trying to define ContT
> >> as an instance of MonadTrans:
> >>
> >> data Cont r a = ...
> >> -- [instances of Monad Cont, blah blah blah]
> >>
> >> type ContT r m a = Cont r (m a)
> >>
> >> instance MonadTrans (ContT r) where  -- This doesn't compile, even if it is
> >> logical
> >>   lift = ...
> >>
> >> For short, type synonyms work for mere aliases, but not for full-fledged
> >> type-level non-inductive functions.
> >> And sometimes we intuitively want to use them as such.
> >>
> >>
> >> 2011/12/7 Dmitry Kulagin <dmitry.kulagin at gmail.com>
> >>>
> >>> > Dmitry, does your code work with LiberalTypeSynonyms extention
> >>> > activated?
> >>> No, the same error:
> >>> Type synonym `StateA' should have 1 argument, but has been given 0
> >>>
> >>> But I have GHC 6.12.3
> >>>
> >>> Dmitry
> >>> 2011/12/7 Yves Parès <limestrael at gmail.com>:
> >>> > This is impossible:
> >>> > in the definition of 'StateT s m a', m must be a monad and then have the
> >>> > *
> >>> > -> * kind.
> >>> > So you cannot pass (StateA a), because it has simply the * kind.
> >>> >
> >>> > Dmitry, does your code work with LiberalTypeSynonyms extention
> >>> > activated?
> >>> >
> >>> >
> >>> > 2011/12/7 Øystein Kolsrud <kolsrud at gmail.com>
> >>> >>
> >>> >> You should be able to write something like this:
> >>> >>
> >>> >> type StateB a b = StateT SomeOtherState (StateA a) b
> >>> >>
> >>> >> Best regards, Øystein Kolsrud
> >>> >>
> >>> >>
> >>> >> On Wed, Dec 7, 2011 at 11:48 AM, Dmitry Kulagin
> >>> >> <dmitry.kulagin at gmail.com>
> >>> >> wrote:
> >>> >>>
> >>> >>> Hi Dan,
> >>> >>>
> >>> >>> I am still pretty new in Haskell, but this problem annoys me already.
> >>> >>>
> >>> >>> If I define certain monad as a type synonym:
> >>> >>>
> >>> >>>    type StateA a = StateT SomeState SomeMonad a
> >>> >>>
> >>> >>> Then I can't declare new monad based on the synonym:
> >>> >>>
> >>> >>>    type StateB a = StateT SomeOtherState StateA a
> >>> >>>
> >>> >>> The only way I know to overcome is to declare StateA without `a':
> >>> >>>
> >>> >>>    type StateA = StateT SomeState SomeMonad
> >>> >>>
> >>> >>> But it is not always possible with existing code base.
> >>> >>>
> >>> >>> I am sorry, if this is offtopic, but it seemed to me that the problem
> >>> >>> is realted to partially applied type synomyms you described.
> >>> >>>
> >>> >>> Thanks!
> >>> >>> Dmitry
> >>> >>>
> >>> >>> On Tue, Dec 6, 2011 at 10:59 PM, Dan Doel <dan.doel at gmail.com> wrote:
> >>> >>> > Greetings,
> >>> >>> >
> >>> >>> > In the process of working on a Haskell-alike language recently, Ed
> >>> >>> > Kmett and I realized that we had (without really thinking about it)
> >>> >>> > implemented type synonyms that are a bit more liberal than GHC's.
> >>> >>> > With
> >>> >>> > LiberalTypeSynonyms enabled, GHC allows:
> >>> >>> >
> >>> >>> >    type Foo a b = b -> a
> >>> >>> >    type Bar f = f String Int
> >>> >>> >
> >>> >>> >    baz :: Bar Foo
> >>> >>> >    baz = show
> >>> >>> >
> >>> >>> > because Bar expands to saturate Foo. However, we had also
> >>> >>> > implemented
> >>> >>> > the following, which fails in GHC:
> >>> >>> >
> >>> >>> >    type Foo a b = b -> a
> >>> >>> >    type Bar f = f (Foo Int) (Foo Int)
> >>> >>> >    type Baz f g = f Int -> g Int
> >>> >>> >
> >>> >>> >    quux :: Bar Baz
> >>> >>> >    quux = id
> >>> >>> >
> >>> >>> > That is: type synonyms are allowed to be partially applied within
> >>> >>> > other type synonyms, as long as similar transitive saturation
> >>> >>> > guarantees are met during their use.
> >>> >>> >
> >>> >>> > I don't know how useful it is, but I was curious if anyone can see
> >>> >>> > anything wrong with allowing this (it seems okay to me after a
> >>> >>> > little
> >>> >>> > thought), and thought I'd float the idea out to the GHC developers,
> >>> >>> > in
> >>> >>> > case they're interested in picking it up.
> >>> >>> >
> >>> >>> > -- Dan
> >>> >>> >
> >>> >>> > _______________________________________________
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> >>> >>>
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> >>> >>
> >>> >>
> >>> >>
> >>> >>
> >>> >> --
> >>> >> Mvh Øystein Kolsrud
> >>> >>
> >>> >> _______________________________________________
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> >>> >>
> >>> >
> >>
> >>
> >
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> 
> 
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