Safe Haskell	None
Language	Haskell2010

Proarrow.Monoid

Documentation

class (Monoidal k, Ob m) => Monoid (m :: k) where Source Comments #

Methods

mempty :: (Unit :: k) ~> m Source Comments #

mappend :: (m ** m) ~> m Source Comments #

Instances

Instances details

Monoid 'TRU Source Comments #
Instance details Defined in Proarrow.Category.Instance.Bool Methods mempty :: (Unit :: BOOL) ~> 'TRU Source Comments # mappend :: ('TRU ** 'TRU) ~> 'TRU Source Comments #
Monoid m => Monoid (m :: Type) Source Comments #
Instance details Defined in Proarrow.Monoid Methods mempty :: (Unit :: Type) ~> m Source Comments # mappend :: (m ** m) ~> m Source Comments #
Monoid ('CNSTRNT ()) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Constraint Methods mempty :: (Unit :: CONSTRAINT) ~> 'CNSTRNT () Source Comments # mappend :: ('CNSTRNT () ** 'CNSTRNT ()) ~> 'CNSTRNT () Source Comments #
Monoid ('P Void) Source Comments #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods mempty :: (Unit :: POINTED) ~> 'P Void Source Comments # mappend :: ('P Void ** 'P Void) ~> 'P Void Source Comments #
Monoid ('P ()) Source Comments #	Conjunction with False = Nothing, True = Just ()
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods mempty :: (Unit :: POINTED) ~> 'P () Source Comments # mappend :: ('P () ** 'P ()) ~> 'P () Source Comments #
Monoid ('P [a] :: POINTED) Source Comments #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods mempty :: (Unit :: POINTED) ~> 'P [a] Source Comments # mappend :: ('P [a] ** 'P [a]) ~> 'P [a] Source Comments #
Monoid ('S 'Z) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Simplex Methods mempty :: (Unit :: Nat) ~> 'S 'Z Source Comments # mappend :: ('S 'Z ** 'S 'Z) ~> 'S 'Z Source Comments #
(Monoidal k, Monoid m) => Monoid (Ap f m :: Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Free Methods mempty :: (Unit :: Type) ~> Ap f m Source Comments # mappend :: (Ap f m ** Ap f m) ~> Ap f m Source Comments #
(Comonoid c, Monoid m, MonoidalProfunctor p) => Monoid (Wrapped p c m :: Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Wrapped Methods mempty :: (Unit :: Type) ~> Wrapped p c m Source Comments # mappend :: (Wrapped p c m ** Wrapped p c m) ~> Wrapped p c m Source Comments #
Comonoid c => Monoid ('OP c :: OPPOSITE k) Source Comments #
Instance details Defined in Proarrow.Category.Opposite Methods mempty :: (Unit :: OPPOSITE k) ~> 'OP c Source Comments # mappend :: ('OP c ** 'OP c) ~> 'OP c Source Comments #
(HasCoproducts k, Ob a) => Monoid ('COPR a :: COPROD k) Source Comments #
Instance details Defined in Proarrow.Monoid Methods mempty :: (Unit :: COPROD k) ~> 'COPR a Source Comments # mappend :: ('COPR a ** 'COPR a) ~> 'COPR a Source Comments #
(Profunctor p, MonoidalProfunctor p) => Monoid (p :: j +-> k) Source Comments #
Instance details Defined in Proarrow.Profunctor.Day Methods mempty :: (Unit :: j +-> k) ~> p Source Comments # mappend :: (p ** p) ~> p Source Comments #
MonoidalProfunctor p => Monoid (Wrapped p :: k2 -> k1 -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Wrapped Methods mempty :: (Unit :: k2 -> k1 -> Type) ~> Wrapped p Source Comments # mappend :: (Wrapped p ** Wrapped p) ~> Wrapped p Source Comments #
(Bicategory kk, Ob (I :: kk a a), Monad m, Ob m) => Monoid ('E m :: ENDO kk a) Source Comments #	Monads are monoids in the category of endo-1-cells.
Instance details Defined in Proarrow.Category.Monoidal.Endo Methods mempty :: (Unit :: ENDO kk a) ~> 'E m Source Comments # mappend :: ('E m ** 'E m) ~> 'E m Source Comments #

newtype GenElt (x :: k) (m :: k) Source Comments #

Constructors

GenElt (x ~> m)

Instances

Instances details

(Monoid m, Cartesian k, Ob x) => Monoid (GenElt x m) Source Comments #
Instance details Defined in Proarrow.Monoid Methods mempty :: GenElt x m Comments # mappend :: GenElt x m -> GenElt x m -> GenElt x m Comments # mconcat :: [GenElt x m] -> GenElt x m Comments #
(Monoid m, Cartesian k) => Semigroup (GenElt x m) Source Comments #
Instance details Defined in Proarrow.Monoid Methods (<>) :: GenElt x m -> GenElt x m -> GenElt x m Comments # sconcat :: NonEmpty (GenElt x m) -> GenElt x m Comments # stimes :: Integral b => b -> GenElt x m -> GenElt x m Comments #

memptyAct :: forall {m} {c} (a :: m) (n :: c). (MonoidalAction m c, Monoid a, Ob n) => n ~> Act a n Source Comments #

mappendAct :: forall {m} {c} (a :: m) (n :: c). (MonoidalAction m c, Monoid a, Ob n) => Act a (Act a n) ~> Act a n Source Comments #

class (MonoidalAction m c, Monoid a, Ob n) => ModuleObject (a :: m) (n :: c) where Source Comments #

Methods

action :: Act a n ~> n Source Comments #

class (Monoidal k, Ob c) => Comonoid (c :: k) where Source Comments #

Methods

counit :: c ~> (Unit :: k) Source Comments #

comult :: c ~> (c ** c) Source Comments #

Instances

Instances details

Comonoid 'FLS Source Comments #
Instance details Defined in Proarrow.Category.Instance.Bool Methods counit :: 'FLS ~> (Unit :: BOOL) Source Comments # comult :: 'FLS ~> ('FLS ** 'FLS) Source Comments #
Comonoid 'TRU Source Comments #
Instance details Defined in Proarrow.Category.Instance.Bool Methods counit :: 'TRU ~> (Unit :: BOOL) Source Comments # comult :: 'TRU ~> ('TRU ** 'TRU) Source Comments #
Comonoid (a :: Type) Source Comments #
Instance details Defined in Proarrow.Monoid Methods counit :: a ~> (Unit :: Type) Source Comments # comult :: a ~> (a ** a) Source Comments #
Comonoid ('CNSTRNT a :: CONSTRAINT) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Constraint Methods counit :: 'CNSTRNT a ~> (Unit :: CONSTRAINT) Source Comments # comult :: 'CNSTRNT a ~> ('CNSTRNT a ** 'CNSTRNT a) Source Comments #
Comonoid ('L (Ur a) :: LINEAR) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Linear Methods counit :: 'L (Ur a) ~> (Unit :: LINEAR) Source Comments # comult :: 'L (Ur a) ~> ('L (Ur a) ** 'L (Ur a)) Source Comments #
Comonoid ('P x :: POINTED) Source Comments #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods counit :: 'P x ~> (Unit :: POINTED) Source Comments # comult :: 'P x ~> ('P x ** 'P x) Source Comments #
Monoid c => Comonoid ('OP c :: OPPOSITE k) Source Comments #
Instance details Defined in Proarrow.Category.Opposite Methods counit :: 'OP c ~> (Unit :: OPPOSITE k) Source Comments # comult :: 'OP c ~> ('OP c ** 'OP c) Source Comments #
(HasProducts k, Ob a) => Comonoid ('PR a :: PROD k) Source Comments #
Instance details Defined in Proarrow.Monoid Methods counit :: 'PR a ~> (Unit :: PROD k) Source Comments # comult :: 'PR a ~> ('PR a ** 'PR a) Source Comments #
CategoryOf k => Comonoid (CatAsComonoid k :: Type -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Nat Methods counit :: CatAsComonoid k ~> (Unit :: Type -> Type) Source Comments # comult :: CatAsComonoid k ~> (CatAsComonoid k ** CatAsComonoid k) Source Comments #
(Bicategory kk, Ob (I :: kk a a), Comonad c, Ob c) => Comonoid ('E c :: ENDO kk a) Source Comments #	Comonads are comonoids in the category of endo-1-cells.
Instance details Defined in Proarrow.Category.Monoidal.Endo Methods counit :: 'E c ~> (Unit :: ENDO kk a) Source Comments # comult :: 'E c ~> ('E c ** 'E c) Source Comments #

counitAct :: forall {m} {c} (a :: m) (n :: c). (MonoidalAction m c, Comonoid a, Ob n) => Act a n ~> n Source Comments #

comultAct :: forall {m} {c} (a :: m) (n :: c). (MonoidalAction m c, Comonoid a, Ob n) => Act a n ~> Act a (Act a n) Source Comments #

data MONOIDK (m :: k) Source Comments #

Constructors

M

Instances

Instances details

Monoid m => CategoryOf (MONOIDK m) Source Comments #

A monoid as a one object category.

Instance details

Defined in Proarrow.Monoid

Associated Types

type (~>)
Instance details Defined in Proarrow.Monoid type (~>) = Mon :: MONOIDK m -> MONOIDK m -> Type

Monoid m => Enriched k (Mon :: MONOIDK m -> MONOIDK m -> Type) Source Comments #

A monoid is a one object enriched category.

Instance details

Defined in Proarrow.Category.Enriched

Methods

underlying :: forall (a :: MONOIDK m) (b :: MONOIDK m). Mon a b -> (Unit :: k) ~> Hom k (Mon :: MONOIDK m -> MONOIDK m -> Type) a b Source Comments #

enriched :: forall (a :: MONOIDK m) (b :: MONOIDK m). (Ob a, Ob b) => ((Unit :: k) ~> Hom k (Mon :: MONOIDK m -> MONOIDK m -> Type) a b) -> Mon a b Source Comments #

Monoid m => Profunctor (Mon :: MONOIDK m -> MONOIDK m -> Type) Source Comments #

Instance details

Defined in Proarrow.Monoid

Methods

dimap :: forall (c :: MONOIDK m) (a :: MONOIDK m) (b :: MONOIDK m) (d :: MONOIDK m). (c ~> a) -> (b ~> d) -> Mon a b -> Mon c d Source Comments #

(\\) :: forall (a :: MONOIDK m) (b :: MONOIDK m) r. ((Ob a, Ob b) => r) -> Mon a b -> r Source Comments #

Monoid m => Promonad (Mon :: MONOIDK m -> MONOIDK m -> Type) Source Comments #

Instance details

Defined in Proarrow.Monoid

Methods

id :: forall (a :: MONOIDK m). Ob a => Mon a a Source Comments #

(.) :: forall (b :: MONOIDK m) (c :: MONOIDK m) (a :: MONOIDK m). Mon b c -> Mon a b -> Mon a c Source Comments #

type (~>) Source Comments #

Instance details

Defined in Proarrow.Monoid

type (~>) = Mon :: MONOIDK m -> MONOIDK m -> Type

type Ob (a :: MONOIDK m) Source Comments #

Instance details

Defined in Proarrow.Monoid

type Ob (a :: MONOIDK m) = a ~ ('M :: MONOIDK m)

type Hom k (Mon :: MONOIDK m -> MONOIDK m -> Type) ('M :: MONOIDK m) ('M :: MONOIDK m) Source Comments #

Instance details

Defined in Proarrow.Category.Enriched

type Hom k (Mon :: MONOIDK m -> MONOIDK m -> Type) ('M :: MONOIDK m) ('M :: MONOIDK m) = m

data Mon (a :: MONOIDK m) (b :: MONOIDK m1) where Source Comments #

Constructors

Mon :: forall {k} {k1} {m1 :: k1} (m :: k). ((Unit :: k) ~> m) -> Mon ('M :: MONOIDK m) ('M :: MONOIDK m1)

Instances

Instances details

Monoid m => Enriched k (Mon :: MONOIDK m -> MONOIDK m -> Type) Source Comments #	A monoid is a one object enriched category.
Instance details Defined in Proarrow.Category.Enriched Methods underlying :: forall (a :: MONOIDK m) (b :: MONOIDK m). Mon a b -> (Unit :: k) ~> Hom k (Mon :: MONOIDK m -> MONOIDK m -> Type) a b Source Comments # enriched :: forall (a :: MONOIDK m) (b :: MONOIDK m). (Ob a, Ob b) => ((Unit :: k) ~> Hom k (Mon :: MONOIDK m -> MONOIDK m -> Type) a b) -> Mon a b Source Comments #
Monoid m => Profunctor (Mon :: MONOIDK m -> MONOIDK m -> Type) Source Comments #
Instance details Defined in Proarrow.Monoid Methods dimap :: forall (c :: MONOIDK m) (a :: MONOIDK m) (b :: MONOIDK m) (d :: MONOIDK m). (c ~> a) -> (b ~> d) -> Mon a b -> Mon c d Source Comments # (\\) :: forall (a :: MONOIDK m) (b :: MONOIDK m) r. ((Ob a, Ob b) => r) -> Mon a b -> r Source Comments #
Monoid m => Promonad (Mon :: MONOIDK m -> MONOIDK m -> Type) Source Comments #
Instance details Defined in Proarrow.Monoid Methods id :: forall (a :: MONOIDK m). Ob a => Mon a a Source Comments # (.) :: forall (b :: MONOIDK m) (c :: MONOIDK m) (a :: MONOIDK m). Mon b c -> Mon a b -> Mon a c Source Comments #
type Hom k (Mon :: MONOIDK m -> MONOIDK m -> Type) ('M :: MONOIDK m) ('M :: MONOIDK m) Source Comments #
Instance details Defined in Proarrow.Category.Enriched type Hom k (Mon :: MONOIDK m -> MONOIDK m -> Type) ('M :: MONOIDK m) ('M :: MONOIDK m) = m