module Data.Extensible.Internal (
Membership
, getMemberId
, mkMembership
, runMembership
, compareMembership
, Member(..)
, remember
, (∈)()
, FindType
, Assoc(..)
, Associate(..)
, FindAssoc
, Elaborate
, Elaborated(..)
, NavHere(..)
, navigate
, here
, navNext
, navL
, navR
, Nat(..)
, KnownPosition(..)
, Succ
, Half
, Head
, Tail
, (++)()
, Map
, Merge
, Concat
, module Data.Type.Equality
, module Data.Proxy
) where
import Data.Type.Equality
import Data.Proxy
#if !MIN_VERSION_base(4,8,0)
import Control.Applicative
import Data.Word
#endif
import Control.Monad
import Unsafe.Coerce
import Data.Typeable
import Language.Haskell.TH hiding (Pred)
import Data.Bits
mkMembership :: Int -> Q Exp
mkMembership n = do
let names = map mkName $ take (n + 1) $ concatMap (flip replicateM ['a'..'z']) [1..]
let rest = mkName "any"
let cons x xs = PromotedConsT `AppT` x `AppT` xs
let t = foldr cons (VarT rest) (map VarT names)
sigE (conE 'Membership `appE` litE (IntegerL $ toInteger n))
$ forallT (PlainTV rest : map PlainTV names) (pure [])
$ conT ''Membership `appT` pure t `appT` varT (names !! n)
newtype Membership (xs :: [k]) (x :: k) = Membership { getMemberId :: Word } deriving Typeable
newtype Remembrance xs x r = Remembrance (Member xs x => r)
remember :: forall xs x r. Membership xs x -> (Member xs x => r) -> r
remember i r = unsafeCoerce (Remembrance r :: Remembrance xs x r) i
class Member xs x where
membership :: Membership xs x
instance (Elaborate x (FindType x xs) ~ 'Expecting pos, KnownPosition pos) => Member xs x where
membership = Membership (theInt (Proxy :: Proxy pos))
data Assoc k v = k :> v
infix 0 :>
class Associate k v xs | k xs -> v where
association :: Membership xs (k ':> v)
instance (Elaborate k (FindAssoc k xs) ~ 'Expecting (n ':> v), KnownPosition n) => Associate k v xs where
association = Membership (theInt (Proxy :: Proxy n))
data Elaborated k v = Expecting v | Missing k | Duplicate k
type family Elaborate (key :: k) (xs :: [v]) :: Elaborated k v where
Elaborate k '[] = 'Missing k
Elaborate k '[x] = 'Expecting x
Elaborate k xs = 'Duplicate k
type family FindAssoc (key :: k) (xs :: [Assoc k v]) where
FindAssoc k ((k ':> v) ': xs) = ('Zero ':> v) ': MapSuccKey (FindAssoc k xs)
FindAssoc k ((k' ':> v) ': xs) = MapSuccKey (FindAssoc k xs)
FindAssoc k '[] = '[]
type family MapSuccKey (xs :: [Assoc Nat v]) :: [Assoc Nat v] where
MapSuccKey '[] = '[]
MapSuccKey ((k ':> x) ': xs) = (Succ k ':> x) ': MapSuccKey xs
instance Show (Membership xs x) where
show (Membership n) = "$(mkMembership " ++ show n ++ ")"
instance Eq (Membership xs x) where
_ == _ = True
instance Ord (Membership xs x) where
compare _ _ = EQ
runMembership :: Membership (y ': xs) x -> (x :~: y -> r) -> (Membership xs x -> r) -> r
runMembership (Membership 0) l _ = l (unsafeCoerce Refl)
runMembership (Membership n) _ r = r (Membership (n 1))
compareMembership :: Membership xs x -> Membership xs y -> Either Ordering (x :~: y)
compareMembership (Membership m) (Membership n) = case compare m n of
EQ -> Right (unsafeCoerce Refl)
x -> Left x
navigate :: (NavHere xs x -> r)
-> (Membership (Half (Tail xs)) x -> r)
-> (Membership (Half (Tail (Tail xs))) x -> r)
-> Membership xs x
-> r
navigate h nl nr = \case
Membership 0 -> h (unsafeCoerce Here)
Membership n -> if n .&. 1 == 0
then nr (Membership (unsafeShiftR (n 1) 1))
else nl (Membership (unsafeShiftR (n 1) 1))
data NavHere xs x where
Here :: NavHere (x ': xs) x
here :: Membership (x ': xs) x
here = Membership 0
navNext :: Membership xs y -> Membership (x ': xs) y
navNext (Membership n) = Membership (n + 1)
navL :: Membership (Half xs) y -> Membership (x ': xs) y
navL (Membership x) = Membership (x * 2 + 1)
navR :: Membership (Half (Tail xs)) y -> Membership (x ': xs) y
navR (Membership x) = Membership (x * 2 + 2)
type x ∈ xs = Member xs x
type family Head (xs :: [k]) :: k where
Head (x ': xs) = x
type family FindType (x :: k) (xs :: [k]) :: [Nat] where
FindType x (x ': xs) = 'Zero ': FindType x xs
FindType x (y ': ys) = MapSucc (FindType x ys)
FindType x '[] = '[]
type family Half (xs :: [k]) :: [k] where
Half '[] = '[]
Half (x ': y ': zs) = x ': Half zs
Half (x ': '[]) = '[x]
type family Tail (xs :: [k]) :: [k] where
Tail (x ': xs) = xs
Tail '[] = '[]
data Nat = Zero | DNat Nat | SDNat Nat
class KnownPosition n where
theInt :: proxy n -> Word
instance KnownPosition 'Zero where
theInt _ = 0
instance KnownPosition n => KnownPosition ('DNat n) where
theInt _ = theInt (Proxy :: Proxy n) `unsafeShiftL` 1
instance KnownPosition n => KnownPosition ('SDNat n) where
theInt _ = (theInt (Proxy :: Proxy n) `unsafeShiftL` 1) + 1
type family Succ (x :: Nat) :: Nat where
Succ 'Zero = 'SDNat 'Zero
Succ ('DNat n) = 'SDNat n
Succ ('SDNat n) = 'DNat (Succ n)
type family MapSucc (xs :: [Nat]) :: [Nat] where
MapSucc '[] = '[]
MapSucc (x ': xs) = Succ x ': MapSucc xs
type family Map (f :: k -> k) (xs :: [k]) :: [k] where
Map f '[] = '[]
Map f (x ': xs) = f x ': Map f xs
type family (++) (xs :: [k]) (ys :: [k]) :: [k] where
'[] ++ ys = ys
(x ': xs) ++ ys = x ': xs ++ ys
infixr 5 ++
type family Concat (xs :: [[k]]) :: [k] where
Concat '[] = '[]
Concat (x ': xs) = x ++ Concat xs
type family Merge (xs :: [k]) (ys :: [k]) :: [k] where
Merge (x ': xs) (y ': ys) = x ': y ': Merge xs ys
Merge xs '[] = xs
Merge '[] ys = ys