[Haskell-cafe] Stuck on a type family problem where kind inference fails
Oliver Charles
ollie at ocharles.org.uk
Thu Mar 17 12:46:47 UTC 2016
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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