Naming issues in type-level programming modules
This page summarizes current type-level programming constructs in modules that ship with GHC. At the bottom is a list of open questions about good names for these operations.
-- Reified equality data a :~: b where Refl :: a :~: a sym :: (a :~: b) -> (b :~: a) trans :: (a :~: b) -> (b :~: c) -> (a :~: c) castWith :: (a :~: b) -> a -> b liftEq :: (a :~: b) -> (f a :~: f b) liftEq2 :: (a :~: a') -> (b :~: b') -> (f a b :~: f a' b') liftEq3 :: (a :~: a') -> (b :~: b') -> (c :~: c') -> (f a b c :~: f a' b' c') liftEq4 :: (a :~: a') -> (b :~: b') -> (c :~: c') -> (d :~: d') -> (f a b c d :~: f a' b' c' d') lower :: (f a :~: f b) -> a :~: b class EqualityT f where equalsT :: f a -> f b -> Maybe (a :~: b) type family a == b where a == a = True a == b = False
-- Reified representational equality data Coercion a b where Coercion :: Coercible a b => Coercion a b coerceWith :: Coercion a b -> a -> b sym :: forall a b. Coercion a b -> Coercion b a trans :: Coercion a b -> Coercion b c -> Coercion a c class CoercionT f where coercionT :: f a -> f b -> Maybe (Coercion a b)
data Proxy t = Proxy data KProxy (t :: *) = KProxy asProxyTypeOf :: a -> Proxy a -> a asProxyTypeOf = const
cast :: forall a b. (Typeable a, Typeable b) => a -> Maybe b eqT :: forall a b. (Typeable a, Typeable b) => Maybe (a :~: b) gcast :: forall a b c. (Typeable a, Typeable b) => c a -> Maybe (c b) gcast1 :: forall c t t' a. (Typeable t, Typeable t') => c (t a) -> Maybe (c (t' a)) gcast2 :: forall c t t' a b. (Typeable t, Typeable t') => c (t a b) -> Maybe (c (t' a b))
data Nat data Symbol class KnownNat (n :: Nat) where natSing :: SNat n class KnownSymbol (n :: Symbol) where symbolSing :: SSymbol n natVal :: forall n proxy. KnownNat n => proxy n -> Integer symbolVal :: forall n proxy. KnownSymbol n => proxy n -> String data SomeNat = forall n. KnownNat n => SomeNat (Proxy n) data SomeSymbol = forall n. KnownSymbol n => SomeSymbol (Proxy n) someNatVal :: Integer -> Maybe SomeNat -- partial because of negative Ints someSymbolVal :: String -> SomeSymbol infix 4 <=?, <= infixl 6 +, - infixl 7 * infixr 8 ^ type x <= y = (x <=? y) ~ True -- Note: in Constraint type family (m :: Nat) <=? (n :: Nat) :: Bool type family (m :: Nat) + (n :: Nat) :: Nat type family (m :: Nat) * (n :: Nat) :: Nat type family (m :: Nat) ^ (n :: Nat) :: Nat type family (m :: Nat) - (n :: Nat) :: Nat
class Coercible a b where coerce :: a -> b
These are in no particular order, but they are numbered for easy reference.
CoercionTsound like monad transformers. I (Richard) have actually been confused by this at one point.
KProxy's data constructor be named
KProxy? Reusing the name here requires users to use a
'every time they want to use the promoted data constructor
There are up to three different ways type-level predicates can be defined: as Constraints, as GADTs wrapping constraints, or as type families returning
Bools. Is there a common naming convention among these? Right now, we have
Data.Type.Equality) have similar names, achieve similar functions, but are subtly different. This may or may not be confusing.
I (Richard) want to add the following function to
gcastWith :: (a :~: b) -> ((a ~ b) => r) -> r gcastWith Refl x = x
I've tested this function in a real setting, and it (that is, type inference for it) works great.