How to write an intersection function for level lists

Question

I work on lists of operating systems at the type level, and I wrote two functions at the type level, one to combine the two lists, and the other to intersect them. I have problems with the intersection function working correctly.

(ghc 7.10.3)

Here, the combine function works as expected:

*Main> (combineSupportedOS debian freeBSD)  :: OSList '[OSDebian, OSFreeBSD]
OSList [OSDebian,OSFreeBSD]

Here's the intersection function, not quite working:

*Main> (intersectSupportedOS debian debian)  :: OSList '[OSDebian]
Couldn't match expected type ‘IntersectOSList ['OSDebian] '['OSDebian]’
            with actual type ‘'['OSDebian]’

How can I convince a type check that it is well printed?

Full code:

{-# LANGUAGE TypeOperators, PolyKinds, DataKinds, TypeFamilies, UndecidableInstances #-}

import Data.Typeable
import Data.String
import Data.Type.Bool
import Data.Type.Equality

data SupportedOS = OSDebian | OSFreeBSD
    deriving (Show, Eq)

data OSList (os :: [SupportedOS]) = OSList [SupportedOS]
    deriving (Show, Eq)

debian :: OSList '[OSDebian]
debian = typeOS OSDebian

freeBSD :: OSList '[OSFreeBSD]
freeBSD = typeOS OSFreeBSD

typeOS :: SupportedOS -> OSList os
typeOS o = OSList [o]

combineSupportedOS
    :: (r ~ ConcatOSList l1 l2)
    => OSList l1
    -> OSList l2
    -> OSList r
combineSupportedOS (OSList l1) (OSList l2) = OSList (l1 ++ l2)

type family ConcatOSList (list1 :: [a]) (list2 :: [a]) :: [a]
type instance ConcatOSList '[] list2 = list2
type instance ConcatOSList (a ': rest) list2 = a ': ConcatOSList rest list2

intersectSupportedOS
    :: (r ~ IntersectOSList l1 l2)
    => OSList l1
    -> OSList l2
    -> OSList r
intersectSupportedOS (OSList l1) (OSList l2) = OSList (filter (`elem` l2) l1)

type family IntersectOSList (list1 :: [a]) (list2 :: [a]) :: [a]
type instance IntersectOSList '[] list2 = list2
type instance IntersectOSList (a ': rest) list2 = 
    If (ElemOSList a list2)
        (a ': IntersectOSList rest list2)
        (IntersectOSList rest list2)

type family ElemOSList a (list :: [b]) :: Bool
type instance ElemOSList a '[] = False
type instance ElemOSList a (b ': bs) = 
    If (a == b)
        True
        (ElemOSList a bs)

type family EqOS (a :: SupportedOS) (b :: SupportedOS) where
    EqOS a a = True
    EqOS a b = False
type instance a == b = EqOS a b

Answer 1

The main fix is ​​as follows:

- type family ElemOSList a (list :: [b]) :: Bool
+ type family ElemOSList (a :: SupportedOS) (list :: [SupportedOS]) :: Bool

Also, as noted, there was an incorrect base case.

Here's the copied code:

type family IntersectOSList (list1 :: [a]) (list2 :: [a]) :: [a]
type instance IntersectOSList '[] list2 = '[]
type instance IntersectOSList (a ': rest) list2 = 
    If (ElemOSList a list2)
            (a ': IntersectOSList rest list2)
            (IntersectOSList rest list2)

type family ElemOSList (a :: SupportedOS) (list :: [SupportedOS]) :: Bool
type instance ElemOSList a '[] = False
type instance ElemOSList a (b ': bs) = a == b || ElemOSList a bs