Safe Haskell	None
Language	Haskell2010

Proarrow.Category.Monoidal.Distributive

Documentation

class (MonoidalProfunctor p, MonoidalProfunctor (Coprod p)) => DistributiveProfunctor (p :: j +-> k) Source Comments #

Instances

Instances details

(MonoidalProfunctor p, MonoidalProfunctor (Coprod p)) => DistributiveProfunctor (p :: j +-> k) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive

class (Monoidal k, HasCoproducts k, DistributiveProfunctor (Id :: k -> k -> Type)) => Distributive k where Source Comments #

Methods

distL :: forall (a :: k) (b :: k) (c :: k). (Ob a, Ob b, Ob c) => (a ** (b || c)) ~> ((a ** b) || (a ** c)) Source Comments #

distR :: forall (a :: k) (b :: k) (c :: k). (Ob a, Ob b, Ob c) => ((a || b) ** c) ~> ((a ** c) || (b ** c)) Source Comments #

distL0 :: forall (a :: k). Ob a => (a ** (InitialObject :: k)) ~> (InitialObject :: k) Source Comments #

distR0 :: forall (a :: k). Ob a => ((InitialObject :: k) ** a) ~> (InitialObject :: k) Source Comments #

Instances

Instances details

Distributive BOOL Source Comments #
Instance details Defined in Proarrow.Category.Instance.Bool Methods distL :: forall (a :: BOOL) (b :: BOOL) (c :: BOOL). (Ob a, Ob b, Ob c) => (a (b \|\| c)) ~> ((a b) \|\| (a c)) Source Comments # distR :: forall (a :: BOOL) (b :: BOOL) (c :: BOOL). (Ob a, Ob b, Ob c) => ((a \|\| b) c) ~> ((a c) \|\| (b c)) Source Comments # distL0 :: forall (a :: BOOL). Ob a => (a (InitialObject :: BOOL)) ~> (InitialObject :: BOOL) Source Comments # distR0 :: forall (a :: BOOL). Ob a => ((InitialObject :: BOOL) a) ~> (InitialObject :: BOOL) Source Comments #
Distributive () Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods distL :: forall (a :: ()) (b :: ()) (c :: ()). (Ob a, Ob b, Ob c) => (a (b \|\| c)) ~> ((a b) \|\| (a c)) Source Comments # distR :: forall (a :: ()) (b :: ()) (c :: ()). (Ob a, Ob b, Ob c) => ((a \|\| b) c) ~> ((a c) \|\| (b c)) Source Comments # distL0 :: forall (a :: ()). Ob a => (a (InitialObject :: ())) ~> (InitialObject :: ()) Source Comments # distR0 :: forall (a :: ()). Ob a => ((InitialObject :: ()) a) ~> (InitialObject :: ()) Source Comments #
Distributive Type Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods distL :: (Ob a, Ob b, Ob c) => (a (b \|\| c)) ~> ((a b) \|\| (a c)) Source Comments # distR :: (Ob a, Ob b, Ob c) => ((a \|\| b) c) ~> ((a c) \|\| (b c)) Source Comments # distL0 :: Ob a => (a (InitialObject :: Type)) ~> (InitialObject :: Type) Source Comments # distR0 :: Ob a => ((InitialObject :: Type) a) ~> (InitialObject :: Type) Source Comments #
BiCCC k => Distributive (PROD k) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods distL :: forall (a :: PROD k) (b :: PROD k) (c :: PROD k). (Ob a, Ob b, Ob c) => (a (b \|\| c)) ~> ((a b) \|\| (a c)) Source Comments # distR :: forall (a :: PROD k) (b :: PROD k) (c :: PROD k). (Ob a, Ob b, Ob c) => ((a \|\| b) c) ~> ((a c) \|\| (b c)) Source Comments # distL0 :: forall (a :: PROD k). Ob a => (a (InitialObject :: PROD k)) ~> (InitialObject :: PROD k) Source Comments # distR0 :: forall (a :: PROD k). Ob a => ((InitialObject :: PROD k) a) ~> (InitialObject :: PROD k) Source Comments #
(Distributive k, Promonad p, DistributiveProfunctor p) => Distributive (KLEISLI p) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods distL :: forall (a :: KLEISLI p) (b :: KLEISLI p) (c :: KLEISLI p). (Ob a, Ob b, Ob c) => (a (b \|\| c)) ~> ((a b) \|\| (a c)) Source Comments # distR :: forall (a :: KLEISLI p) (b :: KLEISLI p) (c :: KLEISLI p). (Ob a, Ob b, Ob c) => ((a \|\| b) c) ~> ((a c) \|\| (b c)) Source Comments # distL0 :: forall (a :: KLEISLI p). Ob a => (a (InitialObject :: KLEISLI p)) ~> (InitialObject :: KLEISLI p) Source Comments # distR0 :: forall (a :: KLEISLI p). Ob a => ((InitialObject :: KLEISLI p) a) ~> (InitialObject :: KLEISLI p) Source Comments #
(Monoidal j, Monoidal k) => Distributive (PRO j k) Source Comments #
Instance details Defined in Proarrow.Profunctor.Day Methods distL :: forall (a :: PRO j k) (b :: PRO j k) (c :: PRO j k). (Ob a, Ob b, Ob c) => (a (b \|\| c)) ~> ((a b) \|\| (a c)) Source Comments # distR :: forall (a :: PRO j k) (b :: PRO j k) (c :: PRO j k). (Ob a, Ob b, Ob c) => ((a \|\| b) c) ~> ((a c) \|\| (b c)) Source Comments # distL0 :: forall (a :: PRO j k). Ob a => (a (InitialObject :: PRO j k)) ~> (InitialObject :: PRO j k) Source Comments # distR0 :: forall (a :: PRO j k). Ob a => ((InitialObject :: PRO j k) a) ~> (InitialObject :: PRO j k) Source Comments #

distLProd :: forall {k} (a :: k) (b :: k) (c :: k). (BiCCC k, Ob a, Ob b, Ob c) => (a && (b || c)) ~> ((a && b) || (a && c)) Source Comments #

distRProd :: forall {k} (a :: k) (b :: k) (c :: k). (BiCCC k, Ob a, Ob b, Ob c) => ((a || b) && c) ~> ((a && c) || (b && c)) Source Comments #

class Profunctor t => Traversable (t :: k +-> k) where Source Comments #

Methods

traverse :: forall (p :: k +-> k). (DistributiveProfunctor p, Strong k p, SelfAction k) => (t :.: p) :~> (p :.: t) Source Comments #

Instances

Instances details

CategoryOf k => Traversable (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods traverse :: forall (p :: k +-> k). (DistributiveProfunctor p, Strong k p, SelfAction k) => ((Id :: k -> k -> Type) :.: p) :~> (p :.: (Id :: k -> k -> Type)) Source Comments #
Traversable (->) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods traverse :: forall (p :: Type +-> Type). (DistributiveProfunctor p, Strong Type p, SelfAction Type) => ((->) :.: p) :~> (p :.: (->)) Source Comments #
Traversable p => Traversable (Fix p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Fix Methods traverse :: forall (p0 :: k +-> k). (DistributiveProfunctor p0, Strong k p0, SelfAction k) => (Fix p :.: p0) :~> (p0 :.: Fix p) Source Comments #
Traversable (Star Maybe) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods traverse :: forall (p :: Type +-> Type). (DistributiveProfunctor p, Strong Type p, SelfAction Type) => (Star Maybe :.: p) :~> (p :.: Star Maybe) Source Comments #
Traversable (Star []) Source Comments #
Instance details Defined in Proarrow.Profunctor.Star Methods traverse :: forall (p :: Type +-> Type). (DistributiveProfunctor p, Strong Type p, SelfAction Type) => (Star [] :.: p) :~> (p :.: Star []) Source Comments #
SelfAction k => Traversable (Constant c :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Constant Methods traverse :: forall (p :: k +-> k). (DistributiveProfunctor p, Strong k p, SelfAction k) => ((Constant c :: k -> k -> Type) :.: p) :~> (p :.: (Constant c :: k -> k -> Type)) Source Comments #
(Monoid w, SelfAction k) => Traversable (Writer w :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Writer Methods traverse :: forall (p :: k +-> k). (DistributiveProfunctor p, Strong k p, SelfAction k) => ((Writer w :: k -> k -> Type) :.: p) :~> (p :.: (Writer w :: k -> k -> Type)) Source Comments #
(Traversable p, Traversable q) => Traversable (p :+: q :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods traverse :: forall (p0 :: k +-> k). (DistributiveProfunctor p0, Strong k p0, SelfAction k) => ((p :+: q) :.: p0) :~> (p0 :.: (p :+: q)) Source Comments #
(Cartesian k, Traversable p, Traversable q) => Traversable (p :*: q :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods traverse :: forall (p0 :: k +-> k). (DistributiveProfunctor p0, Strong k p0, SelfAction k) => ((p :: q) :.: p0) :~> (p0 :.: (p :: q)) Source Comments #
(Traversable p, Traversable q) => Traversable (p :.: q :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods traverse :: forall (p0 :: k +-> k). (DistributiveProfunctor p0, Strong k p0, SelfAction k) => ((p :.: q) :.: p0) :~> (p0 :.: (p :.: q)) Source Comments #

class Profunctor t => Cotraversable (t :: k +-> k) where Source Comments #

Methods

cotraverse :: forall (p :: k +-> k). (DistributiveProfunctor p, Strong k p, SelfAction k) => (p :.: t) :~> (t :.: p) Source Comments #

Instances

Instances details

CategoryOf k => Cotraversable (Id :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods cotraverse :: forall (p :: k +-> k). (DistributiveProfunctor p, Strong k p, SelfAction k) => (p :.: (Id :: k -> k -> Type)) :~> ((Id :: k -> k -> Type) :.: p) Source Comments #
Cotraversable (->) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods cotraverse :: forall (p :: Type +-> Type). (DistributiveProfunctor p, Strong Type p, SelfAction Type) => (p :.: (->)) :~> ((->) :.: p) Source Comments #
Cotraversable p => Cotraversable (Fix p :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Fix Methods cotraverse :: forall (p0 :: k +-> k). (DistributiveProfunctor p0, Strong k p0, SelfAction k) => (p0 :.: Fix p) :~> (Fix p :.: p0) Source Comments #
SelfAction k => Cotraversable (Constant c :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Constant Methods cotraverse :: forall (p :: k +-> k). (DistributiveProfunctor p, Strong k p, SelfAction k) => (p :.: (Constant c :: k -> k -> Type)) :~> ((Constant c :: k -> k -> Type) :.: p) Source Comments #
(Functor t, Traversable (Star t)) => Cotraversable (Costar t :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Costar Methods cotraverse :: forall (p :: k +-> k). (DistributiveProfunctor p, Strong k p, SelfAction k) => (p :.: Costar t) :~> (Costar t :.: p) Source Comments #
(Comonoid r, SelfAction k) => Cotraversable (Reader ('OP r) :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Promonad.Reader Methods cotraverse :: forall (p :: k +-> k). (DistributiveProfunctor p, Strong k p, SelfAction k) => (p :.: (Reader ('OP r) :: k -> k -> Type)) :~> ((Reader ('OP r) :: k -> k -> Type) :.: p) Source Comments #
(Cotraversable p, Cotraversable q) => Cotraversable (p :+: q :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods cotraverse :: forall (p0 :: k +-> k). (DistributiveProfunctor p0, Strong k p0, SelfAction k) => (p0 :.: (p :+: q)) :~> ((p :+: q) :.: p0) Source Comments #
(HasBinaryCoproducts k, Cotraversable p, Cotraversable q) => Cotraversable (p :*: q :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods cotraverse :: forall (p0 :: k +-> k). (DistributiveProfunctor p0, Strong k p0, SelfAction k) => (p0 :.: (p :: q)) :~> ((p :: q) :.: p0) Source Comments #
(Cotraversable p, Cotraversable q) => Cotraversable (p :.: q :: k -> k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Distributive Methods cotraverse :: forall (p0 :: k +-> k). (DistributiveProfunctor p0, Strong k p0, SelfAction k) => (p0 :.: (p :.: q)) :~> ((p :.: q) :.: p0) Source Comments #