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

Minimal complete definition

(<$>)

Methods

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

Instances

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

class Functor g => Apply g where Source #

Subclass of Functor halfway to Applicative

(.) <$> 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

Instances

Apply Empty Source #
Methods (<*>) :: Empty (Arrow p q) -> Empty p -> Empty q Source # liftA2 :: (forall a. p a -> q a -> r a) -> Empty p -> Empty q -> Empty r Source #
Apply g => Apply (Identity g) Source #
Methods (<*>) :: Identity g (Arrow p q) -> Identity g p -> Identity g q Source # liftA2 :: (forall a. p a -> q a -> r a) -> Identity g p -> Identity g q -> Identity g r Source #
Apply (Only x) Source #
Methods (<*>) :: Only x (Arrow p q) -> Only x p -> Only x q Source # liftA2 :: (forall a. p a -> q a -> r a) -> Only x p -> Only x q -> Only x r Source #
(Apply g, Apply h) => Apply (Product g h) Source #
Methods (<*>) :: Product g h (Arrow p q) -> Product g h p -> Product g h q Source # liftA2 :: (forall a. p a -> q a -> r a) -> Product g h p -> Product g h q -> Product g h r 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 Empty Source #
Methods pure :: (forall a. f a) -> Empty f Source #
Applicative g => Applicative (Identity g) Source #
Methods pure :: (forall a. f a) -> Identity g f Source #
Applicative (Only x) Source #
Methods pure :: (forall a. f a) -> Only x f Source #
(Applicative g, Applicative h) => Applicative (Product g h) Source #
Methods pure :: (forall a. f a) -> Product g h 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 Empty Source #
Methods foldMap :: Monoid m => (forall a. p a -> m) -> Empty p -> m Source #
Foldable g => Foldable (Identity g) Source #
Methods foldMap :: Monoid m => (forall a. p a -> m) -> Identity g p -> m Source #
Foldable (Only x) Source #
Methods foldMap :: Monoid m => (forall a. p a -> m) -> Only x p -> m Source #
(Foldable g, Foldable h) => Foldable (Product g h) Source #
Methods foldMap :: Monoid m => (forall a. p a -> m) -> Product g h 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 Empty Source #
Methods traverse :: Applicative m => (forall a. p a -> m (q a)) -> Empty p -> m (Empty q) Source # sequence :: Applicative m => Empty (Compose * * m p) -> m (Empty p) Source #
Traversable g => Traversable (Identity g) Source #
Methods traverse :: Applicative m => (forall a. p a -> m (q a)) -> Identity g p -> m (Identity g q) Source # sequence :: Applicative m => Identity g (Compose * * m p) -> m (Identity g p) Source #
Traversable (Only x) Source #
Methods traverse :: Applicative m => (forall a. p a -> m (q a)) -> Only x p -> m (Only x q) Source # sequence :: Applicative m => Only x (Compose * * m p) -> m (Only x p) Source #
(Traversable g, Traversable h) => Traversable (Product g h) Source #
Methods traverse :: Applicative m => (forall a. p a -> m (q a)) -> Product g h p -> m (Product g h q) Source # sequence :: Applicative m => Product g h (Compose * * m p) -> m (Product g h p) Source #

class Functor g => Distributive g where Source #

Equivalent of Distributive for rank 2 data types

Minimal complete definition

distributeWith

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 #

distributeWith :: Functor f1 => (forall x. f1 (f2 x) -> f x) -> f1 (g f2) -> g f Source #

distributeM :: Monad f => f (g f) -> g f Source #

Instances

Distributive Empty Source #
Methods collect :: Functor f1 => (a -> Empty f2) -> f1 a -> Empty (Compose * * f1 f2) Source # distribute :: Functor f1 => f1 (Empty f2) -> Empty (Compose * * f1 f2) Source # distributeWith :: Functor f1 => (forall x. f1 (f2 x) -> f x) -> f1 (Empty f2) -> Empty f Source # distributeM :: Monad f => f (Empty f) -> Empty f Source #
Distributive g => Distributive (Identity g) Source #
Methods collect :: Functor f1 => (a -> Identity g f2) -> f1 a -> Identity g (Compose * * f1 f2) Source # distribute :: Functor f1 => f1 (Identity g f2) -> Identity g (Compose * * f1 f2) Source # distributeWith :: Functor f1 => (forall x. f1 (f2 x) -> f x) -> f1 (Identity g f2) -> Identity g f Source # distributeM :: Monad f => f (Identity g f) -> Identity g f Source #
Distributive (Only x) Source #
Methods collect :: Functor f1 => (a -> Only x f2) -> f1 a -> Only x (Compose * * f1 f2) Source # distribute :: Functor f1 => f1 (Only x f2) -> Only x (Compose * * f1 f2) Source # distributeWith :: Functor f1 => (forall a. f1 (f2 a) -> f a) -> f1 (Only x f2) -> Only x f Source # distributeM :: Monad f => f (Only x f) -> Only x f Source #
(Distributive g, Distributive h) => Distributive (Product g h) Source #
Methods collect :: Functor f1 => (a -> Product g h f2) -> f1 a -> Product g h (Compose * * f1 f2) Source # distribute :: Functor f1 => f1 (Product g h f2) -> Product g h (Compose * * f1 f2) Source # distributeWith :: Functor f1 => (forall x. f1 (f2 x) -> f x) -> f1 (Product g h f2) -> Product g h f Source # distributeM :: Monad f => f (Product g h f) -> Product g h f Source #

Rank 2 data types

newtype Compose k k1 f g a :: forall k k1. (k1 -> *) -> (k -> k1) -> k -> * 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, Functor g) => Functor (Compose * * f g)
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)
Methods pure :: a -> Compose * * f g a # (<>) :: Compose * f g (a -> b) -> Compose * * f g a -> Compose * * f g b # (>) :: 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)
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)
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) #
Functor f => Generic1 (Compose * * f g)
Associated Types type Rep1 (Compose * * f g :: * -> ) :: -> * # Methods from1 :: Compose * * f g a -> Rep1 (Compose * * f g) a # to1 :: Rep1 (Compose * * f g) a -> Compose * * f g a #
(Eq1 f, Eq1 g) => Eq1 (Compose * * f g)
Methods liftEq :: (a -> b -> Bool) -> Compose * * f g a -> Compose * * f g b -> Bool #
(Ord1 f, Ord1 g) => Ord1 (Compose * * f g)
Methods liftCompare :: (a -> b -> Ordering) -> Compose * * f g a -> Compose * * f g b -> Ordering #
(Read1 f, Read1 g) => Read1 (Compose * * f g)
Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Compose * * f g a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Compose * * f g a] #
(Show1 f, Show1 g) => Show1 (Compose * * f g)
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)
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)
Methods (==) :: Compose * * f g a -> Compose * * f g a -> Bool # (/=) :: Compose * * f g a -> Compose * * f g a -> Bool #
(Data (f (g a)), Typeable * k, Typeable * k1, Typeable (k1 -> k) g, Typeable (k -> *) f, Typeable k1 a) => Data (Compose k1 k f g a)
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall b. b -> c b) -> Compose k1 k f g a -> c (Compose k1 k f g a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Compose k1 k f g a) # toConstr :: Compose k1 k f g a -> Constr # dataTypeOf :: Compose k1 k f g a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Compose k1 k f g a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Compose k1 k f g a)) # gmapT :: (forall b. Data b => b -> b) -> Compose k1 k f g a -> Compose k1 k f g a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Compose k1 k f g a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Compose k1 k f g a -> r # gmapQ :: (forall d. Data d => d -> u) -> Compose k1 k f g a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Compose k1 k f g a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Compose k1 k f g a -> m (Compose k1 k f g a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Compose k1 k f g a -> m (Compose k1 k f g a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Compose k1 k f g a -> m (Compose k1 k f g a) #
(Ord1 f, Ord1 g, Ord a) => Ord (Compose * * f g a)
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)
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)
Methods showsPrec :: Int -> Compose * * f g a -> ShowS # show :: Compose * * f g a -> String # showList :: [Compose * * f g a] -> ShowS #
Generic (Compose k1 k f g a)
Associated Types type Rep (Compose k1 k f g a) :: * -> * # Methods from :: Compose k1 k f g a -> Rep (Compose k1 k f g a) x # to :: Rep (Compose k1 k f g a) x -> Compose k1 k f g a #
type Rep1 (Compose * * f g)
type Rep1 (Compose * * f g) = D1 (MetaData "Compose" "Data.Functor.Compose" "base" True) (C1 (MetaCons "Compose" PrefixI True) (S1 (MetaSel (Just Symbol "getCompose") NoSourceUnpackedness NoSourceStrictness DecidedLazy) ((:.:) f (Rec1 g))))
type Rep (Compose k1 k f g a)
type Rep (Compose k1 k 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

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

newtype Only a f Source #

A rank-2 tuple of only one element

Constructors

Only
Fields fromOnly :: f a

Instances

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

newtype Identity g f Source #

Equivalent of Identity for rank 2 data types

Constructors

Identity
Fields runIdentity :: g f

Instances

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

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

liftA3 :: Apply g => (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