Safe Haskell	None
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

class Functor g where
- (<$>) :: (forall a. p a -> q a) -> g p -> g q
class Functor g => Apply g where
- (<*>) :: g (p ~> q) -> g p -> g q
- liftA2 :: (forall a. p a -> q a -> r a) -> g p -> g q -> g r
- liftA3 :: (forall a. p a -> q a -> r a -> s a) -> g p -> g q -> g r -> g s
class Apply g => Applicative g where
- pure :: (forall a. f a) -> g f
class Foldable g where
- foldMap :: Monoid m => (forall a. p a -> m) -> g p -> m
class (Functor g, Foldable g) => Traversable g where
- traverse :: Applicative m => (forall a. p a -> m (q a)) -> g p -> m (g q)
- sequence :: Applicative m => g (Compose m p) -> m (g p)
class DistributiveTraversable g => Distributive g where
- collect :: Functor f1 => (a -> g f2) -> f1 a -> g (Compose f1 f2)
- distribute :: Functor f1 => f1 (g f2) -> g (Compose f1 f2)
- cotraverse :: Functor m => (forall a. m (p a) -> q a) -> m (g p) -> g q
class Functor g => DistributiveTraversable (g :: (k -> *) -> *) where
- collectTraversable :: Traversable f1 => (a -> g f2) -> f1 a -> g (Compose f1 f2)
- distributeTraversable :: Traversable f1 => f1 (g f2) -> g (Compose f1 f2)
- cotraverseTraversable :: Traversable f1 => (forall x. f1 (f2 x) -> f x) -> f1 (g f2) -> g f
distributeJoin :: (Distributive g, Monad f) => f (g f) -> g f
newtype Compose g p q = Compose {
- getCompose :: g (Compose p q)
}
data Empty f = Empty
newtype Only a f = Only {
- fromOnly :: f a
}
newtype Flip g a f = Flip {
- unFlip :: g (f a)
}
newtype Identity g f = Identity {
- runIdentity :: g f
}
data Product (f :: k -> Type) (g :: k -> Type) (a :: k) = Pair (f a) (g a)
data Sum (f :: k -> Type) (g :: k -> Type) (a :: k)
- = InL (f a)
- | InR (g a)
newtype Arrow p q a = Arrow {
- apply :: p a -> q a
}
type (~>) = Arrow
($) :: Arrow p q a -> p a -> q a
fst :: Product g h p -> g p
snd :: Product g h p -> h p
ap :: Apply g => g (p ~> q) -> g p -> g q
fmap :: Functor g => (forall a. p a -> q a) -> g p -> g q
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
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
fmapTraverse :: (DistributiveTraversable g, Traversable f) => (forall a. f (t a) -> u a) -> f (g t) -> g u
liftA2Traverse1 :: (Apply g, DistributiveTraversable g, Traversable f) => (forall a. f (t a) -> u a -> v a) -> f (g t) -> g u -> g v
liftA2Traverse2 :: (Apply g, DistributiveTraversable g, Traversable f) => (forall a. t a -> f (u a) -> v a) -> g t -> f (g u) -> g v
liftA2TraverseBoth :: (Apply g, DistributiveTraversable g, Traversable f1, Traversable f2) => (forall a. f1 (t a) -> f2 (u a) -> v a) -> f1 (g t) -> f2 (g u) -> g v
distributeWith :: (Distributive g, Functor f) => (forall i. f (a i) -> b i) -> f (g a) -> g b
distributeWithTraversable :: (DistributiveTraversable g, Traversable m) => (forall a. m (p a) -> q a) -> m (g p) -> g q

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)

Methods

(<$>) :: (forall a. p a -> q a) -> g p -> g q infixl 4 Source #

Instances

Instances details

Functor (U1 :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p a -> q a) -> U1 p -> U1 q Source #
Functor (V1 :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p a -> q a) -> V1 p -> V1 q Source #
Functor (Proxy :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p a -> q a) -> Proxy p -> Proxy q Source #
Functor (Empty :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p a -> q a) -> Empty p -> Empty q Source #
Functor f => Functor (Rec1 f :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p a -> q a) -> Rec1 f p -> Rec1 f q Source #
Functor (Const a :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a0 :: k0). p a0 -> q a0) -> Const a p -> Const a q Source #
Functor (Only a :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a0 :: k0). p a0 -> q a0) -> Only a p -> Only a q Source #
Functor g => Functor (Identity g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p a -> q a) -> Identity g p -> Identity g q Source #
(Functor f, Functor g) => Functor (f :*: g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p a -> q a) -> (f :: g) p -> (f :: g) q Source #
(Functor f, Functor g) => Functor (f :+: g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p a -> q a) -> (f :+: g) p -> (f :+: g) q Source #
Functor (K1 i c :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p a -> q a) -> K1 i c p -> K1 i c q Source #
(Functor g, Functor h) => Functor (Sum g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p a -> q a) -> Sum g h p -> Sum g h q Source #
(Functor g, Functor h) => Functor (Product g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p a -> q a) -> Product g h p -> Product g h q Source #
Functor f => Functor (M1 i c f :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p a -> q a) -> M1 i c f p -> M1 i c f q Source #
(Functor g, Functor p) => Functor (Compose g p :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p0 a -> q a) -> Compose g p p0 -> Compose g p q Source #
Functor g => Functor (Flip g a :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a0 :: k0). p a0 -> q a0) -> Flip g a p -> Flip g a 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 (p ~> q) -> g p -> g q infixl 4 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

Instances details

Apply (U1 :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). U1 (p ~> q) -> U1 p -> U1 q Source # liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> U1 p -> U1 q -> U1 r Source # liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> U1 p -> U1 q -> U1 r -> U1 s Source #
Apply (V1 :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). V1 (p ~> q) -> V1 p -> V1 q Source # liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> V1 p -> V1 q -> V1 r Source # liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> V1 p -> V1 q -> V1 r -> V1 s Source #
Apply (Proxy :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). Proxy (p ~> q) -> Proxy p -> Proxy q Source # liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Proxy p -> Proxy q -> Proxy r Source # liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Proxy p -> Proxy q -> Proxy r -> Proxy s Source #
Apply (Empty :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). Empty (p ~> q) -> Empty p -> Empty q Source # liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Empty p -> Empty q -> Empty r Source # liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Empty p -> Empty q -> Empty r -> Empty s Source #
Apply f => Apply (Rec1 f :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). Rec1 f (p ~> q) -> Rec1 f p -> Rec1 f q Source # liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Rec1 f p -> Rec1 f q -> Rec1 f r Source # liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Rec1 f p -> Rec1 f q -> Rec1 f r -> Rec1 f s Source #
Semigroup x => Apply (Const x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). Const x (p ~> q) -> Const x p -> Const x q Source # liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Const x p -> Const x q -> Const x r Source # liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Const x p -> Const x q -> Const x r -> Const x s Source #
Apply (Only x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). Only x (p ~> q) -> Only x p -> Only x q Source # liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Only x p -> Only x q -> Only x r Source # liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Only x p -> Only x q -> Only x r -> Only x s Source #
Apply g => Apply (Identity g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). Identity g (p ~> q) -> Identity g p -> Identity g q Source # liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Identity g p -> Identity g q -> Identity g r Source # liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Identity g p -> Identity g q -> Identity g r -> Identity g s Source #
(Apply f, Apply g) => Apply (f :*: g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). (f :: g) (p ~> q) -> (f :: g) p -> (f :: g) q Source # liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> (f :: g) p -> (f :: g) q -> (f :: g) r Source # liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> (f :: g) p -> (f :: g) q -> (f :: g) r -> (f :*: g) s Source #
Semigroup c => Apply (K1 i c :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). K1 i c (p ~> q) -> K1 i c p -> K1 i c q Source # liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> K1 i c p -> K1 i c q -> K1 i c r Source # liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> K1 i c p -> K1 i c q -> K1 i c r -> K1 i c s Source #
(Apply g, Apply h) => Apply (Product g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). Product g h (p ~> q) -> Product g h p -> Product g h q Source # liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Product g h p -> Product g h q -> Product g h r Source # liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Product g h p -> Product g h q -> Product g h r -> Product g h s Source #
Apply f => Apply (M1 i c f :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). M1 i c f (p ~> q) -> M1 i c f p -> M1 i c f q Source # liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> M1 i c f p -> M1 i c f q -> M1 i c f r Source # liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> M1 i c f p -> M1 i c f q -> M1 i c f r -> M1 i c f s Source #
(Apply g, Applicative p) => Apply (Compose g p :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p0 :: k0 -> Type) (q :: k0 -> Type). Compose g p (p0 ~> q) -> Compose g p p0 -> Compose g p q Source # liftA2 :: (forall (a :: k0). p0 a -> q a -> r a) -> Compose g p p0 -> Compose g p q -> Compose g p r Source # liftA3 :: (forall (a :: k0). p0 a -> q a -> r a -> s a) -> Compose g p p0 -> Compose g p q -> Compose g p r -> Compose g p s Source #
Applicative g => Apply (Flip g a :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). Flip g a (p ~> q) -> Flip g a p -> Flip g a q Source # liftA2 :: (forall (a0 :: k0). p a0 -> q a0 -> r a0) -> Flip g a p -> Flip g a q -> Flip g a r Source # liftA3 :: (forall (a0 :: k0). p a0 -> q a0 -> r a0 -> s a0) -> Flip g a p -> Flip g a q -> Flip g a r -> Flip g a s Source #

class Apply g => Applicative g where Source #

Equivalent of Applicative for rank 2 data types

Methods

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

Instances

Instances details

Applicative (Proxy :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a :: k0). f a) -> Proxy f Source #
Applicative (Empty :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a :: k0). f a) -> Empty f Source #
Applicative f => Applicative (Rec1 f :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a :: k0). f0 a) -> Rec1 f f0 Source #
(Semigroup x, Monoid x) => Applicative (Const x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a :: k0). f a) -> Const x f Source #
Applicative (Only x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a :: k0). f a) -> Only x f Source #
Applicative g => Applicative (Identity g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a :: k0). f a) -> Identity g f Source #
(Applicative f, Applicative g) => Applicative (f :*: g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a :: k0). f0 a) -> (f :*: g) f0 Source #
(Semigroup c, Monoid c) => Applicative (K1 i c :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a :: k0). f a) -> K1 i c f Source #
(Applicative g, Applicative h) => Applicative (Product g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a :: k0). f a) -> Product g h f Source #
Applicative f => Applicative (M1 i c f :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a :: k0). f0 a) -> M1 i c f f0 Source #
(Applicative g, Applicative p) => Applicative (Compose g p :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a :: k0). f a) -> Compose g p f Source #
Applicative g => Applicative (Flip g a :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a0 :: k0). f a0) -> Flip g a f Source #

class Foldable g where Source #

Equivalent of Foldable for rank 2 data types

Methods

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

Instances

Instances details

Foldable (U1 :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> U1 p -> m Source #
Foldable (V1 :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> V1 p -> m Source #
Foldable (Proxy :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Proxy p -> m Source #
Foldable (Empty :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Empty p -> m Source #
Foldable f => Foldable (Rec1 f :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Rec1 f p -> m Source #
Foldable (Const x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Const x p -> m Source #
Foldable (Only x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Only x p -> m Source #
Foldable g => Foldable (Identity g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Identity g p -> m Source #
(Foldable f, Foldable g) => Foldable (f :*: g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> (f :*: g) p -> m Source #
(Foldable f, Foldable g) => Foldable (f :+: g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> (f :+: g) p -> m Source #
Foldable (K1 i c :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> K1 i c p -> m Source #
(Foldable g, Foldable h) => Foldable (Sum g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Sum g h p -> m Source #
(Foldable g, Foldable h) => Foldable (Product g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Product g h p -> m Source #
Foldable f => Foldable (M1 i c f :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> M1 i c f p -> m Source #
(Foldable g, Foldable p) => Foldable (Compose g p :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p0 a -> m) -> Compose g p p0 -> m Source #
Foldable g => Foldable (Flip g a :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a0 :: k0). p a0 -> m) -> Flip g a 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

Instances details

Traversable (U1 :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> U1 p -> m (U1 q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => U1 (Compose m p) -> m (U1 p) Source #
Traversable (V1 :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> V1 p -> m (V1 q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => V1 (Compose m p) -> m (V1 p) Source #
Traversable (Proxy :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Proxy p -> m (Proxy q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => Proxy (Compose m p) -> m (Proxy p) Source #
Traversable (Empty :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Empty p -> m (Empty q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => Empty (Compose m p) -> m (Empty p) Source #
Traversable f => Traversable (Rec1 f :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Rec1 f p -> m (Rec1 f q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => Rec1 f (Compose m p) -> m (Rec1 f p) Source #
Traversable (Const x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Const x p -> m (Const x q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => Const x (Compose m p) -> m (Const x p) Source #
Traversable (Only x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Only x p -> m (Only x q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => Only x (Compose m p) -> m (Only x p) Source #
Traversable g => Traversable (Identity g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Identity g p -> m (Identity g q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => Identity g (Compose m p) -> m (Identity g p) Source #
(Traversable f, Traversable g) => Traversable (f :*: g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> (f :: g) p -> m ((f :: g) q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => (f :: g) (Compose m p) -> m ((f :: g) p) Source #
(Traversable f, Traversable g) => Traversable (f :+: g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> (f :+: g) p -> m ((f :+: g) q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => (f :+: g) (Compose m p) -> m ((f :+: g) p) Source #
Traversable (K1 i c :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> K1 i c p -> m (K1 i c q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => K1 i c (Compose m p) -> m (K1 i c p) Source #
(Traversable g, Traversable h) => Traversable (Sum g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Sum g h p -> m (Sum g h q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => Sum g h (Compose m p) -> m (Sum g h p) Source #
(Traversable g, Traversable h) => Traversable (Product g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Product g h p -> m (Product g h q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => Product g h (Compose m p) -> m (Product g h p) Source #
Traversable f => Traversable (M1 i c f :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> M1 i c f p -> m (M1 i c f q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => M1 i c f (Compose m p) -> m (M1 i c f p) Source #
(Traversable g, Traversable p) => Traversable (Compose g p :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p0 a -> m (q a)) -> Compose g p p0 -> m (Compose g p q) Source # sequence :: forall m (p0 :: k0 -> Type). Applicative m => Compose g p (Compose0 m p0) -> m (Compose g p p0) Source #
Traversable g => Traversable (Flip g a :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a0 :: k0). p a0 -> m (q a0)) -> Flip g a p -> m (Flip g a q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => Flip g a (Compose m p) -> m (Flip g a 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

Instances details

Distributive (Proxy :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collect :: forall f1 a (f2 :: k0 -> Type). Functor f1 => (a -> Proxy f2) -> f1 a -> Proxy (Compose f1 f2) Source # distribute :: forall f1 (f2 :: k0 -> Type). Functor f1 => f1 (Proxy f2) -> Proxy (Compose f1 f2) Source # cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Proxy p) -> Proxy q Source #
Distributive (Empty :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collect :: forall f1 a (f2 :: k0 -> Type). Functor f1 => (a -> Empty f2) -> f1 a -> Empty (Compose f1 f2) Source # distribute :: forall f1 (f2 :: k0 -> Type). Functor f1 => f1 (Empty f2) -> Empty (Compose f1 f2) Source # cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Empty p) -> Empty q Source #
Distributive f => Distributive (Rec1 f :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collect :: forall f1 a (f2 :: k0 -> Type). Functor f1 => (a -> Rec1 f f2) -> f1 a -> Rec1 f (Compose f1 f2) Source # distribute :: forall f1 (f2 :: k0 -> Type). Functor f1 => f1 (Rec1 f f2) -> Rec1 f (Compose f1 f2) Source # cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Rec1 f p) -> Rec1 f q Source #
Distributive (Only x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collect :: forall f1 a (f2 :: k0 -> Type). Functor f1 => (a -> Only x f2) -> f1 a -> Only x (Compose f1 f2) Source # distribute :: forall f1 (f2 :: k0 -> Type). Functor f1 => f1 (Only x f2) -> Only x (Compose f1 f2) Source # cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Only x p) -> Only x q Source #
Distributive g => Distributive (Identity g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collect :: forall f1 a (f2 :: k0 -> Type). Functor f1 => (a -> Identity g f2) -> f1 a -> Identity g (Compose f1 f2) Source # distribute :: forall f1 (f2 :: k0 -> Type). Functor f1 => f1 (Identity g f2) -> Identity g (Compose f1 f2) Source # cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Identity g p) -> Identity g q Source #
(Distributive f, Distributive g) => Distributive (f :*: g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collect :: forall f1 a (f2 :: k0 -> Type). Functor f1 => (a -> (f :: g) f2) -> f1 a -> (f :: g) (Compose f1 f2) Source # distribute :: forall f1 (f2 :: k0 -> Type). Functor f1 => f1 ((f :: g) f2) -> (f :: g) (Compose f1 f2) Source # cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m ((f :: g) p) -> (f :: g) q Source #
(Distributive g, Distributive h) => Distributive (Product g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collect :: forall f1 a (f2 :: k0 -> Type). Functor f1 => (a -> Product g h f2) -> f1 a -> Product g h (Compose f1 f2) Source # distribute :: forall f1 (f2 :: k0 -> Type). Functor f1 => f1 (Product g h f2) -> Product g h (Compose f1 f2) Source # cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Product g h p) -> Product g h q Source #
Distributive f => Distributive (M1 i c f :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collect :: forall f1 a (f2 :: k0 -> Type). Functor f1 => (a -> M1 i c f f2) -> f1 a -> M1 i c f (Compose f1 f2) Source # distribute :: forall f1 (f2 :: k0 -> Type). Functor f1 => f1 (M1 i c f f2) -> M1 i c f (Compose f1 f2) Source # cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (M1 i c f p) -> M1 i c f q Source #
(Distributive g, Distributive p) => Distributive (Compose g p :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collect :: forall f1 a (f2 :: k0 -> Type). Functor f1 => (a -> Compose g p f2) -> f1 a -> Compose g p (Compose0 f1 f2) Source # distribute :: forall f1 (f2 :: k0 -> Type). Functor f1 => f1 (Compose g p f2) -> Compose g p (Compose0 f1 f2) Source # cotraverse :: Functor m => (forall (a :: k0). m (p0 a) -> q a) -> m (Compose g p p0) -> Compose g p q Source #

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

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

Minimal complete definition

Nothing

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 #

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

Instances

Instances details

DistributiveTraversable (Proxy :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collectTraversable :: forall f1 a (f2 :: k0 -> Type). Traversable f1 => (a -> Proxy f2) -> f1 a -> Proxy (Compose f1 f2) Source # distributeTraversable :: forall f1 (f2 :: k0 -> Type). Traversable f1 => f1 (Proxy f2) -> Proxy (Compose f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Proxy f2) -> Proxy f Source #
DistributiveTraversable (Empty :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collectTraversable :: forall f1 a (f2 :: k0 -> Type). Traversable f1 => (a -> Empty f2) -> f1 a -> Empty (Compose f1 f2) Source # distributeTraversable :: forall f1 (f2 :: k0 -> Type). Traversable f1 => f1 (Empty f2) -> Empty (Compose f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Empty f2) -> Empty f Source #
Monoid x => DistributiveTraversable (Const x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collectTraversable :: forall f1 a (f2 :: k0 -> Type). Traversable f1 => (a -> Const x f2) -> f1 a -> Const x (Compose f1 f2) Source # distributeTraversable :: forall f1 (f2 :: k0 -> Type). Traversable f1 => f1 (Const x f2) -> Const x (Compose f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x0 :: k0). f1 (f2 x0) -> f x0) -> f1 (Const x f2) -> Const x f Source #
DistributiveTraversable f => DistributiveTraversable (Rec1 f :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collectTraversable :: forall f1 a (f2 :: k0 -> Type). Traversable f1 => (a -> Rec1 f f2) -> f1 a -> Rec1 f (Compose f1 f2) Source # distributeTraversable :: forall f1 (f2 :: k0 -> Type). Traversable f1 => f1 (Rec1 f f2) -> Rec1 f (Compose f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f0 x) -> f1 (Rec1 f f2) -> Rec1 f f0 Source #
DistributiveTraversable (Only x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collectTraversable :: forall f1 a (f2 :: k0 -> Type). Traversable f1 => (a -> Only x f2) -> f1 a -> Only x (Compose f1 f2) Source # distributeTraversable :: forall f1 (f2 :: k0 -> Type). Traversable f1 => f1 (Only x f2) -> Only x (Compose f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x0 :: k0). f1 (f2 x0) -> f x0) -> f1 (Only x f2) -> Only x f Source #
DistributiveTraversable g => DistributiveTraversable (Identity g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collectTraversable :: forall f1 a (f2 :: k0 -> Type). Traversable f1 => (a -> Identity g f2) -> f1 a -> Identity g (Compose f1 f2) Source # distributeTraversable :: forall f1 (f2 :: k0 -> Type). Traversable f1 => f1 (Identity g f2) -> Identity g (Compose f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Identity g f2) -> Identity g f Source #
Monoid c => DistributiveTraversable (K1 i c :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collectTraversable :: forall f1 a (f2 :: k0 -> Type). Traversable f1 => (a -> K1 i c f2) -> f1 a -> K1 i c (Compose f1 f2) Source # distributeTraversable :: forall f1 (f2 :: k0 -> Type). Traversable f1 => f1 (K1 i c f2) -> K1 i c (Compose f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (K1 i c f2) -> K1 i c f Source #
(DistributiveTraversable f, DistributiveTraversable g) => DistributiveTraversable (f :*: g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collectTraversable :: forall f1 a (f2 :: k0 -> Type). Traversable f1 => (a -> (f :: g) f2) -> f1 a -> (f :: g) (Compose f1 f2) Source # distributeTraversable :: forall f1 (f2 :: k0 -> Type). Traversable f1 => f1 ((f :: g) f2) -> (f :: g) (Compose f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f0 x) -> f1 ((f :: g) f2) -> (f :: g) f0 Source #
(DistributiveTraversable g, DistributiveTraversable h) => DistributiveTraversable (Product g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collectTraversable :: forall f1 a (f2 :: k0 -> Type). Traversable f1 => (a -> Product g h f2) -> f1 a -> Product g h (Compose f1 f2) Source # distributeTraversable :: forall f1 (f2 :: k0 -> Type). Traversable f1 => f1 (Product g h f2) -> Product g h (Compose f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Product g h f2) -> Product g h f Source #
DistributiveTraversable f => DistributiveTraversable (M1 i c f :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collectTraversable :: forall f1 a (f2 :: k0 -> Type). Traversable f1 => (a -> M1 i c f f2) -> f1 a -> M1 i c f (Compose f1 f2) Source # distributeTraversable :: forall f1 (f2 :: k0 -> Type). Traversable f1 => f1 (M1 i c f f2) -> M1 i c f (Compose f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f0 x) -> f1 (M1 i c f f2) -> M1 i c f f0 Source #
(DistributiveTraversable g, Distributive p) => DistributiveTraversable (Compose g p :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collectTraversable :: forall f1 a (f2 :: k0 -> Type). Traversable f1 => (a -> Compose g p f2) -> f1 a -> Compose g p (Compose0 f1 f2) Source # distributeTraversable :: forall f1 (f2 :: k0 -> Type). Traversable f1 => f1 (Compose g p f2) -> Compose g p (Compose0 f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Compose g p f2) -> Compose g p 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 g p q Source #

Equivalent of Compose for rank 2 data types

Constructors

Compose
Fields getCompose :: g (Compose p q)

Instances

Instances details

(DistributiveTraversable g, Distributive p) => DistributiveTraversable (Compose g p :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collectTraversable :: forall f1 a (f2 :: k0 -> Type). Traversable f1 => (a -> Compose g p f2) -> f1 a -> Compose g p (Compose0 f1 f2) Source # distributeTraversable :: forall f1 (f2 :: k0 -> Type). Traversable f1 => f1 (Compose g p f2) -> Compose g p (Compose0 f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Compose g p f2) -> Compose g p f Source #
(Distributive g, Distributive p) => Distributive (Compose g p :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collect :: forall f1 a (f2 :: k0 -> Type). Functor f1 => (a -> Compose g p f2) -> f1 a -> Compose g p (Compose0 f1 f2) Source # distribute :: forall f1 (f2 :: k0 -> Type). Functor f1 => f1 (Compose g p f2) -> Compose g p (Compose0 f1 f2) Source # cotraverse :: Functor m => (forall (a :: k0). m (p0 a) -> q a) -> m (Compose g p p0) -> Compose g p q Source #
(Applicative g, Applicative p) => Applicative (Compose g p :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a :: k0). f a) -> Compose g p f Source #
(Apply g, Applicative p) => Apply (Compose g p :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p0 :: k0 -> Type) (q :: k0 -> Type). Compose g p (p0 ~> q) -> Compose g p p0 -> Compose g p q Source # liftA2 :: (forall (a :: k0). p0 a -> q a -> r a) -> Compose g p p0 -> Compose g p q -> Compose g p r Source # liftA3 :: (forall (a :: k0). p0 a -> q a -> r a -> s a) -> Compose g p p0 -> Compose g p q -> Compose g p r -> Compose g p s Source #
(Traversable g, Traversable p) => Traversable (Compose g p :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p0 a -> m (q a)) -> Compose g p p0 -> m (Compose g p q) Source # sequence :: forall m (p0 :: k0 -> Type). Applicative m => Compose g p (Compose0 m p0) -> m (Compose g p p0) Source #
(Foldable g, Foldable p) => Foldable (Compose g p :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p0 a -> m) -> Compose g p p0 -> m Source #
(Functor g, Functor p) => Functor (Compose g p :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p0 a -> q a) -> Compose g p p0 -> Compose g p q Source #
Eq (g (Compose p q)) => Eq (Compose g p q) Source #
Instance details Defined in Rank2 Methods (==) :: Compose g p q -> Compose g p q -> Bool # (/=) :: Compose g p q -> Compose g p q -> Bool #
Ord (g (Compose p q)) => Ord (Compose g p q) Source #
Instance details Defined in Rank2 Methods compare :: Compose g p q -> Compose g p q -> Ordering # (<) :: Compose g p q -> Compose g p q -> Bool # (<=) :: Compose g p q -> Compose g p q -> Bool # (>) :: Compose g p q -> Compose g p q -> Bool # (>=) :: Compose g p q -> Compose g p q -> Bool # max :: Compose g p q -> Compose g p q -> Compose g p q # min :: Compose g p q -> Compose g p q -> Compose g p q #
Show (g (Compose p q)) => Show (Compose g p q) Source #
Instance details Defined in Rank2 Methods showsPrec :: Int -> Compose g p q -> ShowS # show :: Compose g p q -> String # showList :: [Compose g p q] -> ShowS #

data Empty f Source #

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

Constructors

Empty

Instances

Instances details

DistributiveTraversable (Empty :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collectTraversable :: forall f1 a (f2 :: k0 -> Type). Traversable f1 => (a -> Empty f2) -> f1 a -> Empty (Compose f1 f2) Source # distributeTraversable :: forall f1 (f2 :: k0 -> Type). Traversable f1 => f1 (Empty f2) -> Empty (Compose f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Empty f2) -> Empty f Source #
Distributive (Empty :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collect :: forall f1 a (f2 :: k0 -> Type). Functor f1 => (a -> Empty f2) -> f1 a -> Empty (Compose f1 f2) Source # distribute :: forall f1 (f2 :: k0 -> Type). Functor f1 => f1 (Empty f2) -> Empty (Compose f1 f2) Source # cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Empty p) -> Empty q Source #
Applicative (Empty :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a :: k0). f a) -> Empty f Source #
Apply (Empty :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). Empty (p ~> q) -> Empty p -> Empty q Source # liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Empty p -> Empty q -> Empty r Source # liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Empty p -> Empty q -> Empty r -> Empty s Source #
Traversable (Empty :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Empty p -> m (Empty q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => Empty (Compose m p) -> m (Empty p) Source #
Foldable (Empty :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Empty p -> m Source #
Functor (Empty :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p a -> q a) -> Empty p -> Empty q Source #
Eq (Empty f) Source #
Instance details Defined in Rank2 Methods (==) :: Empty f -> Empty f -> Bool # (/=) :: Empty f -> Empty f -> Bool #
Ord (Empty f) Source #
Instance details Defined in Rank2 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 #
Instance details Defined in Rank2 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

Instances details

DistributiveTraversable (Only x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collectTraversable :: forall f1 a (f2 :: k0 -> Type). Traversable f1 => (a -> Only x f2) -> f1 a -> Only x (Compose f1 f2) Source # distributeTraversable :: forall f1 (f2 :: k0 -> Type). Traversable f1 => f1 (Only x f2) -> Only x (Compose f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x0 :: k0). f1 (f2 x0) -> f x0) -> f1 (Only x f2) -> Only x f Source #
Distributive (Only x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collect :: forall f1 a (f2 :: k0 -> Type). Functor f1 => (a -> Only x f2) -> f1 a -> Only x (Compose f1 f2) Source # distribute :: forall f1 (f2 :: k0 -> Type). Functor f1 => f1 (Only x f2) -> Only x (Compose f1 f2) Source # cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Only x p) -> Only x q Source #
Applicative (Only x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a :: k0). f a) -> Only x f Source #
Apply (Only x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). Only x (p ~> q) -> Only x p -> Only x q Source # liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Only x p -> Only x q -> Only x r Source # liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Only x p -> Only x q -> Only x r -> Only x s Source #
Traversable (Only x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Only x p -> m (Only x q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => Only x (Compose m p) -> m (Only x p) Source #
Foldable (Only x :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Only x p -> m Source #
Functor (Only a :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a0 :: k0). p a0 -> q a0) -> Only a p -> Only a q Source #
Eq (f a) => Eq (Only a f) Source #
Instance details Defined in Rank2 Methods (==) :: Only a f -> Only a f -> Bool # (/=) :: Only a f -> Only a f -> Bool #
Ord (f a) => Ord (Only a f) Source #
Instance details Defined in Rank2 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 #
Instance details Defined in Rank2 Methods showsPrec :: Int -> Only a f -> ShowS # show :: Only a f -> String # showList :: [Only a f] -> ShowS #

newtype Flip g a f Source #

A nested parametric type represented as a rank-2 type

Constructors

Flip
Fields unFlip :: g (f a)

Instances

Instances details

Applicative g => Applicative (Flip g a :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a0 :: k0). f a0) -> Flip g a f Source #
Applicative g => Apply (Flip g a :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). Flip g a (p ~> q) -> Flip g a p -> Flip g a q Source # liftA2 :: (forall (a0 :: k0). p a0 -> q a0 -> r a0) -> Flip g a p -> Flip g a q -> Flip g a r Source # liftA3 :: (forall (a0 :: k0). p a0 -> q a0 -> r a0 -> s a0) -> Flip g a p -> Flip g a q -> Flip g a r -> Flip g a s Source #
Traversable g => Traversable (Flip g a :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a0 :: k0). p a0 -> m (q a0)) -> Flip g a p -> m (Flip g a q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => Flip g a (Compose m p) -> m (Flip g a p) Source #
Foldable g => Foldable (Flip g a :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a0 :: k0). p a0 -> m) -> Flip g a p -> m Source #
Functor g => Functor (Flip g a :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a0 :: k0). p a0 -> q a0) -> Flip g a p -> Flip g a q Source #
Eq (g (f a)) => Eq (Flip g a f) Source #
Instance details Defined in Rank2 Methods (==) :: Flip g a f -> Flip g a f -> Bool # (/=) :: Flip g a f -> Flip g a f -> Bool #
Ord (g (f a)) => Ord (Flip g a f) Source #
Instance details Defined in Rank2 Methods compare :: Flip g a f -> Flip g a f -> Ordering # (<) :: Flip g a f -> Flip g a f -> Bool # (<=) :: Flip g a f -> Flip g a f -> Bool # (>) :: Flip g a f -> Flip g a f -> Bool # (>=) :: Flip g a f -> Flip g a f -> Bool # max :: Flip g a f -> Flip g a f -> Flip g a f # min :: Flip g a f -> Flip g a f -> Flip g a f #
Show (g (f a)) => Show (Flip g a f) Source #
Instance details Defined in Rank2 Methods showsPrec :: Int -> Flip g a f -> ShowS # show :: Flip g a f -> String # showList :: [Flip g a f] -> ShowS #
Semigroup (g (f a)) => Semigroup (Flip g a f) Source #
Instance details Defined in Rank2 Methods (<>) :: Flip g a f -> Flip g a f -> Flip g a f # sconcat :: NonEmpty (Flip g a f) -> Flip g a f # stimes :: Integral b => b -> Flip g a f -> Flip g a f #
Monoid (g (f a)) => Monoid (Flip g a f) Source #
Instance details Defined in Rank2 Methods mempty :: Flip g a f # mappend :: Flip g a f -> Flip g a f -> Flip g a f # mconcat :: [Flip g a f] -> Flip g a f #

newtype Identity g f Source #

Equivalent of Identity for rank 2 data types

Constructors

Identity
Fields runIdentity :: g f

Instances

Instances details

DistributiveTraversable g => DistributiveTraversable (Identity g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collectTraversable :: forall f1 a (f2 :: k0 -> Type). Traversable f1 => (a -> Identity g f2) -> f1 a -> Identity g (Compose f1 f2) Source # distributeTraversable :: forall f1 (f2 :: k0 -> Type). Traversable f1 => f1 (Identity g f2) -> Identity g (Compose f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Identity g f2) -> Identity g f Source #
Distributive g => Distributive (Identity g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collect :: forall f1 a (f2 :: k0 -> Type). Functor f1 => (a -> Identity g f2) -> f1 a -> Identity g (Compose f1 f2) Source # distribute :: forall f1 (f2 :: k0 -> Type). Functor f1 => f1 (Identity g f2) -> Identity g (Compose f1 f2) Source # cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Identity g p) -> Identity g q Source #
Applicative g => Applicative (Identity g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a :: k0). f a) -> Identity g f Source #
Apply g => Apply (Identity g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). Identity g (p ~> q) -> Identity g p -> Identity g q Source # liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Identity g p -> Identity g q -> Identity g r Source # liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Identity g p -> Identity g q -> Identity g r -> Identity g s Source #
Traversable g => Traversable (Identity g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Identity g p -> m (Identity g q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => Identity g (Compose m p) -> m (Identity g p) Source #
Foldable g => Foldable (Identity g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Identity g p -> m Source #
Functor g => Functor (Identity g :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p a -> q a) -> Identity g p -> Identity g q Source #
Eq (g f) => Eq (Identity g f) Source #
Instance details Defined in Rank2 Methods (==) :: Identity g f -> Identity g f -> Bool # (/=) :: Identity g f -> Identity g f -> Bool #
Ord (g f) => Ord (Identity g f) Source #
Instance details Defined in Rank2 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 #
Instance details Defined in Rank2 Methods showsPrec :: Int -> Identity g f -> ShowS # show :: Identity g f -> String # showList :: [Identity g f] -> ShowS #

data Product (f :: k -> Type) (g :: k -> Type) (a :: k) #

Lifted product of functors.

Constructors

Pair (f a) (g a)

Instances

Instances details

Generic1 (Product f g :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Associated Types type Rep1 (Product f g) :: k -> Type # Methods from1 :: forall (a :: k0). Product f g a -> Rep1 (Product f g) a # to1 :: forall (a :: k0). Rep1 (Product f g) a -> Product f g a #
(DistributiveTraversable g, DistributiveTraversable h) => DistributiveTraversable (Product g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collectTraversable :: forall f1 a (f2 :: k0 -> Type). Traversable f1 => (a -> Product g h f2) -> f1 a -> Product g h (Compose f1 f2) Source # distributeTraversable :: forall f1 (f2 :: k0 -> Type). Traversable f1 => f1 (Product g h f2) -> Product g h (Compose f1 f2) Source # cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Product g h f2) -> Product g h f Source #
(Distributive g, Distributive h) => Distributive (Product g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods collect :: forall f1 a (f2 :: k0 -> Type). Functor f1 => (a -> Product g h f2) -> f1 a -> Product g h (Compose f1 f2) Source # distribute :: forall f1 (f2 :: k0 -> Type). Functor f1 => f1 (Product g h f2) -> Product g h (Compose f1 f2) Source # cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Product g h p) -> Product g h q Source #
(Applicative g, Applicative h) => Applicative (Product g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods pure :: (forall (a :: k0). f a) -> Product g h f Source #
(Apply g, Apply h) => Apply (Product g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<*>) :: forall (p :: k0 -> Type) (q :: k0 -> Type). Product g h (p ~> q) -> Product g h p -> Product g h q Source # liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Product g h p -> Product g h q -> Product g h r Source # liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Product g h p -> Product g h q -> Product g h r -> Product g h s Source #
(Traversable g, Traversable h) => Traversable (Product g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Product g h p -> m (Product g h q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => Product g h (Compose m p) -> m (Product g h p) Source #
(Foldable g, Foldable h) => Foldable (Product g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Product g h p -> m Source #
(Functor g, Functor h) => Functor (Product g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p a -> q a) -> Product g h p -> Product g h q Source #
(Monad f, Monad g) => Monad (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods (>>=) :: Product f g a -> (a -> Product f g b) -> Product f g b # (>>) :: Product f g a -> Product f g b -> Product f g b # return :: a -> Product f g a #
(Functor f, Functor g) => Functor (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fmap :: (a -> b) -> Product f g a -> Product f g b # (<$) :: a -> Product f g b -> Product f g a #
(MonadFix f, MonadFix g) => MonadFix (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods mfix :: (a -> Product f g a) -> Product f g a #
(Applicative f, Applicative g) => Applicative (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods pure :: a -> Product f g a # (<>) :: Product f g (a -> b) -> Product f g a -> Product f g b # liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c # (>) :: Product f g a -> Product f g b -> Product f g b # (<*) :: Product f g a -> Product f g b -> Product f g a #
(Foldable f, Foldable g) => Foldable (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fold :: Monoid m => Product f g m -> m # foldMap :: Monoid m => (a -> m) -> Product f g a -> m # foldMap' :: Monoid m => (a -> m) -> Product f g a -> m # foldr :: (a -> b -> b) -> b -> Product f g a -> b # foldr' :: (a -> b -> b) -> b -> Product f g a -> b # foldl :: (b -> a -> b) -> b -> Product f g a -> b # foldl' :: (b -> a -> b) -> b -> Product f g a -> b # foldr1 :: (a -> a -> a) -> Product f g a -> a # foldl1 :: (a -> a -> a) -> Product f g a -> a # toList :: Product f g a -> [a] # null :: Product f g a -> Bool # length :: Product f g a -> Int # elem :: Eq a => a -> Product f g a -> Bool # maximum :: Ord a => Product f g a -> a # minimum :: Ord a => Product f g a -> a # sum :: Num a => Product f g a -> a # product :: Num a => Product f g a -> a #
(Traversable f, Traversable g) => Traversable (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods traverse :: Applicative f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) # sequenceA :: Applicative f0 => Product f g (f0 a) -> f0 (Product f g a) # mapM :: Monad m => (a -> m b) -> Product f g a -> m (Product f g b) # sequence :: Monad m => Product f g (m a) -> m (Product f g a) #
(Eq1 f, Eq1 g) => Eq1 (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods liftEq :: (a -> b -> Bool) -> Product f g a -> Product f g b -> Bool #
(Ord1 f, Ord1 g) => Ord1 (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods liftCompare :: (a -> b -> Ordering) -> Product f g a -> Product f g b -> Ordering #
(Read1 f, Read1 g) => Read1 (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Product f g a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Product f g a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Product f g a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Product f g a] #
(Show1 f, Show1 g) => Show1 (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Product f g a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Product f g a] -> ShowS #
(MonadZip f, MonadZip g) => MonadZip (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods mzip :: Product f g a -> Product f g b -> Product f g (a, b) # mzipWith :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c # munzip :: Product f g (a, b) -> (Product f g a, Product f g b) #
(Alternative f, Alternative g) => Alternative (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods empty :: Product f g a # (<\|>) :: Product f g a -> Product f g a -> Product f g a # some :: Product f g a -> Product f g [a] # many :: Product f g a -> Product f g [a] #
(MonadPlus f, MonadPlus g) => MonadPlus (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods mzero :: Product f g a # mplus :: Product f g a -> Product f g a -> Product f g a #
(Distributive f, Distributive g) => Distributive (Product f g)
Instance details Defined in Data.Distributive Methods distribute :: Functor f0 => f0 (Product f g a) -> Product f g (f0 a) # collect :: Functor f0 => (a -> Product f g b) -> f0 a -> Product f g (f0 b) # distributeM :: Monad m => m (Product f g a) -> Product f g (m a) # collectM :: Monad m => (a -> Product f g b) -> m a -> Product f g (m b) #
(Eq1 f, Eq1 g, Eq a) => Eq (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods (==) :: Product f g a -> Product f g a -> Bool # (/=) :: Product f g a -> Product f g a -> Bool #
(Typeable a, Typeable f, Typeable g, Typeable k, Data (f a), Data (g a)) => Data (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g0. g0 -> c g0) -> Product f g a -> c (Product f g a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product f g a) # toConstr :: Product f g a -> Constr # dataTypeOf :: Product f g a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Product f g a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product f g a)) # gmapT :: (forall b. Data b => b -> b) -> Product f g a -> Product f g a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product f g a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product f g a -> r # gmapQ :: (forall d. Data d => d -> u) -> Product f g a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Product f g a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product f g a -> m (Product f g a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product f g a -> m (Product f g a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product f g a -> m (Product f g a) #
(Ord1 f, Ord1 g, Ord a) => Ord (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods compare :: Product f g a -> Product f g a -> Ordering # (<) :: Product f g a -> Product f g a -> Bool # (<=) :: Product f g a -> Product f g a -> Bool # (>) :: Product f g a -> Product f g a -> Bool # (>=) :: Product f g a -> Product f g a -> Bool # max :: Product f g a -> Product f g a -> Product f g a # min :: Product f g a -> Product f g a -> Product f g a #
(Read1 f, Read1 g, Read a) => Read (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods readsPrec :: Int -> ReadS (Product f g a) # readList :: ReadS [Product f g a] # readPrec :: ReadPrec (Product f g a) # readListPrec :: ReadPrec [Product f g a] #
(Show1 f, Show1 g, Show a) => Show (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods showsPrec :: Int -> Product f g a -> ShowS # show :: Product f g a -> String # showList :: [Product f g a] -> ShowS #
Generic (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Associated Types type Rep (Product f g a) :: Type -> Type # Methods from :: Product f g a -> Rep (Product f g a) x # to :: Rep (Product f g a) x -> Product f g a #
type Rep1 (Product f g :: k -> Type)
Instance details Defined in Data.Functor.Product type Rep1 (Product f g :: k -> Type) = D1 ('MetaData "Product" "Data.Functor.Product" "base" 'False) (C1 ('MetaCons "Pair" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 g)))
type Rep (Product f g a)
Instance details Defined in Data.Functor.Product type Rep (Product f g a) = D1 ('MetaData "Product" "Data.Functor.Product" "base" 'False) (C1 ('MetaCons "Pair" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a)) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (g a))))

data Sum (f :: k -> Type) (g :: k -> Type) (a :: k) #

Lifted sum of functors.

Constructors

InL (f a)
InR (g a)

Instances

Instances details

Generic1 (Sum f g :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Associated Types type Rep1 (Sum f g) :: k -> Type # Methods from1 :: forall (a :: k0). Sum f g a -> Rep1 (Sum f g) a # to1 :: forall (a :: k0). Rep1 (Sum f g) a -> Sum f g a #
(Traversable g, Traversable h) => Traversable (Sum g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Sum g h p -> m (Sum g h q) Source # sequence :: forall m (p :: k0 -> Type). Applicative m => Sum g h (Compose m p) -> m (Sum g h p) Source #
(Foldable g, Foldable h) => Foldable (Sum g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Sum g h p -> m Source #
(Functor g, Functor h) => Functor (Sum g h :: (k -> Type) -> Type) Source #
Instance details Defined in Rank2 Methods (<$>) :: (forall (a :: k0). p a -> q a) -> Sum g h p -> Sum g h q Source #
(Functor f, Functor g) => Functor (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods fmap :: (a -> b) -> Sum f g a -> Sum f g b # (<$) :: a -> Sum f g b -> Sum f g a #
(Foldable f, Foldable g) => Foldable (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods fold :: Monoid m => Sum f g m -> m # foldMap :: Monoid m => (a -> m) -> Sum f g a -> m # foldMap' :: Monoid m => (a -> m) -> Sum f g a -> m # foldr :: (a -> b -> b) -> b -> Sum f g a -> b # foldr' :: (a -> b -> b) -> b -> Sum f g a -> b # foldl :: (b -> a -> b) -> b -> Sum f g a -> b # foldl' :: (b -> a -> b) -> b -> Sum f g a -> b # foldr1 :: (a -> a -> a) -> Sum f g a -> a # foldl1 :: (a -> a -> a) -> Sum f g a -> a # toList :: Sum f g a -> [a] # null :: Sum f g a -> Bool # length :: Sum f g a -> Int # elem :: Eq a => a -> Sum f g a -> Bool # maximum :: Ord a => Sum f g a -> a # minimum :: Ord a => Sum f g a -> a # sum :: Num a => Sum f g a -> a # product :: Num a => Sum f g a -> a #
(Traversable f, Traversable g) => Traversable (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods traverse :: Applicative f0 => (a -> f0 b) -> Sum f g a -> f0 (Sum f g b) # sequenceA :: Applicative f0 => Sum f g (f0 a) -> f0 (Sum f g a) # mapM :: Monad m => (a -> m b) -> Sum f g a -> m (Sum f g b) # sequence :: Monad m => Sum f g (m a) -> m (Sum f g a) #
(Eq1 f, Eq1 g) => Eq1 (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods liftEq :: (a -> b -> Bool) -> Sum f g a -> Sum f g b -> Bool #
(Ord1 f, Ord1 g) => Ord1 (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods liftCompare :: (a -> b -> Ordering) -> Sum f g a -> Sum f g b -> Ordering #
(Read1 f, Read1 g) => Read1 (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Sum f g a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Sum f g a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Sum f g a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Sum f g a] #
(Show1 f, Show1 g) => Show1 (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Sum f g a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Sum f g a] -> ShowS #
(Eq1 f, Eq1 g, Eq a) => Eq (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods (==) :: Sum f g a -> Sum f g a -> Bool # (/=) :: Sum f g a -> Sum f g a -> Bool #
(Typeable a, Typeable f, Typeable g, Typeable k, Data (f a), Data (g a)) => Data (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g0. g0 -> c g0) -> Sum f g a -> c (Sum f g a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum f g a) # toConstr :: Sum f g a -> Constr # dataTypeOf :: Sum f g a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Sum f g a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum f g a)) # gmapT :: (forall b. Data b => b -> b) -> Sum f g a -> Sum f g a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum f g a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum f g a -> r # gmapQ :: (forall d. Data d => d -> u) -> Sum f g a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum f g a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum f g a -> m (Sum f g a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum f g a -> m (Sum f g a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum f g a -> m (Sum f g a) #
(Ord1 f, Ord1 g, Ord a) => Ord (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods compare :: Sum f g a -> Sum f g a -> Ordering # (<) :: Sum f g a -> Sum f g a -> Bool # (<=) :: Sum f g a -> Sum f g a -> Bool # (>) :: Sum f g a -> Sum f g a -> Bool # (>=) :: Sum f g a -> Sum f g a -> Bool # max :: Sum f g a -> Sum f g a -> Sum f g a # min :: Sum f g a -> Sum f g a -> Sum f g a #
(Read1 f, Read1 g, Read a) => Read (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods readsPrec :: Int -> ReadS (Sum f g a) # readList :: ReadS [Sum f g a] # readPrec :: ReadPrec (Sum f g a) # readListPrec :: ReadPrec [Sum f g a] #
(Show1 f, Show1 g, Show a) => Show (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods showsPrec :: Int -> Sum f g a -> ShowS # show :: Sum f g a -> String # showList :: [Sum f g a] -> ShowS #
Generic (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Associated Types type Rep (Sum f g a) :: Type -> Type # Methods from :: Sum f g a -> Rep (Sum f g a) x # to :: Rep (Sum f g a) x -> Sum f g a #
type Rep1 (Sum f g :: k -> Type)
Instance details Defined in Data.Functor.Sum type Rep1 (Sum f g :: k -> Type) = D1 ('MetaData "Sum" "Data.Functor.Sum" "base" 'False) (C1 ('MetaCons "InL" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)) :+: C1 ('MetaCons "InR" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 g)))
type Rep (Sum f g a)
Instance details Defined in Data.Functor.Sum type Rep (Sum f g a) = D1 ('MetaData "Sum" "Data.Functor.Sum" "base" 'False) (C1 ('MetaCons "InL" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))) :+: C1 ('MetaCons "InR" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (g a))))

newtype Arrow p q a Source #

Wrapper for functions that map the argument constructor type

Constructors

Arrow
Fields apply :: p a -> q a

type (~>) = Arrow infixr 0 Source #

Method synonyms and helper functions

($) :: Arrow p q a -> p a -> q a infixr 0 Source #

fst :: Product g h p -> g p Source #

Helper function for accessing the first field of a Pair

snd :: Product g h p -> h p Source #

Helper function for accessing the second field of a Pair

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

Like fmap, but traverses over its argument

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

Like liftA2, but traverses over its first argument

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

Like liftA2, but traverses over its second argument

liftA2TraverseBoth :: (Apply g, DistributiveTraversable g, Traversable f1, Traversable f2) => (forall a. f1 (t a) -> f2 (u a) -> v a) -> f1 (g t) -> f2 (g u) -> g 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