{-# LANGUAGE AllowAmbiguousTypes #-} {-# LANGUAGE ConstraintKinds #-} {-# LANGUAGE DataKinds #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE GADTs #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE PolyKinds #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE TypeApplications #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE TypeFamilyDependencies #-} {-# LANGUAGE TypeOperators #-} {-# LANGUAGE CPP #-} #if __GLASGOW_HASKELL__ < 806 {-# LANGUAGE TypeInType #-} #endif #if __GLASGOW_HASKELL__ >= 810 {-# LANGUAGE UndecidableInstances #-} #endif module Data.Vinyl.TypeLevel where import Data.Coerce import Data.Kind -- | A mere approximation of the natural numbers. And their image as lifted by -- @-XDataKinds@ corresponds to the actual natural numbers. data Nat = Z | S !Nat -- | Produce a runtime 'Int' value corresponding to a 'Nat' type. class NatToInt (n :: Nat) where natToInt :: Int instance NatToInt 'Z where natToInt :: Int natToInt = Int 0 {-# INLINE natToInt #-} instance NatToInt n => NatToInt ('S n) where natToInt :: Int natToInt = Int 1 Int -> Int -> Int forall a. Num a => a -> a -> a + NatToInt n => Int forall (n :: Nat). NatToInt n => Int natToInt @n {-# INLINE natToInt #-} -- | Reify a list of type-level natural number indices as runtime -- 'Int's relying on instances of 'NatToInt'. class IndexWitnesses (is :: [Nat]) where indexWitnesses :: [Int] instance IndexWitnesses '[] where indexWitnesses :: [Int] indexWitnesses = [] {-# INLINE indexWitnesses #-} instance (IndexWitnesses is, NatToInt i) => IndexWitnesses (i ': is) where indexWitnesses :: [Int] indexWitnesses = NatToInt i => Int forall (n :: Nat). NatToInt n => Int natToInt @i Int -> [Int] -> [Int] forall a. a -> [a] -> [a] : IndexWitnesses is => [Int] forall (is :: [Nat]). IndexWitnesses is => [Int] indexWitnesses @is {-# INLINE indexWitnesses #-} -- | Project the first component of a type-level tuple. type family Fst (a :: (k1,k2)) where Fst '(x,y) = x -- | Project the second component of a type-level tuple. type family Snd (a :: (k1,k2)) where Snd '(x,y) = y type family RLength xs where RLength '[] = 'Z RLength (x ': xs) = 'S (RLength xs) -- | A partial relation that gives the index of a value in a list. type family RIndex (r :: k) (rs :: [k]) :: Nat where RIndex r (r ': rs) = 'Z RIndex r (s ': rs) = 'S (RIndex r rs) -- | A partial relation that gives the indices of a sublist in a larger list. type family RImage (rs :: [k]) (ss :: [k]) :: [Nat] where RImage '[] ss = '[] RImage (r ': rs) ss = RIndex r ss ': RImage rs ss -- | Remove the first occurrence of a type from a type-level list. type family RDelete r rs where RDelete r (r ': rs) = rs RDelete r (s ': rs) = s ': RDelete r rs -- | A constraint-former which applies to every field in a record. type family RecAll (f :: u -> *) (rs :: [u]) (c :: * -> Constraint) :: Constraint where RecAll f '[] c = () RecAll f (r ': rs) c = (c (f r), RecAll f rs c) -- | Append for type-level lists. type family (as :: [k]) ++ (bs :: [k]) :: [k] where '[] ++ bs = bs (a ': as) ++ bs = a ': (as ++ bs) -- | Constraint that all types in a type-level list satisfy a -- constraint. type family AllConstrained (c :: u -> Constraint) (ts :: [u]) :: Constraint where AllConstrained c '[] = () AllConstrained c (t ': ts) = (c t, AllConstrained c ts) -- | Constraint that each Constraint in a type-level list is satisfied -- by a particular type. class AllSatisfied cs t where instance AllSatisfied '[] t where instance (c t, AllSatisfied cs t) => AllSatisfied (c ': cs) t where -- | Constraint that all types in a type-level list satisfy each -- constraint from a list of constraints. -- -- @AllAllSat cs ts@ should be equivalent to @AllConstrained -- (AllSatisfied cs) ts@ if partial application of type families were -- legal. type family AllAllSat cs ts :: Constraint where AllAllSat cs '[] = () AllAllSat cs (t ': ts) = (AllSatisfied cs t, AllAllSat cs ts) -- | Apply a type constructor to a record index. Record indexes are -- either 'Type' or @('Symbol', 'Type')@. In the latter case, the type -- constructor is applied to the second component of the tuple. type family ApplyToField (t :: Type -> Type) (a :: k1) = (r :: k1) | r -> t a where ApplyToField t '(s,x) = '(s, t x) ApplyToField t x = t x -- | Apply a type constructor to each element of a type level list -- using 'ApplyOn'. type family MapTyCon t xs = r | r -> xs where MapTyCon t '[] = '[] MapTyCon t (x ': xs) = ApplyToField t x ': MapTyCon t xs -- | This class is used for `consMatchCoercion` with older versions -- of GHC. class Coercible (f x) (g x) => Similar f g (x :: k) instance Coercible (f x) (g x) => Similar f g (x :: k)