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
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 _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe