Safe Haskell	Safe-Inferred
Language	Haskell2010

Generics.Kind

Contents

Generic representation types
- Atoms for Field
- Lists of types
Generic type classes
Getting more instances almost for free
Bridging with GHC.Generics
Re-exported from Atom
- Interpretation of atoms
- Auxiliary data types for interpretation

Description

Main module of kind-generics. Please refer to the README file for documentation on how to use this package.

Synopsis

data ((f :: k -> Type) :+: (g :: k -> Type)) (p :: k)
- = L1 (f p)
- | R1 (g p)
data ((f :: k -> Type) :*: (g :: k -> Type)) (p :: k) = (f p) :*: (g p)
data V1 (p :: k)
data U1 (p :: k) = U1
newtype M1 i (c :: Meta) (f :: k -> Type) (p :: k) = M1 {
- unM1 :: f p
}
newtype Field (t :: Atom d Type) (x :: LoT d) where
- Field :: {..} -> Field t x
data ((c :: Atom d Constraint) :=>: (f :: LoT d -> Type)) (x :: LoT d) where
- SuchThat :: Interpret c x => f x -> (c :=>: f) x
data Exists k (f :: LoT (k -> d) -> Type) (x :: LoT d) where
- Exists :: forall k (t :: k) d (f :: LoT (k -> d) -> Type) (x :: LoT d). {..} -> Exists k f x
data Atom d (k :: TYPE r) where
- Var :: forall d k1. TyVar d k1 -> Atom d k1
- Kon :: forall k1 d. k1 -> Atom d k1
- (:@:) :: forall d k1 k2. Atom d (k1 -> k2) -> Atom d k1 -> Atom d k2
- (:&:) :: forall d. Atom d Constraint -> Atom d Constraint -> Atom d Constraint
- ForAll :: forall d1 d. Atom (d1 -> d) Type -> Atom d Type
- (:=>>:) :: forall d. Atom d Constraint -> Atom d Type -> Atom d Type
- Eval :: forall d k1. Atom d (Exp k1) -> Atom d k1
data TyVar d (k :: TYPE r) where
- VZ :: forall x xs. TyVar (x -> xs) x
- VS :: forall xs k1 x. TyVar xs k1 -> TyVar (x -> xs) k1
type (:$:) (f :: k1 -> k2) (x :: Atom d k1) = ('Kon f :: Atom d (k1 -> k2)) ':@: x
type (:~:) (a :: Atom d k1) (b :: Atom d k1) = (('Kon ((~) :: k1 -> k1 -> Constraint) :: Atom d (k1 -> k1 -> Constraint)) ':@: a) ':@: b
type (:~~:) (a :: Atom d k1) (b :: Atom d k2) = (('Kon ((~~) :: k1 -> k2 -> Constraint) :: Atom d (k1 -> k2 -> Constraint)) ':@: a) ':@: b
type Var0 = 'Var ('VZ :: TyVar (k -> xs) k)
type Var1 = 'Var ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x -> k -> xs) k)
type Var2 = 'Var ('VS ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x1 -> k -> xs) k) :: TyVar (x -> x1 -> k -> xs) k)
type Var3 = 'Var ('VS ('VS ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x2 -> k -> xs) k) :: TyVar (x1 -> x2 -> k -> xs) k) :: TyVar (x -> x1 -> x2 -> k -> xs) k)
type Var4 = 'Var ('VS ('VS ('VS ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x3 -> k -> xs) k) :: TyVar (x2 -> x3 -> k -> xs) k) :: TyVar (x1 -> x2 -> x3 -> k -> xs) k) :: TyVar (x -> x1 -> x2 -> x3 -> k -> xs) k)
type Var5 = 'Var ('VS ('VS ('VS ('VS ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x4 -> k -> xs) k) :: TyVar (x3 -> x4 -> k -> xs) k) :: TyVar (x2 -> x3 -> x4 -> k -> xs) k) :: TyVar (x1 -> x2 -> x3 -> x4 -> k -> xs) k) :: TyVar (x -> x1 -> x2 -> x3 -> x4 -> k -> xs) k)
type Var6 = 'Var ('VS ('VS ('VS ('VS ('VS ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x5 -> k -> xs) k) :: TyVar (x4 -> x5 -> k -> xs) k) :: TyVar (x3 -> x4 -> x5 -> k -> xs) k) :: TyVar (x2 -> x3 -> x4 -> x5 -> k -> xs) k) :: TyVar (x1 -> x2 -> x3 -> x4 -> x5 -> k -> xs) k) :: TyVar (x -> x1 -> x2 -> x3 -> x4 -> x5 -> k -> xs) k)
type Var7 = 'Var ('VS ('VS ('VS ('VS ('VS ('VS ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x6 -> k -> xs) k) :: TyVar (x5 -> x6 -> k -> xs) k) :: TyVar (x4 -> x5 -> x6 -> k -> xs) k) :: TyVar (x3 -> x4 -> x5 -> x6 -> k -> xs) k) :: TyVar (x2 -> x3 -> x4 -> x5 -> x6 -> k -> xs) k) :: TyVar (x1 -> x2 -> x3 -> x4 -> x5 -> x6 -> k -> xs) k) :: TyVar (x -> x1 -> x2 -> x3 -> x4 -> x5 -> x6 -> k -> xs) k)
type Var8 = 'Var ('VS ('VS ('VS ('VS ('VS ('VS ('VS ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x7 -> k -> xs) k) :: TyVar (x6 -> x7 -> k -> xs) k) :: TyVar (x5 -> x6 -> x7 -> k -> xs) k) :: TyVar (x4 -> x5 -> x6 -> x7 -> k -> xs) k) :: TyVar (x3 -> x4 -> x5 -> x6 -> x7 -> k -> xs) k) :: TyVar (x2 -> x3 -> x4 -> x5 -> x6 -> x7 -> k -> xs) k) :: TyVar (x1 -> x2 -> x3 -> x4 -> x5 -> x6 -> x7 -> k -> xs) k) :: TyVar (x -> x1 -> x2 -> x3 -> x4 -> x5 -> x6 -> x7 -> k -> xs) k)
type Var9 = 'Var ('VS ('VS ('VS ('VS ('VS ('VS ('VS ('VS ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x8 -> k -> xs) k) :: TyVar (x7 -> x8 -> k -> xs) k) :: TyVar (x6 -> x7 -> x8 -> k -> xs) k) :: TyVar (x5 -> x6 -> x7 -> x8 -> k -> xs) k) :: TyVar (x4 -> x5 -> x6 -> x7 -> x8 -> k -> xs) k) :: TyVar (x3 -> x4 -> x5 -> x6 -> x7 -> x8 -> k -> xs) k) :: TyVar (x2 -> x3 -> x4 -> x5 -> x6 -> x7 -> x8 -> k -> xs) k) :: TyVar (x1 -> x2 -> x3 -> x4 -> x5 -> x6 -> x7 -> x8 -> k -> xs) k) :: TyVar (x -> x1 -> x2 -> x3 -> x4 -> x5 -> x6 -> x7 -> x8 -> k -> xs) k)
data LoT k where
- LoT0 :: LoT Type
- (:&&:) :: forall k1 ks. k1 -> LoT ks -> LoT (k1 -> ks)
type family (f :: k) :@@: (tys :: LoT k) where ...
type LoT1 (a :: k) = a ':&&: 'LoT0
type LoT2 (a :: k) (b :: k1) = a ':&&: (b ':&&: 'LoT0)
data TyEnv where
- TyEnv :: forall k. k -> LoT k -> TyEnv
class GenericK (f :: k) where
- type RepK f :: LoT k -> Type
- fromK :: (f :@@: x) -> RepK f x
- toK :: RepK f x -> f :@@: x
type GenericF t f x = (GenericK f, x ~ SplitF t f, t ~ (f :@@: x))
fromF :: forall f t x. GenericF t f x => t -> RepK f x
toF :: forall f t x. GenericF t f x => RepK f x -> t
type GenericN n t f x = (GenericK f, 'TyEnv f x ~ SplitN n t, t ~ (f :@@: x))
fromN :: forall n t f x. GenericN n t f x => t -> RepK f x
toN :: forall n t f x. GenericN n t f x => RepK f x -> t
fromRepK :: forall f x xs. (GenericK f, SubstRep' (RepK f) x xs) => (f x :@@: xs) -> SubstRep (RepK f) x xs
toRepK :: forall f x xs. (GenericK f, SubstRep' (RepK f) x xs) => SubstRep (RepK f) x xs -> f x :@@: xs
type family SubstRep f x :: LoT k -> Type
class SubstRep' (f :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k)
type family SubstAtom (f :: Atom (t -> k) d) (x :: t) :: Atom k d where ...
class Conv (gg :: Type -> Type) (kg :: LoT d -> Type) (tys :: LoT d) where
- toGhcGenerics :: kg tys -> gg a
- toKindGenerics :: gg a -> kg tys
type family Interpret (t :: Atom d k) (tys :: LoT d) :: k where ...
type family InterpretVar (t :: TyVar d k) (tys :: LoT d) :: k where ...
type family Satisfies (cs :: [Atom d Constraint]) (tys :: LoT d) where ...
type family ContainsTyVar (v :: TyVar d k) (t :: Atom d p) :: Bool where ...
newtype ForAllI (f :: Atom (d1 -> d) Type) (tys :: LoT d) where
- ForAllI :: forall {d1} {d} (f :: Atom (d1 -> d) Type) (tys :: LoT d). (forall (t :: d1). Interpret f (t ':&&: tys)) -> ForAllI f tys
newtype SuchThatI (c :: Atom d Constraint) (f :: Atom d Type) (tys :: LoT d) where
- SuchThatI :: forall {d} (c :: Atom d Constraint) (tys :: LoT d) (f :: Atom d Type). {..} -> SuchThatI c f tys
newtype WrappedI (f :: Atom d Type) (tys :: LoT d) = WrapI {
- unwrapI :: Interpret f tys
}
toWrappedI :: forall {d1} {ks} (f :: Atom (d1 -> ks) Type) (tys :: LoT ks) (t :: d1). ForAllI f tys -> WrappedI f (t ':&&: tys)
fromWrappedI :: forall {d1} {d} (f :: Atom (d1 -> d) Type) (tys :: LoT d). (forall (t :: d1). WrappedI f (t ':&&: tys)) -> ForAllI f tys

Generic representation types

data ((f :: k -> Type) :+: (g :: k -> Type)) (p :: k) infixr 5 #

Sums: encode choice between constructors

Constructors

L1 (f p)
R1 (g p)

Instances

Instances details

(SubstRep' f x xs, SubstRep' g x xs) => SubstRep' (f :+: g :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k) Source #
Instance details Defined in Generics.Kind Associated Types type SubstRep (f :+: g) x :: LoT k -> Type Source # Methods substRep :: (f :+: g) (x ':&&: xs) -> SubstRep (f :+: g) x xs unsubstRep :: SubstRep (f :+: g) x xs -> (f :+: g) (x ':&&: xs)
Generic1 (f :+: g :: k -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 (f :+: g) :: k -> Type # Methods from1 :: forall (a :: k0). (f :+: g) a -> Rep1 (f :+: g) a # to1 :: forall (a :: k0). Rep1 (f :+: g) a -> (f :+: g) a #
(Conv f f' tys, Conv g g' tys) => Conv (f :+: g) (f' :+: g' :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: (f' :+: g') tys -> (f :+: g) a Source # toKindGenerics :: (f :+: g) a -> (f' :+: g') tys Source #
(Foldable f, Foldable g) => Foldable (f :+: g)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => (f :+: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a # toList :: (f :+: g) a -> [a] # null :: (f :+: g) a -> Bool # length :: (f :+: g) a -> Int # elem :: Eq a => a -> (f :+: g) a -> Bool # maximum :: Ord a => (f :+: g) a -> a # minimum :: Ord a => (f :+: g) a -> a # sum :: Num a => (f :+: g) a -> a # product :: Num a => (f :+: g) a -> a #
(Traversable f, Traversable g) => Traversable (f :+: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a) # mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) # sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) #
(Functor f, Functor g) => Functor (f :+: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b # (<$) :: a -> (f :+: g) b -> (f :+: g) a #
Generic ((f :+: g) p)
Instance details Defined in GHC.Generics Associated Types type Rep ((f :+: g) p) :: Type -> Type # Methods from :: (f :+: g) p -> Rep ((f :+: g) p) x # to :: Rep ((f :+: g) p) x -> (f :+: g) p #
(Read (f p), Read (g p)) => Read ((f :+: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS ((f :+: g) p) # readList :: ReadS [(f :+: g) p] # readPrec :: ReadPrec ((f :+: g) p) # readListPrec :: ReadPrec [(f :+: g) p] #
(Show (f p), Show (g p)) => Show ((f :+: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> (f :+: g) p -> ShowS # show :: (f :+: g) p -> String # showList :: [(f :+: g) p] -> ShowS #
(Eq (f p), Eq (g p)) => Eq ((f :+: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: (f :+: g) p -> (f :+: g) p -> Bool # (/=) :: (f :+: g) p -> (f :+: g) p -> Bool #
(Ord (f p), Ord (g p)) => Ord ((f :+: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: (f :+: g) p -> (f :+: g) p -> Ordering # (<) :: (f :+: g) p -> (f :+: g) p -> Bool # (<=) :: (f :+: g) p -> (f :+: g) p -> Bool # (>) :: (f :+: g) p -> (f :+: g) p -> Bool # (>=) :: (f :+: g) p -> (f :+: g) p -> Bool # max :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p # min :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p #
type SubstRep (f :+: g :: LoT (t -> k) -> Type) (x :: t) Source #
Instance details Defined in Generics.Kind type SubstRep (f :+: g :: LoT (t -> k) -> Type) (x :: t) = SubstRep f x :+: SubstRep g x
type Rep1 (f :+: g :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep1 (f :+: g :: k -> Type) = D1 ('MetaData ":+:" "GHC.Generics" "base" 'False) (C1 ('MetaCons "L1" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)) :+: C1 ('MetaCons "R1" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 g)))
type Rep ((f :+: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics type Rep ((f :+: g) p) = D1 ('MetaData ":+:" "GHC.Generics" "base" 'False) (C1 ('MetaCons "L1" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f p))) :+: C1 ('MetaCons "R1" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (g p))))

data ((f :: k -> Type) :*: (g :: k -> Type)) (p :: k) infixr 6 #

Products: encode multiple arguments to constructors

Constructors

(f p) :*: (g p) infixr 6

Instances

Instances details

(SubstRep' f x xs, SubstRep' g x xs) => SubstRep' (f :*: g :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k) Source #
Instance details Defined in Generics.Kind Associated Types type SubstRep (f :: g) x :: LoT k -> Type Source # Methods substRep :: (f :: g) (x ':&&: xs) -> SubstRep (f :: g) x xs unsubstRep :: SubstRep (f :: g) x xs -> (f :*: g) (x ':&&: xs)
Generic1 (f :*: g :: k -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 (f :: g) :: k -> Type # Methods from1 :: forall (a :: k0). (f :: g) a -> Rep1 (f :: g) a # to1 :: forall (a :: k0). Rep1 (f :: g) a -> (f :*: g) a #
(Conv f f' tys, Conv g g' tys) => Conv (f :: g) (f' :: g' :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: (f' :: g') tys -> (f :: g) a Source # toKindGenerics :: (f :: g) a -> (f' :: g') tys Source #
(Foldable f, Foldable g) => Foldable (f :*: g)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => (f :: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :: g) a -> b # foldr1 :: (a -> a -> a) -> (f :: g) a -> a # foldl1 :: (a -> a -> a) -> (f :: g) a -> a # toList :: (f :: g) a -> [a] # null :: (f :: g) a -> Bool # length :: (f :: g) a -> Int # elem :: Eq a => a -> (f :: g) a -> Bool # maximum :: Ord a => (f :: g) a -> a # minimum :: Ord a => (f :: g) a -> a # sum :: Num a => (f :: g) a -> a # product :: Num a => (f :*: g) a -> a #
(Traversable f, Traversable g) => Traversable (f :*: g)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # sequenceA :: Applicative f0 => (f :: g) (f0 a) -> f0 ((f :: g) a) # mapM :: Monad m => (a -> m b) -> (f :: g) a -> m ((f :: g) b) # sequence :: Monad m => (f :: g) (m a) -> m ((f :: g) a) #
(Alternative f, Alternative g) => Alternative (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: (f :: g) a # (<\|>) :: (f :: g) a -> (f :: g) a -> (f :: g) a # some :: (f :: g) a -> (f :: g) [a] # many :: (f :: g) a -> (f :: g) [a] #
(Applicative f, Applicative g) => Applicative (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> (f :: g) a # (<>) :: (f :: g) (a -> b) -> (f :: g) a -> (f :: g) b # liftA2 :: (a -> b -> c) -> (f :: g) a -> (f :: g) b -> (f :: g) c # (>) :: (f :: g) a -> (f :: g) b -> (f :: g) b # (<) :: (f :: g) a -> (f :: g) b -> (f :: g) a #
(Functor f, Functor g) => Functor (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> (f :: g) a -> (f :: g) b # (<$) :: a -> (f :: g) b -> (f :: g) a #
(Monad f, Monad g) => Monad (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: (f :: g) a -> (a -> (f :: g) b) -> (f :: g) b # (>>) :: (f :: g) a -> (f :: g) b -> (f :: g) b # return :: a -> (f :*: g) a #
(MonadPlus f, MonadPlus g) => MonadPlus (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: (f :: g) a # mplus :: (f :: g) a -> (f :: g) a -> (f :: g) a #
(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :: g) p # mappend :: (f :: g) p -> (f :: g) p -> (f :: g) p # mconcat :: [(f :: g) p] -> (f :: g) p #
(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: (f :: g) p -> (f :: g) p -> (f :: g) p # sconcat :: NonEmpty ((f :: g) p) -> (f :: g) p # stimes :: Integral b => b -> (f :: g) p -> (f :*: g) p #
Generic ((f :*: g) p)
Instance details Defined in GHC.Generics Associated Types type Rep ((f :: g) p) :: Type -> Type # Methods from :: (f :: g) p -> Rep ((f :: g) p) x # to :: Rep ((f :: g) p) x -> (f :*: g) p #
(Read (f p), Read (g p)) => Read ((f :*: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS ((f :: g) p) # readList :: ReadS [(f :: g) p] # readPrec :: ReadPrec ((f :: g) p) # readListPrec :: ReadPrec [(f :: g) p] #
(Show (f p), Show (g p)) => Show ((f :*: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> (f :: g) p -> ShowS # show :: (f :: g) p -> String # showList :: [(f :*: g) p] -> ShowS #
(Eq (f p), Eq (g p)) => Eq ((f :*: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: (f :: g) p -> (f :: g) p -> Bool # (/=) :: (f :: g) p -> (f :: g) p -> Bool #
(Ord (f p), Ord (g p)) => Ord ((f :*: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: (f :: g) p -> (f :: g) p -> Ordering # (<) :: (f :: g) p -> (f :: g) p -> Bool # (<=) :: (f :: g) p -> (f :: g) p -> Bool # (>) :: (f :: g) p -> (f :: g) p -> Bool # (>=) :: (f :: g) p -> (f :: g) p -> Bool # max :: (f :: g) p -> (f :: g) p -> (f :: g) p # min :: (f :: g) p -> (f :: g) p -> (f :: g) p #
type SubstRep (f :*: g :: LoT (t -> k) -> Type) (x :: t) Source #
Instance details Defined in Generics.Kind type SubstRep (f :: g :: LoT (t -> k) -> Type) (x :: t) = SubstRep f x :: SubstRep g x
type Rep1 (f :*: g :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep1 (f :: g :: k -> Type) = D1 ('MetaData "::" "GHC.Generics" "base" 'False) (C1 ('MetaCons "::" ('InfixI 'RightAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f) :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 g)))
type Rep ((f :*: g) p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics type Rep ((f :: g) p) = D1 ('MetaData "::" "GHC.Generics" "base" 'False) (C1 ('MetaCons "::" ('InfixI 'RightAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f p)) :: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (g p))))

data V1 (p :: k) #

Void: used for datatypes without constructors

Instances

Instances details

Generic1 (V1 :: k -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 V1 :: k -> Type # Methods from1 :: forall (a :: k0). V1 a -> Rep1 V1 a # to1 :: forall (a :: k0). Rep1 V1 a -> V1 a #
Foldable (V1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => V1 m -> m # foldMap :: Monoid m => (a -> m) -> V1 a -> m # foldMap' :: Monoid m => (a -> m) -> V1 a -> m # foldr :: (a -> b -> b) -> b -> V1 a -> b # foldr' :: (a -> b -> b) -> b -> V1 a -> b # foldl :: (b -> a -> b) -> b -> V1 a -> b # foldl' :: (b -> a -> b) -> b -> V1 a -> b # foldr1 :: (a -> a -> a) -> V1 a -> a # foldl1 :: (a -> a -> a) -> V1 a -> a # toList :: V1 a -> [a] # null :: V1 a -> Bool # length :: V1 a -> Int # elem :: Eq a => a -> V1 a -> Bool # maximum :: Ord a => V1 a -> a # minimum :: Ord a => V1 a -> a # sum :: Num a => V1 a -> a # product :: Num a => V1 a -> a #
Traversable (V1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b) # sequenceA :: Applicative f => V1 (f a) -> f (V1 a) # mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b) # sequence :: Monad m => V1 (m a) -> m (V1 a) #
Functor (V1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> V1 a -> V1 b # (<$) :: a -> V1 b -> V1 a #
Semigroup (V1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: V1 p -> V1 p -> V1 p # sconcat :: NonEmpty (V1 p) -> V1 p # stimes :: Integral b => b -> V1 p -> V1 p #
Generic (V1 p)
Instance details Defined in GHC.Generics Associated Types type Rep (V1 p) :: Type -> Type # Methods from :: V1 p -> Rep (V1 p) x # to :: Rep (V1 p) x -> V1 p #
Read (V1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS (V1 p) # readList :: ReadS [V1 p] # readPrec :: ReadPrec (V1 p) # readListPrec :: ReadPrec [V1 p] #
Show (V1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> V1 p -> ShowS # show :: V1 p -> String # showList :: [V1 p] -> ShowS #
Eq (V1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: V1 p -> V1 p -> Bool # (/=) :: V1 p -> V1 p -> Bool #
Ord (V1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods compare :: V1 p -> V1 p -> Ordering # (<) :: V1 p -> V1 p -> Bool # (<=) :: V1 p -> V1 p -> Bool # (>) :: V1 p -> V1 p -> Bool # (>=) :: V1 p -> V1 p -> Bool # max :: V1 p -> V1 p -> V1 p # min :: V1 p -> V1 p -> V1 p #
type Rep1 (V1 :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep1 (V1 :: k -> Type) = D1 ('MetaData "V1" "GHC.Generics" "base" 'False) (V1 :: k -> Type)
type Rep (V1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep (V1 p) = D1 ('MetaData "V1" "GHC.Generics" "base" 'False) (V1 :: Type -> Type)

data U1 (p :: k) #

Unit: used for constructors without arguments

Constructors

U1

Instances

Instances details

SubstRep' (U1 :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k) Source #
Instance details Defined in Generics.Kind Associated Types type SubstRep U1 x :: LoT k -> Type Source # Methods substRep :: U1 (x ':&&: xs) -> SubstRep U1 x xs unsubstRep :: SubstRep U1 x xs -> U1 (x ':&&: xs)
Generic1 (U1 :: k -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 U1 :: k -> Type # Methods from1 :: forall (a :: k0). U1 a -> Rep1 U1 a # to1 :: forall (a :: k0). Rep1 U1 a -> U1 a #
Conv (U1 :: Type -> Type) (U1 :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: U1 tys -> U1 a Source # toKindGenerics :: U1 a -> U1 tys Source #
Foldable (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => U1 m -> m # foldMap :: Monoid m => (a -> m) -> U1 a -> m # foldMap' :: Monoid m => (a -> m) -> U1 a -> m # foldr :: (a -> b -> b) -> b -> U1 a -> b # foldr' :: (a -> b -> b) -> b -> U1 a -> b # foldl :: (b -> a -> b) -> b -> U1 a -> b # foldl' :: (b -> a -> b) -> b -> U1 a -> b # foldr1 :: (a -> a -> a) -> U1 a -> a # foldl1 :: (a -> a -> a) -> U1 a -> a # toList :: U1 a -> [a] # null :: U1 a -> Bool # length :: U1 a -> Int # elem :: Eq a => a -> U1 a -> Bool # maximum :: Ord a => U1 a -> a # minimum :: Ord a => U1 a -> a # sum :: Num a => U1 a -> a # product :: Num a => U1 a -> a #
Traversable (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> U1 a -> f (U1 b) # sequenceA :: Applicative f => U1 (f a) -> f (U1 a) # mapM :: Monad m => (a -> m b) -> U1 a -> m (U1 b) # sequence :: Monad m => U1 (m a) -> m (U1 a) #
Alternative (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: U1 a # (<\|>) :: U1 a -> U1 a -> U1 a # some :: U1 a -> U1 [a] # many :: U1 a -> U1 [a] #
Applicative (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> U1 a # (<>) :: U1 (a -> b) -> U1 a -> U1 b # liftA2 :: (a -> b -> c) -> U1 a -> U1 b -> U1 c # (>) :: U1 a -> U1 b -> U1 b # (<*) :: U1 a -> U1 b -> U1 a #
Functor (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> U1 a -> U1 b # (<$) :: a -> U1 b -> U1 a #
Monad (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: U1 a -> (a -> U1 b) -> U1 b # (>>) :: U1 a -> U1 b -> U1 b # return :: a -> U1 a #
MonadPlus (U1 :: Type -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: U1 a # mplus :: U1 a -> U1 a -> U1 a #
Monoid (U1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: U1 p # mappend :: U1 p -> U1 p -> U1 p # mconcat :: [U1 p] -> U1 p #
Semigroup (U1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: U1 p -> U1 p -> U1 p # sconcat :: NonEmpty (U1 p) -> U1 p # stimes :: Integral b => b -> U1 p -> U1 p #
Generic (U1 p)
Instance details Defined in GHC.Generics Associated Types type Rep (U1 p) :: Type -> Type # Methods from :: U1 p -> Rep (U1 p) x # to :: Rep (U1 p) x -> U1 p #
Read (U1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS (U1 p) # readList :: ReadS [U1 p] # readPrec :: ReadPrec (U1 p) # readListPrec :: ReadPrec [U1 p] #
Show (U1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> U1 p -> ShowS # show :: U1 p -> String # showList :: [U1 p] -> ShowS #
Eq (U1 p)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (==) :: U1 p -> U1 p -> Bool # (/=) :: U1 p -> U1 p -> Bool #
Ord (U1 p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: U1 p -> U1 p -> Ordering # (<) :: U1 p -> U1 p -> Bool # (<=) :: U1 p -> U1 p -> Bool # (>) :: U1 p -> U1 p -> Bool # (>=) :: U1 p -> U1 p -> Bool # max :: U1 p -> U1 p -> U1 p # min :: U1 p -> U1 p -> U1 p #
type SubstRep (U1 :: LoT (t -> k) -> Type) (x :: t) Source #
Instance details Defined in Generics.Kind type SubstRep (U1 :: LoT (t -> k) -> Type) (x :: t) = U1 :: LoT k -> Type
type Rep1 (U1 :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep1 (U1 :: k -> Type) = D1 ('MetaData "U1" "GHC.Generics" "base" 'False) (C1 ('MetaCons "U1" 'PrefixI 'False) (U1 :: k -> Type))
type Rep (U1 p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics type Rep (U1 p) = D1 ('MetaData "U1" "GHC.Generics" "base" 'False) (C1 ('MetaCons "U1" 'PrefixI 'False) (U1 :: Type -> Type))

newtype M1 i (c :: Meta) (f :: k -> Type) (p :: k) #

Meta-information (constructor names, etc.)

Constructors

M1
Fields unM1 :: f p

Instances

Instances details

SubstRep' f x xs => SubstRep' (M1 i c f :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k) Source #
Instance details Defined in Generics.Kind Associated Types type SubstRep (M1 i c f) x :: LoT k -> Type Source # Methods substRep :: M1 i c f (x ':&&: xs) -> SubstRep (M1 i c f) x xs unsubstRep :: SubstRep (M1 i c f) x xs -> M1 i c f (x ':&&: xs)
Generic1 (M1 i c f :: k -> Type)
Instance details Defined in GHC.Generics Associated Types type Rep1 (M1 i c f) :: k -> Type # Methods from1 :: forall (a :: k0). M1 i c f a -> Rep1 (M1 i c f) a # to1 :: forall (a :: k0). Rep1 (M1 i c f) a -> M1 i c f a #
Conv f f' tys => Conv (M1 i c f) (f' :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: f' tys -> M1 i c f a Source # toKindGenerics :: M1 i c f a -> f' tys Source #
Conv f f' tys => Conv (M1 i c f) (M1 i c f' :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: M1 i c f' tys -> M1 i c f a Source # toKindGenerics :: M1 i c f a -> M1 i c f' tys Source #
Foldable f => Foldable (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => M1 i c f m -> m # foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m # foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m # foldr :: (a -> b -> b) -> b -> M1 i c f a -> b # foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b # foldl :: (b -> a -> b) -> b -> M1 i c f a -> b # foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b # foldr1 :: (a -> a -> a) -> M1 i c f a -> a # foldl1 :: (a -> a -> a) -> M1 i c f a -> a # toList :: M1 i c f a -> [a] # null :: M1 i c f a -> Bool # length :: M1 i c f a -> Int # elem :: Eq a => a -> M1 i c f a -> Bool # maximum :: Ord a => M1 i c f a -> a # minimum :: Ord a => M1 i c f a -> a # sum :: Num a => M1 i c f a -> a # product :: Num a => M1 i c f a -> a #
Traversable f => Traversable (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> M1 i c f a -> f0 (M1 i c f b) # sequenceA :: Applicative f0 => M1 i c f (f0 a) -> f0 (M1 i c f a) # mapM :: Monad m => (a -> m b) -> M1 i c f a -> m (M1 i c f b) # sequence :: Monad m => M1 i c f (m a) -> m (M1 i c f a) #
Alternative f => Alternative (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods empty :: M1 i c f a # (<\|>) :: M1 i c f a -> M1 i c f a -> M1 i c f a # some :: M1 i c f a -> M1 i c f [a] # many :: M1 i c f a -> M1 i c f [a] #
Applicative f => Applicative (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> M1 i c f a # (<>) :: M1 i c f (a -> b) -> M1 i c f a -> M1 i c f b # liftA2 :: (a -> b -> c0) -> M1 i c f a -> M1 i c f b -> M1 i c f c0 # (>) :: M1 i c f a -> M1 i c f b -> M1 i c f b # (<*) :: M1 i c f a -> M1 i c f b -> M1 i c f a #
Functor f => Functor (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods fmap :: (a -> b) -> M1 i c f a -> M1 i c f b # (<$) :: a -> M1 i c f b -> M1 i c f a #
Monad f => Monad (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods (>>=) :: M1 i c f a -> (a -> M1 i c f b) -> M1 i c f b # (>>) :: M1 i c f a -> M1 i c f b -> M1 i c f b # return :: a -> M1 i c f a #
MonadPlus f => MonadPlus (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods mzero :: M1 i c f a # mplus :: M1 i c f a -> M1 i c f a -> M1 i c f a #
Monoid (f p) => Monoid (M1 i c f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: M1 i c f p # mappend :: M1 i c f p -> M1 i c f p -> M1 i c f p # mconcat :: [M1 i c f p] -> M1 i c f p #
Semigroup (f p) => Semigroup (M1 i c f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods (<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p # sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p # stimes :: Integral b => b -> M1 i c f p -> M1 i c f p #
Generic (M1 i c f p)
Instance details Defined in GHC.Generics Associated Types type Rep (M1 i c f p) :: Type -> Type # Methods from :: M1 i c f p -> Rep (M1 i c f p) x # to :: Rep (M1 i c f p) x -> M1 i c f p #
Read (f p) => Read (M1 i c f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods readsPrec :: Int -> ReadS (M1 i c f p) # readList :: ReadS [M1 i c f p] # readPrec :: ReadPrec (M1 i c f p) # readListPrec :: ReadPrec [M1 i c f p] #
Show (f p) => Show (M1 i c f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods showsPrec :: Int -> M1 i c f p -> ShowS # show :: M1 i c f p -> String # showList :: [M1 i c f p] -> ShowS #
Eq (f p) => Eq (M1 i c f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods (==) :: M1 i c f p -> M1 i c f p -> Bool # (/=) :: M1 i c f p -> M1 i c f p -> Bool #
Ord (f p) => Ord (M1 i c f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics Methods compare :: M1 i c f p -> M1 i c f p -> Ordering # (<) :: M1 i c f p -> M1 i c f p -> Bool # (<=) :: M1 i c f p -> M1 i c f p -> Bool # (>) :: M1 i c f p -> M1 i c f p -> Bool # (>=) :: M1 i c f p -> M1 i c f p -> Bool # max :: M1 i c f p -> M1 i c f p -> M1 i c f p # min :: M1 i c f p -> M1 i c f p -> M1 i c f p #
type SubstRep (M1 i c f :: LoT (t -> k) -> Type) (x :: t) Source #
Instance details Defined in Generics.Kind type SubstRep (M1 i c f :: LoT (t -> k) -> Type) (x :: t) = M1 i c (SubstRep f x)
type Rep1 (M1 i c f :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics type Rep1 (M1 i c f :: k -> Type) = D1 ('MetaData "M1" "GHC.Generics" "base" 'True) (C1 ('MetaCons "M1" 'PrefixI 'True) (S1 ('MetaSel ('Just "unM1") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))
type Rep (M1 i c f p)	Since: base-4.7.0.0
Instance details Defined in GHC.Generics type Rep (M1 i c f p) = D1 ('MetaData "M1" "GHC.Generics" "base" 'True) (C1 ('MetaCons "M1" 'PrefixI 'True) (S1 ('MetaSel ('Just "unM1") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f p))))

newtype Field (t :: Atom d Type) (x :: LoT d) where Source #

Fields: used to represent each of the (visible) arguments to a constructor. Replaces the K1 type from Generics. The type of the field is represented by an Atom from Atom.

instance GenericK [] (a :&&: LoT0) where
  type RepK [] = Field Var0 :*: Field ([] :$: Var0)

Constructors

Field
Fields :: { unField :: Interpret t x } -> Field t x

Instances

Instances details

Interpret (SubstAtom t2 x) xs ~ Interpret t2 (x ':&&: xs) => SubstRep' (Field t2 :: LoT (t1 -> k) -> Type) (x :: t1) (xs :: LoT k) Source #
Instance details Defined in Generics.Kind Associated Types type SubstRep (Field t2) x :: LoT k -> Type Source # Methods substRep :: Field t2 (x ':&&: xs) -> SubstRep (Field t2) x xs unsubstRep :: SubstRep (Field t2) x xs -> Field t2 (x ':&&: xs)
k ~ Interpret t tys => Conv (K1 p k :: Type -> Type) (Field t :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: Field t tys -> K1 p k a Source # toKindGenerics :: K1 p k a -> Field t tys Source #
Monoid (Interpret t x) => Monoid (Field t x) Source #
Instance details Defined in Generics.Kind Methods mempty :: Field t x # mappend :: Field t x -> Field t x -> Field t x # mconcat :: [Field t x] -> Field t x #
Semigroup (Interpret t x) => Semigroup (Field t x) Source #
Instance details Defined in Generics.Kind Methods (<>) :: Field t x -> Field t x -> Field t x # sconcat :: NonEmpty (Field t x) -> Field t x # stimes :: Integral b => b -> Field t x -> Field t x #
Show (Interpret t x) => Show (Field t x) Source #
Instance details Defined in Generics.Kind Methods showsPrec :: Int -> Field t x -> ShowS # show :: Field t x -> String # showList :: [Field t x] -> ShowS #
Eq (Interpret t x) => Eq (Field t x) Source #
Instance details Defined in Generics.Kind Methods (==) :: Field t x -> Field t x -> Bool # (/=) :: Field t x -> Field t x -> Bool #
Ord (Interpret t x) => Ord (Field t x) Source #
Instance details Defined in Generics.Kind Methods compare :: Field t x -> Field t x -> Ordering # (<) :: Field t x -> Field t x -> Bool # (<=) :: Field t x -> Field t x -> Bool # (>) :: Field t x -> Field t x -> Bool # (>=) :: Field t x -> Field t x -> Bool # max :: Field t x -> Field t x -> Field t x # min :: Field t x -> Field t x -> Field t x #
type SubstRep (Field t2 :: LoT (t1 -> k) -> Type) (x :: t1) Source #
Instance details Defined in Generics.Kind type SubstRep (Field t2 :: LoT (t1 -> k) -> Type) (x :: t1) = Field (SubstAtom t2 x)

data ((c :: Atom d Constraint) :=>: (f :: LoT d -> Type)) (x :: LoT d) where Source #

Constraints: used to represent constraints in a constructor. Replaces the (:=>:) type from GHC.Generics.Extra.

data Showable a = Show a => a -> X a

instance GenericK Showable (a :&&: LoT0) where
  type RepK Showable = (Show :$: a) :=>: (Field Var0)

Constructors

SuchThat :: Interpret c x => f x -> (c :=>: f) x

Instances

Instances details

(Interpret (SubstAtom c x) xs => InterpretCons c x xs, Interpret c (x ':&&: xs) => InterpretSubst c x xs, SubstRep' f x xs) => SubstRep' (c :=>: f :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k) Source #
Instance details Defined in Generics.Kind Associated Types type SubstRep (c :=>: f) x :: LoT k -> Type Source # Methods substRep :: (c :=>: f) (x ':&&: xs) -> SubstRep (c :=>: f) x xs unsubstRep :: SubstRep (c :=>: f) x xs -> (c :=>: f) (x ':&&: xs)
(k ~ Interpret t tys, Conv f f' tys) => Conv (k :=>: f) (t :=>: f' :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: (t :=>: f') tys -> (k :=>: f) a Source # toKindGenerics :: (k :=>: f) a -> (t :=>: f') tys Source #
(Interpret c x => Show (f x)) => Show ((c :=>: f) x) Source #
Instance details Defined in Generics.Kind Methods showsPrec :: Int -> (c :=>: f) x -> ShowS # show :: (c :=>: f) x -> String # showList :: [(c :=>: f) x] -> ShowS #
(Interpret c x => Eq (f x)) => Eq ((c :=>: f) x) Source #
Instance details Defined in Generics.Kind Methods (==) :: (c :=>: f) x -> (c :=>: f) x -> Bool # (/=) :: (c :=>: f) x -> (c :=>: f) x -> Bool #
(Interpret c x => Ord (f x)) => Ord ((c :=>: f) x) Source #
Instance details Defined in Generics.Kind Methods compare :: (c :=>: f) x -> (c :=>: f) x -> Ordering # (<) :: (c :=>: f) x -> (c :=>: f) x -> Bool # (<=) :: (c :=>: f) x -> (c :=>: f) x -> Bool # (>) :: (c :=>: f) x -> (c :=>: f) x -> Bool # (>=) :: (c :=>: f) x -> (c :=>: f) x -> Bool # max :: (c :=>: f) x -> (c :=>: f) x -> (c :=>: f) x # min :: (c :=>: f) x -> (c :=>: f) x -> (c :=>: f) x #
type SubstRep (c :=>: f :: LoT (t -> k) -> Type) (x :: t) Source #
Instance details Defined in Generics.Kind type SubstRep (c :=>: f :: LoT (t -> k) -> Type) (x :: t) = SubstAtom c x :=>: SubstRep f x

data Exists k (f :: LoT (k -> d) -> Type) (x :: LoT d) where Source #

Existentials: a representation of the form E f describes a constructor whose inner type is represented by f, and where the type variable at index 0, Var0, is existentially quantified.

data E where
 E :: t -> Exists

instance GenericK E LoT0 where
  type RepK E = Exists Type (Field Var0)

Constructors

Exists
Fields :: forall k (t :: k) d (f :: LoT (k -> d) -> Type) (x :: LoT d). { unExists :: f (t ':&&: x) } -> Exists k f x

Instances

Instances details

(forall (t :: k). Show (f (t ':&&: x))) => Show (Exists k f x) Source #
Instance details Defined in Generics.Kind Methods showsPrec :: Int -> Exists k f x -> ShowS # show :: Exists k f x -> String # showList :: [Exists k f x] -> ShowS #

Atoms for `Field`

data Atom d (k :: TYPE r) where #

Constructors

Var :: forall d k1. TyVar d k1 -> Atom d k1
Kon :: forall k1 d. k1 -> Atom d k1
(:@:) :: forall d k1 k2. Atom d (k1 -> k2) -> Atom d k1 -> Atom d k2
(:&:) :: forall d. Atom d Constraint -> Atom d Constraint -> Atom d Constraint
ForAll :: forall d1 d. Atom (d1 -> d) Type -> Atom d Type
(:=>>:) :: forall d. Atom d Constraint -> Atom d Type -> Atom d Type
Eval :: forall d k1. Atom d (Exp k1) -> Atom d k1

data TyVar d (k :: TYPE r) where #

Constructors

VZ :: forall x xs. TyVar (x -> xs) x
VS :: forall xs k1 x. TyVar xs k1 -> TyVar (x -> xs) k1

type (:$:) (f :: k1 -> k2) (x :: Atom d k1) = ('Kon f :: Atom d (k1 -> k2)) ':@: x #

type (:~:) (a :: Atom d k1) (b :: Atom d k1) = (('Kon ((~) :: k1 -> k1 -> Constraint) :: Atom d (k1 -> k1 -> Constraint)) ':@: a) ':@: b #

type (:~~:) (a :: Atom d k1) (b :: Atom d k2) = (('Kon ((~~) :: k1 -> k2 -> Constraint) :: Atom d (k1 -> k2 -> Constraint)) ':@: a) ':@: b #

type Var0 = 'Var ('VZ :: TyVar (k -> xs) k) #

type Var1 = 'Var ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x -> k -> xs) k) #

type Var2 = 'Var ('VS ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x1 -> k -> xs) k) :: TyVar (x -> x1 -> k -> xs) k) #

type Var3 = 'Var ('VS ('VS ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x2 -> k -> xs) k) :: TyVar (x1 -> x2 -> k -> xs) k) :: TyVar (x -> x1 -> x2 -> k -> xs) k) #

type Var4 = 'Var ('VS ('VS ('VS ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x3 -> k -> xs) k) :: TyVar (x2 -> x3 -> k -> xs) k) :: TyVar (x1 -> x2 -> x3 -> k -> xs) k) :: TyVar (x -> x1 -> x2 -> x3 -> k -> xs) k) #

type Var5 = 'Var ('VS ('VS ('VS ('VS ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x4 -> k -> xs) k) :: TyVar (x3 -> x4 -> k -> xs) k) :: TyVar (x2 -> x3 -> x4 -> k -> xs) k) :: TyVar (x1 -> x2 -> x3 -> x4 -> k -> xs) k) :: TyVar (x -> x1 -> x2 -> x3 -> x4 -> k -> xs) k) #

type Var6 = 'Var ('VS ('VS ('VS ('VS ('VS ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x5 -> k -> xs) k) :: TyVar (x4 -> x5 -> k -> xs) k) :: TyVar (x3 -> x4 -> x5 -> k -> xs) k) :: TyVar (x2 -> x3 -> x4 -> x5 -> k -> xs) k) :: TyVar (x1 -> x2 -> x3 -> x4 -> x5 -> k -> xs) k) :: TyVar (x -> x1 -> x2 -> x3 -> x4 -> x5 -> k -> xs) k) #

type Var7 = 'Var ('VS ('VS ('VS ('VS ('VS ('VS ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x6 -> k -> xs) k) :: TyVar (x5 -> x6 -> k -> xs) k) :: TyVar (x4 -> x5 -> x6 -> k -> xs) k) :: TyVar (x3 -> x4 -> x5 -> x6 -> k -> xs) k) :: TyVar (x2 -> x3 -> x4 -> x5 -> x6 -> k -> xs) k) :: TyVar (x1 -> x2 -> x3 -> x4 -> x5 -> x6 -> k -> xs) k) :: TyVar (x -> x1 -> x2 -> x3 -> x4 -> x5 -> x6 -> k -> xs) k) #

type Var8 = 'Var ('VS ('VS ('VS ('VS ('VS ('VS ('VS ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x7 -> k -> xs) k) :: TyVar (x6 -> x7 -> k -> xs) k) :: TyVar (x5 -> x6 -> x7 -> k -> xs) k) :: TyVar (x4 -> x5 -> x6 -> x7 -> k -> xs) k) :: TyVar (x3 -> x4 -> x5 -> x6 -> x7 -> k -> xs) k) :: TyVar (x2 -> x3 -> x4 -> x5 -> x6 -> x7 -> k -> xs) k) :: TyVar (x1 -> x2 -> x3 -> x4 -> x5 -> x6 -> x7 -> k -> xs) k) :: TyVar (x -> x1 -> x2 -> x3 -> x4 -> x5 -> x6 -> x7 -> k -> xs) k) #

type Var9 = 'Var ('VS ('VS ('VS ('VS ('VS ('VS ('VS ('VS ('VS ('VZ :: TyVar (k -> xs) k) :: TyVar (x8 -> k -> xs) k) :: TyVar (x7 -> x8 -> k -> xs) k) :: TyVar (x6 -> x7 -> x8 -> k -> xs) k) :: TyVar (x5 -> x6 -> x7 -> x8 -> k -> xs) k) :: TyVar (x4 -> x5 -> x6 -> x7 -> x8 -> k -> xs) k) :: TyVar (x3 -> x4 -> x5 -> x6 -> x7 -> x8 -> k -> xs) k) :: TyVar (x2 -> x3 -> x4 -> x5 -> x6 -> x7 -> x8 -> k -> xs) k) :: TyVar (x1 -> x2 -> x3 -> x4 -> x5 -> x6 -> x7 -> x8 -> k -> xs) k) :: TyVar (x -> x1 -> x2 -> x3 -> x4 -> x5 -> x6 -> x7 -> x8 -> k -> xs) k) #

Lists of types

data LoT k where #

Constructors

LoT0 :: LoT Type
(:&&:) :: forall k1 ks. k1 -> LoT ks -> LoT (k1 -> ks)

Instances

Instances details

SubstRep' (U1 :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k) Source #
Instance details Defined in Generics.Kind Associated Types type SubstRep U1 x :: LoT k -> Type Source # Methods substRep :: U1 (x ':&&: xs) -> SubstRep U1 x xs unsubstRep :: SubstRep U1 x xs -> U1 (x ':&&: xs)
(SubstRep' f x xs, SubstRep' g x xs) => SubstRep' (f :*: g :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k) Source #
Instance details Defined in Generics.Kind Associated Types type SubstRep (f :: g) x :: LoT k -> Type Source # Methods substRep :: (f :: g) (x ':&&: xs) -> SubstRep (f :: g) x xs unsubstRep :: SubstRep (f :: g) x xs -> (f :*: g) (x ':&&: xs)
(SubstRep' f x xs, SubstRep' g x xs) => SubstRep' (f :+: g :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k) Source #
Instance details Defined in Generics.Kind Associated Types type SubstRep (f :+: g) x :: LoT k -> Type Source # Methods substRep :: (f :+: g) (x ':&&: xs) -> SubstRep (f :+: g) x xs unsubstRep :: SubstRep (f :+: g) x xs -> (f :+: g) (x ':&&: xs)
SubstRep' f x xs => SubstRep' (M1 i c f :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k) Source #
Instance details Defined in Generics.Kind Associated Types type SubstRep (M1 i c f) x :: LoT k -> Type Source # Methods substRep :: M1 i c f (x ':&&: xs) -> SubstRep (M1 i c f) x xs unsubstRep :: SubstRep (M1 i c f) x xs -> M1 i c f (x ':&&: xs)
Conv (U1 :: Type -> Type) (U1 :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: U1 tys -> U1 a Source # toKindGenerics :: U1 a -> U1 tys Source #
(Conv f f' tys, Conv g g' tys) => Conv (f :: g) (f' :: g' :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: (f' :: g') tys -> (f :: g) a Source # toKindGenerics :: (f :: g) a -> (f' :: g') tys Source #
(Conv f f' tys, Conv g g' tys) => Conv (f :+: g) (f' :+: g' :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: (f' :+: g') tys -> (f :+: g) a Source # toKindGenerics :: (f :+: g) a -> (f' :+: g') tys Source #
Conv f f' tys => Conv (M1 i c f) (M1 i c f' :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: M1 i c f' tys -> M1 i c f a Source # toKindGenerics :: M1 i c f a -> M1 i c f' tys Source #
type SubstRep (U1 :: LoT (t -> k) -> Type) (x :: t) Source #
Instance details Defined in Generics.Kind type SubstRep (U1 :: LoT (t -> k) -> Type) (x :: t) = U1 :: LoT k -> Type
type SubstRep (f :*: g :: LoT (t -> k) -> Type) (x :: t) Source #
Instance details Defined in Generics.Kind type SubstRep (f :: g :: LoT (t -> k) -> Type) (x :: t) = SubstRep f x :: SubstRep g x
type SubstRep (f :+: g :: LoT (t -> k) -> Type) (x :: t) Source #
Instance details Defined in Generics.Kind type SubstRep (f :+: g :: LoT (t -> k) -> Type) (x :: t) = SubstRep f x :+: SubstRep g x
type SubstRep (M1 i c f :: LoT (t -> k) -> Type) (x :: t) Source #
Instance details Defined in Generics.Kind type SubstRep (M1 i c f :: LoT (t -> k) -> Type) (x :: t) = M1 i c (SubstRep f x)

type family (f :: k) :@@: (tys :: LoT k) where ... #

Equations

(f :: Type) :@@: (_1 :: LoT Type) = f
(f :: k -> k') :@@: (as :: LoT (k -> k')) = f (HeadLoT as) :@@: TailLoT as

type LoT1 (a :: k) = a ':&&: 'LoT0 #

type LoT2 (a :: k) (b :: k1) = a ':&&: (b ':&&: 'LoT0) #

data TyEnv where #

Constructors

TyEnv :: forall k. k -> LoT k -> TyEnv

Generic type classes

class GenericK (f :: k) where Source #

Representable types of any kind. Examples:

instance GenericK Int
instance GenericK []
instance GenericK Either
instance GenericK (Either a)
instance GenericK (Either a b)

Minimal complete definition

Nothing

Associated Types

type RepK f :: LoT k -> Type Source #

Methods

fromK :: (f :@@: x) -> RepK f x Source #

Convert the data type to its representation.

default fromK :: (Generic (f :@@: x), Conv (Rep (f :@@: x)) (RepK f) x) => (f :@@: x) -> RepK f x Source #

toK :: RepK f x -> f :@@: x Source #

Convert from a representation to its corresponding data type.

default toK :: (Generic (f :@@: x), Conv (Rep (f :@@: x)) (RepK f) x) => RepK f x -> f :@@: x Source #

Instances

Instances details

GenericK Ranky Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK Ranky :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (Ranky :@@: x) -> RepK Ranky x Source # toK :: forall (x :: LoT k). RepK Ranky x -> Ranky :@@: x Source #
GenericK (HappyFamily (Maybe a) :: Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK (HappyFamily (Maybe a)) :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (HappyFamily (Maybe a) :@@: x) -> RepK (HappyFamily (Maybe a)) x Source # toK :: forall (x :: LoT k). RepK (HappyFamily (Maybe a)) x -> HappyFamily (Maybe a) :@@: x Source #
GenericK (HappyFamily [a] :: Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK (HappyFamily [a]) :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (HappyFamily [a] :@@: x) -> RepK (HappyFamily [a]) x Source # toK :: forall (x :: LoT k). RepK (HappyFamily [a]) x -> HappyFamily [a] :@@: x Source #
GenericK (Tree a :: Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK (Tree a) :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (Tree a :@@: x) -> RepK (Tree a) x Source # toK :: forall (x :: LoT k). RepK (Tree a) x -> Tree a :@@: x Source #
GenericK (WeirdTreeR a :: Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK (WeirdTreeR a) :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (WeirdTreeR a :@@: x) -> RepK (WeirdTreeR a) x Source # toK :: forall (x :: LoT k). RepK (WeirdTreeR a) x -> WeirdTreeR a :@@: x Source #
GenericK (Maybe a :: Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK (Maybe a) :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (Maybe a :@@: x) -> RepK (Maybe a) x Source # toK :: forall (x :: LoT k). RepK (Maybe a) x -> Maybe a :@@: x Source #
GenericK ([a] :: Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK [a] :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). ([a] :@@: x) -> RepK [a] x Source # toK :: forall (x :: LoT k). RepK [a] x -> [a] :@@: x Source #
GenericK (Either a b :: Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK (Either a b) :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (Either a b :@@: x) -> RepK (Either a b) x Source # toK :: forall (x :: LoT k). RepK (Either a b) x -> Either a b :@@: x Source #
GenericK (SimpleIndex a b :: Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK (SimpleIndex a b) :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (SimpleIndex a b :@@: x) -> RepK (SimpleIndex a b) x Source # toK :: forall (x :: LoT k). RepK (SimpleIndex a b) x -> SimpleIndex a b :@@: x Source #
GenericK (Hkd f a :: Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK (Hkd f a) :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (Hkd f a :@@: x) -> RepK (Hkd f a) x Source # toK :: forall (x :: LoT k). RepK (Hkd f a) x -> Hkd f a :@@: x Source #
GenericK (TTY m a :: Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK (TTY m a) :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (TTY m a :@@: x) -> RepK (TTY m a) x Source # toK :: forall (x :: LoT k). RepK (TTY m a) x -> TTY m a :@@: x Source #
GenericK Either Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK Either :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (Either :@@: x) -> RepK Either x Source # toK :: forall (x :: LoT k). RepK Either x -> Either :@@: x Source #
GenericK SimpleIndex Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK SimpleIndex :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (SimpleIndex :@@: x) -> RepK SimpleIndex x Source # toK :: forall (x :: LoT k). RepK SimpleIndex x -> SimpleIndex :@@: x Source #
GenericK HappyFamily Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK HappyFamily :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (HappyFamily :@@: x) -> RepK HappyFamily x Source # toK :: forall (x :: LoT k). RepK HappyFamily x -> HappyFamily :@@: x Source #
GenericK Ranky2 Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK Ranky2 :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (Ranky2 :@@: x) -> RepK Ranky2 x Source # toK :: forall (x :: LoT k). RepK Ranky2 x -> Ranky2 :@@: x Source #
GenericK Shower Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK Shower :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (Shower :@@: x) -> RepK Shower x Source # toK :: forall (x :: LoT k). RepK Shower x -> Shower :@@: x Source #
GenericK Tree Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK Tree :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (Tree :@@: x) -> RepK Tree x Source # toK :: forall (x :: LoT k). RepK Tree x -> Tree :@@: x Source #
GenericK WeirdTree Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK WeirdTree :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (WeirdTree :@@: x) -> RepK WeirdTree x Source # toK :: forall (x :: LoT k). RepK WeirdTree x -> WeirdTree :@@: x Source #
GenericK WeirdTreeR Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK WeirdTreeR :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (WeirdTreeR :@@: x) -> RepK WeirdTreeR x Source # toK :: forall (x :: LoT k). RepK WeirdTreeR x -> WeirdTreeR :@@: x Source #
GenericK Maybe Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK Maybe :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (Maybe :@@: x) -> RepK Maybe x Source # toK :: forall (x :: LoT k). RepK Maybe x -> Maybe :@@: x Source #
GenericK [] Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK [] :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). ([] :@@: x) -> RepK [] x Source # toK :: forall (x :: LoT k). RepK [] x -> [] :@@: x Source #
GenericK (Hkd :: (k -> Exp Type) -> k -> Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK Hkd :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k0). (Hkd :@@: x) -> RepK Hkd x Source # toK :: forall (x :: LoT k0). RepK Hkd x -> Hkd :@@: x Source #
GenericK (P' :: Type -> k -> Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK P' :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k0). (P' :@@: x) -> RepK P' x Source # toK :: forall (x :: LoT k0). RepK P' x -> P' :@@: x Source #
GenericK (Either a :: Type -> Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK (Either a) :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (Either a :@@: x) -> RepK (Either a) x Source # toK :: forall (x :: LoT k). RepK (Either a) x -> Either a :@@: x Source #
GenericK (SimpleIndex a :: Type -> Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK (SimpleIndex a) :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k). (SimpleIndex a :@@: x) -> RepK (SimpleIndex a) x Source # toK :: forall (x :: LoT k). RepK (SimpleIndex a) x -> SimpleIndex a :@@: x Source #
GenericK (P k :: k -> Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK (P k) :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k0). (P k :@@: x) -> RepK (P k) x Source # toK :: forall (x :: LoT k0). RepK (P k) x -> P k :@@: x Source #
GenericK (T :: k -> Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK T :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k0). (T :@@: x) -> RepK T x Source # toK :: forall (x :: LoT k0). RepK T x -> T :@@: x Source #
GenericK (Hkd f :: k -> Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK (Hkd f) :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k0). (Hkd f :@@: x) -> RepK (Hkd f) x Source # toK :: forall (x :: LoT k0). RepK (Hkd f) x -> Hkd f :@@: x Source #
GenericK (P' j :: k -> Type) Source #
Instance details Defined in Generics.Kind.Examples Associated Types type RepK (P' j) :: LoT k -> Type Source # Methods fromK :: forall (x :: LoT k0). (P' j :@@: x) -> RepK (P' j) x Source # toK :: forall (x :: LoT k0). RepK (P' j) x -> P' j :@@: x Source #

type GenericF t f x = (GenericK f, x ~ SplitF t f, t ~ (f :@@: x)) Source #

fromF :: forall f t x. GenericF t f x => t -> RepK f x Source #

toF :: forall f t x. GenericF t f x => RepK f x -> t Source #

type GenericN n t f x = (GenericK f, 'TyEnv f x ~ SplitN n t, t ~ (f :@@: x)) Source #

fromN :: forall n t f x. GenericN n t f x => t -> RepK f x Source #

toN :: forall n t f x. GenericN n t f x => RepK f x -> t Source #

Getting more instances almost for free

fromRepK :: forall f x xs. (GenericK f, SubstRep' (RepK f) x xs) => (f x :@@: xs) -> SubstRep (RepK f) x xs Source #

toRepK :: forall f x xs. (GenericK f, SubstRep' (RepK f) x xs) => SubstRep (RepK f) x xs -> f x :@@: xs Source #

type family SubstRep f x :: LoT k -> Type Source #

Instances

Instances details

type SubstRep (U1 :: LoT (t -> k) -> Type) (x :: t) Source #
Instance details Defined in Generics.Kind type SubstRep (U1 :: LoT (t -> k) -> Type) (x :: t) = U1 :: LoT k -> Type
type SubstRep (Field t2 :: LoT (t1 -> k) -> Type) (x :: t1) Source #
Instance details Defined in Generics.Kind type SubstRep (Field t2 :: LoT (t1 -> k) -> Type) (x :: t1) = Field (SubstAtom t2 x)
type SubstRep (f :*: g :: LoT (t -> k) -> Type) (x :: t) Source #
Instance details Defined in Generics.Kind type SubstRep (f :: g :: LoT (t -> k) -> Type) (x :: t) = SubstRep f x :: SubstRep g x
type SubstRep (f :+: g :: LoT (t -> k) -> Type) (x :: t) Source #
Instance details Defined in Generics.Kind type SubstRep (f :+: g :: LoT (t -> k) -> Type) (x :: t) = SubstRep f x :+: SubstRep g x
type SubstRep (c :=>: f :: LoT (t -> k) -> Type) (x :: t) Source #
Instance details Defined in Generics.Kind type SubstRep (c :=>: f :: LoT (t -> k) -> Type) (x :: t) = SubstAtom c x :=>: SubstRep f x
type SubstRep (M1 i c f :: LoT (t -> k) -> Type) (x :: t) Source #
Instance details Defined in Generics.Kind type SubstRep (M1 i c f :: LoT (t -> k) -> Type) (x :: t) = M1 i c (SubstRep f x)

class SubstRep' (f :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k) Source #

Minimal complete definition

substRep, unsubstRep

Instances

Instances details

SubstRep' (U1 :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k) Source #
Instance details Defined in Generics.Kind Associated Types type SubstRep U1 x :: LoT k -> Type Source # Methods substRep :: U1 (x ':&&: xs) -> SubstRep U1 x xs unsubstRep :: SubstRep U1 x xs -> U1 (x ':&&: xs)
Interpret (SubstAtom t2 x) xs ~ Interpret t2 (x ':&&: xs) => SubstRep' (Field t2 :: LoT (t1 -> k) -> Type) (x :: t1) (xs :: LoT k) Source #
Instance details Defined in Generics.Kind Associated Types type SubstRep (Field t2) x :: LoT k -> Type Source # Methods substRep :: Field t2 (x ':&&: xs) -> SubstRep (Field t2) x xs unsubstRep :: SubstRep (Field t2) x xs -> Field t2 (x ':&&: xs)
(SubstRep' f x xs, SubstRep' g x xs) => SubstRep' (f :*: g :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k) Source #
Instance details Defined in Generics.Kind Associated Types type SubstRep (f :: g) x :: LoT k -> Type Source # Methods substRep :: (f :: g) (x ':&&: xs) -> SubstRep (f :: g) x xs unsubstRep :: SubstRep (f :: g) x xs -> (f :*: g) (x ':&&: xs)
(SubstRep' f x xs, SubstRep' g x xs) => SubstRep' (f :+: g :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k) Source #
Instance details Defined in Generics.Kind Associated Types type SubstRep (f :+: g) x :: LoT k -> Type Source # Methods substRep :: (f :+: g) (x ':&&: xs) -> SubstRep (f :+: g) x xs unsubstRep :: SubstRep (f :+: g) x xs -> (f :+: g) (x ':&&: xs)
(Interpret (SubstAtom c x) xs => InterpretCons c x xs, Interpret c (x ':&&: xs) => InterpretSubst c x xs, SubstRep' f x xs) => SubstRep' (c :=>: f :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k) Source #
Instance details Defined in Generics.Kind Associated Types type SubstRep (c :=>: f) x :: LoT k -> Type Source # Methods substRep :: (c :=>: f) (x ':&&: xs) -> SubstRep (c :=>: f) x xs unsubstRep :: SubstRep (c :=>: f) x xs -> (c :=>: f) (x ':&&: xs)
SubstRep' f x xs => SubstRep' (M1 i c f :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k) Source #
Instance details Defined in Generics.Kind Associated Types type SubstRep (M1 i c f) x :: LoT k -> Type Source # Methods substRep :: M1 i c f (x ':&&: xs) -> SubstRep (M1 i c f) x xs unsubstRep :: SubstRep (M1 i c f) x xs -> M1 i c f (x ':&&: xs)

type family SubstAtom (f :: Atom (t -> k) d) (x :: t) :: Atom k d where ... Source #

Equations

SubstAtom ('Var 'VZ) x = 'Kon x
SubstAtom ('Var ('VS v)) x = 'Var v
SubstAtom ('Kon t) x = 'Kon t
SubstAtom (t1 ':@: t2) x = SubstAtom t1 x ':@: SubstAtom t2 x
SubstAtom (t1 ':&: t2) x = SubstAtom t1 x ':&: SubstAtom t2 x

Bridging with GHC.Generics

class Conv (gg :: Type -> Type) (kg :: LoT d -> Type) (tys :: LoT d) where Source #

Bridges a representation of a data type using the combinators in GHC.Generics with a representation using this module. You are never expected to manipulate this type class directly, it is part of the deriving mechanism for GenericK.

Methods

toGhcGenerics :: kg tys -> gg a Source #

toKindGenerics :: gg a -> kg tys Source #

Instances

Instances details

Conv (U1 :: Type -> Type) (U1 :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: U1 tys -> U1 a Source # toKindGenerics :: U1 a -> U1 tys Source #
k ~ Interpret t tys => Conv (K1 p k :: Type -> Type) (Field t :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: Field t tys -> K1 p k a Source # toKindGenerics :: K1 p k a -> Field t tys Source #
(Conv f f' tys, Conv g g' tys) => Conv (f :: g) (f' :: g' :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: (f' :: g') tys -> (f :: g) a Source # toKindGenerics :: (f :: g) a -> (f' :: g') tys Source #
(Conv f f' tys, Conv g g' tys) => Conv (f :+: g) (f' :+: g' :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: (f' :+: g') tys -> (f :+: g) a Source # toKindGenerics :: (f :+: g) a -> (f' :+: g') tys Source #
(k ~ Interpret t tys, Conv f f' tys) => Conv (k :=>: f) (t :=>: f' :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: (t :=>: f') tys -> (k :=>: f) a Source # toKindGenerics :: (k :=>: f) a -> (t :=>: f') tys Source #
Conv f f' tys => Conv (M1 i c f) (f' :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: f' tys -> M1 i c f a Source # toKindGenerics :: M1 i c f a -> f' tys Source #
Conv f f' tys => Conv (M1 i c f) (M1 i c f' :: LoT d -> Type) (tys :: LoT d) Source #
Instance details Defined in Generics.Kind Methods toGhcGenerics :: M1 i c f' tys -> M1 i c f a Source # toKindGenerics :: M1 i c f a -> M1 i c f' tys Source #

Re-exported from `Atom`

Interpretation of atoms

type family Interpret (t :: Atom d k) (tys :: LoT d) :: k where ... #

Equations

Interpret ('Var v :: Atom d k) (tys :: LoT d) = InterpretVar v tys
Interpret ('Kon t :: Atom d k) (tys :: LoT d) = t
Interpret (f ':@: x :: Atom d k2) (tys :: LoT d) = Interpret f tys (Interpret x tys)
Interpret (c ':&: d2 :: Atom d1 Constraint) (tys :: LoT d1) = (Interpret c tys, Interpret d2 tys)
Interpret ('ForAll f :: Atom d Type) (tys :: LoT d) = ForAllI f tys
Interpret (c ':=>>: f :: Atom d Type) (tys :: LoT d) = SuchThatI c f tys
Interpret ('Eval f :: Atom d a) (tys :: LoT d) = Eval (Interpret f tys)

type family InterpretVar (t :: TyVar d k) (tys :: LoT d) :: k where ... #

Equations

InterpretVar ('VZ :: TyVar (k -> k') k) (tys :: LoT (k -> k')) = HeadLoT tys
InterpretVar ('VS v :: TyVar (k2 -> k') k1) (tys :: LoT (k2 -> k')) = InterpretVar v (TailLoT tys)

type family Satisfies (cs :: [Atom d Constraint]) (tys :: LoT d) where ... #

Equations

Satisfies ('[] :: [Atom d Constraint]) (tys :: LoT d) = ()
Satisfies (c ': cs :: [Atom d Constraint]) (tys :: LoT d) = (Interpret c tys, Satisfies cs tys)

type family ContainsTyVar (v :: TyVar d k) (t :: Atom d p) :: Bool where ... #

Equations

ContainsTyVar (v :: TyVar d p) ('Var v :: Atom d p) = 'True
ContainsTyVar (v :: TyVar d k) ('Var w :: Atom d p) = 'False
ContainsTyVar (v :: TyVar d k) ('Kon t :: Atom d p) = 'False
ContainsTyVar (v :: TyVar d k) (f ':@: x :: Atom d p2) = Or (ContainsTyVar v f) (ContainsTyVar v x)
ContainsTyVar (v :: TyVar d k) (x ':&: y :: Atom d Constraint) = Or (ContainsTyVar v x) (ContainsTyVar v y)
ContainsTyVar (v :: TyVar d k) (c ':=>>: f :: Atom d Type) = Or (ContainsTyVar v c) (ContainsTyVar v f)
ContainsTyVar (v :: TyVar xs k) ('ForAll f :: Atom xs Type) = ContainsTyVar ('VS v :: TyVar (x -> xs) k) f

Auxiliary data types for interpretation

newtype ForAllI (f :: Atom (d1 -> d) Type) (tys :: LoT d) where #

Constructors

ForAllI :: forall {d1} {d} (f :: Atom (d1 -> d) Type) (tys :: LoT d). (forall (t :: d1). Interpret f (t ':&&: tys)) -> ForAllI f tys

newtype SuchThatI (c :: Atom d Constraint) (f :: Atom d Type) (tys :: LoT d) where #

Constructors

SuchThatI
Fields :: forall {d} (c :: Atom d Constraint) (tys :: LoT d) (f :: Atom d Type). { unSuchThatI :: Interpret c tys => Interpret f tys } -> SuchThatI c f tys

newtype WrappedI (f :: Atom d Type) (tys :: LoT d) #

Constructors

WrapI
Fields unwrapI :: Interpret f tys

toWrappedI :: forall {d1} {ks} (f :: Atom (d1 -> ks) Type) (tys :: LoT ks) (t :: d1). ForAllI f tys -> WrappedI f (t ':&&: tys) #

fromWrappedI :: forall {d1} {d} (f :: Atom (d1 -> d) Type) (tys :: LoT d). (forall (t :: d1). WrappedI f (t ':&&: tys)) -> ForAllI f tys #

Generic representation types

Instances

Instances

Instances

Instances

Instances

Instances

Instances

Instances

Atoms for Field

Lists of types

Instances

Generic type classes

Instances

Getting more instances almost for free

Instances

Instances

Bridging with GHC.Generics

Instances

Re-exported from Atom

Interpretation of atoms

Auxiliary data types for interpretation

Atoms for `Field`

Re-exported from `Atom`