Data.Bifunctor.Monoidal

Documentation

class (Associative t1 cat, Associative t2 cat, Associative to cat) => Semigroupal cat t1 t2 to f where

Methods

combine :: cat (to (f x y) (f x' y')) (f (t1 x x') (t2 y y'))

Instances

Semigroupal ((->) :: Type -> Type -> Type) Either Either Either Either

Defined in Data.Bifunctor.Monoidal

Methods

combine :: Either (Either x y) (Either x' y') -> Either (Either x x') (Either y y')

Semigroupal ((->) :: Type -> Type -> Type) Either Either Either (,)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: Either (x, y) (x', y') -> (Either x x', Either y y')

Semigroupal ((->) :: Type -> Type -> Type) Either (,) (,) Either

Defined in Data.Bifunctor.Monoidal

Methods

combine :: (Either x y, Either x' y') -> Either (Either x x') (y, y')

Profunctor p => Semigroupal ((->) :: Type -> Type -> Type) (,) Either Either p

Defined in Data.Bifunctor.Monoidal

Methods

combine :: Either (p x y) (p x' y') -> p (x, x') (Either y y')

Semigroupal ((->) :: Type -> Type -> Type) (,) (,) (,) (,)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: ((x, y), (x', y')) -> ((x, x'), (y, y'))

Semigroupal ((->) :: Type -> Type -> Type) These (,) (,) Either

Defined in Data.Bifunctor.Monoidal

Methods

combine :: (Either x y, Either x' y') -> Either (These x x') (y, y')

(Strong p, Semigroupoid p) => Semigroupal ((->) :: Type -> Type -> Type) (,) (,) (,) (StrongCategory p)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: (StrongCategory p x y, StrongCategory p x' y') -> StrongCategory p (x, x') (y, y')

Alternative f => Semigroupal ((->) :: Type -> Type -> Type) Either Either Either (Star f)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: Either (Star f x y) (Star f x' y') -> Star f (Either x x') (Either y y')

Alternative f => Semigroupal ((->) :: Type -> Type -> Type) Either Either Either (Forget (f r) :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: Either (Forget (f r) x y) (Forget (f r) x' y') -> Forget (f r) (Either x x') (Either y y')

Semigroupal ((->) :: Type -> Type -> Type) Either Either (,) ((->) :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: (x -> y, x' -> y') -> (Either x x' -> Either y y')

Functor f => Semigroupal ((->) :: Type -> Type -> Type) Either Either (,) (Star f)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: (Star f x y, Star f x' y') -> Star f (Either x x') (Either y y')

Semigroupal ((->) :: Type -> Type -> Type) Either Either (,) (Forget (f r) :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: (Forget (f r) x y, Forget (f r) x' y') -> Forget (f r) (Either x x') (Either y y')

Alternative f => Semigroupal ((->) :: Type -> Type -> Type) (,) Either (,) (Star f)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: (Star f x y, Star f x' y') -> Star f (x, x') (Either y y')

Alternative f => Semigroupal ((->) :: Type -> Type -> Type) (,) Either (,) (Forget (f r) :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: (Forget (f r) x y, Forget (f r) x' y') -> Forget (f r) (x, x') (Either y y')

Semigroupal ((->) :: Type -> Type -> Type) (,) (,) (,) ((->) :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: (x -> y, x' -> y') -> ((x, x') -> (y, y'))

Applicative f => Semigroupal ((->) :: Type -> Type -> Type) (,) (,) (,) (Star f)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: (Star f x y, Star f x' y') -> Star f (x, x') (y, y')

Alternative f => Semigroupal ((->) :: Type -> Type -> Type) (,) (,) (,) (Forget (f r) :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: (Forget (f r) x y, Forget (f r) x' y') -> Forget (f r) (x, x') (y, y')

Functor f => Semigroupal ((->) :: Type -> Type -> Type) Either Either Either (Joker f :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: Either (Joker f x y) (Joker f x' y') -> Joker f (Either x x') (Either y y')

Alternative f => Semigroupal ((->) :: Type -> Type -> Type) Either Either (,) (Joker f :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: (Joker f x y, Joker f x' y') -> Joker f (Either x x') (Either y y')

Alternative f => Semigroupal ((->) :: Type -> Type -> Type) Either Either (,) (Clown f :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: (Clown f x y, Clown f x' y') -> Clown f (Either x x') (Either y y')

Applicative f => Semigroupal ((->) :: Type -> Type -> Type) (,) (,) (,) (Joker f :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: (Joker f x y, Joker f x' y') -> Joker f (x, x') (y, y')

Applicative f => Semigroupal ((->) :: Type -> Type -> Type) (,) (,) (,) (Clown f :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: (Clown f x y, Clown f x' y') -> Clown f (x, x') (y, y')

class Unital cat i1 i2 io f where

Methods

introduce :: cat io (f i1 i2)

Instances

Unital ((->) :: Type -> Type -> Type) () () () (,)

Defined in Data.Bifunctor.Monoidal

Methods

introduce :: () -> ((), ())

Unital ((->) :: Type -> Type -> Type) Void () () Either

Defined in Data.Bifunctor.Monoidal

Methods

introduce :: () -> Either Void ()

Unital ((->) :: Type -> Type -> Type) Void Void Void Either

Defined in Data.Bifunctor.Monoidal

Methods

introduce :: Void -> Either Void Void

Unital ((->) :: Type -> Type -> Type) Void Void Void (,)

Defined in Data.Bifunctor.Monoidal

Methods

introduce :: Void -> (Void, Void)

(Profunctor p, Category p) => Unital ((->) :: Type -> Type -> Type) () () () (StrongCategory p)

Defined in Data.Bifunctor.Monoidal

Methods

introduce :: () -> StrongCategory p () ()

Unital ((->) :: Type -> Type -> Type) () () () ((->) :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

introduce :: () -> (() -> ())

Applicative f => Unital ((->) :: Type -> Type -> Type) () () () (Star f)

Defined in Data.Bifunctor.Monoidal

Methods

introduce :: () -> Star f () ()

Alternative f => Unital ((->) :: Type -> Type -> Type) () Void () (Star f)

Defined in Data.Bifunctor.Monoidal

Methods

introduce :: () -> Star f () Void

Unital ((->) :: Type -> Type -> Type) Void Void () ((->) :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

introduce :: () -> (Void -> Void)

Unital ((->) :: Type -> Type -> Type) Void Void () (Star f)

Defined in Data.Bifunctor.Monoidal

Methods

introduce :: () -> Star f Void Void

Unital ((->) :: Type -> Type -> Type) Void Void Void ((->) :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

introduce :: Void -> (Void -> Void)

Alternative f => Unital ((->) :: Type -> Type -> Type) Void Void Void (Star f)

Defined in Data.Bifunctor.Monoidal

Methods

introduce :: Void -> Star f Void Void

Applicative f => Unital ((->) :: Type -> Type -> Type) () () () (Joker f :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

introduce :: () -> Joker f () ()

Alternative f => Unital ((->) :: Type -> Type -> Type) Void Void () (Joker f :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

introduce :: () -> Joker f Void Void

Unital ((->) :: Type -> Type -> Type) Void Void Void (Joker f :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

introduce :: Void -> Joker f Void Void

class (Tensor t1 i1 cat, Tensor t2 i2 cat, Tensor to io cat, Semigroupal cat t1 t2 to f, Unital cat i1 i2 io f) => Monoidal cat t1 i1 t2 i2 to io f

Instances

Monoidal ((->) :: Type -> Type -> Type) Either Void Either Void Either Void Either

Defined in Data.Bifunctor.Monoidal

Monoidal ((->) :: Type -> Type -> Type) Either Void Either Void Either Void (,)

Defined in Data.Bifunctor.Monoidal

Monoidal ((->) :: Type -> Type -> Type) Either Void (,) () (,) () Either

Defined in Data.Bifunctor.Monoidal

Monoidal ((->) :: Type -> Type -> Type) (,) () (,) () (,) () (,)

Defined in Data.Bifunctor.Monoidal

Monoidal ((->) :: Type -> Type -> Type) These Void (,) () (,) () Either

Defined in Data.Bifunctor.Monoidal

(Strong p, Semigroupoid p, Category p) => Monoidal ((->) :: Type -> Type -> Type) (,) () (,) () (,) () (StrongCategory p)

Defined in Data.Bifunctor.Monoidal

Alternative f => Monoidal ((->) :: Type -> Type -> Type) Either Void Either Void Either Void (Star f)

Defined in Data.Bifunctor.Monoidal

Monoidal ((->) :: Type -> Type -> Type) Either Void Either Void (,) () ((->) :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Functor f => Monoidal ((->) :: Type -> Type -> Type) Either Void Either Void (,) () (Star f)

Defined in Data.Bifunctor.Monoidal

Alternative f => Monoidal ((->) :: Type -> Type -> Type) (,) () Either Void (,) () (Star f)

Defined in Data.Bifunctor.Monoidal

Monoidal ((->) :: Type -> Type -> Type) (,) () (,) () (,) () ((->) :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Applicative f => Monoidal ((->) :: Type -> Type -> Type) (,) () (,) () (,) () (Star f)

Defined in Data.Bifunctor.Monoidal

Functor f => Monoidal ((->) :: Type -> Type -> Type) Either Void Either Void Either Void (Joker f :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Alternative f => Monoidal ((->) :: Type -> Type -> Type) Either Void Either Void (,) () (Joker f :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Applicative f => Monoidal ((->) :: Type -> Type -> Type) (,) () (,) () (,) () (Joker f :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

newtype StrongCategory p a b

Constructors

StrongCategory (p a b)

Instances

Profunctor p => Profunctor (StrongCategory p)

Defined in Data.Bifunctor.Monoidal

Methods

dimap :: (a -> b) -> (c -> d) -> StrongCategory p b c -> StrongCategory p a d

lmap :: (a -> b) -> StrongCategory p b c -> StrongCategory p a c

rmap :: (b -> c) -> StrongCategory p a b -> StrongCategory p a c

(#.) :: forall a b c q. Coercible c b => q b c -> StrongCategory p a b -> StrongCategory p a c

(.#) :: forall a b c q. Coercible b a => StrongCategory p b c -> q a b -> StrongCategory p a c

Category p => Category (StrongCategory p :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

id :: forall (a :: k). StrongCategory p a a

(.) :: forall (b :: k) (c :: k) (a :: k). StrongCategory p b c -> StrongCategory p a b -> StrongCategory p a c

Semigroupoid p => Semigroupoid (StrongCategory p :: Type -> Type -> Type)

Defined in Data.Bifunctor.Monoidal

Methods

o :: forall (j :: k) (k1 :: k) (i :: k). StrongCategory p j k1 -> StrongCategory p i j -> StrongCategory p i k1

Monad (p a) => Monad (StrongCategory p a)

Defined in Data.Bifunctor.Monoidal

Methods

(>>=) :: StrongCategory p a a0 -> (a0 -> StrongCategory p a b) -> StrongCategory p a b

(>>) :: StrongCategory p a a0 -> StrongCategory p a b -> StrongCategory p a b

return :: a0 -> StrongCategory p a a0

Functor (p a) => Functor (StrongCategory p a)

Defined in Data.Bifunctor.Monoidal

Methods

fmap :: (a0 -> b) -> StrongCategory p a a0 -> StrongCategory p a b

(<$) :: a0 -> StrongCategory p a b -> StrongCategory p a a0

Applicative (p a) => Applicative (StrongCategory p a)

Defined in Data.Bifunctor.Monoidal

Methods

pure :: a0 -> StrongCategory p a a0

(<*>) :: StrongCategory p a (a0 -> b) -> StrongCategory p a a0 -> StrongCategory p a b

liftA2 :: (a0 -> b -> c) -> StrongCategory p a a0 -> StrongCategory p a b -> StrongCategory p a c

(*>) :: StrongCategory p a a0 -> StrongCategory p a b -> StrongCategory p a b

(<*) :: StrongCategory p a a0 -> StrongCategory p a b -> StrongCategory p a a0

(Strong p, Semigroupoid p, Category p) => Monoidal ((->) :: Type -> Type -> Type) (,) () (,) () (,) () (StrongCategory p)

Defined in Data.Bifunctor.Monoidal

(Profunctor p, Category p) => Unital ((->) :: Type -> Type -> Type) () () () (StrongCategory p)

Defined in Data.Bifunctor.Monoidal

Methods

introduce :: () -> StrongCategory p () ()

(Strong p, Semigroupoid p) => Semigroupal ((->) :: Type -> Type -> Type) (,) (,) (,) (StrongCategory p)

Defined in Data.Bifunctor.Monoidal

Methods

combine :: (StrongCategory p x y, StrongCategory p x' y') -> StrongCategory p (x, x') (y, y')