Rank2

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.

Rank 2 classes

class Functor g where

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

Instances

Functor (U1 :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p a -> q a) -> U1 p -> U1 q

Functor (V1 :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p a -> q a) -> V1 p -> V1 q

Functor (Proxy :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p a -> q a) -> Proxy p -> Proxy q

Functor (Empty :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p a -> q a) -> Empty p -> Empty q

Functor f => Functor (Rec1 f :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p a -> q a) -> Rec1 f p -> Rec1 f q

Functor (Const a :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a0 :: k0). p a0 -> q a0) -> Const a p -> Const a q

Functor (Only a :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a0 :: k0). p a0 -> q a0) -> Only a p -> Only a q

Functor g => Functor (Identity g :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p a -> q a) -> Identity g p -> Identity g q

(Functor f, Functor g) => Functor (f :*: g :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p a -> q a) -> (f :*: g) p -> (f :*: g) q

(Functor f, Functor g) => Functor (f :+: g :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p a -> q a) -> (f :+: g) p -> (f :+: g) q

Functor (K1 i c :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p a -> q a) -> K1 i c p -> K1 i c q

(Functor g, Functor h) => Functor (Sum g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p a -> q a) -> Sum g h p -> Sum g h q

(Functor g, Functor h) => Functor (Product g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p a -> q a) -> Product g h p -> Product g h q

Functor f => Functor (M1 i c f :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p a -> q a) -> M1 i c f p -> M1 i c f q

(Functor g, Functor p) => Functor (Compose g p :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p0 a -> q a) -> Compose g p p0 -> Compose g p q

Functor g => Functor (Flip g a :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a0 :: k0). p a0 -> q a0) -> Flip g a p -> Flip g a q

class Functor g => Apply g where

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

Equivalent of <*> for rank 2 data types

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

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

Equivalent of liftA3 for rank 2 data types

Instances

Apply (U1 :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: U1 (p ~> q) -> U1 p -> U1 q

liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> U1 p -> U1 q -> U1 r

liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> U1 p -> U1 q -> U1 r -> U1 s

Apply (V1 :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: V1 (p ~> q) -> V1 p -> V1 q

liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> V1 p -> V1 q -> V1 r

liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> V1 p -> V1 q -> V1 r -> V1 s

Apply (Proxy :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: Proxy (p ~> q) -> Proxy p -> Proxy q

liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Proxy p -> Proxy q -> Proxy r

liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Proxy p -> Proxy q -> Proxy r -> Proxy s

Apply (Empty :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: Empty (p ~> q) -> Empty p -> Empty q

liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Empty p -> Empty q -> Empty r

liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Empty p -> Empty q -> Empty r -> Empty s

Apply f => Apply (Rec1 f :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: Rec1 f (p ~> q) -> Rec1 f p -> Rec1 f q

liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Rec1 f p -> Rec1 f q -> Rec1 f r

liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Rec1 f p -> Rec1 f q -> Rec1 f r -> Rec1 f s

Semigroup x => Apply (Const x :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: Const x (p ~> q) -> Const x p -> Const x q

liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Const x p -> Const x q -> Const x r

liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Const x p -> Const x q -> Const x r -> Const x s

Apply (Only x :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: Only x (p ~> q) -> Only x p -> Only x q

liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Only x p -> Only x q -> Only x r

liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Only x p -> Only x q -> Only x r -> Only x s

Apply g => Apply (Identity g :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: Identity g (p ~> q) -> Identity g p -> Identity g q

liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Identity g p -> Identity g q -> Identity g r

liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Identity g p -> Identity g q -> Identity g r -> Identity g s

(Apply f, Apply g) => Apply (f :*: g :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: (f :*: g) (p ~> q) -> (f :*: g) p -> (f :*: g) q

liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> (f :*: g) p -> (f :*: g) q -> (f :*: g) r

liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> (f :*: g) p -> (f :*: g) q -> (f :*: g) r -> (f :*: g) s

Semigroup c => Apply (K1 i c :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: K1 i c (p ~> q) -> K1 i c p -> K1 i c q

liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> K1 i c p -> K1 i c q -> K1 i c r

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

(Apply g, Apply h) => Apply (Product g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: Product g h (p ~> q) -> Product g h p -> Product g h q

liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Product g h p -> Product g h q -> Product g h r

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

Apply f => Apply (M1 i c f :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: M1 i c f (p ~> q) -> M1 i c f p -> M1 i c f q

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

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

(Apply g, Applicative p) => Apply (Compose g p :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: Compose g p (p0 ~> q) -> Compose g p p0 -> Compose g p q

liftA2 :: (forall (a :: k0). p0 a -> q a -> r a) -> Compose g p p0 -> Compose g p q -> Compose g p r

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

Applicative g => Apply (Flip g a :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: Flip g a (p ~> q) -> Flip g a p -> Flip g a q

liftA2 :: (forall (a0 :: k0). p a0 -> q a0 -> r a0) -> Flip g a p -> Flip g a q -> Flip g a r

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

class Apply g => Applicative g where

Equivalent of Applicative for rank 2 data types

Methods

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

Instances

Applicative (Proxy :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a :: k0). f a) -> Proxy f

Applicative (Empty :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a :: k0). f a) -> Empty f

Applicative f => Applicative (Rec1 f :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a :: k0). f0 a) -> Rec1 f f0

(Semigroup x, Monoid x) => Applicative (Const x :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a :: k0). f a) -> Const x f

Applicative (Only x :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a :: k0). f a) -> Only x f

Applicative g => Applicative (Identity g :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a :: k0). f a) -> Identity g f

(Applicative f, Applicative g) => Applicative (f :*: g :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a :: k0). f0 a) -> (f :*: g) f0

(Semigroup c, Monoid c) => Applicative (K1 i c :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a :: k0). f a) -> K1 i c f

(Applicative g, Applicative h) => Applicative (Product g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a :: k0). f a) -> Product g h f

Applicative f => Applicative (M1 i c f :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a :: k0). f0 a) -> M1 i c f f0

(Applicative g, Applicative p) => Applicative (Compose g p :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a :: k0). f a) -> Compose g p f

Applicative g => Applicative (Flip g a :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a0 :: k0). f a0) -> Flip g a f

class Foldable g where

Equivalent of Foldable for rank 2 data types

Methods

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

Instances

Foldable (U1 :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> U1 p -> m

Foldable (V1 :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> V1 p -> m

Foldable (Proxy :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Proxy p -> m

Foldable (Empty :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Empty p -> m

Foldable f => Foldable (Rec1 f :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Rec1 f p -> m

Foldable (Const x :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Const x p -> m

Foldable (Only x :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Only x p -> m

Foldable g => Foldable (Identity g :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Identity g p -> m

(Foldable f, Foldable g) => Foldable (f :*: g :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> (f :*: g) p -> m

(Foldable f, Foldable g) => Foldable (f :+: g :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> (f :+: g) p -> m

Foldable (K1 i c :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> K1 i c p -> m

(Foldable g, Foldable h) => Foldable (Sum g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Sum g h p -> m

(Foldable g, Foldable h) => Foldable (Product g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Product g h p -> m

Foldable f => Foldable (M1 i c f :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> M1 i c f p -> m

(Foldable g, Foldable p) => Foldable (Compose g p :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p0 a -> m) -> Compose g p p0 -> m

Foldable g => Foldable (Flip g a :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a0 :: k0). p a0 -> m) -> Flip g a p -> m

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

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)

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

Instances

Traversable (U1 :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> U1 p -> m (U1 q)

sequence :: Applicative m => U1 (Compose m p) -> m (U1 p)

Traversable (V1 :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> V1 p -> m (V1 q)

sequence :: Applicative m => V1 (Compose m p) -> m (V1 p)

Traversable (Proxy :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Proxy p -> m (Proxy q)

sequence :: Applicative m => Proxy (Compose m p) -> m (Proxy p)

Traversable (Empty :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Empty p -> m (Empty q)

sequence :: Applicative m => Empty (Compose m p) -> m (Empty p)

Traversable f => Traversable (Rec1 f :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Rec1 f p -> m (Rec1 f q)

sequence :: Applicative m => Rec1 f (Compose m p) -> m (Rec1 f p)

Traversable (Const x :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Const x p -> m (Const x q)

sequence :: Applicative m => Const x (Compose m p) -> m (Const x p)

Traversable (Only x :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Only x p -> m (Only x q)

sequence :: Applicative m => Only x (Compose m p) -> m (Only x p)

Traversable g => Traversable (Identity g :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Identity g p -> m (Identity g q)

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

(Traversable f, Traversable g) => Traversable (f :*: g :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> (f :*: g) p -> m ((f :*: g) q)

sequence :: Applicative m => (f :*: g) (Compose m p) -> m ((f :*: g) p)

(Traversable f, Traversable g) => Traversable (f :+: g :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> (f :+: g) p -> m ((f :+: g) q)

sequence :: Applicative m => (f :+: g) (Compose m p) -> m ((f :+: g) p)

Traversable (K1 i c :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> K1 i c p -> m (K1 i c q)

sequence :: Applicative m => K1 i c (Compose m p) -> m (K1 i c p)

(Traversable g, Traversable h) => Traversable (Sum g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Sum g h p -> m (Sum g h q)

sequence :: Applicative m => Sum g h (Compose m p) -> m (Sum g h p)

(Traversable g, Traversable h) => Traversable (Product g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Product g h p -> m (Product g h q)

sequence :: Applicative m => Product g h (Compose m p) -> m (Product g h p)

Traversable f => Traversable (M1 i c f :: (k -> Type) -> Type)

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)

sequence :: Applicative m => M1 i c f (Compose m p) -> m (M1 i c f p)

(Traversable g, Traversable p) => Traversable (Compose g p :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p0 a -> m (q a)) -> Compose g p p0 -> m (Compose g p q)

sequence :: Applicative m => Compose g p (Compose0 m p0) -> m (Compose g p p0)

Traversable g => Traversable (Flip g a :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a0 :: k0). p a0 -> m (q a0)) -> Flip g a p -> m (Flip g a q)

sequence :: Applicative m => Flip g a (Compose m p) -> m (Flip g a p)

class DistributiveTraversable g => Distributive g where

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)

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

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

Instances

Distributive (Proxy :: (k -> Type) -> Type)

Defined in Rank2

Methods

collect :: Functor f1 => (a -> Proxy f2) -> f1 a -> Proxy (Compose f1 f2)

distribute :: Functor f1 => f1 (Proxy f2) -> Proxy (Compose f1 f2)

cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Proxy p) -> Proxy q

Distributive (Empty :: (k -> Type) -> Type)

Defined in Rank2

Methods

collect :: Functor f1 => (a -> Empty f2) -> f1 a -> Empty (Compose f1 f2)

distribute :: Functor f1 => f1 (Empty f2) -> Empty (Compose f1 f2)

cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Empty p) -> Empty q

Distributive f => Distributive (Rec1 f :: (k -> Type) -> Type)

Defined in Rank2

Methods

collect :: Functor f1 => (a -> Rec1 f f2) -> f1 a -> Rec1 f (Compose f1 f2)

distribute :: Functor f1 => f1 (Rec1 f f2) -> Rec1 f (Compose f1 f2)

cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Rec1 f p) -> Rec1 f q

Distributive (Only x :: (k -> Type) -> Type)

Defined in Rank2

Methods

collect :: Functor f1 => (a -> Only x f2) -> f1 a -> Only x (Compose f1 f2)

distribute :: Functor f1 => f1 (Only x f2) -> Only x (Compose f1 f2)

cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Only x p) -> Only x q

Distributive g => Distributive (Identity g :: (k -> Type) -> Type)

Defined in Rank2

Methods

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

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

cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Identity g p) -> Identity g q

(Distributive f, Distributive g) => Distributive (f :*: g :: (k -> Type) -> Type)

Defined in Rank2

Methods

collect :: Functor f1 => (a -> (f :*: g) f2) -> f1 a -> (f :*: g) (Compose f1 f2)

distribute :: Functor f1 => f1 ((f :*: g) f2) -> (f :*: g) (Compose f1 f2)

cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m ((f :*: g) p) -> (f :*: g) q

(Distributive g, Distributive h) => Distributive (Product g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

collect :: Functor f1 => (a -> Product g h f2) -> f1 a -> Product g h (Compose f1 f2)

distribute :: Functor f1 => f1 (Product g h f2) -> Product g h (Compose f1 f2)

cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Product g h p) -> Product g h q

Distributive f => Distributive (M1 i c f :: (k -> Type) -> Type)

Defined in Rank2

Methods

collect :: Functor f1 => (a -> M1 i c f f2) -> f1 a -> M1 i c f (Compose f1 f2)

distribute :: Functor f1 => f1 (M1 i c f f2) -> M1 i c f (Compose f1 f2)

cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (M1 i c f p) -> M1 i c f q

(Distributive g, Distributive p) => Distributive (Compose g p :: (k -> Type) -> Type)

Defined in Rank2

Methods

collect :: Functor f1 => (a -> Compose g p f2) -> f1 a -> Compose g p (Compose0 f1 f2)

distribute :: Functor f1 => f1 (Compose g p f2) -> Compose g p (Compose0 f1 f2)

cotraverse :: Functor m => (forall (a :: k0). m (p0 a) -> q a) -> m (Compose g p p0) -> Compose g p q

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

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)

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

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

Instances

DistributiveTraversable (Proxy :: (k -> Type) -> Type)

Defined in Rank2

Methods

collectTraversable :: Traversable f1 => (a -> Proxy f2) -> f1 a -> Proxy (Compose f1 f2)

distributeTraversable :: Traversable f1 => f1 (Proxy f2) -> Proxy (Compose f1 f2)

cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Proxy f2) -> Proxy f

DistributiveTraversable (Empty :: (k -> Type) -> Type)

Defined in Rank2

Methods

collectTraversable :: Traversable f1 => (a -> Empty f2) -> f1 a -> Empty (Compose f1 f2)

distributeTraversable :: Traversable f1 => f1 (Empty f2) -> Empty (Compose f1 f2)

cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Empty f2) -> Empty f

Monoid x => DistributiveTraversable (Const x :: (k -> Type) -> Type)

Defined in Rank2

Methods

collectTraversable :: Traversable f1 => (a -> Const x f2) -> f1 a -> Const x (Compose f1 f2)

distributeTraversable :: Traversable f1 => f1 (Const x f2) -> Const x (Compose f1 f2)

cotraverseTraversable :: Traversable f1 => (forall (x0 :: k0). f1 (f2 x0) -> f x0) -> f1 (Const x f2) -> Const x f

DistributiveTraversable f => DistributiveTraversable (Rec1 f :: (k -> Type) -> Type)

Defined in Rank2

Methods

collectTraversable :: Traversable f1 => (a -> Rec1 f f2) -> f1 a -> Rec1 f (Compose f1 f2)

distributeTraversable :: Traversable f1 => f1 (Rec1 f f2) -> Rec1 f (Compose f1 f2)

cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f0 x) -> f1 (Rec1 f f2) -> Rec1 f f0

DistributiveTraversable (Only x :: (k -> Type) -> Type)

Defined in Rank2

Methods

collectTraversable :: Traversable f1 => (a -> Only x f2) -> f1 a -> Only x (Compose f1 f2)

distributeTraversable :: Traversable f1 => f1 (Only x f2) -> Only x (Compose f1 f2)

cotraverseTraversable :: Traversable f1 => (forall (x0 :: k0). f1 (f2 x0) -> f x0) -> f1 (Only x f2) -> Only x f

DistributiveTraversable g => DistributiveTraversable (Identity g :: (k -> Type) -> Type)

Defined in Rank2

Methods

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

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

cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Identity g f2) -> Identity g f

Monoid c => DistributiveTraversable (K1 i c :: (k -> Type) -> Type)

Defined in Rank2

Methods

collectTraversable :: Traversable f1 => (a -> K1 i c f2) -> f1 a -> K1 i c (Compose f1 f2)

distributeTraversable :: Traversable f1 => f1 (K1 i c f2) -> K1 i c (Compose f1 f2)

cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (K1 i c f2) -> K1 i c f

(DistributiveTraversable f, DistributiveTraversable g) => DistributiveTraversable (f :*: g :: (k -> Type) -> Type)

Defined in Rank2

Methods

collectTraversable :: Traversable f1 => (a -> (f :*: g) f2) -> f1 a -> (f :*: g) (Compose f1 f2)

distributeTraversable :: Traversable f1 => f1 ((f :*: g) f2) -> (f :*: g) (Compose f1 f2)

cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f0 x) -> f1 ((f :*: g) f2) -> (f :*: g) f0

(DistributiveTraversable g, DistributiveTraversable h) => DistributiveTraversable (Product g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

collectTraversable :: Traversable f1 => (a -> Product g h f2) -> f1 a -> Product g h (Compose f1 f2)

distributeTraversable :: Traversable f1 => f1 (Product g h f2) -> Product g h (Compose f1 f2)

cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Product g h f2) -> Product g h f

DistributiveTraversable f => DistributiveTraversable (M1 i c f :: (k -> Type) -> Type)

Defined in Rank2

Methods

collectTraversable :: Traversable f1 => (a -> M1 i c f f2) -> f1 a -> M1 i c f (Compose f1 f2)

distributeTraversable :: Traversable f1 => f1 (M1 i c f f2) -> M1 i c f (Compose f1 f2)

cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f0 x) -> f1 (M1 i c f f2) -> M1 i c f f0

(DistributiveTraversable g, Distributive p) => DistributiveTraversable (Compose g p :: (k -> Type) -> Type)

Defined in Rank2

Methods

collectTraversable :: Traversable f1 => (a -> Compose g p f2) -> f1 a -> Compose g p (Compose0 f1 f2)

distributeTraversable :: Traversable f1 => f1 (Compose g p f2) -> Compose g p (Compose0 f1 f2)

cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Compose g p f2) -> Compose g p f

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

A variant of distribute convenient with Monad instances

Rank 2 data types

newtype Compose g p q

Equivalent of Compose for rank 2 data types

Constructors

Compose

Fields

• getCompose :: g (Compose p q)

Instances

(DistributiveTraversable g, Distributive p) => DistributiveTraversable (Compose g p :: (k -> Type) -> Type)

Defined in Rank2

Methods

collectTraversable :: Traversable f1 => (a -> Compose g p f2) -> f1 a -> Compose g p (Compose0 f1 f2)

distributeTraversable :: Traversable f1 => f1 (Compose g p f2) -> Compose g p (Compose0 f1 f2)

cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Compose g p f2) -> Compose g p f

(Distributive g, Distributive p) => Distributive (Compose g p :: (k -> Type) -> Type)

Defined in Rank2

Methods

collect :: Functor f1 => (a -> Compose g p f2) -> f1 a -> Compose g p (Compose0 f1 f2)

distribute :: Functor f1 => f1 (Compose g p f2) -> Compose g p (Compose0 f1 f2)

cotraverse :: Functor m => (forall (a :: k0). m (p0 a) -> q a) -> m (Compose g p p0) -> Compose g p q

(Applicative g, Applicative p) => Applicative (Compose g p :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a :: k0). f a) -> Compose g p f

(Apply g, Applicative p) => Apply (Compose g p :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: Compose g p (p0 ~> q) -> Compose g p p0 -> Compose g p q

liftA2 :: (forall (a :: k0). p0 a -> q a -> r a) -> Compose g p p0 -> Compose g p q -> Compose g p r

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

(Traversable g, Traversable p) => Traversable (Compose g p :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p0 a -> m (q a)) -> Compose g p p0 -> m (Compose g p q)

sequence :: Applicative m => Compose g p (Compose0 m p0) -> m (Compose g p p0)

(Foldable g, Foldable p) => Foldable (Compose g p :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p0 a -> m) -> Compose g p p0 -> m

(Functor g, Functor p) => Functor (Compose g p :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p0 a -> q a) -> Compose g p p0 -> Compose g p q

Eq (g (Compose p q)) => Eq (Compose g p q)

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)

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)

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

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

Constructors

Empty

Instances

DistributiveTraversable (Empty :: (k -> Type) -> Type)

Defined in Rank2

Methods

collectTraversable :: Traversable f1 => (a -> Empty f2) -> f1 a -> Empty (Compose f1 f2)

distributeTraversable :: Traversable f1 => f1 (Empty f2) -> Empty (Compose f1 f2)

cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Empty f2) -> Empty f

Distributive (Empty :: (k -> Type) -> Type)

Defined in Rank2

Methods

collect :: Functor f1 => (a -> Empty f2) -> f1 a -> Empty (Compose f1 f2)

distribute :: Functor f1 => f1 (Empty f2) -> Empty (Compose f1 f2)

cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Empty p) -> Empty q

Applicative (Empty :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a :: k0). f a) -> Empty f

Apply (Empty :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: Empty (p ~> q) -> Empty p -> Empty q

liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Empty p -> Empty q -> Empty r

liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Empty p -> Empty q -> Empty r -> Empty s

Traversable (Empty :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Empty p -> m (Empty q)

sequence :: Applicative m => Empty (Compose m p) -> m (Empty p)

Foldable (Empty :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Empty p -> m

Functor (Empty :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p a -> q a) -> Empty p -> Empty q

Eq (Empty f)

Defined in Rank2

Methods

(==) :: Empty f -> Empty f -> Bool

(/=) :: Empty f -> Empty f -> Bool

Ord (Empty f)

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)

Defined in Rank2

Methods

showsPrec :: Int -> Empty f -> ShowS

show :: Empty f -> String

showList :: [Empty f] -> ShowS

newtype Only a f

A rank-2 tuple of only one element

Constructors

Only

Fields

• fromOnly :: f a

Instances

DistributiveTraversable (Only x :: (k -> Type) -> Type)

Defined in Rank2

Methods

collectTraversable :: Traversable f1 => (a -> Only x f2) -> f1 a -> Only x (Compose f1 f2)

distributeTraversable :: Traversable f1 => f1 (Only x f2) -> Only x (Compose f1 f2)

cotraverseTraversable :: Traversable f1 => (forall (x0 :: k0). f1 (f2 x0) -> f x0) -> f1 (Only x f2) -> Only x f

Distributive (Only x :: (k -> Type) -> Type)

Defined in Rank2

Methods

collect :: Functor f1 => (a -> Only x f2) -> f1 a -> Only x (Compose f1 f2)

distribute :: Functor f1 => f1 (Only x f2) -> Only x (Compose f1 f2)

cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Only x p) -> Only x q

Applicative (Only x :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a :: k0). f a) -> Only x f

Apply (Only x :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: Only x (p ~> q) -> Only x p -> Only x q

liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Only x p -> Only x q -> Only x r

liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Only x p -> Only x q -> Only x r -> Only x s

Traversable (Only x :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Only x p -> m (Only x q)

sequence :: Applicative m => Only x (Compose m p) -> m (Only x p)

Foldable (Only x :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Only x p -> m

Functor (Only a :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a0 :: k0). p a0 -> q a0) -> Only a p -> Only a q

Eq (f a) => Eq (Only a f)

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)

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)

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

A nested parametric type represented as a rank-2 type

Constructors

Flip

Fields

• unFlip :: g (f a)

Instances

Applicative g => Applicative (Flip g a :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a0 :: k0). f a0) -> Flip g a f

Applicative g => Apply (Flip g a :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: Flip g a (p ~> q) -> Flip g a p -> Flip g a q

liftA2 :: (forall (a0 :: k0). p a0 -> q a0 -> r a0) -> Flip g a p -> Flip g a q -> Flip g a r

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

Traversable g => Traversable (Flip g a :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a0 :: k0). p a0 -> m (q a0)) -> Flip g a p -> m (Flip g a q)

sequence :: Applicative m => Flip g a (Compose m p) -> m (Flip g a p)

Foldable g => Foldable (Flip g a :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a0 :: k0). p a0 -> m) -> Flip g a p -> m

Functor g => Functor (Flip g a :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a0 :: k0). p a0 -> q a0) -> Flip g a p -> Flip g a q

Eq (g (f a)) => Eq (Flip g a f)

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)

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)

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)

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)

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

Equivalent of Identity for rank 2 data types

Constructors

Identity

Fields

• runIdentity :: g f

Instances

DistributiveTraversable g => DistributiveTraversable (Identity g :: (k -> Type) -> Type)

Defined in Rank2

Methods

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

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

cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Identity g f2) -> Identity g f

Distributive g => Distributive (Identity g :: (k -> Type) -> Type)

Defined in Rank2

Methods

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

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

cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Identity g p) -> Identity g q

Applicative g => Applicative (Identity g :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a :: k0). f a) -> Identity g f

Apply g => Apply (Identity g :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: Identity g (p ~> q) -> Identity g p -> Identity g q

liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Identity g p -> Identity g q -> Identity g r

liftA3 :: (forall (a :: k0). p a -> q a -> r a -> s a) -> Identity g p -> Identity g q -> Identity g r -> Identity g s

Traversable g => Traversable (Identity g :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Identity g p -> m (Identity g q)

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

Foldable g => Foldable (Identity g :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Identity g p -> m

Functor g => Functor (Identity g :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p a -> q a) -> Identity g p -> Identity g q

Eq (g f) => Eq (Identity g f)

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)

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)

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) :: forall k. (k -> Type) -> (k -> Type) -> k -> Type

Lifted product of functors.

Constructors

Pair (f a) (g a)

Instances

Generic1 (Product f g :: k -> Type)

Defined in Data.Functor.Product

Associated Types

type Rep1 (Product f g) :: k -> Type

Methods

from1 :: Product f g a -> Rep1 (Product f g) a

to1 :: Rep1 (Product f g) a -> Product f g a

(DistributiveTraversable g, DistributiveTraversable h) => DistributiveTraversable (Product g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

collectTraversable :: Traversable f1 => (a -> Product g h f2) -> f1 a -> Product g h (Compose f1 f2)

distributeTraversable :: Traversable f1 => f1 (Product g h f2) -> Product g h (Compose f1 f2)

cotraverseTraversable :: Traversable f1 => (forall (x :: k0). f1 (f2 x) -> f x) -> f1 (Product g h f2) -> Product g h f

(Distributive g, Distributive h) => Distributive (Product g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

collect :: Functor f1 => (a -> Product g h f2) -> f1 a -> Product g h (Compose f1 f2)

distribute :: Functor f1 => f1 (Product g h f2) -> Product g h (Compose f1 f2)

cotraverse :: Functor m => (forall (a :: k0). m (p a) -> q a) -> m (Product g h p) -> Product g h q

(Applicative g, Applicative h) => Applicative (Product g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

pure :: (forall (a :: k0). f a) -> Product g h f

(Apply g, Apply h) => Apply (Product g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<*>) :: Product g h (p ~> q) -> Product g h p -> Product g h q

liftA2 :: (forall (a :: k0). p a -> q a -> r a) -> Product g h p -> Product g h q -> Product g h r

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

(Traversable g, Traversable h) => Traversable (Product g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Product g h p -> m (Product g h q)

sequence :: Applicative m => Product g h (Compose m p) -> m (Product g h p)

(Foldable g, Foldable h) => Foldable (Product g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Product g h p -> m

(Functor g, Functor h) => Functor (Product g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p a -> q a) -> Product g h p -> Product g h q

(Monad f, Monad g) => Monad (Product f g)

Since: base-4.9.0.0

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

fail :: String -> Product f g a

(Functor f, Functor g) => Functor (Product f g)

Since: base-4.9.0.0

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

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

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

Defined in Data.Functor.Product

Methods

fold :: Monoid m => Product f g m -> 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

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

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

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

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

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

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

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

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)

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

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

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 :: (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

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

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

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)

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)

Since: base-4.9.0.0

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)

Since: base-4.9.0.0

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) :: forall k. (k -> Type) -> (k -> Type) -> k -> Type

Lifted sum of functors.

Constructors

InL (f a)

InR (g a)

Instances

Generic1 (Sum f g :: k -> Type)

Defined in Data.Functor.Sum

Associated Types

type Rep1 (Sum f g) :: k -> Type

Methods

from1 :: Sum f g a -> Rep1 (Sum f g) a

to1 :: Rep1 (Sum f g) a -> Sum f g a

(Traversable g, Traversable h) => Traversable (Sum g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

traverse :: Applicative m => (forall (a :: k0). p a -> m (q a)) -> Sum g h p -> m (Sum g h q)

sequence :: Applicative m => Sum g h (Compose m p) -> m (Sum g h p)

(Foldable g, Foldable h) => Foldable (Sum g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

foldMap :: Monoid m => (forall (a :: k0). p a -> m) -> Sum g h p -> m

(Functor g, Functor h) => Functor (Sum g h :: (k -> Type) -> Type)

Defined in Rank2

Methods

(<$>) :: (forall (a :: k0). p a -> q a) -> Sum g h p -> Sum g h q

(Functor f, Functor g) => Functor (Sum f g)

Since: base-4.9.0.0

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

Defined in Data.Functor.Sum

Methods

fold :: Monoid m => Sum f g m -> 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

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

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

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

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

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

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

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 :: (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

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

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

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)

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)

Since: base-4.9.0.0

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)

Since: base-4.9.0.0

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

Wrapper for functions that map the argument constructor type

Constructors

Arrow

Fields

• apply :: p a -> q a

type (~>) = Arrow infixr 0

Method synonyms and helper functions

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

fst :: Product g h p -> g p

Helper function for accessing the first field of a Pair

snd :: Product g h p -> h p

Helper function for accessing the second field of a Pair

ap :: Apply g => g (p ~> q) -> g p -> g q

Alphabetical synonym for <*>

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

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

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

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

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

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

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

Deprecated: Use cotraverse instead.

Synonym for cotraverse

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

Deprecated: Use cotraverseTraversable instead.

Synonym for cotraverseTraversable