CategoriesInstances

Provides instances for the definition of category constrained on the objects.

Documentation

class Any x

Instances

Any (x :: k)

Defined in CategoriesInstances

Monad m => Bifunctor (Algebra m :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,)

Defined in CategoriesInstances

Methods

bimap :: (Algebra m x1, Algebra m x2, Any y1, Any y2) => (x1 -> x2) -> (y1 -> y2) -> (x1, y1) -> (x2, y2)

Bifunctor (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Either

Defined in CategoriesInstances

Methods

bimap :: (Any x1, Any x2, Any y1, Any y2) => (x1 -> x2) -> (y1 -> y2) -> Either x1 y1 -> Either x2 y2

Bifunctor (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,)

Defined in CategoriesInstances

Methods

bimap :: (Any x1, Any x2, Any y1, Any y2) => (x1 -> x2) -> (y1 -> y2) -> (x1, y1) -> (x2, y2)

Monad m => Bifunctor (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) (Kleisli m :: Type -> Type -> Type) (Any :: Type -> Constraint) (Kleisli m :: Type -> Type -> Type) (,)

Defined in CategoriesInstances

Methods

bimap :: (Any x1, Any x2, Any y1, Any y2) => (x1 -> x2) -> Kleisli m y1 y2 -> Kleisli m (x1, y1) (x2, y2)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Algebra []) ((->) :: Type -> Type -> Type) (,) () (,) (,) (Aggregating a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Algebra [] w) => Aggregating a b x y -> Aggregating a b (w, x) (w, y)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Either Void Either Either (Replacing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Any w) => Replacing a b x y -> Replacing a b (Either w x) (Either w y)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Either Void Either Either (Setting a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Any w) => Setting a b x y -> Setting a b (Either w x) (Either w y)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,) () (,) (,) (Replacing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Any w) => Replacing a b x y -> Replacing a b (w, x) (w, y)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,) () (,) (,) (Setting a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Any w) => Setting a b x y -> Setting a b (w, x) (w, y)

Monad m => Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Algebra m :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,) () (,) (,) (Classifying m a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Algebra m w) => Classifying m a b x y -> Classifying m a b (w, x) (w, y)

Monad m => Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Algebra m :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,) () (,) (,) (Viewing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Algebra m w) => Viewing a b x y -> Viewing a b (w, x) (w, y)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Either Void Either Either (Previewing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Any w) => Previewing a b x y -> Previewing a b (Either w x) (Either w y)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,) () (,) (,) (Previewing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Any w) => Previewing a b x y -> Previewing a b (w, x) (w, y)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,) () (,) (,) (Viewing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Any w) => Viewing a b x y -> Viewing a b (w, x) (w, y)

Monad m => Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) (Kleisli m :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,) () (,) (,) (Updating m a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Any w) => Updating m a b x y -> Updating m a b (w, x) (w, y)

Monad m => MonoidalAction (Algebra m :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,) () (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,)

Defined in CategoriesInstances

Methods

unitor :: Any x => ((), x) -> x

unitorinv :: Any x => x -> ((), x)

multiplicator :: (Any x, Algebra m p, Algebra m q) => (p, (q, x)) -> ((p, q), x)

multiplicatorinv :: (Any x, Algebra m p, Algebra m q) => ((p, q), x) -> (p, (q, x))

Monad m => MonoidalAction (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,) () (Any :: Type -> Constraint) (Kleisli m :: Type -> Type -> Type) (,)

Defined in CategoriesInstances

Methods

unitor :: Any x => Kleisli m ((), x) x

unitorinv :: Any x => Kleisli m x ((), x)

multiplicator :: (Any x, Any p, Any q) => Kleisli m (p, (q, x)) ((p, q), x)

multiplicatorinv :: (Any x, Any p, Any q) => Kleisli m ((p, q), x) (p, (q, x))

Profunctor (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Replacing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

dimap :: (Any x1, Any x2, Any y1, Any y2) => (x2 -> x1) -> (y1 -> y2) -> Replacing a b x1 y1 -> Replacing a b x2 y2

Profunctor (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Aggregating a b :: Type -> Type -> Type)

Defined in Combinators

Methods

dimap :: (Any x1, Any x2, Any y1, Any y2) => (x2 -> x1) -> (y1 -> y2) -> Aggregating a b x1 y1 -> Aggregating a b x2 y2

Profunctor (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Setting a b :: Type -> Type -> Type)

Defined in Combinators

Methods

dimap :: (Any x1, Any x2, Any y1, Any y2) => (x2 -> x1) -> (y1 -> y2) -> Setting a b x1 y1 -> Setting a b x2 y2

Monad m => Profunctor (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Updating m a b :: Type -> Type -> Type)

Defined in Combinators

Methods

dimap :: (Any x1, Any x2, Any y1, Any y2) => (x2 -> x1) -> (y1 -> y2) -> Updating m a b x1 y1 -> Updating m a b x2 y2

Monad m => Profunctor (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Classifying m a b :: Type -> Type -> Type)

Defined in Combinators

Methods

dimap :: (Any x1, Any x2, Any y1, Any y2) => (x2 -> x1) -> (y1 -> y2) -> Classifying m a b x1 y1 -> Classifying m a b x2 y2

Profunctor (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Previewing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

dimap :: (Any x1, Any x2, Any y1, Any y2) => (x2 -> x1) -> (y1 -> y2) -> Previewing a b x1 y1 -> Previewing a b x2 y2

Profunctor (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Viewing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

dimap :: (Any x1, Any x2, Any y1, Any y2) => (x2 -> x1) -> (y1 -> y2) -> Viewing a b x1 y1 -> Viewing a b x2 y2

Monad m => Profunctor (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) (Kleisli m :: Type -> Type -> Type) (Updating m a b :: Type -> Type -> Type)

Defined in Combinators

Methods

dimap :: (Any x1, Any x2, Any y1, Any y2) => (x2 -> x1) -> Kleisli m y1 y2 -> Updating m a b x1 y1 -> Updating m a b x2 y2

Category (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type)

Defined in CategoriesInstances

Methods

unit :: Any x => x -> x

comp :: Any x => (y -> z) -> (x -> y) -> x -> z

Monad m => Category (Any :: Type -> Constraint) (Kleisli m :: Type -> Type -> Type)

Defined in CategoriesInstances

Methods

unit :: Any x => Kleisli m x x

comp :: Any x => Kleisli m y z -> Kleisli m x y -> Kleisli m x z

MonoidalCategory (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Either Void

Defined in CategoriesInstances

Methods

alpha :: (Any x, Any y, Any z) => Either x (Either y z) -> Either (Either x y) z

alphainv :: (Any x, Any y, Any z) => Either (Either x y) z -> Either x (Either y z)

lambda :: Any x => Either x Void -> x

lambdainv :: Any x => x -> Either x Void

rho :: Any x => Either Void x -> x

rhoinv :: Any x => x -> Either Void x

MonoidalCategory (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,) ()

Defined in CategoriesInstances

Methods

alpha :: (Any x, Any y, Any z) => (x, (y, z)) -> ((x, y), z)

alphainv :: (Any x, Any y, Any z) => ((x, y), z) -> (x, (y, z))

lambda :: Any x => (x, ()) -> x

lambdainv :: Any x => x -> (x, ())

rho :: Any x => ((), x) -> x

rhoinv :: Any x => x -> ((), x)

MonoidalAction Functor (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

unitor :: Any x => App Identity x -> x

unitorinv :: Any x => x -> App Identity x

multiplicator :: (Any x, Functor p, Functor q) => App p (App q x) -> App (Compose p q) x

multiplicatorinv :: (Any x, Functor p, Functor q) => App (Compose p q) x -> App p (App q x)

MonoidalAction Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

unitor :: Any x => App Identity x -> x

unitorinv :: Any x => x -> App Identity x

multiplicator :: (Any x, Applicative p, Applicative q) => App p (App q x) -> App (Compose p q) x

multiplicatorinv :: (Any x, Applicative p, Applicative q) => App (Compose p q) x -> App p (App q x)

MonoidalAction Traversable (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

unitor :: Any x => App Identity x -> x

unitorinv :: Any x => x -> App Identity x

multiplicator :: (Any x, Traversable p, Traversable q) => App p (App q x) -> App (Compose p q) x

multiplicatorinv :: (Any x, Traversable p, Traversable q) => App (Compose p q) x -> App p (App q x)

Bifunctor Functor (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

bimap :: (Functor x1, Functor x2, Any y1, Any y2) => Nat x1 x2 -> (y1 -> y2) -> App x1 y1 -> App x2 y2

Bifunctor Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

bimap :: (Applicative x1, Applicative x2, Any y1, Any y2) => Nat x1 x2 -> (y1 -> y2) -> App x1 y1 -> App x2 y2

Bifunctor Traversable (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

bimap :: (Traversable x1, Traversable x2, Any y1, Any y2) => Nat x1 x2 -> (y1 -> y2) -> App x1 y1 -> App x2 y2

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Functor (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (App :: (Type -> Type) -> Type -> Type) (App :: (Type -> Type) -> Type -> Type) (Replacing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Functor w) => Replacing a b x y -> Replacing a b (App w x) (App w y)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (App :: (Type -> Type) -> Type -> Type) (App :: (Type -> Type) -> Type -> Type) (Replacing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Applicative w) => Replacing a b x y -> Replacing a b (App w x) (App w y)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (App :: (Type -> Type) -> Type -> Type) (App :: (Type -> Type) -> Type -> Type) (Aggregating a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Applicative w) => Aggregating a b x y -> Aggregating a b (App w x) (App w y)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Traversable (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (App :: (Type -> Type) -> Type -> Type) (App :: (Type -> Type) -> Type -> Type) (Replacing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Traversable w) => Replacing a b x y -> Replacing a b (App w x) (App w y)

newtype Nat f g

Constructors

Nat

Fields

• nat :: forall x. f x -> g x

Instances

Category Functor (Nat :: (Type -> Type) -> (Type -> Type) -> Type)

Defined in CategoriesInstances

Methods

unit :: Functor x => Nat x x

comp :: Functor x => Nat y z -> Nat x y -> Nat x z

Category Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type)

Defined in CategoriesInstances

Methods

unit :: Applicative x => Nat x x

comp :: Applicative x => Nat y z -> Nat x y -> Nat x z

Category Traversable (Nat :: (Type -> Type) -> (Type -> Type) -> Type)

Defined in CategoriesInstances

Methods

unit :: Traversable x => Nat x x

comp :: Traversable x => Nat y z -> Nat x y -> Nat x z

MonoidalCategory Functor (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity

Defined in CategoriesInstances

Methods

alpha :: (Functor x, Functor y, Functor z) => Nat (Compose x (Compose y z)) (Compose (Compose x y) z)

alphainv :: (Functor x, Functor y, Functor z) => Nat (Compose (Compose x y) z) (Compose x (Compose y z))

lambda :: Functor x => Nat (Compose x Identity) x

lambdainv :: Functor x => Nat x (Compose x Identity)

rho :: Functor x => Nat (Compose Identity x) x

rhoinv :: Functor x => Nat x (Compose Identity x)

MonoidalCategory Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity

Defined in CategoriesInstances

Methods

alpha :: (Applicative x, Applicative y, Applicative z) => Nat (Compose x (Compose y z)) (Compose (Compose x y) z)

alphainv :: (Applicative x, Applicative y, Applicative z) => Nat (Compose (Compose x y) z) (Compose x (Compose y z))

lambda :: Applicative x => Nat (Compose x Identity) x

lambdainv :: Applicative x => Nat x (Compose x Identity)

rho :: Applicative x => Nat (Compose Identity x) x

rhoinv :: Applicative x => Nat x (Compose Identity x)

MonoidalCategory Traversable (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity

Defined in CategoriesInstances

Methods

alpha :: (Traversable x, Traversable y, Traversable z) => Nat (Compose x (Compose y z)) (Compose (Compose x y) z)

alphainv :: (Traversable x, Traversable y, Traversable z) => Nat (Compose (Compose x y) z) (Compose x (Compose y z))

lambda :: Traversable x => Nat (Compose x Identity) x

lambdainv :: Traversable x => Nat x (Compose x Identity)

rho :: Traversable x => Nat (Compose Identity x) x

rhoinv :: Traversable x => Nat x (Compose Identity x)

MonoidalAction Functor (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

unitor :: Any x => App Identity x -> x

unitorinv :: Any x => x -> App Identity x

multiplicator :: (Any x, Functor p, Functor q) => App p (App q x) -> App (Compose p q) x

multiplicatorinv :: (Any x, Functor p, Functor q) => App (Compose p q) x -> App p (App q x)

MonoidalAction Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

unitor :: Any x => App Identity x -> x

unitorinv :: Any x => x -> App Identity x

multiplicator :: (Any x, Applicative p, Applicative q) => App p (App q x) -> App (Compose p q) x

multiplicatorinv :: (Any x, Applicative p, Applicative q) => App (Compose p q) x -> App p (App q x)

MonoidalAction Traversable (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

unitor :: Any x => App Identity x -> x

unitorinv :: Any x => x -> App Identity x

multiplicator :: (Any x, Traversable p, Traversable q) => App p (App q x) -> App (Compose p q) x

multiplicatorinv :: (Any x, Traversable p, Traversable q) => App (Compose p q) x -> App p (App q x)

Bifunctor Functor (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

bimap :: (Functor x1, Functor x2, Any y1, Any y2) => Nat x1 x2 -> (y1 -> y2) -> App x1 y1 -> App x2 y2

Bifunctor Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

bimap :: (Applicative x1, Applicative x2, Any y1, Any y2) => Nat x1 x2 -> (y1 -> y2) -> App x1 y1 -> App x2 y2

Bifunctor Traversable (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

bimap :: (Traversable x1, Traversable x2, Any y1, Any y2) => Nat x1 x2 -> (y1 -> y2) -> App x1 y1 -> App x2 y2

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Functor (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (App :: (Type -> Type) -> Type -> Type) (App :: (Type -> Type) -> Type -> Type) (Replacing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Functor w) => Replacing a b x y -> Replacing a b (App w x) (App w y)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (App :: (Type -> Type) -> Type -> Type) (App :: (Type -> Type) -> Type -> Type) (Replacing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Applicative w) => Replacing a b x y -> Replacing a b (App w x) (App w y)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (App :: (Type -> Type) -> Type -> Type) (App :: (Type -> Type) -> Type -> Type) (Aggregating a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Applicative w) => Aggregating a b x y -> Aggregating a b (App w x) (App w y)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Traversable (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (App :: (Type -> Type) -> Type -> Type) (App :: (Type -> Type) -> Type -> Type) (Replacing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Traversable w) => Replacing a b x y -> Replacing a b (App w x) (App w y)

Bifunctor Functor (Nat :: (Type -> Type) -> (Type -> Type) -> Type) Functor (Nat :: (Type -> Type) -> (Type -> Type) -> Type) Functor (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

bimap :: (Functor x1, Functor x2, Functor y1, Functor y2) => Nat x1 x2 -> Nat y1 y2 -> Nat (Compose x1 y1) (Compose x2 y2)

Bifunctor Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type) Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type) Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

bimap :: (Applicative x1, Applicative x2, Applicative y1, Applicative y2) => Nat x1 x2 -> Nat y1 y2 -> Nat (Compose x1 y1) (Compose x2 y2)

Bifunctor Traversable (Nat :: (Type -> Type) -> (Type -> Type) -> Type) Traversable (Nat :: (Type -> Type) -> (Type -> Type) -> Type) Traversable (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

bimap :: (Traversable x1, Traversable x2, Traversable y1, Traversable y2) => Nat x1 x2 -> Nat y1 y2 -> Nat (Compose x1 y1) (Compose x2 y2)

newtype App f a

Constructors

App

Fields

• getApp :: f a

Instances

MonoidalAction Functor (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

unitor :: Any x => App Identity x -> x

unitorinv :: Any x => x -> App Identity x

multiplicator :: (Any x, Functor p, Functor q) => App p (App q x) -> App (Compose p q) x

multiplicatorinv :: (Any x, Functor p, Functor q) => App (Compose p q) x -> App p (App q x)

MonoidalAction Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

unitor :: Any x => App Identity x -> x

unitorinv :: Any x => x -> App Identity x

multiplicator :: (Any x, Applicative p, Applicative q) => App p (App q x) -> App (Compose p q) x

multiplicatorinv :: (Any x, Applicative p, Applicative q) => App (Compose p q) x -> App p (App q x)

MonoidalAction Traversable (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

unitor :: Any x => App Identity x -> x

unitorinv :: Any x => x -> App Identity x

multiplicator :: (Any x, Traversable p, Traversable q) => App p (App q x) -> App (Compose p q) x

multiplicatorinv :: (Any x, Traversable p, Traversable q) => App (Compose p q) x -> App p (App q x)

Bifunctor Functor (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

bimap :: (Functor x1, Functor x2, Any y1, Any y2) => Nat x1 x2 -> (y1 -> y2) -> App x1 y1 -> App x2 y2

Bifunctor Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

bimap :: (Applicative x1, Applicative x2, Any y1, Any y2) => Nat x1 x2 -> (y1 -> y2) -> App x1 y1 -> App x2 y2

Bifunctor Traversable (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (App :: (Type -> Type) -> Type -> Type)

Defined in CategoriesInstances

Methods

bimap :: (Traversable x1, Traversable x2, Any y1, Any y2) => Nat x1 x2 -> (y1 -> y2) -> App x1 y1 -> App x2 y2

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Functor (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (App :: (Type -> Type) -> Type -> Type) (App :: (Type -> Type) -> Type -> Type) (Replacing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Functor w) => Replacing a b x y -> Replacing a b (App w x) (App w y)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (App :: (Type -> Type) -> Type -> Type) (App :: (Type -> Type) -> Type -> Type) (Replacing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Applicative w) => Replacing a b x y -> Replacing a b (App w x) (App w y)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Applicative (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (App :: (Type -> Type) -> Type -> Type) (App :: (Type -> Type) -> Type -> Type) (Aggregating a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Applicative w) => Aggregating a b x y -> Aggregating a b (App w x) (App w y)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) Traversable (Nat :: (Type -> Type) -> (Type -> Type) -> Type) (Compose :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity (App :: (Type -> Type) -> Type -> Type) (App :: (Type -> Type) -> Type -> Type) (Replacing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Traversable w) => Replacing a b x y -> Replacing a b (App w x) (App w y)

class Monad m => Algebra m a where

Methods

algebra :: m a -> a

Instances

Monad m => Algebra m ()

Defined in CategoriesInstances

Methods

algebra :: m () -> ()

Monad m => Algebra m (m a)

Defined in CategoriesInstances

Methods

algebra :: m (m a) -> m a

(Monad m, Algebra m x, Algebra m y) => Algebra m (x, y)

Defined in CategoriesInstances

Methods

algebra :: m (x, y) -> (x, y)

Monad m => Bifunctor (Algebra m :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,)

Defined in CategoriesInstances

Methods

bimap :: (Algebra m x1, Algebra m x2, Any y1, Any y2) => (x1 -> x2) -> (y1 -> y2) -> (x1, y1) -> (x2, y2)

Monad m => Bifunctor (Algebra m :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Algebra m :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Algebra m :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,)

Defined in CategoriesInstances

Methods

bimap :: (Algebra m x1, Algebra m x2, Algebra m y1, Algebra m y2) => (x1 -> x2) -> (y1 -> y2) -> (x1, y1) -> (x2, y2)

Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Algebra []) ((->) :: Type -> Type -> Type) (,) () (,) (,) (Aggregating a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Algebra [] w) => Aggregating a b x y -> Aggregating a b (w, x) (w, y)

Monad m => Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Algebra m :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,) () (,) (,) (Classifying m a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Algebra m w) => Classifying m a b x y -> Classifying m a b (w, x) (w, y)

Monad m => Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Algebra m :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,) () (,) (,) (Viewing a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Algebra m w) => Viewing a b x y -> Viewing a b (w, x) (w, y)

Monad m => MonoidalAction (Algebra m :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,) () (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,)

Defined in CategoriesInstances

Methods

unitor :: Any x => ((), x) -> x

unitorinv :: Any x => x -> ((), x)

multiplicator :: (Any x, Algebra m p, Algebra m q) => (p, (q, x)) -> ((p, q), x)

multiplicatorinv :: (Any x, Algebra m p, Algebra m q) => ((p, q), x) -> (p, (q, x))

Monad m => Category (Algebra m :: Type -> Constraint) ((->) :: Type -> Type -> Type)

Defined in CategoriesInstances

Methods

unit :: Algebra m x => x -> x

comp :: Algebra m x => (y -> z) -> (x -> y) -> x -> z

Monad m => MonoidalCategory (Algebra m :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,) ()

Defined in CategoriesInstances

Methods

alpha :: (Algebra m x, Algebra m y, Algebra m z) => (x, (y, z)) -> ((x, y), z)

alphainv :: (Algebra m x, Algebra m y, Algebra m z) => ((x, y), z) -> (x, (y, z))

lambda :: Algebra m x => (x, ()) -> x

lambdainv :: Algebra m x => x -> (x, ())

rho :: Algebra m x => ((), x) -> x

rhoinv :: Algebra m x => x -> ((), x)

data FunList s a b

Constructors

Done b

More s (FunList s a (a -> b))

Instances

Functor (FunList s a)

Defined in CategoriesInstances

Methods

fmap :: (a0 -> b) -> FunList s a a0 -> FunList s a b

(<$) :: a0 -> FunList s a b -> FunList s a a0

Applicative (FunList s a)

Defined in CategoriesInstances

Methods

pure :: a0 -> FunList s a a0

(<*>) :: FunList s a (a0 -> b) -> FunList s a a0 -> FunList s a b

liftA2 :: (a0 -> b -> c) -> FunList s a a0 -> FunList s a b -> FunList s a c

(*>) :: FunList s a a0 -> FunList s a b -> FunList s a b

(<*) :: FunList s a a0 -> FunList s a b -> FunList s a a0

newtype Kleisli m a b

Constructors

Kleisli

Fields

• getKleisli :: a -> m b

Instances

Monad m => Bifunctor (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) (Kleisli m :: Type -> Type -> Type) (Any :: Type -> Constraint) (Kleisli m :: Type -> Type -> Type) (,)

Defined in CategoriesInstances

Methods

bimap :: (Any x1, Any x2, Any y1, Any y2) => (x1 -> x2) -> Kleisli m y1 y2 -> Kleisli m (x1, y1) (x2, y2)

Monad m => Tambara (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) (Kleisli m :: Type -> Type -> Type) (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,) () (,) (,) (Updating m a b :: Type -> Type -> Type)

Defined in Combinators

Methods

tambara :: (Any x, Any y, Any w) => Updating m a b x y -> Updating m a b (w, x) (w, y)

Monad m => MonoidalAction (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (,) () (Any :: Type -> Constraint) (Kleisli m :: Type -> Type -> Type) (,)

Defined in CategoriesInstances

Methods

unitor :: Any x => Kleisli m ((), x) x

unitorinv :: Any x => Kleisli m x ((), x)

multiplicator :: (Any x, Any p, Any q) => Kleisli m (p, (q, x)) ((p, q), x)

multiplicatorinv :: (Any x, Any p, Any q) => Kleisli m ((p, q), x) (p, (q, x))

Monad m => Profunctor (Any :: Type -> Constraint) ((->) :: Type -> Type -> Type) (Any :: Type -> Constraint) (Kleisli m :: Type -> Type -> Type) (Updating m a b :: Type -> Type -> Type)

Defined in Combinators

Methods

dimap :: (Any x1, Any x2, Any y1, Any y2) => (x2 -> x1) -> Kleisli m y1 y2 -> Updating m a b x1 y1 -> Updating m a b x2 y2

Monad m => Category (Any :: Type -> Constraint) (Kleisli m :: Type -> Type -> Type)

Defined in CategoriesInstances

Methods

unit :: Any x => Kleisli m x x

comp :: Any x => Kleisli m y z -> Kleisli m x y -> Kleisli m x z

Orphan instances

MonoidalCategory objm m o i => MonoidalAction (objm :: k -> Constraint) (m :: k -> k -> Type) (o :: k -> k -> k) (i :: k) (objm :: k -> Constraint) (m :: k -> k -> Type) (o :: k -> k -> k)

Methods

unitor :: objm x => m (o i x) x

unitorinv :: objm x => m x (o i x)

multiplicator :: (objm x, objm p, objm q) => m (o p (o q x)) (o (o p q) x)

multiplicatorinv :: (objm x, objm p, objm q) => m (o (o p q) x) (o p (o q x))