Safe Haskell	None
Language	GHC2024

Proarrow.Category.Monoidal.Action

Documentation

type Act (t :: (m, k) +-> k) (a :: m) (x :: k) = t % '(a, x) Source Github #

class (Representable t, Monoidal m) => MonoidalAction (t :: (m, k) +-> k) where Source Github #

Methods

unitor :: forall (x :: k). Ob x => Act t (Unit :: m) x ~> x Source Github #

unitorInv :: forall (x :: k). Ob x => x ~> Act t (Unit :: m) x Source Github #

multiplicator :: forall (a :: m) (b :: m) (x :: k). (Ob a, Ob b, Ob x) => Act t (a ** b) x ~> Act t a (Act t b x) Source Github #

multiplicatorInv :: forall (a :: m) (b :: m) (x :: k). (Ob a, Ob b, Ob x) => Act t a (Act t b x) ~> Act t (a ** b) x Source Github #

Instances

Instances details

Monoidal k => MonoidalAction (Tensor :: k -> (k, k) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action Methods unitor :: forall (x :: k). Ob x => Act (Tensor :: k -> (k, k) -> Type) (Unit :: k) x ~> x Source Github # unitorInv :: forall (x :: k). Ob x => x ~> Act (Tensor :: k -> (k, k) -> Type) (Unit :: k) x Source Github # multiplicator :: forall (a :: k) (b :: k) (x :: k). (Ob a, Ob b, Ob x) => Act (Tensor :: k -> (k, k) -> Type) (a b) x ~> Act (Tensor :: k -> (k, k) -> Type) a (Act (Tensor :: k -> (k, k) -> Type) b x) Source Github # multiplicatorInv :: forall (a :: k) (b :: k) (x :: k). (Ob a, Ob b, Ob x) => Act (Tensor :: k -> (k, k) -> Type) a (Act (Tensor :: k -> (k, k) -> Type) b x) ~> Act (Tensor :: k -> (k, k) -> Type) (a b) x Source Github #
CategoryOf k => MonoidalAction (Rep (NoAction :: ((), k) +-> k) :: k -> ((), k) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action Methods unitor :: forall (x :: k). Ob x => Act (Rep (NoAction :: ((), k) +-> k)) (Unit :: ()) x ~> x Source Github # unitorInv :: forall (x :: k). Ob x => x ~> Act (Rep (NoAction :: ((), k) +-> k)) (Unit :: ()) x Source Github # multiplicator :: forall (a :: ()) (b :: ()) (x :: k). (Ob a, Ob b, Ob x) => Act (Rep (NoAction :: ((), k) +-> k)) (a b) x ~> Act (Rep (NoAction :: ((), k) +-> k)) a (Act (Rep (NoAction :: ((), k) +-> k)) b x) Source Github # multiplicatorInv :: forall (a :: ()) (b :: ()) (x :: k). (Ob a, Ob b, Ob x) => Act (Rep (NoAction :: ((), k) +-> k)) a (Act (Rep (NoAction :: ((), k) +-> k)) b x) ~> Act (Rep (NoAction :: ((), k) +-> k)) (a b) x Source Github #
HasCoproducts k => MonoidalAction (CoprodAction :: k -> (COPROD k, k) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action Methods unitor :: forall (x :: k). Ob x => Act (CoprodAction :: k -> (COPROD k, k) -> Type) (Unit :: COPROD k) x ~> x Source Github # unitorInv :: forall (x :: k). Ob x => x ~> Act (CoprodAction :: k -> (COPROD k, k) -> Type) (Unit :: COPROD k) x Source Github # multiplicator :: forall (a :: COPROD k) (b :: COPROD k) (x :: k). (Ob a, Ob b, Ob x) => Act (CoprodAction :: k -> (COPROD k, k) -> Type) (a b) x ~> Act (CoprodAction :: k -> (COPROD k, k) -> Type) a (Act (CoprodAction :: k -> (COPROD k, k) -> Type) b x) Source Github # multiplicatorInv :: forall (a :: COPROD k) (b :: COPROD k) (x :: k). (Ob a, Ob b, Ob x) => Act (CoprodAction :: k -> (COPROD k, k) -> Type) a (Act (CoprodAction :: k -> (COPROD k, k) -> Type) b x) ~> Act (CoprodAction :: k -> (COPROD k, k) -> Type) (a b) x Source Github #
HasProducts k => MonoidalAction (ProdAction :: k -> (PROD k, k) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action Methods unitor :: forall (x :: k). Ob x => Act (ProdAction :: k -> (PROD k, k) -> Type) (Unit :: PROD k) x ~> x Source Github # unitorInv :: forall (x :: k). Ob x => x ~> Act (ProdAction :: k -> (PROD k, k) -> Type) (Unit :: PROD k) x Source Github # multiplicator :: forall (a :: PROD k) (b :: PROD k) (x :: k). (Ob a, Ob b, Ob x) => Act (ProdAction :: k -> (PROD k, k) -> Type) (a b) x ~> Act (ProdAction :: k -> (PROD k, k) -> Type) a (Act (ProdAction :: k -> (PROD k, k) -> Type) b x) Source Github # multiplicatorInv :: forall (a :: PROD k) (b :: PROD k) (x :: k). (Ob a, Ob b, Ob x) => Act (ProdAction :: k -> (PROD k, k) -> Type) a (Act (ProdAction :: k -> (PROD k, k) -> Type) b x) ~> Act (ProdAction :: k -> (PROD k, k) -> Type) (a b) x Source Github #
MonoidalAction t => MonoidalAction (Rep (OpAction t) :: OPPOSITE k -> (OPPOSITE m, OPPOSITE k) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action Methods unitor :: forall (x :: OPPOSITE k). Ob x => Act (Rep (OpAction t)) (Unit :: OPPOSITE m) x ~> x Source Github # unitorInv :: forall (x :: OPPOSITE k). Ob x => x ~> Act (Rep (OpAction t)) (Unit :: OPPOSITE m) x Source Github # multiplicator :: forall (a :: OPPOSITE m) (b :: OPPOSITE m) (x :: OPPOSITE k). (Ob a, Ob b, Ob x) => Act (Rep (OpAction t)) (a b) x ~> Act (Rep (OpAction t)) a (Act (Rep (OpAction t)) b x) Source Github # multiplicatorInv :: forall (a :: OPPOSITE m) (b :: OPPOSITE m) (x :: OPPOSITE k). (Ob a, Ob b, Ob x) => Act (Rep (OpAction t)) a (Act (Rep (OpAction t)) b x) ~> Act (Rep (OpAction t)) (a b) x Source Github #
MonoidalAction ApplyAction Source Github #
Instance details Defined in Proarrow.Category.Instance.Nat Methods unitor :: Ob x => Act ApplyAction (Unit :: Type -> Type) x ~> x Source Github # unitorInv :: Ob x => x ~> Act ApplyAction (Unit :: Type -> Type) x Source Github # multiplicator :: forall (a :: Type -> Type) (b :: Type -> Type) x. (Ob a, Ob b, Ob x) => Act ApplyAction (a b) x ~> Act ApplyAction a (Act ApplyAction b x) Source Github # multiplicatorInv :: forall (a :: Type -> Type) (b :: Type -> Type) x. (Ob a, Ob b, Ob x) => Act ApplyAction a (Act ApplyAction b x) ~> Act ApplyAction (a b) x Source Github #
(Monoidal k2, Monoidal (SUBCAT ob), MonoidalAction t) => MonoidalAction (SubAction ob t :: k1 -> (SUBCAT ob, k1) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action Methods unitor :: forall (x :: k1). Ob x => Act (SubAction ob t) (Unit :: SUBCAT ob) x ~> x Source Github # unitorInv :: forall (x :: k1). Ob x => x ~> Act (SubAction ob t) (Unit :: SUBCAT ob) x Source Github # multiplicator :: forall (a :: SUBCAT ob) (b :: SUBCAT ob) (x :: k1). (Ob a, Ob b, Ob x) => Act (SubAction ob t) (a b) x ~> Act (SubAction ob t) a (Act (SubAction ob t) b x) Source Github # multiplicatorInv :: forall (a :: SUBCAT ob) (b :: SUBCAT ob) (x :: k1). (Ob a, Ob b, Ob x) => Act (SubAction ob t) a (Act (SubAction ob t) b x) ~> Act (SubAction ob t) (a b) x Source Github #

actHom :: forall {m} {k} (t :: (m, k) +-> k) (a :: m) (b :: m) (x :: k) (y :: k). Representable t => (a ~> b) -> (x ~> y) -> Act t a x ~> Act t b y Source Github #

composeActs :: forall {m} {k} (t :: (m, k) +-> k) (x :: m) (y :: m) (c :: k) (a :: k) (b :: k). (MonoidalAction t, Ob x, Ob y, Ob c) => (a ~> Act t x b) -> (b ~> Act t y c) -> a ~> Act t (x ** y) c Source Github #

decomposeActs :: forall {m} {k} (t :: (m, k) +-> k) (x :: m) (y :: m) (c :: k) (a :: k) (b :: k). (MonoidalAction t, Ob x, Ob y, Ob c) => (Act t y c ~> b) -> (Act t x b ~> a) -> Act t (x ** y) c ~> a Source Github #

data family NoAction :: ((), k) +-> k Source Github #

Instances

Instances details

CategoryOf k => MonoidalAction (Rep (NoAction :: ((), k) +-> k) :: k -> ((), k) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action Methods unitor :: forall (x :: k). Ob x => Act (Rep (NoAction :: ((), k) +-> k)) (Unit :: ()) x ~> x Source Github # unitorInv :: forall (x :: k). Ob x => x ~> Act (Rep (NoAction :: ((), k) +-> k)) (Unit :: ()) x Source Github # multiplicator :: forall (a :: ()) (b :: ()) (x :: k). (Ob a, Ob b, Ob x) => Act (Rep (NoAction :: ((), k) +-> k)) (a b) x ~> Act (Rep (NoAction :: ((), k) +-> k)) a (Act (Rep (NoAction :: ((), k) +-> k)) b x) Source Github # multiplicatorInv :: forall (a :: ()) (b :: ()) (x :: k). (Ob a, Ob b, Ob x) => Act (Rep (NoAction :: ((), k) +-> k)) a (Act (Rep (NoAction :: ((), k) +-> k)) b x) ~> Act (Rep (NoAction :: ((), k) +-> k)) (a b) x Source Github #
CategoryOf k => FunctorForRep (NoAction :: ((), k) +-> k) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action Methods fmap :: forall (a :: ((), k)) (b :: ((), k)). (a ~> b) -> ((NoAction :: ((), k) +-> k) @ a) ~> ((NoAction :: ((), k) +-> k) @ b) Source Github #
type (NoAction :: ((), k) +-> k) @ ('(a, x) :: ((), k)) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action type (NoAction :: ((), k) +-> k) @ ('(a, x) :: ((), k)) = x

data family OpAction :: ((m, k) +-> k) -> (OPPOSITE m, OPPOSITE k) +-> OPPOSITE k Source Github #

Instances

Instances details

MonoidalAction t => MonoidalAction (Rep (OpAction t) :: OPPOSITE k -> (OPPOSITE m, OPPOSITE k) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action Methods unitor :: forall (x :: OPPOSITE k). Ob x => Act (Rep (OpAction t)) (Unit :: OPPOSITE m) x ~> x Source Github # unitorInv :: forall (x :: OPPOSITE k). Ob x => x ~> Act (Rep (OpAction t)) (Unit :: OPPOSITE m) x Source Github # multiplicator :: forall (a :: OPPOSITE m) (b :: OPPOSITE m) (x :: OPPOSITE k). (Ob a, Ob b, Ob x) => Act (Rep (OpAction t)) (a b) x ~> Act (Rep (OpAction t)) a (Act (Rep (OpAction t)) b x) Source Github # multiplicatorInv :: forall (a :: OPPOSITE m) (b :: OPPOSITE m) (x :: OPPOSITE k). (Ob a, Ob b, Ob x) => Act (Rep (OpAction t)) a (Act (Rep (OpAction t)) b x) ~> Act (Rep (OpAction t)) (a b) x Source Github #
(Representable t, CategoryOf m) => FunctorForRep (OpAction t :: (OPPOSITE m, OPPOSITE k) +-> OPPOSITE k) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action Methods fmap :: forall (a :: (OPPOSITE m, OPPOSITE k)) (b :: (OPPOSITE m, OPPOSITE k)). (a ~> b) -> (OpAction t @ a) ~> (OpAction t @ b) Source Github #
type (OpAction t :: (OPPOSITE m, OPPOSITE k) +-> OPPOSITE k) @ ('('OP a, 'OP x) :: (OPPOSITE m, OPPOSITE k)) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action type (OpAction t :: (OPPOSITE m, OPPOSITE k) +-> OPPOSITE k) @ ('('OP a, 'OP x) :: (OPPOSITE m, OPPOSITE k)) = 'OP (t % '(a, x))

type SubAction (ob :: OB m) (t :: (m, k) +-> k) = Rep (SubAction' ob t) Source Github #

data family SubAction' :: forall (ob :: OB m) -> ((m, k) +-> k) -> (SUBCAT ob, k) +-> k Source Github #

Instances

Instances details

Monad m => Strong (AlgAction m :: Type -> (SUBCAT (Algebra m), Type) -> Type) (Classifying m a b :: Type -> Type -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods act :: forall (a0 :: SUBCAT (Algebra m)) x y. Ob a0 => Classifying m a b x y -> Classifying m a b (Act (AlgAction m) a0 x) (Act (AlgAction m) a0 y) Source Github #
(Monoidal k2, Monoidal (SUBCAT ob), MonoidalAction t) => MonoidalAction (SubAction ob t :: k1 -> (SUBCAT ob, k1) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action Methods unitor :: forall (x :: k1). Ob x => Act (SubAction ob t) (Unit :: SUBCAT ob) x ~> x Source Github # unitorInv :: forall (x :: k1). Ob x => x ~> Act (SubAction ob t) (Unit :: SUBCAT ob) x Source Github # multiplicator :: forall (a :: SUBCAT ob) (b :: SUBCAT ob) (x :: k1). (Ob a, Ob b, Ob x) => Act (SubAction ob t) (a b) x ~> Act (SubAction ob t) a (Act (SubAction ob t) b x) Source Github # multiplicatorInv :: forall (a :: SUBCAT ob) (b :: SUBCAT ob) (x :: k1). (Ob a, Ob b, Ob x) => Act (SubAction ob t) a (Act (SubAction ob t) b x) ~> Act (SubAction ob t) (a b) x Source Github #
(Monoidal k2, Monoidal (SUBCAT ob), Representable t) => FunctorForRep (SubAction' ob t :: (SUBCAT ob, k1) +-> k1) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action Methods fmap :: forall (a :: (SUBCAT ob, k1)) (b :: (SUBCAT ob, k1)). (a ~> b) -> (SubAction' ob t @ a) ~> (SubAction' ob t @ b) Source Github #
Applicative f => Strong (SubAction Traversable ApplyAction) (Star (Prelude f) :: Type -> Type -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Star Methods act :: forall (a :: SUBCAT Traversable) x y. Ob a => Star (Prelude f) x y -> Star (Prelude f) (Act (SubAction Traversable ApplyAction) a x) (Act (SubAction Traversable ApplyAction) a y) Source Github #
type (SubAction' ob t :: (SUBCAT ob, k2) +-> k2) @ ('('SUB a :: SUBCAT ob, x) :: (SUBCAT ob, k2)) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action type (SubAction' ob t :: (SUBCAT ob, k2) +-> k2) @ ('('SUB a :: SUBCAT ob, x) :: (SUBCAT ob, k2)) = t % '(a, x)

type ProdAction = Rep (ProdAction' :: (PROD k, k) +-> k) Source Github #

data family ProdAction' :: (PROD k, k) +-> k Source Github #

Instances

Instances details

HasProducts k => MonoidalAction (ProdAction :: k -> (PROD k, k) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action Methods unitor :: forall (x :: k). Ob x => Act (ProdAction :: k -> (PROD k, k) -> Type) (Unit :: PROD k) x ~> x Source Github # unitorInv :: forall (x :: k). Ob x => x ~> Act (ProdAction :: k -> (PROD k, k) -> Type) (Unit :: PROD k) x Source Github # multiplicator :: forall (a :: PROD k) (b :: PROD k) (x :: k). (Ob a, Ob b, Ob x) => Act (ProdAction :: k -> (PROD k, k) -> Type) (a b) x ~> Act (ProdAction :: k -> (PROD k, k) -> Type) a (Act (ProdAction :: k -> (PROD k, k) -> Type) b x) Source Github # multiplicatorInv :: forall (a :: PROD k) (b :: PROD k) (x :: k). (Ob a, Ob b, Ob x) => Act (ProdAction :: k -> (PROD k, k) -> Type) a (Act (ProdAction :: k -> (PROD k, k) -> Type) b x) ~> Act (ProdAction :: k -> (PROD k, k) -> Type) (a b) x Source Github #
Cartesian k => Costrong (ProdAction :: k -> (PROD k, k) -> Type) (Fold :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Fold Methods coact :: forall (a :: PROD k) (x :: k) (y :: k). (Ob a, Ob x, Ob y) => Fold (Act (ProdAction :: k -> (PROD k, k) -> Type) a x) (Act (ProdAction :: k -> (PROD k, k) -> Type) a y) -> Fold x y Source Github #
Strong (ProdAction :: Type -> (PROD Type, Type) -> Type) (Previewing a b :: Type -> Type -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods act :: forall (a0 :: PROD Type) x y. Ob a0 => Previewing a b x y -> Previewing a b (Act (ProdAction :: Type -> (PROD Type, Type) -> Type) a0 x) (Act (ProdAction :: Type -> (PROD Type, Type) -> Type) a0 y) Source Github #
Functor f => Strong (ProdAction :: Type -> (PROD Type, Type) -> Type) (Star (Prelude f) :: Type -> Type -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Star Methods act :: forall (a :: PROD Type) x y. Ob a => Star (Prelude f) x y -> Star (Prelude f) (Act (ProdAction :: Type -> (PROD Type, Type) -> Type) a x) (Act (ProdAction :: Type -> (PROD Type, Type) -> Type) a y) Source Github #
(Cartesian k, Ob c) => Strong (ProdAction :: k -> (PROD k, k) -> Type) (Rep (Constant c) :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods act :: forall (a :: PROD k) (x :: k) (y :: k). Ob a => Rep (Constant c) x y -> Rep (Constant c) (Act (ProdAction :: k -> (PROD k, k) -> Type) a x) (Act (ProdAction :: k -> (PROD k, k) -> Type) a y) Source Github #
HasProducts k => FunctorForRep (ProdAction' :: (PROD k, k) +-> k) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action Methods fmap :: forall (a :: (PROD k, k)) (b :: (PROD k, k)). (a ~> b) -> ((ProdAction' :: (PROD k, k) +-> k) @ a) ~> ((ProdAction' :: (PROD k, k) +-> k) @ b) Source Github #
type (ProdAction' :: (PROD k, k) +-> k) @ ('('PR a, b) :: (PROD k, k)) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action type (ProdAction' :: (PROD k, k) +-> k) @ ('('PR a, b) :: (PROD k, k)) = a && b

type CoprodAction = Rep (CoprodAction' :: (COPROD k, k) +-> k) Source Github #

data family CoprodAction' :: (COPROD k, k) +-> k Source Github #

Instances

Instances details

HasCoproducts k => MonoidalAction (CoprodAction :: k -> (COPROD k, k) -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action Methods unitor :: forall (x :: k). Ob x => Act (CoprodAction :: k -> (COPROD k, k) -> Type) (Unit :: COPROD k) x ~> x Source Github # unitorInv :: forall (x :: k). Ob x => x ~> Act (CoprodAction :: k -> (COPROD k, k) -> Type) (Unit :: COPROD k) x Source Github # multiplicator :: forall (a :: COPROD k) (b :: COPROD k) (x :: k). (Ob a, Ob b, Ob x) => Act (CoprodAction :: k -> (COPROD k, k) -> Type) (a b) x ~> Act (CoprodAction :: k -> (COPROD k, k) -> Type) a (Act (CoprodAction :: k -> (COPROD k, k) -> Type) b x) Source Github # multiplicatorInv :: forall (a :: COPROD k) (b :: COPROD k) (x :: k). (Ob a, Ob b, Ob x) => Act (CoprodAction :: k -> (COPROD k, k) -> Type) a (Act (CoprodAction :: k -> (COPROD k, k) -> Type) b x) ~> Act (CoprodAction :: k -> (COPROD k, k) -> Type) (a b) x Source Github #
Costrong (CoprodAction :: LINEAR -> (COPROD LINEAR, LINEAR) -> Type) Linear Source Github #
Instance details Defined in Proarrow.Category.Instance.Linear Methods coact :: forall (a :: COPROD LINEAR) (x :: LINEAR) (y :: LINEAR). (Ob a, Ob x, Ob y) => Linear (Act (CoprodAction :: LINEAR -> (COPROD LINEAR, LINEAR) -> Type) a x) (Act (CoprodAction :: LINEAR -> (COPROD LINEAR, LINEAR) -> Type) a y) -> Linear x y Source Github #
MonadPlus m => Strong (CoprodAction :: Type -> (COPROD Type, Type) -> Type) (Kleisli m :: Type -> Type -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Arrow Methods act :: forall (a :: COPROD Type) x y. Ob a => Kleisli m x y -> Kleisli m (Act (CoprodAction :: Type -> (COPROD Type, Type) -> Type) a x) (Act (CoprodAction :: Type -> (COPROD Type, Type) -> Type) a y) Source Github #
BiCCC k => Strong (CoprodAction :: k -> (COPROD k, k) -> Type) (Fold :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Instance.Fold Methods act :: forall (a :: COPROD k) (x :: k) (y :: k). Ob a => Fold x y -> Fold (Act (CoprodAction :: k -> (COPROD k, k) -> Type) a x) (Act (CoprodAction :: k -> (COPROD k, k) -> Type) a y) Source Github #
Strong (CoprodAction :: Type -> (COPROD Type, Type) -> Type) (Previewing a b :: Type -> Type -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods act :: forall (a0 :: COPROD Type) x y. Ob a0 => Previewing a b x y -> Previewing a b (Act (CoprodAction :: Type -> (COPROD Type, Type) -> Type) a0 x) (Act (CoprodAction :: Type -> (COPROD Type, Type) -> Type) a0 y) Source Github #
Strong (CoprodAction :: Type -> (COPROD Type, Type) -> Type) (Replacing a b :: Type -> Type -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods act :: forall (a0 :: COPROD Type) x y. Ob a0 => Replacing a b x y -> Replacing a b (Act (CoprodAction :: Type -> (COPROD Type, Type) -> Type) a0 x) (Act (CoprodAction :: Type -> (COPROD Type, Type) -> Type) a0 y) Source Github #
Strong (CoprodAction :: Type -> (COPROD Type, Type) -> Type) (Rep (Constant (First c)) :: Type -> Type -> Type) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Optic Methods act :: forall (a :: COPROD Type) x y. Ob a => Rep (Constant (First c)) x y -> Rep (Constant (First c)) (Act (CoprodAction :: Type -> (COPROD Type, Type) -> Type) a x) (Act (CoprodAction :: Type -> (COPROD Type, Type) -> Type) a y) Source Github #
HasCoproducts k => FunctorForRep (CoprodAction' :: (COPROD k, k) +-> k) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action Methods fmap :: forall (a :: (COPROD k, k)) (b :: (COPROD k, k)). (a ~> b) -> ((CoprodAction' :: (COPROD k, k) +-> k) @ a) ~> ((CoprodAction' :: (COPROD k, k) +-> k) @ b) Source Github #
type (CoprodAction' :: (COPROD k, k) +-> k) @ ('('COPR a, x) :: (COPROD k, k)) Source Github #
Instance details Defined in Proarrow.Category.Monoidal.Action type (CoprodAction' :: (COPROD k, k) +-> k) @ ('('COPR a, x) :: (COPROD k, k)) = a \|\| x