PolyKind issue in GHC 7.6.1rc1: How to make a kind a functional dependency?
Edward Kmett
ekmett at gmail.com
Fri Aug 31 14:44:54 CEST 2012
Hrmm. This seems to render product kinds rather useless, as there is no way
to refine the code to reflect the knowledge that they are inhabited by a
single constructor. =(
For instance, there doesn't even seem to be a way to make the following
code compile, either.
{-# LANGUAGE PolyKinds, DataKinds, TypeOperators, GADTs #-}
module Product where
import Prelude hiding (id,(.))
class Category k where
id :: k a a
(.) :: k b c -> k a b -> k a c
data (*) :: (x -> x -> *) -> (y -> y -> *) -> (x,y) -> (x,y) -> * where
(:*) :: x a b -> y c d -> (x * y) '(a,c) '(b,d)
instance (Category x, Category y) => Category (x * y) where
id = id :* id
(xf :* yf) . (xg :* yg) = (xf . xg) :* (yf . yg)
This all works perfectly fine in Conor's SHE, (as does the thrist example)
so I'm wondering where the impedence mismatch comes in and how to gain
knowledge of this injectivity to make it work.
Also, does it ever make sense for the kind of a kind variable mentioned in
a type not to get a functional dependency on the type?
e.g. should
class Foo (m :: k -> *)
always be
class Foo (m :: k -> *) | m -> k
?
Honest question. I can't come up with a scenario, but you might have one I
don't know.
-Edward
On Fri, Aug 31, 2012 at 5:55 AM, Simon Peyton-Jones
<simonpj at microsoft.com>wrote:
> With the code below, I get this error message with HEAD. And that looks
> right to me, no?****
>
> The current 7.6 branch gives the same message printed less prettily.****
>
> ** **
>
> If I replace the defn of irt with****
>
> irt :: a '(i,j) -> Thrist a '(i,j)****
>
> irt ax = ax :- Nil****
>
> ** **
>
> then it typechecks.****
>
> ** **
>
> Simon****
>
> ** **
>
> ** **
>
> Knett.hs:20:10:****
>
> Couldn't match type `x' with '(i0, k0)****
>
> `x' is a rigid type variable bound by****
>
> the type signature for irt :: a x -> Thrist k a x at
> Knett.hs:19:8****
>
> Expected type: Thrist k a x****
>
> Actual type: Thrist k a '(i0, k0)****
>
> In the expression: ax :- Nil****
>
> In an equation for `irt': irt ax = ax :- Nil****
>
> simonpj at cam-05-unx:~/tmp$****
>
> ** **
>
> ** **
>
> {-# LANGUAGE FunctionalDependencies, GADTs, KindSignatures,
> MultiParamTypeClasses, PolyKinds, ****
>
> RankNTypes, TypeOperators, DefaultSignatures, DataKinds, ****
>
> FlexibleInstances, UndecidableInstances #-}****
>
> ** **
>
> module Knett where****
>
> ** **
>
> class IMonad (m :: (k -> *) -> k -> *) | m -> k where ****
>
> ireturn :: a x -> m a x****
>
> ** **
>
> infixr 5 :-****
>
> ** **
>
> data Thrist :: ((i,i) -> *) -> (i,i) -> * where****
>
> Nil :: Thrist a '(i,i)****
>
> (:-) :: a '(i,j) -> Thrist a '(j,k) -> Thrist a '(i,k)****
>
> ** **
>
> -- instance IMonad Thrist where****
>
> -- ireturn a = a :- Nil****
>
> ** **
>
> irt :: a x -> Thrist a x****
>
> irt ax = ax :- Nil****
>
> ** **
>
> ** **
>
> *From:* glasgow-haskell-users-bounces at haskell.org [mailto:
> glasgow-haskell-users-bounces at haskell.org] *On Behalf Of *Edward Kmett
> *Sent:* 31 August 2012 03:38
> *To:* glasgow-haskell-users at haskell.org
> *Subject:* PolyKind issue in GHC 7.6.1rc1: How to make a kind a
> functional dependency?****
>
> ** **
>
> If I define the following****
>
> ** **
>
> {-# LANGUAGE FunctionalDependencies, GADTs, KindSignatures,
> MultiParamTypeClasses, PolyKinds, RankNTypes, TypeOperators,
> DefaultSignatures, DataKinds, FlexibleInstances, UndecidableInstances #-}*
> ***
>
> module Indexed.Test where****
>
> ** **
>
> class IMonad (m :: (k -> *) -> k -> *) where ****
>
> ireturn :: a x -> m a x****
>
> ** **
>
> infixr 5 :-****
>
> data Thrist :: ((i,i) -> *) -> (i,i) -> * where****
>
> Nil :: Thrist a '(i,i)****
>
> (:-) :: a '(i,j) -> Thrist a '(j,k) -> Thrist a '(i,k)****
>
> ** **
>
> instance IMonad Thrist where****
>
> ireturn a = a :- Nil****
>
> ** **
>
> Then 'ireturn' complains (correctly) that it can't match the k with the
> kind (i,i). The reason it can't is because when you look at the resulting
> signature for the MPTC it generates it looks like****
>
> ** **
>
> class IMonad k m where****
>
> ireturn :: a x -> m a x****
>
> ** **
>
> However, there doesn't appear to be a way to say that the kind k should be
> determined by m. ****
>
> ** **
>
> I tried doing:****
>
> ** **
>
> class IMonad (m :: (k -> *) -> k -> *) | m -> k where ****
>
> ireturn :: a x -> m a x****
>
> ** **
>
> Surprisingly (to me) this compiles and generates the correct constraints
> for IMonad:****
>
> ** **
>
> ghci> :set -XPolyKinds -XKindSignatures -XFunctionalDependencies
> -XDataKinds -XGADTs****
>
> ghci> class IMonad (m :: (k -> *) -> k -> *) | m -> k where ireturn :: a x
> -> m a x****
>
> ghci> :info IMonad****
>
> class IMonad k m | m -> k where****
>
> ireturn :: a x -> m a x****
>
> ** **
>
> But when I add ****
>
> ** **
>
> ghci> :{****
>
> Prelude| data Thrist :: ((i,i) -> *) -> (i,i) -> * where****
>
> Prelude| Nil :: Thrist a '(i,i)****
>
> Prelude| (:-) :: a '(i,j) -> Thrist a '(j,k) -> Thrist a '(i,k)****
>
> Prelude| :}****
>
> ** **
>
> and attempt to introduce the instance, I crash:****
>
> ** **
>
> ghci> instance IMonad Thrist where ireturn a = a :- Nil****
>
> ghc: panic! (the 'impossible' happened)****
>
> (GHC version 7.6.0.20120810 for x86_64-apple-darwin):****
>
> lookupVarEnv_NF: Nothing****
>
> ** **
>
> Please report this as a GHC bug: http://www.haskell.org/ghc/reportabug***
> *
>
> ** **
>
> Moreover, attempting to compile them in separate modules leads to a
> different issue. ****
>
> ** **
>
> Within the module, IMonad has a type that includes the kind k and the
> constraint on it from m. But from the other module, :info shows no such
> constraint, and the above code again fails to typecheck, but upon trying to
> recompile, when GHC goes to load the IMonad instance from the core file, it
> panicks again differently about references to a variable not present in the
> core.****
>
> ** **
>
> Is there any way to make such a constraint that determines a kind from a
> type parameter in GHC 7.6 at this time?****
>
> ** **
>
> I tried the Kind hack used in GHC.TypeLits, but it doesn't seem to be
> applicable to this situation.****
>
> ** **
>
> -Edward****
>
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