Safe Haskell	Safe
Language	Haskell2010

Rank2

Contents

Rank 2 classes
Rank 2 data types
Method synonyms and helper functions

Description

Import this module qualified, like this:

import qualified Rank2

This will bring into scope the standard classes Functor, Applicative, Foldable, and Traversable, but with a Rank2. prefix and a twist that their methods operate on a heterogenous collection. The same property is shared by the two less standard classes Apply and Distributive.

Synopsis

Rank 2 classes

class Functor g where Source #

Equivalent of Functor for rank 2 data types, satisfying the usual functor laws

id <$> g == g
(p . q) <$> g == p <$> (q <$> g)

Minimal complete definition

(<$>)

Methods

(<$>) :: (forall a. p a -> q a) -> g p -> g q Source #

Instances

Functor k (Empty (k -> *)) Source #
Methods (<$>) :: (forall (a :: Empty (k -> *)). p a -> q a) -> g p -> g q Source #
Functor k (Only k a) Source #
Methods (<$>) :: (forall (b :: Only k a). p b -> q b) -> g p -> g q Source #
Functor k g => Functor k (Identity (k -> *) g) Source #
Methods (<$>) :: (forall (a :: Identity (k -> *) g). p a -> q a) -> g p -> g q Source #
(Functor k g, Functor k h) => Functor k (Product (k -> *) g h) Source #
Methods (<$>) :: (forall (a :: Product (k -> *) g h). p a -> q a) -> g p -> g q Source #

class Functor g => Apply g where Source #

Subclass of Functor halfway to Applicative, satisfying

(.) <$> u <*> v <*> w == u <*> (v <*> w)

Minimal complete definition

liftA2 | (<*>)

Methods

(<*>) :: g (Arrow p q) -> g p -> g q Source #

Equivalent of <*> for rank 2 data types

liftA2 :: (forall a. p a -> q a -> r a) -> g p -> g q -> g r Source #

Equivalent of liftA2 for rank 2 data types

liftA3 :: (forall a. p a -> q a -> r a -> s a) -> g p -> g q -> g r -> g s Source #

Equivalent of liftA3 for rank 2 data types

Instances

Apply k (Empty (k -> *)) Source #
Methods (<>) :: g (Arrow (Empty (k -> )) p q) -> g p -> g q Source # liftA2 :: (forall (a :: Empty (k -> )). p a -> q a -> r a) -> g p -> g q -> g r Source # liftA3 :: (forall (a :: Empty (k -> )). p a -> q a -> r a -> s a) -> g p -> g q -> g r -> g s Source #
Apply k (Only k x) Source #
Methods (<*>) :: g (Arrow (Only k x) p q) -> g p -> g q Source # liftA2 :: (forall (a :: Only k x). p a -> q a -> r a) -> g p -> g q -> g r Source # liftA3 :: (forall (a :: Only k x). p a -> q a -> r a -> s a) -> g p -> g q -> g r -> g s Source #
Apply k g => Apply k (Identity (k -> *) g) Source #
Methods (<>) :: g (Arrow (Identity (k -> ) g) p q) -> g p -> g q Source # liftA2 :: (forall (a :: Identity (k -> ) g). p a -> q a -> r a) -> g p -> g q -> g r Source # liftA3 :: (forall (a :: Identity (k -> ) g). p a -> q a -> r a -> s a) -> g p -> g q -> g r -> g s Source #
(Apply k g, Apply k h) => Apply k (Product (k -> *) g h) Source #
Methods (<>) :: g (Arrow (Product (k -> ) g h) p q) -> g p -> g q Source # liftA2 :: (forall (a :: Product (k -> ) g h). p a -> q a -> r a) -> g p -> g q -> g r Source # liftA3 :: (forall (a :: Product (k -> ) g h). p a -> q a -> r a -> s a) -> g p -> g q -> g r -> g s Source #

class Apply g => Applicative g where Source #

Equivalent of Applicative for rank 2 data types

Minimal complete definition

pure

Methods

pure :: (forall a. f a) -> g f Source #

Instances

Applicative k (Empty (k -> *)) Source #
Methods pure :: (forall (a :: Empty (k -> *)). f a) -> g f Source #
Applicative k (Only k x) Source #
Methods pure :: (forall (a :: Only k x). f a) -> g f Source #
Applicative k g => Applicative k (Identity (k -> *) g) Source #
Methods pure :: (forall (a :: Identity (k -> *) g). f a) -> g f Source #
(Applicative k g, Applicative k h) => Applicative k (Product (k -> *) g h) Source #
Methods pure :: (forall (a :: Product (k -> *) g h). f a) -> g f Source #

class Foldable g where Source #

Equivalent of Foldable for rank 2 data types

Minimal complete definition

foldMap

Methods

foldMap :: Monoid m => (forall a. p a -> m) -> g p -> m Source #

Instances

Foldable k (Empty (k -> *)) Source #
Methods foldMap :: Monoid m => (forall (a :: Empty (k -> *)). p a -> m) -> g p -> m Source #
Foldable k (Only k x) Source #
Methods foldMap :: Monoid m => (forall (a :: Only k x). p a -> m) -> g p -> m Source #
Foldable k g => Foldable k (Identity (k -> *) g) Source #
Methods foldMap :: Monoid m => (forall (a :: Identity (k -> *) g). p a -> m) -> g p -> m Source #
(Foldable k g, Foldable k h) => Foldable k (Product (k -> *) g h) Source #
Methods foldMap :: Monoid m => (forall (a :: Product (k -> *) g h). p a -> m) -> g p -> m Source #

class (Functor g, Foldable g) => Traversable g where Source #

Equivalent of Traversable for rank 2 data types

Minimal complete definition

traverse | sequence

Methods

traverse :: Applicative m => (forall a. p a -> m (q a)) -> g p -> m (g q) Source #

sequence :: Applicative m => g (Compose m p) -> m (g p) Source #

Instances

Traversable k (Empty (k -> *)) Source #
Methods traverse :: Applicative m => (forall (a :: Empty (k -> )). p a -> m (q a)) -> g p -> m (g q) Source # sequence :: Applicative m => g (Compose (Empty (k -> *)) m p) -> m (g p) Source #
Traversable k (Only k x) Source #
Methods traverse :: Applicative m => (forall (a :: Only k x). p a -> m (q a)) -> g p -> m (g q) Source # sequence :: Applicative m => g (Compose * (Only k x) m p) -> m (g p) Source #
Traversable k g => Traversable k (Identity (k -> *) g) Source #
Methods traverse :: Applicative m => (forall (a :: Identity (k -> ) g). p a -> m (q a)) -> g p -> m (g q) Source # sequence :: Applicative m => g (Compose (Identity (k -> *) g) m p) -> m (g p) Source #
(Traversable k g, Traversable k h) => Traversable k (Product (k -> *) g h) Source #
Methods traverse :: Applicative m => (forall (a :: Product (k -> ) g h). p a -> m (q a)) -> g p -> m (g q) Source # sequence :: Applicative m => g (Compose (Product (k -> *) g h) m p) -> m (g p) Source #

class DistributiveTraversable g => Distributive g where Source #

Equivalent of Distributive for rank 2 data types

Minimal complete definition

cotraverse | distribute

Methods

collect :: Functor f1 => (a -> g f2) -> f1 a -> g (Compose f1 f2) Source #

distribute :: Functor f1 => f1 (g f2) -> g (Compose f1 f2) Source #

cotraverse :: Functor m => (forall a. m (p a) -> q a) -> m (g p) -> g q Source #

Dual of traverse, equivalent of cotraverse for rank 2 data types

Instances

Distributive k (Empty (k -> *)) Source #
Methods collect :: Functor f1 => (a -> g f2) -> f1 a -> g (Compose * (Empty (k -> )) f1 f2) Source # distribute :: Functor f1 => f1 (g f2) -> g (Compose (Empty (k -> )) f1 f2) Source # cotraverse :: Functor m => (forall (a :: Empty (k -> )). m (p a) -> q a) -> m (g p) -> g q Source #
Distributive k (Only k x) Source #
Methods collect :: Functor f1 => (a -> g f2) -> f1 a -> g (Compose * (Only k x) f1 f2) Source # distribute :: Functor f1 => f1 (g f2) -> g (Compose * (Only k x) f1 f2) Source # cotraverse :: Functor m => (forall (a :: Only k x). m (p a) -> q a) -> m (g p) -> g q Source #
Distributive k g => Distributive k (Identity (k -> *) g) Source #
Methods collect :: Functor f1 => (a -> g f2) -> f1 a -> g (Compose * (Identity (k -> ) g) f1 f2) Source # distribute :: Functor f1 => f1 (g f2) -> g (Compose (Identity (k -> ) g) f1 f2) Source # cotraverse :: Functor m => (forall (a :: Identity (k -> ) g). m (p a) -> q a) -> m (g p) -> g q Source #
(Distributive k g, Distributive k h) => Distributive k (Product (k -> *) g h) Source #
Methods collect :: Functor f1 => (a -> g f2) -> f1 a -> g (Compose * (Product (k -> ) g h) f1 f2) Source # distribute :: Functor f1 => f1 (g f2) -> g (Compose (Product (k -> ) g h) f1 f2) Source # cotraverse :: Functor m => (forall (a :: Product (k -> ) g h). m (p a) -> q a) -> m (g p) -> g q Source #

class Functor g => DistributiveTraversable (g :: (k -> *) -> *) where Source #

A weaker Distributive that requires Traversable to use, not just a Functor.

Methods

collectTraversable :: Traversable f1 => (a -> g f2) -> f1 a -> g (Compose f1 f2) Source #

distributeTraversable :: Traversable f1 => f1 (g f2) -> g (Compose f1 f2) Source #

cotraverseTraversable :: Traversable f1 => (forall x. f1 (f2 x) -> f x) -> f1 (g f2) -> g f Source #

cotraverseTraversable :: (Traversable m, Distributive g) => (forall a. m (p a) -> q a) -> m (g p) -> g q Source #

Instances

DistributiveTraversable k (Empty (k -> *)) Source #
Methods collectTraversable :: Traversable f1 => (a -> g f2) -> f1 a -> g (Compose * (Empty (k -> )) f1 f2) Source # distributeTraversable :: Traversable f1 => f1 (g f2) -> g (Compose (Empty (k -> )) f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: Empty (k -> )). f1 (f2 x) -> f x) -> f1 (g f2) -> g f Source #
DistributiveTraversable k (Only k x) Source #
Methods collectTraversable :: Traversable f1 => (a -> g f2) -> f1 a -> g (Compose * (Only k x) f1 f2) Source # distributeTraversable :: Traversable f1 => f1 (g f2) -> g (Compose * (Only k x) f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (a :: Only k x). f1 (f2 a) -> f a) -> f1 (g f2) -> g f Source #
DistributiveTraversable k g => DistributiveTraversable k (Identity (k -> *) g) Source #
Methods collectTraversable :: Traversable f1 => (a -> g f2) -> f1 a -> g (Compose * (Identity (k -> ) g) f1 f2) Source # distributeTraversable :: Traversable f1 => f1 (g f2) -> g (Compose (Identity (k -> ) g) f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: Identity (k -> ) g). f1 (f2 x) -> f x) -> f1 (g f2) -> g f Source #
(DistributiveTraversable k g, DistributiveTraversable k h) => DistributiveTraversable k (Product (k -> *) g h) Source #
Methods collectTraversable :: Traversable f1 => (a -> g f2) -> f1 a -> g (Compose * (Product (k -> ) g h) f1 f2) Source # distributeTraversable :: Traversable f1 => f1 (g f2) -> g (Compose (Product (k -> ) g h) f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: Product (k -> ) g h). f1 (f2 x) -> f x) -> f1 (g f2) -> g f Source #

distributeJoin :: (Distributive g, Monad f) => f (g f) -> g f Source #

A variant of distribute convenient with Monad instances

Rank 2 data types

newtype Compose k k1 (f :: k -> *) (g :: k1 -> k) (a :: k1) :: forall k k1. (k -> *) -> (k1 -> k) -> k1 -> * infixr 9 #

Right-to-left composition of functors. The composition of applicative functors is always applicative, but the composition of monads is not always a monad.

Constructors

Compose infixr 9
Fields getCompose :: f (g a)

Instances

Functor f => Generic1 k (Compose * k f g)
Associated Types type Rep1 (Compose * k f g) (f :: Compose * k f g -> ) :: k -> # Methods from1 :: f a -> Rep1 (Compose * k f g) f a # to1 :: Rep1 (Compose * k f g) f a -> f a #
(Functor f, Functor g) => Functor (Compose * * f g)	Since: 4.9.0.0
Methods fmap :: (a -> b) -> Compose * * f g a -> Compose * * f g b # (<$) :: a -> Compose * * f g b -> Compose * * f g a #
(Applicative f, Applicative g) => Applicative (Compose * * f g)	Since: 4.9.0.0
Methods pure :: a -> Compose * * f g a # (<>) :: Compose * f g (a -> b) -> Compose * * f g a -> Compose * * f g b # liftA2 :: (a -> b -> c) -> Compose * * f g a -> Compose * * f g b -> Compose * * f g c # (>) :: Compose * f g a -> Compose * * f g b -> Compose * * f g b # (<) :: Compose * f g a -> Compose * * f g b -> Compose * * f g a #
(Foldable f, Foldable g) => Foldable (Compose * * f g)	Since: 4.9.0.0
Methods fold :: Monoid m => Compose * * f g m -> m # foldMap :: Monoid m => (a -> m) -> Compose * * f g a -> m # foldr :: (a -> b -> b) -> b -> Compose * * f g a -> b # foldr' :: (a -> b -> b) -> b -> Compose * * f g a -> b # foldl :: (b -> a -> b) -> b -> Compose * * f g a -> b # foldl' :: (b -> a -> b) -> b -> Compose * * f g a -> b # foldr1 :: (a -> a -> a) -> Compose * * f g a -> a # foldl1 :: (a -> a -> a) -> Compose * * f g a -> a # toList :: Compose * * f g a -> [a] # null :: Compose * * f g a -> Bool # length :: Compose * * f g a -> Int # elem :: Eq a => a -> Compose * * f g a -> Bool # maximum :: Ord a => Compose * * f g a -> a # minimum :: Ord a => Compose * * f g a -> a # sum :: Num a => Compose * * f g a -> a # product :: Num a => Compose * * f g a -> a #
(Traversable f, Traversable g) => Traversable (Compose * * f g)	Since: 4.9.0.0
Methods traverse :: Applicative f => (a -> f b) -> Compose * * f g a -> f (Compose * * f g b) # sequenceA :: Applicative f => Compose * * f g (f a) -> f (Compose * * f g a) # mapM :: Monad m => (a -> m b) -> Compose * * f g a -> m (Compose * * f g b) # sequence :: Monad m => Compose * * f g (m a) -> m (Compose * * f g a) #
(Eq1 f, Eq1 g) => Eq1 (Compose * * f g)	Since: 4.9.0.0
Methods liftEq :: (a -> b -> Bool) -> Compose * * f g a -> Compose * * f g b -> Bool #
(Ord1 f, Ord1 g) => Ord1 (Compose * * f g)	Since: 4.9.0.0
Methods liftCompare :: (a -> b -> Ordering) -> Compose * * f g a -> Compose * * f g b -> Ordering #
(Read1 f, Read1 g) => Read1 (Compose * * f g)	Since: 4.9.0.0
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Compose * * f g a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Compose * * f g a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Compose * * f g a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Compose * * f g a] #
(Show1 f, Show1 g) => Show1 (Compose * * f g)	Since: 4.9.0.0
Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Compose * * f g a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Compose * * f g a] -> ShowS #
(Alternative f, Applicative g) => Alternative (Compose * * f g)	Since: 4.9.0.0
Methods empty :: Compose * * f g a # (<\|>) :: Compose * * f g a -> Compose * * f g a -> Compose * * f g a # some :: Compose * * f g a -> Compose * * f g [a] # many :: Compose * * f g a -> Compose * * f g [a] #
(Eq1 f, Eq1 g, Eq a) => Eq (Compose * * f g a)	Since: 4.9.0.0
Methods (==) :: Compose * * f g a -> Compose * * f g a -> Bool # (/=) :: Compose * * f g a -> Compose * * f g a -> Bool #
(Data (f (g a)), Typeable * k2, Typeable * k1, Typeable (k2 -> k1) g, Typeable (k1 -> *) f, Typeable k2 a) => Data (Compose k1 k2 f g a)
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall b. b -> c b) -> Compose k1 k2 f g a -> c (Compose k1 k2 f g a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Compose k1 k2 f g a) # toConstr :: Compose k1 k2 f g a -> Constr # dataTypeOf :: Compose k1 k2 f g a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Compose k1 k2 f g a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Compose k1 k2 f g a)) # gmapT :: (forall b. Data b => b -> b) -> Compose k1 k2 f g a -> Compose k1 k2 f g a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Compose k1 k2 f g a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Compose k1 k2 f g a -> r # gmapQ :: (forall d. Data d => d -> u) -> Compose k1 k2 f g a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Compose k1 k2 f g a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Compose k1 k2 f g a -> m (Compose k1 k2 f g a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Compose k1 k2 f g a -> m (Compose k1 k2 f g a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Compose k1 k2 f g a -> m (Compose k1 k2 f g a) #
(Ord1 f, Ord1 g, Ord a) => Ord (Compose * * f g a)	Since: 4.9.0.0
Methods compare :: Compose * * f g a -> Compose * * f g a -> Ordering # (<) :: Compose * * f g a -> Compose * * f g a -> Bool # (<=) :: Compose * * f g a -> Compose * * f g a -> Bool # (>) :: Compose * * f g a -> Compose * * f g a -> Bool # (>=) :: Compose * * f g a -> Compose * * f g a -> Bool # max :: Compose * * f g a -> Compose * * f g a -> Compose * * f g a # min :: Compose * * f g a -> Compose * * f g a -> Compose * * f g a #
(Read1 f, Read1 g, Read a) => Read (Compose * * f g a)	Since: 4.9.0.0
Methods readsPrec :: Int -> ReadS (Compose * * f g a) # readList :: ReadS [Compose * * f g a] # readPrec :: ReadPrec (Compose * * f g a) # readListPrec :: ReadPrec [Compose * * f g a] #
(Show1 f, Show1 g, Show a) => Show (Compose * * f g a)	Since: 4.9.0.0
Methods showsPrec :: Int -> Compose * * f g a -> ShowS # show :: Compose * * f g a -> String # showList :: [Compose * * f g a] -> ShowS #
Generic (Compose k1 k2 f g a)
Associated Types type Rep (Compose k1 k2 f g a) :: * -> * # Methods from :: Compose k1 k2 f g a -> Rep (Compose k1 k2 f g a) x # to :: Rep (Compose k1 k2 f g a) x -> Compose k1 k2 f g a #
type Rep1 k (Compose * k f g)
type Rep1 k (Compose * k f g) = D1 k (MetaData "Compose" "Data.Functor.Compose" "base" True) (C1 k (MetaCons "Compose" PrefixI True) (S1 k (MetaSel (Just Symbol "getCompose") NoSourceUnpackedness NoSourceStrictness DecidedLazy) ((:.:) * k f (Rec1 k g))))
type Rep (Compose k1 k2 f g a)
type Rep (Compose k1 k2 f g a) = D1 * (MetaData "Compose" "Data.Functor.Compose" "base" True) (C1 * (MetaCons "Compose" PrefixI True) (S1 * (MetaSel (Just Symbol "getCompose") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (f (g a)))))

data Empty f Source #

A rank-2 equivalent of '()', a zero-element tuple

Constructors

Empty

Instances

DistributiveTraversable k (Empty (k -> *)) Source #
Methods collectTraversable :: Traversable f1 => (a -> g f2) -> f1 a -> g (Compose * (Empty (k -> )) f1 f2) Source # distributeTraversable :: Traversable f1 => f1 (g f2) -> g (Compose (Empty (k -> )) f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: Empty (k -> )). f1 (f2 x) -> f x) -> f1 (g f2) -> g f Source #
Distributive k (Empty (k -> *)) Source #
Methods collect :: Functor f1 => (a -> g f2) -> f1 a -> g (Compose * (Empty (k -> )) f1 f2) Source # distribute :: Functor f1 => f1 (g f2) -> g (Compose (Empty (k -> )) f1 f2) Source # cotraverse :: Functor m => (forall (a :: Empty (k -> )). m (p a) -> q a) -> m (g p) -> g q Source #
Applicative k (Empty (k -> *)) Source #
Methods pure :: (forall (a :: Empty (k -> *)). f a) -> g f Source #
Apply k (Empty (k -> *)) Source #
Methods (<>) :: g (Arrow (Empty (k -> )) p q) -> g p -> g q Source # liftA2 :: (forall (a :: Empty (k -> )). p a -> q a -> r a) -> g p -> g q -> g r Source # liftA3 :: (forall (a :: Empty (k -> )). p a -> q a -> r a -> s a) -> g p -> g q -> g r -> g s Source #
Traversable k (Empty (k -> *)) Source #
Methods traverse :: Applicative m => (forall (a :: Empty (k -> )). p a -> m (q a)) -> g p -> m (g q) Source # sequence :: Applicative m => g (Compose (Empty (k -> *)) m p) -> m (g p) Source #
Foldable k (Empty (k -> *)) Source #
Methods foldMap :: Monoid m => (forall (a :: Empty (k -> *)). p a -> m) -> g p -> m Source #
Functor k (Empty (k -> *)) Source #
Methods (<$>) :: (forall (a :: Empty (k -> *)). p a -> q a) -> g p -> g q Source #
Eq (Empty k f) Source #
Methods (==) :: Empty k f -> Empty k f -> Bool # (/=) :: Empty k f -> Empty k f -> Bool #
Ord (Empty k f) Source #
Methods compare :: Empty k f -> Empty k f -> Ordering # (<) :: Empty k f -> Empty k f -> Bool # (<=) :: Empty k f -> Empty k f -> Bool # (>) :: Empty k f -> Empty k f -> Bool # (>=) :: Empty k f -> Empty k f -> Bool # max :: Empty k f -> Empty k f -> Empty k f # min :: Empty k f -> Empty k f -> Empty k f #
Show (Empty k f) Source #
Methods showsPrec :: Int -> Empty k f -> ShowS # show :: Empty k f -> String # showList :: [Empty k f] -> ShowS #

newtype Only a f Source #

A rank-2 tuple of only one element

Constructors

Only
Fields fromOnly :: f a

Instances

DistributiveTraversable k (Only k x) Source #
Methods collectTraversable :: Traversable f1 => (a -> g f2) -> f1 a -> g (Compose * (Only k x) f1 f2) Source # distributeTraversable :: Traversable f1 => f1 (g f2) -> g (Compose * (Only k x) f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (a :: Only k x). f1 (f2 a) -> f a) -> f1 (g f2) -> g f Source #
Distributive k (Only k x) Source #
Methods collect :: Functor f1 => (a -> g f2) -> f1 a -> g (Compose * (Only k x) f1 f2) Source # distribute :: Functor f1 => f1 (g f2) -> g (Compose * (Only k x) f1 f2) Source # cotraverse :: Functor m => (forall (a :: Only k x). m (p a) -> q a) -> m (g p) -> g q Source #
Applicative k (Only k x) Source #
Methods pure :: (forall (a :: Only k x). f a) -> g f Source #
Apply k (Only k x) Source #
Methods (<*>) :: g (Arrow (Only k x) p q) -> g p -> g q Source # liftA2 :: (forall (a :: Only k x). p a -> q a -> r a) -> g p -> g q -> g r Source # liftA3 :: (forall (a :: Only k x). p a -> q a -> r a -> s a) -> g p -> g q -> g r -> g s Source #
Traversable k (Only k x) Source #
Methods traverse :: Applicative m => (forall (a :: Only k x). p a -> m (q a)) -> g p -> m (g q) Source # sequence :: Applicative m => g (Compose * (Only k x) m p) -> m (g p) Source #
Foldable k (Only k x) Source #
Methods foldMap :: Monoid m => (forall (a :: Only k x). p a -> m) -> g p -> m Source #
Functor k (Only k a) Source #
Methods (<$>) :: (forall (b :: Only k a). p b -> q b) -> g p -> g q Source #
Eq (f a) => Eq (Only k a f) Source #
Methods (==) :: Only k a f -> Only k a f -> Bool # (/=) :: Only k a f -> Only k a f -> Bool #
Ord (f a) => Ord (Only k a f) Source #
Methods compare :: Only k a f -> Only k a f -> Ordering # (<) :: Only k a f -> Only k a f -> Bool # (<=) :: Only k a f -> Only k a f -> Bool # (>) :: Only k a f -> Only k a f -> Bool # (>=) :: Only k a f -> Only k a f -> Bool # max :: Only k a f -> Only k a f -> Only k a f # min :: Only k a f -> Only k a f -> Only k a f #
Show (f a) => Show (Only k a f) Source #
Methods showsPrec :: Int -> Only k a f -> ShowS # show :: Only k a f -> String # showList :: [Only k a f] -> ShowS #

newtype Identity g f Source #

Equivalent of Identity for rank 2 data types

Constructors

Identity
Fields runIdentity :: g f

Instances

DistributiveTraversable k g => DistributiveTraversable k (Identity (k -> *) g) Source #
Methods collectTraversable :: Traversable f1 => (a -> g f2) -> f1 a -> g (Compose * (Identity (k -> ) g) f1 f2) Source # distributeTraversable :: Traversable f1 => f1 (g f2) -> g (Compose (Identity (k -> ) g) f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: Identity (k -> ) g). f1 (f2 x) -> f x) -> f1 (g f2) -> g f Source #
Distributive k g => Distributive k (Identity (k -> *) g) Source #
Methods collect :: Functor f1 => (a -> g f2) -> f1 a -> g (Compose * (Identity (k -> ) g) f1 f2) Source # distribute :: Functor f1 => f1 (g f2) -> g (Compose (Identity (k -> ) g) f1 f2) Source # cotraverse :: Functor m => (forall (a :: Identity (k -> ) g). m (p a) -> q a) -> m (g p) -> g q Source #
Applicative k g => Applicative k (Identity (k -> *) g) Source #
Methods pure :: (forall (a :: Identity (k -> *) g). f a) -> g f Source #
Apply k g => Apply k (Identity (k -> *) g) Source #
Methods (<>) :: g (Arrow (Identity (k -> ) g) p q) -> g p -> g q Source # liftA2 :: (forall (a :: Identity (k -> ) g). p a -> q a -> r a) -> g p -> g q -> g r Source # liftA3 :: (forall (a :: Identity (k -> ) g). p a -> q a -> r a -> s a) -> g p -> g q -> g r -> g s Source #
Traversable k g => Traversable k (Identity (k -> *) g) Source #
Methods traverse :: Applicative m => (forall (a :: Identity (k -> ) g). p a -> m (q a)) -> g p -> m (g q) Source # sequence :: Applicative m => g (Compose (Identity (k -> *) g) m p) -> m (g p) Source #
Foldable k g => Foldable k (Identity (k -> *) g) Source #
Methods foldMap :: Monoid m => (forall (a :: Identity (k -> *) g). p a -> m) -> g p -> m Source #
Functor k g => Functor k (Identity (k -> *) g) Source #
Methods (<$>) :: (forall (a :: Identity (k -> *) g). p a -> q a) -> g p -> g q Source #
Eq (g f) => Eq (Identity k g f) Source #
Methods (==) :: Identity k g f -> Identity k g f -> Bool # (/=) :: Identity k g f -> Identity k g f -> Bool #
Ord (g f) => Ord (Identity k g f) Source #
Methods compare :: Identity k g f -> Identity k g f -> Ordering # (<) :: Identity k g f -> Identity k g f -> Bool # (<=) :: Identity k g f -> Identity k g f -> Bool # (>) :: Identity k g f -> Identity k g f -> Bool # (>=) :: Identity k g f -> Identity k g f -> Bool # max :: Identity k g f -> Identity k g f -> Identity k g f # min :: Identity k g f -> Identity k g f -> Identity k g f #
Show (g f) => Show (Identity k g f) Source #
Methods showsPrec :: Int -> Identity k g f -> ShowS # show :: Identity k g f -> String # showList :: [Identity k g f] -> ShowS #

data Product g h f Source #

Equivalent of Product for rank 2 data types

Constructors

Pair
Fields fst :: g f snd :: h f

Instances

(DistributiveTraversable k g, DistributiveTraversable k h) => DistributiveTraversable k (Product (k -> *) g h) Source #
Methods collectTraversable :: Traversable f1 => (a -> g f2) -> f1 a -> g (Compose * (Product (k -> ) g h) f1 f2) Source # distributeTraversable :: Traversable f1 => f1 (g f2) -> g (Compose (Product (k -> ) g h) f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: Product (k -> ) g h). f1 (f2 x) -> f x) -> f1 (g f2) -> g f Source #
(Distributive k g, Distributive k h) => Distributive k (Product (k -> *) g h) Source #
Methods collect :: Functor f1 => (a -> g f2) -> f1 a -> g (Compose * (Product (k -> ) g h) f1 f2) Source # distribute :: Functor f1 => f1 (g f2) -> g (Compose (Product (k -> ) g h) f1 f2) Source # cotraverse :: Functor m => (forall (a :: Product (k -> ) g h). m (p a) -> q a) -> m (g p) -> g q Source #
(Applicative k g, Applicative k h) => Applicative k (Product (k -> *) g h) Source #
Methods pure :: (forall (a :: Product (k -> *) g h). f a) -> g f Source #
(Apply k g, Apply k h) => Apply k (Product (k -> *) g h) Source #
Methods (<>) :: g (Arrow (Product (k -> ) g h) p q) -> g p -> g q Source # liftA2 :: (forall (a :: Product (k -> ) g h). p a -> q a -> r a) -> g p -> g q -> g r Source # liftA3 :: (forall (a :: Product (k -> ) g h). p a -> q a -> r a -> s a) -> g p -> g q -> g r -> g s Source #
(Traversable k g, Traversable k h) => Traversable k (Product (k -> *) g h) Source #
Methods traverse :: Applicative m => (forall (a :: Product (k -> ) g h). p a -> m (q a)) -> g p -> m (g q) Source # sequence :: Applicative m => g (Compose (Product (k -> *) g h) m p) -> m (g p) Source #
(Foldable k g, Foldable k h) => Foldable k (Product (k -> *) g h) Source #
Methods foldMap :: Monoid m => (forall (a :: Product (k -> *) g h). p a -> m) -> g p -> m Source #
(Functor k g, Functor k h) => Functor k (Product (k -> *) g h) Source #
Methods (<$>) :: (forall (a :: Product (k -> *) g h). p a -> q a) -> g p -> g q Source #
(Eq (h f), Eq (g f)) => Eq (Product k g h f) Source #
Methods (==) :: Product k g h f -> Product k g h f -> Bool # (/=) :: Product k g h f -> Product k g h f -> Bool #
(Ord (h f), Ord (g f)) => Ord (Product k g h f) Source #
Methods compare :: Product k g h f -> Product k g h f -> Ordering # (<) :: Product k g h f -> Product k g h f -> Bool # (<=) :: Product k g h f -> Product k g h f -> Bool # (>) :: Product k g h f -> Product k g h f -> Bool # (>=) :: Product k g h f -> Product k g h f -> Bool # max :: Product k g h f -> Product k g h f -> Product k g h f # min :: Product k g h f -> Product k g h f -> Product k g h f #
(Show (h f), Show (g f)) => Show (Product k g h f) Source #
Methods showsPrec :: Int -> Product k g h f -> ShowS # show :: Product k g h f -> String # showList :: [Product k g h f] -> ShowS #

newtype Arrow p q a Source #

Wrapper for functions that map the argument constructor type

Constructors

Arrow
Fields apply :: p a -> q a

Method synonyms and helper functions

ap :: Apply g => g (Arrow p q) -> g p -> g q Source #

Alphabetical synonym for <*>

fmap :: Functor g => (forall a. p a -> q a) -> g p -> g q Source #

Alphabetical synonym for <$>

liftA4 :: Apply g => (forall a. p a -> q a -> r a -> s a -> t a) -> g p -> g q -> g r -> g s -> g t Source #

liftA5 :: Apply g => (forall a. p a -> q a -> r a -> s a -> t a -> u a) -> g p -> g q -> g r -> g s -> g t -> g u Source #

fmapTraverse :: (DistributiveTraversable f, Traversable g) => (forall a. g (t a) -> u a) -> g (f t) -> f u Source #

Like fmap, but traverses over its argument

liftA2Traverse1 :: (Apply f, DistributiveTraversable f, Traversable g) => (forall a. g (t a) -> u a -> v a) -> g (f t) -> f u -> f v Source #

Like liftA2, but traverses over its first argument

liftA2Traverse2 :: (Apply f, DistributiveTraversable f, Traversable g) => (forall a. t a -> g (u a) -> v a) -> f t -> g (f u) -> f v Source #

Like liftA2, but traverses over its second argument

liftA2TraverseBoth :: (Apply f, DistributiveTraversable f, Traversable g1, Traversable g2) => (forall a. g1 (t a) -> g2 (u a) -> v a) -> g1 (f t) -> g2 (f u) -> f v Source #

Like liftA2, but traverses over both its arguments

distributeWith :: (Distributive g, Functor f) => (forall i. f (a i) -> b i) -> f (g a) -> g b Source #

Deprecated: Use cotraverse instead.

Synonym for cotraverse

distributeWithTraversable :: (DistributiveTraversable g, Traversable m) => (forall a. m (p a) -> q a) -> m (g p) -> g q Source #

Deprecated: Use cotraverseTraversable instead.

Synonym for cotraverseTraversable