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

[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
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