Copyright	(C) 2014-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	Rank2Types
Safe Haskell	Safe
Language	Haskell2010

Data.Profunctor.Strong

Contents

Strength
Costrength

Description

Synopsis

class Profunctor p => Strong p where
- first' :: p a b -> p (a, c) (b, c)
- second' :: p a b -> p (c, a) (c, b)
uncurry' :: Strong p => p a (b -> c) -> p (a, b) c
strong :: Strong p => (a -> b -> c) -> p a b -> p a c
newtype Tambara p a b = Tambara {
- runTambara :: forall c. p (a, c) (b, c)
}
tambara :: Strong p => (p :-> q) -> p :-> Tambara q
untambara :: Profunctor q => (p :-> Tambara q) -> p :-> q
data Pastro p a b where
- Pastro :: ((y, z) -> b) -> p x y -> (a -> (x, z)) -> Pastro p a b
pastro :: Strong q => (p :-> q) -> Pastro p :-> q
unpastro :: ( Pastro p :-> q) -> p :-> q
class Profunctor p => Costrong p where
- unfirst :: p (a, d) (b, d) -> p a b
- unsecond :: p (d, a) (d, b) -> p a b
data Cotambara q a b where
- Cotambara :: Costrong r => (r :-> q) -> r a b -> Cotambara q a b
cotambara :: Costrong p => (p :-> q) -> p :-> Cotambara q
uncotambara :: Profunctor q => (p :-> Cotambara q) -> p :-> q
newtype Copastro p a b = Copastro {
- runCopastro :: forall r. Costrong r => ( forall x y. p x y -> r x y) -> r a b
}

Strength

class Profunctor p => Strong p where Source #

Generalizing Star of a strong Functor

Note: Every Functor in Haskell is strong with respect to (,) .

This describes profunctor strength with respect to the product structure of Hask.

http://www.riec.tohoku.ac.jp/~asada/papers/arrStrMnd.pdf

Minimal complete definition

first' | second'

Methods

first' :: p a b -> p (a, c) (b, c) Source #

Laws:

first' ≡ dimap swap swap . second'
lmap fst ≡ rmap fst . first'
lmap (second' f) . first' ≡ rmap (second' f) . first'
first' . first' ≡ dimap assoc unassoc . first' where
  assoc ((a,b),c) = (a,(b,c))
  unassoc (a,(b,c)) = ((a,b),c)

second' :: p a b -> p (c, a) (c, b) Source #

Laws:

second' ≡ dimap swap swap . first'
lmap snd ≡ rmap snd . second'
lmap (first' f) . second' ≡ rmap (first' f) . second'
second' . second' ≡ dimap unassoc assoc . second' where
  assoc ((a,b),c) = (a,(b,c))
  unassoc (a,(b,c)) = ((a,b),c)

Instances

Instances details

Monad m => Strong ( Kleisli m) Source #
Instance details Defined in Data.Profunctor.Strong Methods first' :: Kleisli m a b -> Kleisli m (a, c) (b, c) Source # second' :: Kleisli m a b -> Kleisli m (c, a) (c, b) Source #
Strong ( Pastro p) Source #
Instance details Defined in Data.Profunctor.Strong Methods first' :: Pastro p a b -> Pastro p (a, c) (b, c) Source # second' :: Pastro p a b -> Pastro p (c, a) (c, b) Source #
Profunctor p => Strong ( Tambara p) Source #
Instance details Defined in Data.Profunctor.Strong Methods first' :: Tambara p a b -> Tambara p (a, c) (b, c) Source # second' :: Tambara p a b -> Tambara p (c, a) (c, b) Source #
Strong p => Strong ( Closure p) Source #
Instance details Defined in Data.Profunctor.Closed Methods first' :: Closure p a b -> Closure p (a, c) (b, c) Source # second' :: Closure p a b -> Closure p (c, a) (c, b) Source #
Strong ( FreeTraversing p) Source #
Instance details Defined in Data.Profunctor.Traversing Methods first' :: FreeTraversing p a b -> FreeTraversing p (a, c) (b, c) Source # second' :: FreeTraversing p a b -> FreeTraversing p (c, a) (c, b) Source #
Profunctor p => Strong ( CofreeTraversing p) Source #
Instance details Defined in Data.Profunctor.Traversing Methods first' :: CofreeTraversing p a b -> CofreeTraversing p (a, c) (b, c) Source # second' :: CofreeTraversing p a b -> CofreeTraversing p (c, a) (c, b) Source #
Strong ( FreeMapping p) Source #
Instance details Defined in Data.Profunctor.Mapping Methods first' :: FreeMapping p a b -> FreeMapping p (a, c) (b, c) Source # second' :: FreeMapping p a b -> FreeMapping p (c, a) (c, b) Source #
Profunctor p => Strong ( CofreeMapping p) Source #
Instance details Defined in Data.Profunctor.Mapping Methods first' :: CofreeMapping p a b -> CofreeMapping p (a, c) (b, c) Source # second' :: CofreeMapping p a b -> CofreeMapping p (c, a) (c, b) Source #
Strong p => Strong ( Coyoneda p) Source #
Instance details Defined in Data.Profunctor.Yoneda Methods first' :: Coyoneda p a b -> Coyoneda p (a, c) (b, c) Source # second' :: Coyoneda p a b -> Coyoneda p (c, a) (c, b) Source #
Strong p => Strong ( Yoneda p) Source #
Instance details Defined in Data.Profunctor.Yoneda Methods first' :: Yoneda p a b -> Yoneda p (a, c) (b, c) Source # second' :: Yoneda p a b -> Yoneda p (c, a) (c, b) Source #
Strong ((->) :: Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Strong Methods first' :: (a -> b) -> (a, c) -> (b, c) Source # second' :: (a -> b) -> (c, a) -> (c, b) Source #
Strong ( Forget r :: Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Strong Methods first' :: Forget r a b -> Forget r (a, c) (b, c) Source # second' :: Forget r a b -> Forget r (c, a) (c, b) Source #
Functor m => Strong ( Star m) Source #
Instance details Defined in Data.Profunctor.Strong Methods first' :: Star m a b -> Star m (a, c) (b, c) Source # second' :: Star m a b -> Star m (c, a) (c, b) Source #
Contravariant f => Strong ( Clown f :: Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Strong Methods first' :: Clown f a b -> Clown f (a, c) (b, c) Source # second' :: Clown f a b -> Clown f (c, a) (c, b) Source #
Arrow p => Strong ( WrappedArrow p) Source #	`Arrow` is `Strong` `Category`
Instance details Defined in Data.Profunctor.Strong Methods first' :: WrappedArrow p a b -> WrappedArrow p (a, c) (b, c) Source # second' :: WrappedArrow p a b -> WrappedArrow p (c, a) (c, b) Source #
( Strong p, Strong q) => Strong ( Sum p q) Source #
Instance details Defined in Data.Profunctor.Strong Methods first' :: Sum p q a b -> Sum p q (a, c) (b, c) Source # second' :: Sum p q a b -> Sum p q (c, a) (c, b) Source #
( Strong p, Strong q) => Strong ( Product p q) Source #
Instance details Defined in Data.Profunctor.Strong Methods first' :: Product p q a b -> Product p q (a, c) (b, c) Source # second' :: Product p q a b -> Product p q (c, a) (c, b) Source #
( Functor f, Strong p) => Strong ( Tannen f p) Source #
Instance details Defined in Data.Profunctor.Strong Methods first' :: Tannen f p a b -> Tannen f p (a, c) (b, c) Source # second' :: Tannen f p a b -> Tannen f p (c, a) (c, b) Source #
( Strong p, Strong q) => Strong ( Procompose p q) Source #
Instance details Defined in Data.Profunctor.Composition Methods first' :: Procompose p q a b -> Procompose p q (a, c) (b, c) Source # second' :: Procompose p q a b -> Procompose p q (c, a) (c, b) Source #
( Functor f, Strong p) => Strong ( Cayley f p) Source #
Instance details Defined in Data.Profunctor.Cayley Methods first' :: Cayley f p a b -> Cayley f p (a, c) (b, c) Source # second' :: Cayley f p a b -> Cayley f p (c, a) (c, b) Source #

uncurry' :: Strong p => p a (b -> c) -> p (a, b) c Source #

strong :: Strong p => (a -> b -> c) -> p a b -> p a c Source #

newtype Tambara p a b Source #

Tambara cofreely makes any Profunctor Strong .

Constructors

Tambara
Fields runTambara :: forall c. p (a, c) (b, c)

Instances

Instances details

ProfunctorComonad Tambara Source #
Instance details Defined in Data.Profunctor.Strong Methods proextract :: forall (p :: Type -> Type -> Type ). Profunctor p => Tambara p :-> p Source # produplicate :: forall (p :: Type -> Type -> Type ). Profunctor p => Tambara p :-> Tambara ( Tambara p) Source #
ProfunctorAdjunction Pastro Tambara Source #
Instance details Defined in Data.Profunctor.Strong Methods unit :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> Tambara ( Pastro p) Source # counit :: forall (p :: Type -> Type -> Type ). Profunctor p => Pastro ( Tambara p) :-> p Source #
Arrow p => Arrow ( Tambara p) Source #
Instance details Defined in Data.Profunctor.Strong Methods arr :: (b -> c) -> Tambara p b c Source # first :: Tambara p b c -> Tambara p (b, d) (c, d) Source # second :: Tambara p b c -> Tambara p (d, b) (d, c) Source # (***) :: Tambara p b c -> Tambara p b' c' -> Tambara p (b, b') (c, c') Source # (&&&) :: Tambara p b c -> Tambara p b c' -> Tambara p b (c, c') Source #
ArrowZero p => ArrowZero ( Tambara p) Source #
Instance details Defined in Data.Profunctor.Strong Methods zeroArrow :: Tambara p b c Source #
ArrowPlus p => ArrowPlus ( Tambara p) Source #
Instance details Defined in Data.Profunctor.Strong Methods (<+>) :: Tambara p b c -> Tambara p b c -> Tambara p b c Source #
ArrowChoice p => ArrowChoice ( Tambara p) Source #
Instance details Defined in Data.Profunctor.Strong Methods left :: Tambara p b c -> Tambara p ( Either b d) ( Either c d) Source # right :: Tambara p b c -> Tambara p ( Either d b) ( Either d c) Source # (+++) :: Tambara p b c -> Tambara p b' c' -> Tambara p ( Either b b') ( Either c c') Source # (\|\|\|) :: Tambara p b d -> Tambara p c d -> Tambara p ( Either b c) d Source #
ArrowApply p => ArrowApply ( Tambara p) Source #
Instance details Defined in Data.Profunctor.Strong Methods app :: Tambara p ( Tambara p b c, b) c Source #
ArrowLoop p => ArrowLoop ( Tambara p) Source #
Instance details Defined in Data.Profunctor.Strong Methods loop :: Tambara p (b, d) (c, d) -> Tambara p b c Source #
Profunctor p => Profunctor ( Tambara p) Source #
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Tambara p b c -> Tambara p a d Source # lmap :: (a -> b) -> Tambara p b c -> Tambara p a c Source # rmap :: (b -> c) -> Tambara p a b -> Tambara p a c Source # (#.) :: forall a b c q. Coercible c b => q b c -> Tambara p a b -> Tambara p a c Source # (.#) :: forall a b c q. Coercible b a => Tambara p b c -> q a b -> Tambara p a c Source #
Profunctor p => Strong ( Tambara p) Source #
Instance details Defined in Data.Profunctor.Strong Methods first' :: Tambara p a b -> Tambara p (a, c) (b, c) Source # second' :: Tambara p a b -> Tambara p (c, a) (c, b) Source #
Choice p => Choice ( Tambara p) Source #
Instance details Defined in Data.Profunctor.Choice Methods left' :: Tambara p a b -> Tambara p ( Either a c) ( Either b c) Source # right' :: Tambara p a b -> Tambara p ( Either c a) ( Either c b) Source #
Category p => Category ( Tambara p :: Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Strong Methods id :: forall (a :: k). Tambara p a a Source # (.) :: forall (b :: k) (c :: k) (a :: k). Tambara p b c -> Tambara p a b -> Tambara p a c Source #
ProfunctorFunctor Tambara Source #
Instance details Defined in Data.Profunctor.Strong Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> Tambara p :-> Tambara q Source #
Profunctor p => Functor ( Tambara p a) Source #
Instance details Defined in Data.Profunctor.Strong Methods fmap :: (a0 -> b) -> Tambara p a a0 -> Tambara p a b Source # (<$) :: a0 -> Tambara p a b -> Tambara p a a0 Source #
( Profunctor p, Arrow p) => Applicative ( Tambara p a) Source #
Instance details Defined in Data.Profunctor.Strong Methods pure :: a0 -> Tambara p a a0 Source # (<>) :: Tambara p a (a0 -> b) -> Tambara p a a0 -> Tambara p a b Source # liftA2 :: (a0 -> b -> c) -> Tambara p a a0 -> Tambara p a b -> Tambara p a c Source # (>) :: Tambara p a a0 -> Tambara p a b -> Tambara p a b Source # (<*) :: Tambara p a a0 -> Tambara p a b -> Tambara p a a0 Source #
( Profunctor p, ArrowPlus p) => Alternative ( Tambara p a) Source #
Instance details Defined in Data.Profunctor.Strong Methods empty :: Tambara p a a0 Source # (<\|>) :: Tambara p a a0 -> Tambara p a a0 -> Tambara p a a0 Source # some :: Tambara p a a0 -> Tambara p a [a0] Source # many :: Tambara p a a0 -> Tambara p a [a0] Source #
ArrowPlus p => Semigroup ( Tambara p a b) Source #
Instance details Defined in Data.Profunctor.Strong Methods (<>) :: Tambara p a b -> Tambara p a b -> Tambara p a b Source # sconcat :: NonEmpty ( Tambara p a b) -> Tambara p a b Source # stimes :: Integral b0 => b0 -> Tambara p a b -> Tambara p a b Source #
ArrowPlus p => Monoid ( Tambara p a b) Source #
Instance details Defined in Data.Profunctor.Strong Methods mempty :: Tambara p a b Source # mappend :: Tambara p a b -> Tambara p a b -> Tambara p a b Source # mconcat :: [ Tambara p a b] -> Tambara p a b Source #

tambara :: Strong p => (p :-> q) -> p :-> Tambara q Source #

tambara (untambara f) ≡ f
untambara (tambara f) ≡ f

untambara :: Profunctor q => (p :-> Tambara q) -> p :-> q Source #

tambara (untambara f) ≡ f
untambara (tambara f) ≡ f

data Pastro p a b where Source #

Pastro -| Tambara

Pastro p ~ exists z. Costar ((,)z) Procompose p Procompose Star ((,)z)

Pastro freely makes any Profunctor Strong .

Constructors

Pastro :: ((y, z) -> b) -> p x y -> (a -> (x, z)) -> Pastro p a b

Instances

Instances details

ProfunctorMonad Pastro Source #
Instance details Defined in Data.Profunctor.Strong Methods proreturn :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> Pastro p Source # projoin :: forall (p :: Type -> Type -> Type ). Profunctor p => Pastro ( Pastro p) :-> Pastro p Source #
ProfunctorAdjunction Pastro Tambara Source #
Instance details Defined in Data.Profunctor.Strong Methods unit :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> Tambara ( Pastro p) Source # counit :: forall (p :: Type -> Type -> Type ). Profunctor p => Pastro ( Tambara p) :-> p Source #
Profunctor ( Pastro p) Source #
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Pastro p b c -> Pastro p a d Source # lmap :: (a -> b) -> Pastro p b c -> Pastro p a c Source # rmap :: (b -> c) -> Pastro p a b -> Pastro p a c Source # (#.) :: forall a b c q. Coercible c b => q b c -> Pastro p a b -> Pastro p a c Source # (.#) :: forall a b c q. Coercible b a => Pastro p b c -> q a b -> Pastro p a c Source #
Strong ( Pastro p) Source #
Instance details Defined in Data.Profunctor.Strong Methods first' :: Pastro p a b -> Pastro p (a, c) (b, c) Source # second' :: Pastro p a b -> Pastro p (c, a) (c, b) Source #
ProfunctorFunctor Pastro Source #
Instance details Defined in Data.Profunctor.Strong Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> Pastro p :-> Pastro q Source #
Functor ( Pastro p a) Source #
Instance details Defined in Data.Profunctor.Strong Methods fmap :: (a0 -> b) -> Pastro p a a0 -> Pastro p a b Source # (<$) :: a0 -> Pastro p a b -> Pastro p a a0 Source #

pastro :: Strong q => (p :-> q) -> Pastro p :-> q Source #

pastro (unpastro f) ≡ f
unpastro (pastro f) ≡ f

unpastro :: ( Pastro p :-> q) -> p :-> q Source #

pastro (unpastro f) ≡ f
unpastro (pastro f) ≡ f

Costrength

class Profunctor p => Costrong p where Source #

Analogous to ArrowLoop , loop = unfirst

Minimal complete definition

unfirst | unsecond

Methods

unfirst :: p (a, d) (b, d) -> p a b Source #

Laws:

unfirst ≡ unsecond . dimap swap swap
lmap (,()) ≡ unfirst . rmap (,())
unfirst . lmap (second f) ≡ unfirst . rmap (second f)
unfirst . unfirst = unfirst . dimap assoc unassoc where
  assoc ((a,b),c) = (a,(b,c))
  unassoc (a,(b,c)) = ((a,b),c)

unsecond :: p (d, a) (d, b) -> p a b Source #

Laws:

unsecond ≡ unfirst . dimap swap swap
lmap ((),) ≡ unsecond . rmap ((),)
unsecond . lmap (first f) ≡ unsecond . rmap (first f)
unsecond . unsecond = unsecond . dimap unassoc assoc where
  assoc ((a,b),c) = (a,(b,c))
  unassoc (a,(b,c)) = ((a,b),c)

Instances

Instances details

MonadFix m => Costrong ( Kleisli m) Source #
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Kleisli m (a, d) (b, d) -> Kleisli m a b Source # unsecond :: Kleisli m (d, a) (d, b) -> Kleisli m a b Source #
Costrong ( Tagged :: Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Tagged (a, d) (b, d) -> Tagged a b Source # unsecond :: Tagged (d, a) (d, b) -> Tagged a b Source #
Costrong ( Copastro p) Source #
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Copastro p (a, d) (b, d) -> Copastro p a b Source # unsecond :: Copastro p (d, a) (d, b) -> Copastro p a b Source #
Costrong ( Cotambara p) Source #
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Cotambara p (a, d) (b, d) -> Cotambara p a b Source # unsecond :: Cotambara p (d, a) (d, b) -> Cotambara p a b Source #
Costrong p => Costrong ( Coyoneda p) Source #
Instance details Defined in Data.Profunctor.Yoneda Methods unfirst :: Coyoneda p (a, d) (b, d) -> Coyoneda p a b Source # unsecond :: Coyoneda p (d, a) (d, b) -> Coyoneda p a b Source #
Costrong p => Costrong ( Yoneda p) Source #
Instance details Defined in Data.Profunctor.Yoneda Methods unfirst :: Yoneda p (a, d) (b, d) -> Yoneda p a b Source # unsecond :: Yoneda p (d, a) (d, b) -> Yoneda p a b Source #
Costrong ((->) :: Type -> Type -> Type ) Source #
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: ((a, d) -> (b, d)) -> a -> b Source # unsecond :: ((d, a) -> (d, b)) -> a -> b Source #
Functor f => Costrong ( Cokleisli f) Source #
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Cokleisli f (a, d) (b, d) -> Cokleisli f a b Source # unsecond :: Cokleisli f (d, a) (d, b) -> Cokleisli f a b Source #
Functor f => Costrong ( Costar f) Source #
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Costar f (a, d) (b, d) -> Costar f a b Source # unsecond :: Costar f (d, a) (d, b) -> Costar f a b Source #
ArrowLoop p => Costrong ( WrappedArrow p) Source #
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: WrappedArrow p (a, d) (b, d) -> WrappedArrow p a b Source # unsecond :: WrappedArrow p (d, a) (d, b) -> WrappedArrow p a b Source #
( Costrong p, Costrong q) => Costrong ( Sum p q) Source #
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Sum p q (a, d) (b, d) -> Sum p q a b Source # unsecond :: Sum p q (d, a) (d, b) -> Sum p q a b Source #
( Costrong p, Costrong q) => Costrong ( Product p q) Source #
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Product p q (a, d) (b, d) -> Product p q a b Source # unsecond :: Product p q (d, a) (d, b) -> Product p q a b Source #
( Functor f, Costrong p) => Costrong ( Tannen f p) Source #
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Tannen f p (a, d) (b, d) -> Tannen f p a b Source # unsecond :: Tannen f p (d, a) (d, b) -> Tannen f p a b Source #
( Corepresentable p, Corepresentable q) => Costrong ( Procompose p q) Source #
Instance details Defined in Data.Profunctor.Composition Methods unfirst :: Procompose p q (a, d) (b, d) -> Procompose p q a b Source # unsecond :: Procompose p q (d, a) (d, b) -> Procompose p q a b Source #
( Functor f, Costrong p) => Costrong ( Cayley f p) Source #
Instance details Defined in Data.Profunctor.Cayley Methods unfirst :: Cayley f p (a, d) (b, d) -> Cayley f p a b Source # unsecond :: Cayley f p (d, a) (d, b) -> Cayley f p a b Source #

data Cotambara q a b where Source #

Cotambara cofreely constructs costrength

Constructors

Cotambara :: Costrong r => (r :-> q) -> r a b -> Cotambara q a b

Instances

Instances details

ProfunctorComonad Cotambara Source #
Instance details Defined in Data.Profunctor.Strong Methods proextract :: forall (p :: Type -> Type -> Type ). Profunctor p => Cotambara p :-> p Source # produplicate :: forall (p :: Type -> Type -> Type ). Profunctor p => Cotambara p :-> Cotambara ( Cotambara p) Source #
ProfunctorAdjunction Copastro Cotambara Source #
Instance details Defined in Data.Profunctor.Strong Methods unit :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> Cotambara ( Copastro p) Source # counit :: forall (p :: Type -> Type -> Type ). Profunctor p => Copastro ( Cotambara p) :-> p Source #
Profunctor ( Cotambara p) Source #
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Cotambara p b c -> Cotambara p a d Source # lmap :: (a -> b) -> Cotambara p b c -> Cotambara p a c Source # rmap :: (b -> c) -> Cotambara p a b -> Cotambara p a c Source # (#.) :: forall a b c q. Coercible c b => q b c -> Cotambara p a b -> Cotambara p a c Source # (.#) :: forall a b c q. Coercible b a => Cotambara p b c -> q a b -> Cotambara p a c Source #
Costrong ( Cotambara p) Source #
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Cotambara p (a, d) (b, d) -> Cotambara p a b Source # unsecond :: Cotambara p (d, a) (d, b) -> Cotambara p a b Source #
ProfunctorFunctor Cotambara Source #
Instance details Defined in Data.Profunctor.Strong Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> Cotambara p :-> Cotambara q Source #
Functor ( Cotambara p a) Source #
Instance details Defined in Data.Profunctor.Strong Methods fmap :: (a0 -> b) -> Cotambara p a a0 -> Cotambara p a b Source # (<$) :: a0 -> Cotambara p a b -> Cotambara p a a0 Source #

cotambara :: Costrong p => (p :-> q) -> p :-> Cotambara q Source #

cotambara . uncotambara ≡ id
uncotambara . cotambara ≡ id

uncotambara :: Profunctor q => (p :-> Cotambara q) -> p :-> q Source #

cotambara . uncotambara ≡ id
uncotambara . cotambara ≡ id

newtype Copastro p a b Source #

Copastro -| Cotambara

Copastro freely constructs costrength

Constructors

Copastro
Fields runCopastro :: forall r. Costrong r => ( forall x y. p x y -> r x y) -> r a b

Instances

Instances details

ProfunctorMonad Copastro Source #
Instance details Defined in Data.Profunctor.Strong Methods proreturn :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> Copastro p Source # projoin :: forall (p :: Type -> Type -> Type ). Profunctor p => Copastro ( Copastro p) :-> Copastro p Source #
ProfunctorAdjunction Copastro Cotambara Source #
Instance details Defined in Data.Profunctor.Strong Methods unit :: forall (p :: Type -> Type -> Type ). Profunctor p => p :-> Cotambara ( Copastro p) Source # counit :: forall (p :: Type -> Type -> Type ). Profunctor p => Copastro ( Cotambara p) :-> p Source #
Profunctor ( Copastro p) Source #
Instance details Defined in Data.Profunctor.Strong Methods dimap :: (a -> b) -> (c -> d) -> Copastro p b c -> Copastro p a d Source # lmap :: (a -> b) -> Copastro p b c -> Copastro p a c Source # rmap :: (b -> c) -> Copastro p a b -> Copastro p a c Source # (#.) :: forall a b c q. Coercible c b => q b c -> Copastro p a b -> Copastro p a c Source # (.#) :: forall a b c q. Coercible b a => Copastro p b c -> q a b -> Copastro p a c Source #
Costrong ( Copastro p) Source #
Instance details Defined in Data.Profunctor.Strong Methods unfirst :: Copastro p (a, d) (b, d) -> Copastro p a b Source # unsecond :: Copastro p (d, a) (d, b) -> Copastro p a b Source #
ProfunctorFunctor Copastro Source #
Instance details Defined in Data.Profunctor.Strong Methods promap :: forall (p :: Type -> Type -> Type ) (q :: Type -> Type -> Type ). Profunctor p => (p :-> q) -> Copastro p :-> Copastro q Source #
Functor ( Copastro p a) Source #
Instance details Defined in Data.Profunctor.Strong Methods fmap :: (a0 -> b) -> Copastro p a a0 -> Copastro p a b Source # (<$) :: a0 -> Copastro p a b -> Copastro p a a0 Source #