Generics.Kind

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

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

(SubstRep' f x xs, SubstRep' g x xs) => SubstRep' (f :+: g :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k)

Defined in Generics.Kind

Associated Types

type SubstRep (f :+: g) x :: LoT k -> Type

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)

Since: base-4.9.0.0

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)

Defined in Generics.Kind

Methods

toGhcGenerics :: (f' :+: g') tys -> (f :+: g) a

toKindGenerics :: (f :+: g) a -> (f' :+: g') tys

(Functor f, Functor g) => Functor (f :+: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b

(<$) :: a -> (f :+: g) b -> (f :+: g) a

(Foldable f, Foldable g) => Foldable (f :+: g)

Since: base-4.9.0.0

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

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)

(Eq (f p), Eq (g p)) => Eq ((f :+: g) p)

Since: base-4.7.0.0

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

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

(Read (f p), Read (g p)) => Read ((f :+: g) p)

Since: base-4.7.0.0

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

Defined in GHC.Generics

Methods

showsPrec :: Int -> (f :+: g) p -> ShowS

show :: (f :+: g) p -> String

showList :: [(f :+: g) p] -> ShowS

Generic ((f :+: g) p)

Since: base-4.7.0.0

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

type SubstRep (f :+: g :: LoT (t -> k) -> Type) (x :: t)

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)

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)

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

(SubstRep' f x xs, SubstRep' g x xs) => SubstRep' (f :*: g :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k)

Defined in Generics.Kind

Associated Types

type SubstRep (f :*: g) x :: LoT k -> Type

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)

Since: base-4.9.0.0

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)

Defined in Generics.Kind

Methods

toGhcGenerics :: (f' :*: g') tys -> (f :*: g) a

toKindGenerics :: (f :*: g) a -> (f' :*: g') tys

(Monad f, Monad g) => Monad (f :*: g)

Since: base-4.9.0.0

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

(Functor f, Functor g) => Functor (f :*: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> (f :*: g) a -> (f :*: g) b

(<$) :: a -> (f :*: g) b -> (f :*: g) a

(Applicative f, Applicative g) => Applicative (f :*: g)

Since: base-4.9.0.0

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

(Foldable f, Foldable g) => Foldable (f :*: g)

Since: base-4.9.0.0

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

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

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]

(MonadPlus f, MonadPlus g) => MonadPlus (f :*: g)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

mzero :: (f :*: g) a

mplus :: (f :*: g) a -> (f :*: g) a -> (f :*: g) a

(Eq (f p), Eq (g p)) => Eq ((f :*: g) p)

Since: base-4.7.0.0

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

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

(Read (f p), Read (g p)) => Read ((f :*: g) p)

Since: base-4.7.0.0

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

Defined in GHC.Generics

Methods

showsPrec :: Int -> (f :*: g) p -> ShowS

show :: (f :*: g) p -> String

showList :: [(f :*: g) p] -> ShowS

Generic ((f :*: g) p)

Since: base-4.7.0.0

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

(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p)

Since: base-4.12.0.0

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

(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p)

Since: base-4.12.0.0

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

type SubstRep (f :*: g :: LoT (t -> k) -> Type) (x :: t)

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)

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)

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

Generic1 (V1 :: k -> Type)

Since: base-4.9.0.0

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

Functor (V1 :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> V1 a -> V1 b

(<$) :: a -> V1 b -> V1 a

Foldable (V1 :: Type -> Type)

Since: base-4.9.0.0

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

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)

Eq (V1 p)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

(==) :: V1 p -> V1 p -> Bool

(/=) :: V1 p -> V1 p -> Bool

Ord (V1 p)

Since: base-4.9.0.0

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

Read (V1 p)

Since: base-4.9.0.0

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

Defined in GHC.Generics

Methods

showsPrec :: Int -> V1 p -> ShowS

show :: V1 p -> String

showList :: [V1 p] -> ShowS

Generic (V1 p)

Since: base-4.9.0.0

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

Semigroup (V1 p)

Since: base-4.12.0.0

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

type Rep1 (V1 :: k -> Type)

Defined in GHC.Generics

type Rep1 (V1 :: k -> Type) = D1 ('MetaData "V1" "GHC.Generics" "base" 'False) (V1 :: k -> Type)

type Rep (V1 p)

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

SubstRep' (U1 :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k)

Defined in Generics.Kind

Associated Types

type SubstRep U1 x :: LoT k -> Type

Methods

substRep :: U1 (x :&&: xs) -> SubstRep U1 x xs

unsubstRep :: SubstRep U1 x xs -> U1 (x :&&: xs)

Generic1 (U1 :: k -> Type)

Since: base-4.9.0.0

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)

Defined in Generics.Kind

Methods

toGhcGenerics :: U1 tys -> U1 a

toKindGenerics :: U1 a -> U1 tys

Monad (U1 :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

(>>=) :: U1 a -> (a -> U1 b) -> U1 b

(>>) :: U1 a -> U1 b -> U1 b

return :: a -> U1 a

Functor (U1 :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

fmap :: (a -> b) -> U1 a -> U1 b

(<$) :: a -> U1 b -> U1 a

Applicative (U1 :: Type -> Type)

Since: base-4.9.0.0

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

Foldable (U1 :: Type -> Type)

Since: base-4.9.0.0

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

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

Defined in GHC.Generics

Methods

empty :: U1 a

(<|>) :: U1 a -> U1 a -> U1 a

some :: U1 a -> U1 [a]

many :: U1 a -> U1 [a]

MonadPlus (U1 :: Type -> Type)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

mzero :: U1 a

mplus :: U1 a -> U1 a -> U1 a

Eq (U1 p)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

(==) :: U1 p -> U1 p -> Bool

(/=) :: U1 p -> U1 p -> Bool

Ord (U1 p)

Since: base-4.7.0.0

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

Read (U1 p)

Since: base-4.9.0.0

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

Defined in GHC.Generics

Methods

showsPrec :: Int -> U1 p -> ShowS

show :: U1 p -> String

showList :: [U1 p] -> ShowS

Generic (U1 p)

Since: base-4.7.0.0

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

Semigroup (U1 p)

Since: base-4.12.0.0

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

Monoid (U1 p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

mempty :: U1 p

mappend :: U1 p -> U1 p -> U1 p

mconcat :: [U1 p] -> U1 p

type SubstRep (U1 :: LoT (t -> k) -> Type) (x :: t)

Defined in Generics.Kind

type SubstRep (U1 :: LoT (t -> k) -> Type) (x :: t) = U1 :: LoT k -> Type

type Rep1 (U1 :: k -> Type)

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)

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

SubstRep' f x xs => SubstRep' (M1 i c f :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k)

Defined in Generics.Kind

Associated Types

type SubstRep (M1 i c f) x :: LoT k -> Type

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)

Since: base-4.9.0.0

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)

Defined in Generics.Kind

Methods

toGhcGenerics :: f' tys -> M1 i c f a

toKindGenerics :: M1 i c f a -> f' tys

Conv f f' tys => Conv (M1 i c f) (M1 i c f' :: LoT d -> Type) (tys :: LoT d)

Defined in Generics.Kind

Methods

toGhcGenerics :: M1 i c f' tys -> M1 i c f a

toKindGenerics :: M1 i c f a -> M1 i c f' tys

Monad f => Monad (M1 i c f)

Since: base-4.9.0.0

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

Functor f => Functor (M1 i c f)

Since: base-4.9.0.0

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

Applicative f => Applicative (M1 i c f)

Since: base-4.9.0.0

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

Foldable f => Foldable (M1 i c f)

Since: base-4.9.0.0

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

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

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]

MonadPlus f => MonadPlus (M1 i c f)

Since: base-4.9.0.0

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

Eq (f p) => Eq (M1 i c f p)

Since: base-4.7.0.0

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

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

Read (f p) => Read (M1 i c f p)

Since: base-4.7.0.0

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

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

Generic (M1 i c f p)

Since: base-4.7.0.0

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

Semigroup (f p) => Semigroup (M1 i c f p)

Since: base-4.12.0.0

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

Monoid (f p) => Monoid (M1 i c f p)

Since: base-4.12.0.0

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

type SubstRep (M1 i c f :: LoT (t -> k) -> Type) (x :: t)

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)

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)

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

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

Interpret (SubstAtom t2 x) xs ~ Interpret t2 (x :&&: xs) => SubstRep' (Field t2 :: LoT (t1 -> k) -> Type) (x :: t1) (xs :: LoT k)

Defined in Generics.Kind

Associated Types

type SubstRep (Field t2) x :: LoT k -> Type

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)

Defined in Generics.Kind

Methods

toGhcGenerics :: Field t tys -> K1 p k a

toKindGenerics :: K1 p k a -> Field t tys

Show (Interpret t x) => Show (Field t x)

Defined in Generics.Kind

Methods

showsPrec :: Int -> Field t x -> ShowS

show :: Field t x -> String

showList :: [Field t x] -> ShowS

type SubstRep (Field t2 :: LoT (t1 -> k) -> Type) (x :: t1)

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

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

(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)

Defined in Generics.Kind

Associated Types

type SubstRep (c :=>: f) x :: LoT k -> Type

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)

Defined in Generics.Kind

Methods

toGhcGenerics :: (t :=>: f') tys -> (k :=>: f) a

toKindGenerics :: (k :=>: f) a -> (t :=>: f') tys

(Interpret c x => Show (f x)) => Show ((c :=>: f) x)

Defined in Generics.Kind

Methods

showsPrec :: Int -> (c :=>: f) x -> ShowS

show :: (c :=>: f) x -> String

showList :: [(c :=>: f) x] -> ShowS

type SubstRep (c :=>: f :: LoT (t -> k) -> Type) (x :: t)

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

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

(forall (t :: k). Show (f (t :&&: x))) => Show (Exists k f x)

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

Shape of a type, possibly with type variables.

>>> :kind Kon [] :@: Var0 -- the type [a] for unknown a
Kon [] :@: Var0 :: Atom (* -> xs) *

Constructors

Var :: forall d k1. TyVar d k1 -> Atom d k1

Represents a type variable.

Kon :: forall k1 d. k1 -> Atom d k1

Represents a constant type, like Int.

(:@:) :: forall d k1 k2. Atom d (k1 -> k2) -> Atom d k1 -> Atom d k2

Represents type application.

(:&:) :: forall d. Atom d Constraint -> Atom d Constraint -> Atom d Constraint infixr 5

Represents the conjunction of two constraints.

ForAll :: forall d1 d. Atom (d1 -> d) Type -> Atom d Type

Represents universal quantification.

(:=>>:) :: forall d. Atom d Constraint -> Atom d Type -> Atom d Type infixr 5

Represents constraint requirement, the "thick arrow" =>.

data TyVar d (k :: TYPE r) where

Well-scoped de Bruijn representation of type variables. TyVar d represents all the possible type variables which can refer to the holes in kind d.

We recommend using the aliases Var0, Var1, ... instead of the constructors, for further clarity.

Constructors

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

First hole in d.

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

Successor hole, increases the hole reference by 1.

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

Represents an applied constructor. Instead of Kon [] :: Var0$ you can write @[] :$: Var0$.

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

Represents (homogeneous) type equality.

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

Represents heterogeneous type equality.

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

LoT k represents a list of types which can be applied to a data type of kind k.

Constructors

LoT0 :: LoT Type

Empty list of types.

(:&&:) :: forall k1 ks. k1 -> LoT ks -> LoT (k1 -> ks) infixr 5

Cons a type with a list of types.

Instances

SubstRep' (U1 :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k)

Defined in Generics.Kind

Associated Types

type SubstRep U1 x :: LoT k -> Type

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)

Defined in Generics.Kind

Associated Types

type SubstRep (f :*: g) x :: LoT k -> Type

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)

Defined in Generics.Kind

Associated Types

type SubstRep (f :+: g) x :: LoT k -> Type

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)

Defined in Generics.Kind

Associated Types

type SubstRep (M1 i c f) x :: LoT k -> Type

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)

Defined in Generics.Kind

Methods

toGhcGenerics :: U1 tys -> U1 a

toKindGenerics :: U1 a -> U1 tys

(Conv f f' tys, Conv g g' tys) => Conv (f :*: g) (f' :*: g' :: LoT d -> Type) (tys :: LoT d)

Defined in Generics.Kind

Methods

toGhcGenerics :: (f' :*: g') tys -> (f :*: g) a

toKindGenerics :: (f :*: g) a -> (f' :*: g') tys

(Conv f f' tys, Conv g g' tys) => Conv (f :+: g) (f' :+: g' :: LoT d -> Type) (tys :: LoT d)

Defined in Generics.Kind

Methods

toGhcGenerics :: (f' :+: g') tys -> (f :+: g) a

toKindGenerics :: (f :+: g) a -> (f' :+: g') tys

Conv f f' tys => Conv (M1 i c f) (M1 i c f' :: LoT d -> Type) (tys :: LoT d)

Defined in Generics.Kind

Methods

toGhcGenerics :: M1 i c f' tys -> M1 i c f a

toKindGenerics :: M1 i c f a -> M1 i c f' tys

type SubstRep (U1 :: LoT (t -> k) -> Type) (x :: t)

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)

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)

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)

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 ...

Apply a list of types to a type constructor.

>>> :kind! Either :@@: (Int :&&: Bool :&&: LoT0)
Either Int Bool :: Type

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

List of types with a single element.

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

List of types with two elements.

data TyEnv where

A type constructor and a list of types that can be applied to it.

Constructors

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

Generic type classes

class GenericK (f :: k) where

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

Methods

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

Convert the data type to its representation.

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

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

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

Instances

GenericK (SimpleIndex a b :: Type)

Defined in Generics.Kind.Examples

Associated Types

type RepK (SimpleIndex a b) :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (SimpleIndex a b :@@: x) -> RepK (SimpleIndex a b) x

toK :: forall (x :: LoT k). RepK (SimpleIndex a b) x -> SimpleIndex a b :@@: x

GenericK Ranky

Defined in Generics.Kind.Examples

Associated Types

type RepK Ranky :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (Ranky :@@: x) -> RepK Ranky x

toK :: forall (x :: LoT k). RepK Ranky x -> Ranky :@@: x

GenericK ([a] :: Type)

Defined in Generics.Kind.Examples

Associated Types

type RepK [a] :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). ([a] :@@: x) -> RepK [a] x

toK :: forall (x :: LoT k). RepK [a] x -> [a] :@@: x

GenericK (Maybe a :: Type)

Defined in Generics.Kind.Examples

Associated Types

type RepK (Maybe a) :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (Maybe a :@@: x) -> RepK (Maybe a) x

toK :: forall (x :: LoT k). RepK (Maybe a) x -> Maybe a :@@: x

GenericK (WeirdTreeR a :: Type)

Defined in Generics.Kind.Examples

Associated Types

type RepK (WeirdTreeR a) :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (WeirdTreeR a :@@: x) -> RepK (WeirdTreeR a) x

toK :: forall (x :: LoT k). RepK (WeirdTreeR a) x -> WeirdTreeR a :@@: x

GenericK (HappyFamily [a] :: Type)

Defined in Generics.Kind.Examples

Associated Types

type RepK (HappyFamily [a]) :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (HappyFamily [a] :@@: x) -> RepK (HappyFamily [a]) x

toK :: forall (x :: LoT k). RepK (HappyFamily [a]) x -> HappyFamily [a] :@@: x

GenericK (HappyFamily (Maybe a) :: Type)

Defined in Generics.Kind.Examples

Associated Types

type RepK (HappyFamily (Maybe a)) :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (HappyFamily (Maybe a) :@@: x) -> RepK (HappyFamily (Maybe a)) x

toK :: forall (x :: LoT k). RepK (HappyFamily (Maybe a)) x -> HappyFamily (Maybe a) :@@: x

GenericK (Tree a :: Type)

Defined in Generics.Kind.Examples

Associated Types

type RepK (Tree a) :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (Tree a :@@: x) -> RepK (Tree a) x

toK :: forall (x :: LoT k). RepK (Tree a) x -> Tree a :@@: x

GenericK (Either a b :: Type)

Defined in Generics.Kind.Examples

Associated Types

type RepK (Either a b) :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (Either a b :@@: x) -> RepK (Either a b) x

toK :: forall (x :: LoT k). RepK (Either a b) x -> Either a b :@@: x

GenericK (TTY m a :: Type)

Defined in Generics.Kind.Examples

Associated Types

type RepK (TTY m a) :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (TTY m a :@@: x) -> RepK (TTY m a) x

toK :: forall (x :: LoT k). RepK (TTY m a) x -> TTY m a :@@: x

GenericK SimpleIndex

Defined in Generics.Kind.Examples

Associated Types

type RepK SimpleIndex :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (SimpleIndex :@@: x) -> RepK SimpleIndex x

toK :: forall (x :: LoT k). RepK SimpleIndex x -> SimpleIndex :@@: x

GenericK Either

Defined in Generics.Kind.Examples

Associated Types

type RepK Either :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (Either :@@: x) -> RepK Either x

toK :: forall (x :: LoT k). RepK Either x -> Either :@@: x

GenericK []

Defined in Generics.Kind.Examples

Associated Types

type RepK [] :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). ([] :@@: x) -> RepK [] x

toK :: forall (x :: LoT k). RepK [] x -> [] :@@: x

GenericK Maybe

Defined in Generics.Kind.Examples

Associated Types

type RepK Maybe :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (Maybe :@@: x) -> RepK Maybe x

toK :: forall (x :: LoT k). RepK Maybe x -> Maybe :@@: x

GenericK Shower

Defined in Generics.Kind.Examples

Associated Types

type RepK Shower :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (Shower :@@: x) -> RepK Shower x

toK :: forall (x :: LoT k). RepK Shower x -> Shower :@@: x

GenericK Ranky2

Defined in Generics.Kind.Examples

Associated Types

type RepK Ranky2 :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (Ranky2 :@@: x) -> RepK Ranky2 x

toK :: forall (x :: LoT k). RepK Ranky2 x -> Ranky2 :@@: x

GenericK WeirdTreeR

Defined in Generics.Kind.Examples

Associated Types

type RepK WeirdTreeR :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (WeirdTreeR :@@: x) -> RepK WeirdTreeR x

toK :: forall (x :: LoT k). RepK WeirdTreeR x -> WeirdTreeR :@@: x

GenericK WeirdTree

Defined in Generics.Kind.Examples

Associated Types

type RepK WeirdTree :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (WeirdTree :@@: x) -> RepK WeirdTree x

toK :: forall (x :: LoT k). RepK WeirdTree x -> WeirdTree :@@: x

GenericK HappyFamily

Defined in Generics.Kind.Examples

Associated Types

type RepK HappyFamily :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (HappyFamily :@@: x) -> RepK HappyFamily x

toK :: forall (x :: LoT k). RepK HappyFamily x -> HappyFamily :@@: x

GenericK Tree

Defined in Generics.Kind.Examples

Associated Types

type RepK Tree :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (Tree :@@: x) -> RepK Tree x

toK :: forall (x :: LoT k). RepK Tree x -> Tree :@@: x

GenericK (P' :: Type -> k -> Type)

Defined in Generics.Kind.Examples

Associated Types

type RepK P' :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k0). (P' :@@: x) -> RepK P' x

toK :: forall (x :: LoT k0). RepK P' x -> P' :@@: x

GenericK (SimpleIndex a :: Type -> Type)

Defined in Generics.Kind.Examples

Associated Types

type RepK (SimpleIndex a) :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (SimpleIndex a :@@: x) -> RepK (SimpleIndex a) x

toK :: forall (x :: LoT k). RepK (SimpleIndex a) x -> SimpleIndex a :@@: x

GenericK (Either a :: Type -> Type)

Defined in Generics.Kind.Examples

Associated Types

type RepK (Either a) :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k). (Either a :@@: x) -> RepK (Either a) x

toK :: forall (x :: LoT k). RepK (Either a) x -> Either a :@@: x

GenericK (P k :: k -> Type)

Defined in Generics.Kind.Examples

Associated Types

type RepK (P k) :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k0). (P k :@@: x) -> RepK (P k) x

toK :: forall (x :: LoT k0). RepK (P k) x -> P k :@@: x

GenericK (T :: k -> Type)

Defined in Generics.Kind.Examples

Associated Types

type RepK T :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k0). (T :@@: x) -> RepK T x

toK :: forall (x :: LoT k0). RepK T x -> T :@@: x

GenericK (P' j :: k -> Type)

Defined in Generics.Kind.Examples

Associated Types

type RepK (P' j) :: LoT k -> Type

Methods

fromK :: forall (x :: LoT k0). (P' j :@@: x) -> RepK (P' j) x

toK :: forall (x :: LoT k0). RepK (P' j) x -> P' j :@@: 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

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

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

Instances

type SubstRep (U1 :: LoT (t -> k) -> Type) (x :: t)

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)

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)

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)

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)

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)

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)

Minimal complete definition

substRep, unsubstRep

Instances

SubstRep' (U1 :: LoT (t -> k) -> Type) (x :: t) (xs :: LoT k)

Defined in Generics.Kind

Associated Types

type SubstRep U1 x :: LoT k -> Type

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)

Defined in Generics.Kind

Associated Types

type SubstRep (Field t2) x :: LoT k -> Type

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)

Defined in Generics.Kind

Associated Types

type SubstRep (f :*: g) x :: LoT k -> Type

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)

Defined in Generics.Kind

Associated Types

type SubstRep (f :+: g) x :: LoT k -> Type

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)

Defined in Generics.Kind

Associated Types

type SubstRep (c :=>: f) x :: LoT k -> Type

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)

Defined in Generics.Kind

Associated Types

type SubstRep (M1 i c f) x :: LoT k -> Type

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 ...

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

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

toKindGenerics :: gg a -> kg tys

Instances

Conv (U1 :: Type -> Type) (U1 :: LoT d -> Type) (tys :: LoT d)

Defined in Generics.Kind

Methods

toGhcGenerics :: U1 tys -> U1 a

toKindGenerics :: U1 a -> U1 tys

k ~ Interpret t tys => Conv (K1 p k :: Type -> Type) (Field t :: LoT d -> Type) (tys :: LoT d)

Defined in Generics.Kind

Methods

toGhcGenerics :: Field t tys -> K1 p k a

toKindGenerics :: K1 p k a -> Field t tys

(k ~ Interpret t tys, Conv f f' tys) => Conv (k :=>: f) (t :=>: f' :: LoT d -> Type) (tys :: LoT d)

Defined in Generics.Kind

Methods

toGhcGenerics :: (t :=>: f') tys -> (k :=>: f) a

toKindGenerics :: (k :=>: f) a -> (t :=>: f') tys

(Conv f f' tys, Conv g g' tys) => Conv (f :*: g) (f' :*: g' :: LoT d -> Type) (tys :: LoT d)

Defined in Generics.Kind

Methods

toGhcGenerics :: (f' :*: g') tys -> (f :*: g) a

toKindGenerics :: (f :*: g) a -> (f' :*: g') tys

(Conv f f' tys, Conv g g' tys) => Conv (f :+: g) (f' :+: g' :: LoT d -> Type) (tys :: LoT d)

Defined in Generics.Kind

Methods

toGhcGenerics :: (f' :+: g') tys -> (f :+: g) a

toKindGenerics :: (f :+: g) a -> (f' :+: g') tys

Conv f f' tys => Conv (M1 i c f) (f' :: LoT d -> Type) (tys :: LoT d)

Defined in Generics.Kind

Methods

toGhcGenerics :: f' tys -> M1 i c f a

toKindGenerics :: M1 i c f a -> f' tys

Conv f f' tys => Conv (M1 i c f) (M1 i c f' :: LoT d -> Type) (tys :: LoT d)

Defined in Generics.Kind

Methods

toGhcGenerics :: M1 i c f' tys -> M1 i c f a

toKindGenerics :: M1 i c f a -> M1 i c f' tys

Re-exported from Atom

Interpretation of atoms

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

Replaces the holes in the Atom t by the elements of the list of types tys. The amount and kind of types in tys must match statically those required by the Atom.

>>> :kind! Interpret ([] :$: Var0) (LoT1 Int)
Interpret ([] :$: Var0) (LoT1 Int) :: *
= [Int]

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

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

Obtains the type in the list tys referenced by the type variable t.

>>> :kind! Interpret Var0 (LoT2 Int Bool)
Interpret Var0 (LoT2 Int Bool) :: *
= Int
>>> :kind! Interpret Var1 (LoT2 Int Bool)
Interpret Var1 (LoT2 Int Bool) :: *
= Bool

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 ...

Interprets a list of Atoms representing constraints into the actual constraints. This is a specialization of Interpret for the case of constraints.

>>> :kind! Satisfies '[Eq :$: Var0, Show :$: Var0] (LoT1 Int)
Satisfies '[Eq :$: Var0, Show :$: Var0] (LoT1 Int) :: Constraint
= (Eq Int, (Show Int, () :: Constraint))

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 ...

Determines whether a given type variable v is used within an Atom t. If not, we know that the atom is constant with respect to that variable.

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

Auxiliary type for interpretation of the ForAll atom. Required because a type family like Interpret cannot return a polymorphic type.

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

Auxiliary type for interpretation of the (:=>>:) atom. Required because a type family like Interpret cannot return a type with constraints.

Constructors

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

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

Records a value of type f applied to the list tys.

>>> :t WrapI [1] :: WrappedI ([] :$: Var0) (LoT1 Int)
WrapI [1] :: WrappedI ([] :$: Var0) (LoT1 Int)

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