Generics.SOP.BasicFunctors

Basic functors.

Definitions of the type-level equivalents of const, id, and (.), and a definition of the lifted function space.

These datatypes are generally useful, but in this library, they're primarily used as parameters for the NP, NS, POP, and SOP types.

Documentation

newtype K a b

The constant type functor.

Like Constant, but kind-polymorphic in its second argument and with a shorter name.

Constructors

K a

Instances

Functor (K * a)

Methods

fmap :: (a -> b) -> K * a a -> K * a b

(<$) :: a -> K * a b -> K * a a

Monoid a => Applicative (K * a)

Methods

pure :: a -> K * a a

(<*>) :: K * a (a -> b) -> K * a a -> K * a b

(*>) :: K * a a -> K * a b -> K * a b

(<*) :: K * a a -> K * a b -> K * a a

Foldable (K * a)

Methods

fold :: Monoid m => K * a m -> m

foldMap :: Monoid m => (a -> m) -> K * a a -> m

foldr :: (a -> b -> b) -> b -> K * a a -> b

foldr' :: (a -> b -> b) -> b -> K * a a -> b

foldl :: (b -> a -> b) -> b -> K * a a -> b

foldl' :: (b -> a -> b) -> b -> K * a a -> b

foldr1 :: (a -> a -> a) -> K * a a -> a

foldl1 :: (a -> a -> a) -> K * a a -> a

toList :: K * a a -> [a]

null :: K * a a -> Bool

length :: K * a a -> Int

elem :: Eq a => a -> K * a a -> Bool

maximum :: Ord a => K * a a -> a

minimum :: Ord a => K * a a -> a

sum :: Num a => K * a a -> a

product :: Num a => K * a a -> a

Traversable (K * a)

Methods

traverse :: Applicative f => (a -> f b) -> K * a a -> f (K * a b)

sequenceA :: Applicative f => K * a (f a) -> f (K * a a)

mapM :: Monad m => (a -> m b) -> K * a a -> m (K * a b)

sequence :: Monad m => K * a (m a) -> m (K * a a)

Show a => Show (K k a b)

Methods

showsPrec :: Int -> K k a b -> ShowS

show :: K k a b -> String

showList :: [K k a b] -> ShowS

Generic (K k a b)

Associated Types

type Rep (K k a b) :: * -> *

Methods

from :: K k a b -> Rep (K k a b) x

to :: Rep (K k a b) x -> K k a b

type Rep (K k a b)

type Rep (K k a b) = D1 (MetaData "K" "Generics.SOP.BasicFunctors" "generics-sop-0.2.2.0-9w3u9oOObG6ENcL8IZfj8x" True) (C1 (MetaCons "K" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

type Code (K * a0 b0)

type Code (K * a0 b0) = (:) [*] ((:) * a0 ([] *)) ([] [*])

unK :: K a b -> a

Extract the contents of a K value.

newtype I a

The identity type functor.

Like Identity, but with a shorter name.

Constructors

I a

Instances

Monad I

Methods

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

(>>) :: I a -> I b -> I b

return :: a -> I a

fail :: String -> I a

Functor I

Methods

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

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

Applicative I

Methods

pure :: a -> I a

(<*>) :: I (a -> b) -> I a -> I b

(*>) :: I a -> I b -> I b

(<*) :: I a -> I b -> I a

Foldable I

Methods

fold :: Monoid m => I m -> m

foldMap :: Monoid m => (a -> m) -> I a -> m

foldr :: (a -> b -> b) -> b -> I a -> b

foldr' :: (a -> b -> b) -> b -> I a -> b

foldl :: (b -> a -> b) -> b -> I a -> b

foldl' :: (b -> a -> b) -> b -> I a -> b

foldr1 :: (a -> a -> a) -> I a -> a

foldl1 :: (a -> a -> a) -> I a -> a

toList :: I a -> [a]

null :: I a -> Bool

length :: I a -> Int

elem :: Eq a => a -> I a -> Bool

maximum :: Ord a => I a -> a

minimum :: Ord a => I a -> a

sum :: Num a => I a -> a

product :: Num a => I a -> a

Traversable I

Methods

traverse :: Applicative f => (a -> f b) -> I a -> f (I b)

sequenceA :: Applicative f => I (f a) -> f (I a)

mapM :: Monad m => (a -> m b) -> I a -> m (I b)

sequence :: Monad m => I (m a) -> m (I a)

Show a => Show (I a)

Methods

showsPrec :: Int -> I a -> ShowS

show :: I a -> String

showList :: [I a] -> ShowS

Generic (I a)

Associated Types

type Rep (I a) :: * -> *

Methods

from :: I a -> Rep (I a) x

to :: Rep (I a) x -> I a

type Rep (I a)

type Rep (I a) = D1 (MetaData "I" "Generics.SOP.BasicFunctors" "generics-sop-0.2.2.0-9w3u9oOObG6ENcL8IZfj8x" True) (C1 (MetaCons "I" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

type Code (I a0)

type Code (I a0) = (:) [*] ((:) * a0 ([] *)) ([] [*])

unI :: I a -> a

Extract the contents of an I value.

newtype (f :.: g) p infixr 7

Composition of functors.

Like Compose, but kind-polymorphic and with a shorter name.

Constructors

Comp (f (g p))

Instances

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

Methods

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

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

Show (f (g p)) => Show ((:.:) k l f g p)

Methods

showsPrec :: Int -> (k :.: l) f g p -> ShowS

show :: (k :.: l) f g p -> String

showList :: [(k :.: l) f g p] -> ShowS

Generic ((:.:) k l f g p)

Associated Types

type Rep ((:.:) k l f g p) :: * -> *

Methods

from :: (k :.: l) f g p -> Rep ((k :.: l) f g p) x

to :: Rep ((k :.: l) f g p) x -> (k :.: l) f g p

type Rep ((:.:) k l f g p)

type Rep ((:.:) k l f g p) = D1 (MetaData ":.:" "Generics.SOP.BasicFunctors" "generics-sop-0.2.2.0-9w3u9oOObG6ENcL8IZfj8x" True) (C1 (MetaCons "Comp" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f (g p)))))

type Code ((:.:) * * f0 g0 p0)

type Code ((:.:) * * f0 g0 p0) = (:) [*] ((:) * (f0 (g0 p0)) ([] *)) ([] [*])

unComp :: (f :.: g) p -> f (g p)

Extract the contents of a Comp value.