Opened 13 months ago
Last modified 4 months ago
#12369 new feature request
data families shouldn't be required to have return kind *, data instances should
Reported by: | ekmett | Owned by: | |
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Priority: | normal | Milestone: | 8.4.1 |
Component: | Compiler (Type checker) | Version: | 8.0.1 |
Keywords: | TypeInType | Cc: | Iceland_jack |
Operating System: | Unknown/Multiple | Architecture: | Unknown/Multiple |
Type of failure: | None/Unknown | Test Case: | |
Blocked By: | Blocking: | ||
Related Tickets: | Differential Rev(s): | ||
Wiki Page: |
Description
I'd like to be able to define
{-# language PolyKinds, KindSignatures, GADTs, TypeFamilies #-} data family Fix :: (k -> *) -> k newtype instance Fix f = In { out :: f (Fix f) }
But currently this is disallowed:
Fix.hs:2:1: error: • Kind signature on data type declaration has non-* return kind (k -> *) -> k • In the data family declaration for ‘Fix’
Ultimately I think the issue here is that data instances should be required to end in kind *, not the families, but this generalization didn't mean anything until we had PolyKinds
.
As an example of a usecase, with the above, I could define a bifunctor fixed point such as
newtype instance Fix f a = In2 { out2 :: f (Fix f a) a }
Change History (11)
comment:1 Changed 13 months ago by
comment:2 Changed 10 months ago by
Cc: | Iceland_jack added |
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comment:3 Changed 9 months ago by
Is this another example of this
type f ~> g = forall a. f a -> g a type f ~~> g = forall a b. f a b -> g a b newtype Free0 :: (Type -> Constraint) -> (Type -> Type) where Free0 :: (forall q. k q => (p -> q) -> q) -> Free0 k p newtype Free1 :: ((k -> Type) -> Constraint) -> ((k -> Type) -> (k -> Type)) where Free1 :: (forall q. k q => (p ~> q) -> q a) -> Free1 k p a newtype Free2 :: ((k1 -> k2 -> Type) -> Constraint) -> ((k1 -> k2 -> Type) -> (k1 -> k2 -> Type)) where Free2 :: (forall q. k q => (p ~~> q) -> q a b) -> Free2 k p a b
They all follow the pattern type FREE ĸ = (ĸ -> Constraint) -> (ĸ -> ĸ)
Free0 :: FREE Type Free1 :: FREE (k -> Type) Free2 :: FREE (k1 -> k2 -> Type)
Maybe you could write it as?
data family Free :: FREE k newtype instance Free :: FREE Type where Free0 :: (forall q. k q => (p -> q) -> q) -> Free k p newtype instance Free :: forall k. FREE (k -> Type) where Free1 :: (forall q. k q => (p ~> q) -> q a) -> Free k p a newtype instance Free :: forall k1 k2. FREE (k1 -> k2 -> Type) where Free2 :: (forall q. k q => (p ~~> q) -> q a b) -> Free2 k p a b
comment:4 Changed 9 months ago by
Should it be
type FIX k = (* -> k) -> k data family Fix :: FIX k
which fits the type of newtype Fix2 f a = In2 (f (Fix2 f a) a)
Fix2 :: FIX (k -> Type)
or
type FIX k = (k -> k) -> k data family Fix :: FIX k
which fits newtype Fix_ f a = In_ (f (Fix_ f) a)
's type
Fix_ :: FIX (k -> Type)
I would be very interested if this somehow tied in with the example of a fixed point of mutually recursive types from s
Definition 2. In Haskell, mutually recursive types can be modelled as follows.
newtype Fix_1 f1 f2 = In_1 (f1 (Fix_1 f1 f2) (Fix_2 f1 f2)) newtype Fix_2 f1 f2 = In_2 (f2 (Fix_1 f1 f2) (Fix_2 f1 f2))Since Haskell has no concept of pairs on the type level, that is, no product kinds, we have to curry the type constructors:
Fix_1 f1 f2 = Outl (Fix <f1, f2>)
andFix_2 f1 f2 = Outr (Fix <f1, f2>)
.
We can get close to an arrow in a product category
-- Beautiful definition btw data (×) :: Cat x -> Cat y -> Cat (x, y) where Prod :: c1 a a_ -> c2 b b_ -> (c1 × c2) '(a, b) '(a_, b_)
but the closest I've gotten to modelling an endofunctor over a product category
F <A, B> = <Nat × B, 1 + A × B>
is
type family F (pair :: (*, *)) :: (*, *) where F '(a, b) = '((Int, b), Either () (a, b))
and the desired FixProd
would probably have a type like ((*, *) -> (*, *)) -> (*, *)
(kinds can probably be generalised)
newtype FixProd :: FIX (*, *) where FixProd :: ...
Except this requires a non-Type
return kind, I appreciate any pointers and if having a value of type (*, *)
might ever make sense
comment:5 follow-up: 6 Changed 9 months ago by
A data family defines a family of datatypes. An example shows best how this works:
data family Array a -- compact storage of elements of type a data instance Array Bool = MkArrayBool ByteArray data instance Array Int = MkArrayInt (Vector Int)With such a definition, we can have a different runtime representation for
Array Bool
than we do forArray Int
, something not possible with more traditional parameterized types.
The part about runtime representation made me wonder if you could define
-- × × × FAILS × × × data family Array a :: TYPE rep
I dunno about the instances, maybe using Proposal 3: Allow newtypes over unlifted types
newtype instance Array Int# :: TYPE PtrRepUnlifted where MkInt# :: ByteArray# -> Array Int# newtype instance Array (##) :: TYPE IntRep where MkInt# :: Int# -> Array (##)
I don't really understand representation polymorphism, may suffer from same problem as #11471.
-- WORKS FINE data family Array (a :: TYPE rep) :: Type -- × × × FAILS × × × -- -- Unexpected type ‘Int#’ data Array Int# -- Should this fail?
comment:6 follow-up: 7 Changed 9 months ago by
Replying to Iceland_jack:
The part about runtime representation made me wonder if you could define
-- × × × FAILS × × × data family Array a :: TYPE repI dunno about the instances, maybe using Proposal 3: Allow newtypes over unlifted types
While there's nothing very wrong about the data family definition, the instances would be a problem, because we don't yet have a way to make user-written unlifted types. It would indeed be useful to have this, but we don't. So I think this kind of construct is best off waiting until we solve the simpler case of normal unlifted datatypes before we try unlifted data families.
-- WORKS FINE data family Array (a :: TYPE rep) :: Type -- × × × FAILS × × × -- -- Unexpected type ‘Int#’ data Array Int# -- Should this fail?
You just want to say data instance Array Int#
, which indeed works fine.
comment:7 Changed 9 months ago by
Replying to goldfire:
So I think this kind of construct is best off waiting until we solve the simpler case of normal unlifted datatypes before we try unlifted data families.
Awesome! Maybe you can combine them into fixed point that is rep-poly ;)
You just want to say
data instance Array Int#
, which indeed works fine.
Haha oops.
comment:8 follow-up: 9 Changed 9 months ago by
Keywords: | TypeInType added |
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The stuff about representation-polymorphism is a bit of a red herring; make a new ticket.
Let's not lose track of the original request here, which is well described in the Description.
Richard: it might need no more than removing a test, namely the test that data families return *?
comment:10 Changed 5 months ago by
To avoid clutter I will add further examples to this gist.
This feature is starting to look very attractive.
comment:11 Changed 4 months ago by
Milestone: | 8.2.1 → 8.4.1 |
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Given that 8.2.1-rc1 is imminent, I'm bumping these off to the 8.4
Interesting idea. I can't see a technical problem with it, so maybe we could just allow it. If someone would like to have a go, I'd be a willing reviewer.
Alternatively, if it becomes Important to a bunch of people, I could have a go myself.
Simon