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

Yes, please do, with your use case. These examples are very helpful! Thanks, Richard On Mar 17, 2016, at 4:29 PM, Oliver Charles wrote:

Rats. Shall I open something in Trac?

On Thu, 17 Mar 2016 8:26 pm Richard Eisenberg, 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:

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import Data.Kind

data TyFun :: * -> * -> * type a ~> b = TyFun a b -> *

type family (f :: a ~> b) @@ (x :: a) :: b

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data Null a = Nullable a | NotNullable a

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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 wrote:

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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, 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:

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data Null a = Nullable a | NotNullable a

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notNullableType :: (forall a. a -> Type) -> Null a -> Type

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notNullableType k (NotNullable a) = baseType k a

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nullableType :: (forall a. a -> Type) -> Null a -> Type

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nullableType k (Nullable a) = baseType (k . Nullable) a

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baseType :: (forall a. a -> Type) -> forall b. b -> Type

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baseType k a = k a

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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 wrote:

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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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