[Haskell-cafe] Stuck on a type family problem where kind inference fails

Richard Eisenberg eir at cis.upenn.edu
Thu Mar 17 21:42:20 UTC 2016


Yes, please do, with your use case. These examples are very helpful!

Thanks,
Richard

On Mar 17, 2016, at 4:29 PM, Oliver Charles <ollie at ocharles.org.uk> wrote:

> Rats. Shall I open something in Trac?
> 
> 
> On Thu, 17 Mar 2016 8:26 pm Richard Eisenberg, <eir at cis.upenn.edu> wrote:
> Bah. I've just tried to mock something up, but GHC 8 doesn't support higher-rank kinds in type families. They work fine in datatypes and classes, but not in type families. I know exactly why this is failing, and I'm pretty sure I know how to fix it, but it's certainly not going to make it for GHC 8 -- there's a significant engineering hurdle before we can allow type family arguments' kinds to be fancy.
> 
> Sorry to disappoint here. Perhaps there's a way to work around the problem, maybe by burying the higher-rank kind under a newtype or some similar trick.
> 
> Just to show what I tried:
> 
>> import Data.Kind
>> 
>> data TyFun :: * -> * -> *
>> type a ~> b = TyFun a b -> *
>> 
>> type family (f :: a ~> b) @@ (x :: a) :: b
> 
>> 
>> data Null a = Nullable a | NotNullable a
>> 
> 
>> type family ((f :: b ~> c) ∘ (g :: a ~> b)) (x :: a) :: c where
>>   (f ∘ g) x = f @@ (g @@ x)
>> 
>> type family BaseType (k :: forall a. a ~> Type) (x :: b) :: Type where   -- this fails :(
>> --  BaseType k x = (@@) k x
> 
> (By the way, Type and * are synonyms in GHC 8. There's no rhyme nor reason for why I used both in this example.)
> 
> Richard
> 
> On Mar 17, 2016, at 4:12 PM, Oliver Charles <ollie at ocharles.org.uk> wrote:
> 
>> Your term level stuff is exactly what I got to - a need for rank-2 type.. Err, kinds! I was trying to do that within a class but gave up on GHC 7. Great to hear GHC 8 will get me there, is there anything I can look at in the mean time? I don't need singletons entirely, so I'm happy to reimplement small parts.
>> 
>> - Ollie
>> 
>> 
>> On Thu, 17 Mar 2016 7:05 pm Richard Eisenberg, <eir at cis.upenn.edu> wrote:
>> Interesting use case!
>> 
>> You need a higher-rank kind.
>> 
>> All the typey stuff is getting in the way of understanding. I've implemented what you want at the term level:
>> 
>> 
>>> data Null a = Nullable a | NotNullable a
>>> 
>> 
>>> notNullableType :: (forall a. a -> Type) -> Null a -> Type
>> 
>>> notNullableType k (NotNullable a) = baseType k a
>>> 
>> 
>>> nullableType :: (forall a. a -> Type) -> Null a -> Type
>> 
>>> nullableType k (Nullable a) = baseType (k . Nullable) a
>>> 
>> 
>>> baseType :: (forall a. a -> Type) -> forall b. b -> Type
>> 
>>> baseType k a = k a
>>> 
>> 
>>> exprTyFun :: Null b -> (forall a. a -> Type) -> Null b -> Type
>>> exprTyFun (NotNullable _) = notNullableType
>>> exprTyFun (Nullable _) = nullableType
>> 
>> 
>> It's critical that notNullableType and nullableType have the same type, which is achievable only with higher-rank types.
>> 
>> Happily, GHC 8.0 comes equipped with higher-rank kinds. `singletons` doesn't yet build on 8.0, but it will in the future, for a sufficiently expansive definition of future. Christiaan Baaij is working on this, but I've been all-consumed by getting GHC 8 out and haven't given Christiaan's contributions the attention they deserve. So: all in good time!
>> 
>> I hope this answers your question.
>> 
>> Richard
>> 
>> On Mar 17, 2016, at 8:46 AM, Oliver Charles <ollie at ocharles.org.uk> wrote:
>> 
>>> Hi all,
>>> 
>>> This is a little tricky to explain, so bear with me. I'm working on some code that roughly models a PostgreSQL schema. Users begin by defining their tables as Haskell records, parametrized over some f :: k -> *, and use a special Col type family that applies some normalisation:
>>> 
>>> data Table f = Table { tableId :: Col f ('NotNullable 'DBInt)
>>>                      , tableX :: Col f ('Nullable 'DBString) }
>>> 
>>> is one such example.
>>> 
>>> The idea behind Col is that sometimes we don't need information about the "full type" when we know more about f.
>>> 
>>> One such choice of f is Expr, which corresponds to expressions inside a query. In this case, I would desire
>>> 
>>> tableId :: Col Expr ('NotNullable 'DBInt)  =  tableId :: Expr 'DBInt
>>> tableX :: Col Expr ('Nullable 'DBString)   =  tableX :: Expr ('Nullable 'DBString)
>>> 
>>> Notice here that if you use 'NotNullable, then this information is erased - but it's important if the column is 'Nullable.
>>> 
>>> However, I'm struggling to work out any way to actually pull this off in the general case. Here's what I've been attempting:
>>> 
>>> {-# LANGUAGE FunctionalDependencies #-}
>>> {-# LANGUAGE FlexibleInstances #-}
>>> {-# LANGUAGE RankNTypes #-}
>>> {-# LANGUAGE MultiParamTypeClasses #-}
>>> {-# LANGUAGE DataKinds #-}
>>> {-# LANGUAGE TypeOperators #-}
>>> {-# LANGUAGE TypeFamilies #-}
>>> {-# LANGUAGE KindSignatures #-}
>>> {-# LANGUAGE PolyKinds #-}
>>> {-# LANGUAGE TemplateHaskell #-}
>>> {-# LANGUAGE GADTs #-}
>>> {-# LANGUAGE UndecidableInstances #-}
>>> {-# LANGUAGE ScopedTypeVariables #-}
>>> 
>>> module ExprTest where
>>> 
>>> import Data.Singletons
>>> import Data.Singletons.Prelude hiding (Null)
>>> import Data.Singletons.TH
>>> 
>>> data Expr (a :: k)
>>> 
>>> data MyExprSym :: TyFun k * -> *
>>> type instance Apply MyExprSym (x :: k) = Expr x
>>> 
>>> $(singletons [d|
>>>   data Null a = Nullable a | NotNullable a
>>>   |])
>>> 
>>> $(promote [d|
>>>   notNullableType k (NotNullable a) = baseType k a
>>>   nullableType k (Nullable a) = baseType (k . Nullable) a
>>>   baseType k a = k a
>>>   |])
>>> 
>>> So far, this seems to work well. If I ask GHCI:
>>> 
>>> *ExprTest> :kind! Apply (Apply NullableTypeSym0 MyExprSym) ('Nullable 'DBString)
>>> Apply (Apply NullableTypeSym0 MyExprSym) ('Nullable 'DBString) :: *
>>> = Expr ('Nullable 'DBString)
>>> 
>>> *ExprTest> :kind! Apply (Apply NotNullableTypeSym0 MyExprSym) ('NotNullable 'DBInt)
>>> Apply (Apply NotNullableTypeSym0 MyExprSym) ('NotNullable 'DBInt) :: *
>>> = Expr 'DBInt
>>> 
>>> This is exactly what I want, but note that I had to choose the necessary symbols NullableTypeSym0 and NotNullableTypeSym0. I would like to calculate those symbols from the column type itself. Looking at the kinds of these symbols though, they are both different:
>>> 
>>> *ExprTest> :kind! NotNullableTypeSym0
>>> NotNullableTypeSym0 :: TyFun
>>>                          (TyFun k1 k -> *) (TyFun (Null k1) k -> *)
>>>                        -> *
>>> = NotNullableTypeSym0
>>> *ExprTest> :kind! NullableTypeSym0
>>> NullableTypeSym0 :: TyFun
>>>                       (TyFun (Null k1) k -> *) (TyFun (Null k1) k -> *)
>>>                     -> *
>>> = NullableTypeSym0
>>> 
>>> So I can't see a way to write a single type family that returns them.
>>> 
>>> 
>>> To summarise, I'd like a way to write this following instance for Col:
>>> 
>>> type instance Col Expr x = Apply (Apply ?? MyExprSym) x
>>> 
>>> such that 
>>> 
>>> Col Expr ('Nullable a) = Expr ('Nullable a') and
>>> Col Expr ('NotNullable a) = Expr a
>>> 
>>> but I cannot work out how to write the placeholder ?? above.
>>> 
>>> One attempt is 
>>> 
>>> type family ExprTyfun (col :: colK) :: TyFun (TyFun k * -> *) (TyFun j * -> *) -> *
>>> type instance ExprTyfun ('NotNullable a) = NotNullableTypeSym0
>>> type instance ExprTyfun ('Nullable a) = NullableTypeSym0
>>> 
>>> But neither of these instances actually normalise as I'd like, presumably because of k and j being forall'd in the return type:
>>> 
>>> *ExprTest> :set -fprint-explicit-kinds
>>> 
>>> 
>>> *ExprTest> :kind! ExprTyfun ('Nullable 'DBInt)
>>> ExprTyfun ('Nullable 'DBInt) :: TyFun
>>>                                   (TyFun k * -> *) (TyFun k1 * -> *)
>>>                                 -> *
>>> = ExprTyfun k k1 (Null DBType) ('Nullable DBType 'DBInt)
>>> 
>>> 
>>> *ExprTest> :kind! ExprTyfun ('NotNullable 'DBInt)
>>> ExprTyfun ('NotNullable 'DBInt) :: TyFun
>>>                                      (TyFun k * -> *) (TyFun k1 * -> *)
>>>                                    -> *
>>> = ExprTyfun k k1 (Null DBType) ('NotNullable DBType 'DBInt)
>>> 
>>> 
>>> *ExprTest> :i ExprTyfun
>>> type family ExprTyfun (k :: BOX)
>>>                       (j :: BOX)
>>>                       (colK :: BOX)
>>>                       (col :: colK) ::
>>>   TyFun (TyFun k * -> *) (TyFun j * -> *) -> *
>>>   	-- Defined at src/Opaleye/TF/ExprTest.hs:39:1
>>> type instance ExprTyfun
>>>                 (Null k) (Null k) (Null k1) ('Nullable k1 a)
>>>   = NullableTypeSym0 * k
>>>   	-- Defined at src/Opaleye/TF/ExprTest.hs:41:1
>>> type instance ExprTyfun k (Null k) (Null k1) ('NotNullable k1 a)
>>>   = NotNullableTypeSym0 * k
>>>   	-- Defined at src/Opaleye/TF/ExprTest.hs:40:1
>>> 
>>> 
>>> I'd also like to point out that in my full code the types to Col can be a lot bigger, and I'd like to not assume any ordering. For example, here's a possible type:
>>> 
>>>   userId :: Col f ('Column "id" ('NotNullable ('HasDefault 'DBInt)))
>>> 
>>> In this case Col Expr ('Column "id" ('NotNullable ('HasDefault 'DBInt))) = Expr 'DBInt
>>> 
>>> I hope this question is understandable! Please let me know if there's anything I can do to provide more clarity.
>>> 
>>> - Ollie
>> 
>>> _______________________________________________
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>> 
> 

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