Safe Haskell	None
Language	GHC2024

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 #
Monoid a => Monoid ('R a :: REV k) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Rev Methods mempty :: (Unit :: REV k) ~> 'R a Source Comments # mappend :: ('R a ** 'R a) ~> 'R a Source Comments #
Comonoid c => Monoid ('OP c :: OPPOSITE k) Source Comments #
Instance details Defined in Proarrow.Monoid 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 #

combine :: forall {k} (m :: k). Monoid m => ((Unit :: k) ~> m) -> ((Unit :: k) ~> m) -> (Unit :: k) ~> m Source Comments #

class Monoid m => CommutativeMonoid (m :: k) 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

Ob a => Comonoid (a :: BOOL) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Bool Methods counit :: a ~> (Unit :: BOOL) Source Comments # comult :: a ~> (a ** a) Source Comments #
Ob a => Comonoid (a :: KIND) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods counit :: a ~> (Unit :: KIND) Source Comments # comult :: a ~> (a ** a) Source Comments #
Comonoid '() Source Comments #
Instance details Defined in Proarrow.Monoid Methods counit :: '() ~> (Unit :: ()) Source Comments # comult :: '() ~> ('() ** '()) 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 #
Comonoid a => Comonoid ('R a :: REV k) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Rev Methods counit :: 'R a ~> (Unit :: REV k) Source Comments # comult :: 'R a ~> ('R a ** 'R a) Source Comments #
Monoid c => Comonoid ('OP c :: OPPOSITE k) Source Comments #
Instance details Defined in Proarrow.Monoid 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 #
(Monoidal j, Monoidal k, Supplies k (Comonoid :: k -> Constraint), Supplies j (Monoid :: j -> Constraint), Profunctor p) => Comonoid (p :: j +-> k) Source Comments #
Instance details Defined in Proarrow.Profunctor.Day Methods counit :: p ~> (Unit :: j +-> k) Source Comments # comult :: p ~> (p ** p) 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 #

class Monoidal k => CopyDiscard k where Source Comments #

Minimal complete definition

Nothing

Methods

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

default copy :: forall (a :: k). (Supplies k (Comonoid :: k -> Constraint), Ob a) => a ~> (a ** a) Source Comments #

discard :: forall (a :: k). Ob a => a ~> (Unit :: k) Source Comments #

default discard :: forall (a :: k). (Supplies k (Comonoid :: k -> Constraint), Ob a) => a ~> (Unit :: k) Source Comments #

Instances

Instances details

CopyDiscard BOOL Source Comments #
Instance details Defined in Proarrow.Category.Instance.Bool Methods copy :: forall (a :: BOOL). Ob a => a ~> (a ** a) Source Comments # discard :: forall (a :: BOOL). Ob a => a ~> (Unit :: BOOL) Source Comments #
CopyDiscard KIND Source Comments #
Instance details Defined in Proarrow.Category.Instance.Cat Methods copy :: forall (a :: KIND). Ob a => a ~> (a ** a) Source Comments # discard :: forall (a :: KIND). Ob a => a ~> (Unit :: KIND) Source Comments #
CopyDiscard CONSTRAINT Source Comments #
Instance details Defined in Proarrow.Category.Instance.Constraint Methods copy :: forall (a :: CONSTRAINT). Ob a => a ~> (a ** a) Source Comments # discard :: forall (a :: CONSTRAINT). Ob a => a ~> (Unit :: CONSTRAINT) Source Comments #
CopyDiscard POINTED Source Comments #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods copy :: forall (a :: POINTED). Ob a => a ~> (a ** a) Source Comments # discard :: forall (a :: POINTED). Ob a => a ~> (Unit :: POINTED) Source Comments #
CopyDiscard () Source Comments #
Instance details Defined in Proarrow.Monoid Methods copy :: forall (a :: ()). Ob a => a ~> (a ** a) Source Comments # discard :: forall (a :: ()). Ob a => a ~> (Unit :: ()) Source Comments #
CopyDiscard Type Source Comments #
Instance details Defined in Proarrow.Monoid Methods copy :: Ob a => a ~> (a ** a) Source Comments # discard :: Ob a => a ~> (Unit :: Type) Source Comments #
CopyDiscard k => CopyDiscard (REV k) Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Rev Methods copy :: forall (a :: REV k). Ob a => a ~> (a ** a) Source Comments # discard :: forall (a :: REV k). Ob a => a ~> (Unit :: REV k) Source Comments #
HasProducts k => CopyDiscard (PROD k) Source Comments #
Instance details Defined in Proarrow.Monoid Methods copy :: forall (a :: PROD k). Ob a => a ~> (a ** a) Source Comments # discard :: forall (a :: PROD k). Ob a => a ~> (Unit :: PROD k) Source Comments #
(SymMonoidal k, CopyDiscard k) => CopyDiscard [k] Source Comments #
Instance details Defined in Proarrow.Category.Monoidal.Strictified Methods copy :: forall (a :: [k]). Ob a => a ~> (a ** a) Source Comments # discard :: forall (a :: [k]). Ob a => a ~> (Unit :: [k]) Source Comments #
(Promonad p, MonoidalProfunctor p, CopyDiscard k) => CopyDiscard (KLEISLI p) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Kleisli Methods copy :: forall (a :: KLEISLI p). Ob a => a ~> (a ** a) Source Comments # discard :: forall (a :: KLEISLI p). Ob a => a ~> (Unit :: KLEISLI p) Source Comments #
(SubMonoidal ob, CopyDiscard k) => CopyDiscard (SUBCAT ob) Source Comments #
Instance details Defined in Proarrow.Category.Instance.Sub Methods copy :: forall (a :: SUBCAT ob). Ob a => a ~> (a ** a) Source Comments # discard :: forall (a :: SUBCAT ob). Ob a => a ~> (Unit :: SUBCAT ob) Source Comments #
(CopyDiscard k, Monoidal j, Supplies j (Monoid :: j -> Constraint)) => CopyDiscard (j +-> k) Source Comments #
Instance details Defined in Proarrow.Profunctor.Day Methods copy :: forall (a :: j +-> k). Ob a => a ~> (a ** a) Source Comments # discard :: forall (a :: j +-> k). Ob a => a ~> (Unit :: j +-> k) Source Comments #
(CopyDiscard j, CopyDiscard k) => CopyDiscard (j, k) Source Comments #
Instance details Defined in Proarrow.Monoid Methods copy :: forall (a :: (j, k)). Ob a => a ~> (a ** a) Source Comments # discard :: forall (a :: (j, k)). Ob a => a ~> (Unit :: (j, k)) Source Comments #

data MONOIDK (m :: k) Source Comments #

Constructors

M

Instances

Instances details

CommutativeMonoid m => Monoidal (MONOIDK m) Source Comments #

Instance details

Defined in Proarrow.Monoid

Associated Types

type Unit
Instance details Defined in Proarrow.Monoid type Unit = 'M :: MONOIDK m

Methods

withOb2 :: forall (a :: MONOIDK m) (b :: MONOIDK m) r. (Ob a, Ob b) => (Ob (a ** b) => r) -> r Source Comments #

leftUnitor :: forall (a :: MONOIDK m). Ob a => ((Unit :: MONOIDK m) ** a) ~> a Source Comments #

leftUnitorInv :: forall (a :: MONOIDK m). Ob a => a ~> ((Unit :: MONOIDK m) ** a) Source Comments #

rightUnitor :: forall (a :: MONOIDK m). Ob a => (a ** (Unit :: MONOIDK m)) ~> a Source Comments #

rightUnitorInv :: forall (a :: MONOIDK m). Ob a => a ~> (a ** (Unit :: MONOIDK m)) Source Comments #

associator :: forall (a :: MONOIDK m) (b :: MONOIDK m) (c :: MONOIDK m). (Ob a, Ob b, Ob c) => ((a ** b) ** c) ~> (a ** (b ** c)) Source Comments #

associatorInv :: forall (a :: MONOIDK m) (b :: MONOIDK m) (c :: MONOIDK m). (Ob a, Ob b, Ob c) => (a ** (b ** c)) ~> ((a ** b) ** c) Source Comments #

CommutativeMonoid m => SymMonoidal (MONOIDK m) Source Comments #

Instance details

Defined in Proarrow.Monoid

Methods

swap :: forall (a :: MONOIDK m) (b :: MONOIDK m). (Ob a, Ob b) => (a ** b) ~> (b ** a) Source Comments #

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 => HasBinaryCoproducts (MONOIDK m) Source Comments #

Instance details

Defined in Proarrow.Monoid

Methods

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

lft :: forall (a :: MONOIDK m) (b :: MONOIDK m). (Ob a, Ob b) => a ~> (a || b) Source Comments #

rgt :: forall (a :: MONOIDK m) (b :: MONOIDK m). (Ob a, Ob b) => b ~> (a || b) Source Comments #

(|||) :: forall (x :: MONOIDK m) (a :: MONOIDK m) (y :: MONOIDK m). (x ~> a) -> (y ~> a) -> (x || y) ~> a Source Comments #

(+++) :: forall (a :: MONOIDK m) (b :: MONOIDK m) (x :: MONOIDK m) (y :: MONOIDK m). (a ~> x) -> (b ~> y) -> (a || b) ~> (x || y) Source Comments #

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

Instance details

Defined in Proarrow.Monoid

Methods

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

fst :: forall (a :: MONOIDK m) (b :: MONOIDK m). (Ob a, Ob b) => (a && b) ~> a Source Comments #

snd :: forall (a :: MONOIDK m) (b :: MONOIDK m). (Ob a, Ob b) => (a && b) ~> b Source Comments #

(&&&) :: forall (a :: MONOIDK m) (x :: MONOIDK m) (y :: MONOIDK m). (a ~> x) -> (a ~> y) -> a ~> (x && y) Source Comments #

(***) :: forall (a :: MONOIDK m) (b :: MONOIDK m) (x :: MONOIDK m) (y :: MONOIDK m). (a ~> x) -> (b ~> y) -> (a && b) ~> (x && y) Source Comments #

CommutativeMonoid m => CompactClosed (MONOIDK m) Source Comments #

Instance details

Defined in Proarrow.Monoid

Methods

distribDual :: forall (a :: MONOIDK m) (b :: MONOIDK m). (Ob a, Ob b) => Dual (a ** b) ~> (Dual a ** Dual b) Source Comments #

dualUnit :: Dual (Unit :: MONOIDK m) ~> (Unit :: MONOIDK m) Source Comments #

CommutativeMonoid m => StarAutonomous (MONOIDK m) Source Comments #

Instance details

Defined in Proarrow.Monoid

Methods

dual :: forall (a :: MONOIDK m) (b :: MONOIDK m). (a ~> b) -> Dual b ~> Dual a Source Comments #

dualInv :: forall (a :: MONOIDK m) (b :: MONOIDK m). (Ob a, Ob b) => (Dual a ~> Dual b) -> b ~> a Source Comments #

linDist :: forall (a :: MONOIDK m) (b :: MONOIDK m) (c :: MONOIDK m). (Ob a, Ob b, Ob c) => ((a ** b) ~> Dual c) -> a ~> Dual (b ** c) Source Comments #

linDistInv :: forall (a :: MONOIDK m) (b :: MONOIDK m) (c :: MONOIDK m). (Ob a, Ob b, Ob c) => (a ~> Dual (b ** c)) -> (a ** b) ~> Dual c Source Comments #

CommutativeMonoid m => Closed (MONOIDK m) Source Comments #

Instance details

Defined in Proarrow.Monoid

Methods

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

curry :: forall (a :: MONOIDK m) (b :: MONOIDK m) (c :: MONOIDK m). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Comments #

apply :: forall (a :: MONOIDK m) (b :: MONOIDK m). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Comments #

(^^^) :: forall (a :: MONOIDK m) (b :: MONOIDK m) (x :: MONOIDK m) (y :: MONOIDK m). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Comments #

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

Instance details

Defined in Proarrow.Monoid

Associated Types

type InitialObject
Instance details Defined in Proarrow.Monoid type InitialObject = 'M :: MONOIDK m

Methods

initiate :: forall (a :: MONOIDK m). Ob a => (InitialObject :: MONOIDK m) ~> a Source Comments #

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

Instance details

Defined in Proarrow.Monoid

Associated Types

type TerminalObject
Instance details Defined in Proarrow.Monoid type TerminalObject = 'M :: MONOIDK m

Methods

terminate :: forall (a :: MONOIDK m). Ob a => a ~> (TerminalObject :: MONOIDK m) Source Comments #

Monoid m => EnrichedProfunctor (Clone 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

withProObj :: forall (a :: MONOIDK m) (b :: MONOIDK m) r. (Ob a, Ob b) => (Ob (ProObj (Clone k) (Mon :: MONOIDK m -> MONOIDK m -> Type) a b) => r) -> r Source Comments #

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

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

rmap :: forall (a :: MONOIDK m) (b :: MONOIDK m) (c :: MONOIDK m). (Ob a, Ob b, Ob c) => (HomObj (Clone k) b c ** ProObj (Clone k) (Mon :: MONOIDK m -> MONOIDK m -> Type) a b) ~> ProObj (Clone k) (Mon :: MONOIDK m -> MONOIDK m -> Type) a c Source Comments #

lmap :: forall (a :: MONOIDK m) (b :: MONOIDK m) (c :: MONOIDK m). (Ob a, Ob b, Ob c) => (HomObj (Clone k) c a ** ProObj (Clone k) (Mon :: MONOIDK m -> MONOIDK m -> Type) a b) ~> ProObj (Clone k) (Mon :: MONOIDK m -> MONOIDK m -> Type) c b Source Comments #

CommutativeMonoid m => MonoidalProfunctor (Mon :: MONOIDK m -> MONOIDK m -> Type) Source Comments #

Instance details

Defined in Proarrow.Monoid

Methods

par0 :: Mon (Unit :: MONOIDK m) (Unit :: MONOIDK m) Source Comments #

par :: forall (x1 :: MONOIDK m) (x2 :: MONOIDK m) (y1 :: MONOIDK m) (y2 :: MONOIDK m). Mon x1 x2 -> Mon y1 y2 -> Mon (x1 ** y1) (x2 ** y2) 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 Unit Source Comments #

Instance details

Defined in Proarrow.Monoid

type Unit = 'M :: MONOIDK m

type (~>) Source Comments #

Instance details

Defined in Proarrow.Monoid

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

type InitialObject Source Comments #

Instance details

Defined in Proarrow.Monoid

type InitialObject = 'M :: MONOIDK m

type TerminalObject Source Comments #

Instance details

Defined in Proarrow.Monoid

type TerminalObject = 'M :: MONOIDK m

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

Instance details

Defined in Proarrow.Monoid

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

type (a :: MONOIDK m) || (b :: MONOIDK m) Source Comments #

Instance details

Defined in Proarrow.Monoid

type (a :: MONOIDK m) || (b :: MONOIDK m) = 'M :: MONOIDK m

type (a :: MONOIDK m) && (b :: MONOIDK m) Source Comments #

Instance details

Defined in Proarrow.Monoid

type (a :: MONOIDK m) && (b :: MONOIDK m) = 'M :: MONOIDK m

type (a :: MONOIDK m) ~~> (b :: MONOIDK m) Source Comments #

Instance details

Defined in Proarrow.Monoid

type (a :: MONOIDK m) ~~> (b :: MONOIDK m) = 'M :: MONOIDK m

type Dual ('M :: MONOIDK m) Source Comments #

Instance details

Defined in Proarrow.Monoid

type Dual ('M :: MONOIDK m) = 'M :: MONOIDK m

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

Instance details

Defined in Proarrow.Category.Enriched

type ProObj (Clone k) (Mon :: MONOIDK m -> MONOIDK m -> Type) ('M :: MONOIDK m) ('M :: MONOIDK m) = 'SUB m :: SUBCAT (Any :: k -> Constraint)

type ('M :: MONOIDK m) ** ('M :: MONOIDK m) Source Comments #

Instance details

Defined in Proarrow.Monoid

type ('M :: MONOIDK m) ** ('M :: MONOIDK m) = 'M :: MONOIDK 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 => EnrichedProfunctor (Clone 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 withProObj :: forall (a :: MONOIDK m) (b :: MONOIDK m) r. (Ob a, Ob b) => (Ob (ProObj (Clone k) (Mon :: MONOIDK m -> MONOIDK m -> Type) a b) => r) -> r Source Comments # underlying :: forall (a :: MONOIDK m) (b :: MONOIDK m). Mon a b -> (Unit :: Clone k) ~> ProObj (Clone k) (Mon :: MONOIDK m -> MONOIDK m -> Type) a b Source Comments # enriched :: forall (a :: MONOIDK m) (b :: MONOIDK m). (Ob a, Ob b) => ((Unit :: Clone k) ~> ProObj (Clone k) (Mon :: MONOIDK m -> MONOIDK m -> Type) a b) -> Mon a b Source Comments # rmap :: forall (a :: MONOIDK m) (b :: MONOIDK m) (c :: MONOIDK m). (Ob a, Ob b, Ob c) => (HomObj (Clone k) b c ProObj (Clone k) (Mon :: MONOIDK m -> MONOIDK m -> Type) a b) ~> ProObj (Clone k) (Mon :: MONOIDK m -> MONOIDK m -> Type) a c Source Comments # lmap :: forall (a :: MONOIDK m) (b :: MONOIDK m) (c :: MONOIDK m). (Ob a, Ob b, Ob c) => (HomObj (Clone k) c a ProObj (Clone k) (Mon :: MONOIDK m -> MONOIDK m -> Type) a b) ~> ProObj (Clone k) (Mon :: MONOIDK m -> MONOIDK m -> Type) c b Source Comments #
CommutativeMonoid m => MonoidalProfunctor (Mon :: MONOIDK m -> MONOIDK m -> Type) Source Comments #
Instance details Defined in Proarrow.Monoid Methods par0 :: Mon (Unit :: MONOIDK m) (Unit :: MONOIDK m) Source Comments # par :: forall (x1 :: MONOIDK m) (x2 :: MONOIDK m) (y1 :: MONOIDK m) (y2 :: MONOIDK m). Mon x1 x2 -> Mon y1 y2 -> Mon (x1 y1) (x2 y2) 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 ProObj (Clone k) (Mon :: MONOIDK m -> MONOIDK m -> Type) ('M :: MONOIDK m) ('M :: MONOIDK m) Source Comments #
Instance details Defined in Proarrow.Category.Enriched type ProObj (Clone k) (Mon :: MONOIDK m -> MONOIDK m -> Type) ('M :: MONOIDK m) ('M :: MONOIDK m) = 'SUB m :: SUBCAT (Any :: k -> Constraint)