-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Profunctors
--   
--   Profunctors
@package profunctors
@version 5.1.2


module Data.Profunctor.Trace

-- | Coend of <a>Profunctor</a> from <tt>Hask -&gt; Hask</tt>.
data Trace f
Trace :: f a a -> Trace f


-- | For a good explanation of profunctors in Haskell see Dan Piponi's
--   article:
--   
--   <a>http://blog.sigfpe.com/2011/07/profunctors-in-haskell.html</a>
--   
--   This module includes <i>unsafe</i> composition operators that are
--   useful in practice when it comes to generating optimal core in GHC.
--   
--   If you import this module you are taking upon yourself the obligation
--   that you will only call the operators with <tt>#</tt> in their names
--   with functions that are operationally identity such as
--   <tt>newtype</tt> constructors or the field accessor of a
--   <tt>newtype</tt>.
--   
--   If you are ever in doubt, use <a>rmap</a> or <a>lmap</a>.
module Data.Profunctor.Unsafe

-- | Formally, the class <a>Profunctor</a> represents a profunctor from
--   <tt>Hask</tt> -&gt; <tt>Hask</tt>.
--   
--   Intuitively it is a bifunctor where the first argument is
--   contravariant and the second argument is covariant.
--   
--   You can define a <a>Profunctor</a> by either defining <a>dimap</a> or
--   by defining both <a>lmap</a> and <a>rmap</a>.
--   
--   If you supply <a>dimap</a>, you should ensure that:
--   
--   <pre>
--   <a>dimap</a> <a>id</a> <a>id</a> ≡ <a>id</a>
--   </pre>
--   
--   If you supply <a>lmap</a> and <a>rmap</a>, ensure:
--   
--   <pre>
--   <a>lmap</a> <a>id</a> ≡ <a>id</a>
--   <a>rmap</a> <a>id</a> ≡ <a>id</a>
--   </pre>
--   
--   If you supply both, you should also ensure:
--   
--   <pre>
--   <a>dimap</a> f g ≡ <a>lmap</a> f <a>.</a> <a>rmap</a> g
--   </pre>
--   
--   These ensure by parametricity:
--   
--   <pre>
--   <a>dimap</a> (f <a>.</a> g) (h <a>.</a> i) ≡ <a>dimap</a> g h <a>.</a> <a>dimap</a> f i
--   <a>lmap</a> (f <a>.</a> g) ≡ <a>lmap</a> g <a>.</a> <a>lmap</a> f
--   <a>rmap</a> (f <a>.</a> g) ≡ <a>rmap</a> f <a>.</a> <a>rmap</a> g
--   </pre>
class Profunctor p where dimap f g = lmap f . rmap g lmap f = dimap f id rmap = dimap id (#.) = \ f -> \ p -> p `seq` rmap f p (.#) = \ p -> p `seq` \ f -> lmap f p

-- | Map over both arguments at the same time.
--   
--   <pre>
--   <a>dimap</a> f g ≡ <a>lmap</a> f <a>.</a> <a>rmap</a> g
--   </pre>
dimap :: Profunctor p => (a -> b) -> (c -> d) -> p b c -> p a d

-- | Map the first argument contravariantly.
--   
--   <pre>
--   <a>lmap</a> f ≡ <a>dimap</a> f <a>id</a>
--   </pre>
lmap :: Profunctor p => (a -> b) -> p b c -> p a c

-- | Map the second argument covariantly.
--   
--   <pre>
--   <a>rmap</a> ≡ <a>dimap</a> <a>id</a>
--   </pre>
rmap :: Profunctor p => (b -> c) -> p a b -> p a c

-- | Strictly map the second argument argument covariantly with a function
--   that is assumed operationally to be a cast, such as a newtype
--   constructor.
--   
--   <i>Note:</i> This operation is explicitly <i>unsafe</i> since an
--   implementation may choose to use <tt>unsafeCoerce</tt> to implement
--   this combinator and it has no way to validate that your function meets
--   the requirements.
--   
--   If you implement this combinator with <tt>unsafeCoerce</tt>, then you
--   are taking upon yourself the obligation that you don't use GADT-like
--   tricks to distinguish values.
--   
--   If you import <a>Data.Profunctor.Unsafe</a> you are taking upon
--   yourself the obligation that you will only call this with a first
--   argument that is operationally identity.
--   
--   The semantics of this function with respect to bottoms should match
--   the default definition:
--   
--   <pre>
--   (<a>#.</a>) ≡ \f -&gt; \p -&gt; p `seq` <a>rmap</a> f p
--   </pre>
(#.) :: (Profunctor p, Coercible c b) => (b -> c) -> p a b -> p a c

-- | Strictly map the first argument argument contravariantly with a
--   function that is assumed operationally to be a cast, such as a newtype
--   constructor.
--   
--   <i>Note:</i> This operation is explicitly <i>unsafe</i> since an
--   implementation may choose to use <tt>unsafeCoerce</tt> to implement
--   this combinator and it has no way to validate that your function meets
--   the requirements.
--   
--   If you implement this combinator with <tt>unsafeCoerce</tt>, then you
--   are taking upon yourself the obligation that you don't use GADT-like
--   tricks to distinguish values.
--   
--   If you import <a>Data.Profunctor.Unsafe</a> you are taking upon
--   yourself the obligation that you will only call this with a second
--   argument that is operationally identity.
--   
--   <pre>
--   (<a>.#</a>) ≡ \p -&gt; p `seq` \f -&gt; <a>lmap</a> f p
--   </pre>
(.#) :: (Profunctor p, Coercible b a) => p b c -> (a -> b) -> p a c
instance Data.Profunctor.Unsafe.Profunctor (->)
instance Data.Profunctor.Unsafe.Profunctor Data.Tagged.Tagged
instance GHC.Base.Monad m => Data.Profunctor.Unsafe.Profunctor (Control.Arrow.Kleisli m)
instance GHC.Base.Functor w => Data.Profunctor.Unsafe.Profunctor (Control.Comonad.Cokleisli w)
instance Data.Functor.Contravariant.Contravariant f => Data.Profunctor.Unsafe.Profunctor (Data.Bifunctor.Clown.Clown f)
instance GHC.Base.Functor f => Data.Profunctor.Unsafe.Profunctor (Data.Bifunctor.Joker.Joker f)


-- | For a good explanation of profunctors in Haskell see Dan Piponi's
--   article:
--   
--   <a>http://blog.sigfpe.com/2011/07/profunctors-in-haskell.html</a>
--   
--   For more information on strength and costrength, see:
--   
--   <a>http://comonad.com/reader/2008/deriving-strength-from-laziness/</a>
module Data.Profunctor

-- | Formally, the class <a>Profunctor</a> represents a profunctor from
--   <tt>Hask</tt> -&gt; <tt>Hask</tt>.
--   
--   Intuitively it is a bifunctor where the first argument is
--   contravariant and the second argument is covariant.
--   
--   You can define a <a>Profunctor</a> by either defining <a>dimap</a> or
--   by defining both <a>lmap</a> and <a>rmap</a>.
--   
--   If you supply <a>dimap</a>, you should ensure that:
--   
--   <pre>
--   <a>dimap</a> <a>id</a> <a>id</a> ≡ <a>id</a>
--   </pre>
--   
--   If you supply <a>lmap</a> and <a>rmap</a>, ensure:
--   
--   <pre>
--   <a>lmap</a> <a>id</a> ≡ <a>id</a>
--   <a>rmap</a> <a>id</a> ≡ <a>id</a>
--   </pre>
--   
--   If you supply both, you should also ensure:
--   
--   <pre>
--   <a>dimap</a> f g ≡ <a>lmap</a> f <a>.</a> <a>rmap</a> g
--   </pre>
--   
--   These ensure by parametricity:
--   
--   <pre>
--   <a>dimap</a> (f <a>.</a> g) (h <a>.</a> i) ≡ <a>dimap</a> g h <a>.</a> <a>dimap</a> f i
--   <a>lmap</a> (f <a>.</a> g) ≡ <a>lmap</a> g <a>.</a> <a>lmap</a> f
--   <a>rmap</a> (f <a>.</a> g) ≡ <a>rmap</a> f <a>.</a> <a>rmap</a> g
--   </pre>
class Profunctor p where dimap f g = lmap f . rmap g lmap f = dimap f id rmap = dimap id (#.) = \ f -> \ p -> p `seq` rmap f p (.#) = \ p -> p `seq` \ f -> lmap f p

-- | Map over both arguments at the same time.
--   
--   <pre>
--   <a>dimap</a> f g ≡ <a>lmap</a> f <a>.</a> <a>rmap</a> g
--   </pre>
dimap :: Profunctor p => (a -> b) -> (c -> d) -> p b c -> p a d

-- | Map the first argument contravariantly.
--   
--   <pre>
--   <a>lmap</a> f ≡ <a>dimap</a> f <a>id</a>
--   </pre>
lmap :: Profunctor p => (a -> b) -> p b c -> p a c

-- | Map the second argument covariantly.
--   
--   <pre>
--   <a>rmap</a> ≡ <a>dimap</a> <a>id</a>
--   </pre>
rmap :: Profunctor p => (b -> c) -> p a b -> p a c

-- | Generalizing <a>Star</a> of a strong <a>Functor</a>
--   
--   <i>Note:</i> Every <a>Functor</a> in Haskell is strong with respect to
--   <tt>(,)</tt>.
--   
--   This describes profunctor strength with respect to the product
--   structure of Hask.
--   
--   <a>http://www-kb.is.s.u-tokyo.ac.jp/~asada/papers/arrStrMnd.pdf</a>
class Profunctor p => Strong p where first' = dimap swap swap . second' second' = dimap swap swap . first'
first' :: Strong p => p a b -> p (a, c) (b, c)
second' :: Strong p => p a b -> p (c, a) (c, b)

-- | The generalization of <a>Costar</a> of <a>Functor</a> that is strong
--   with respect to <a>Either</a>.
--   
--   Note: This is also a notion of strength, except with regards to
--   another monoidal structure that we can choose to equip Hask with: the
--   cocartesian coproduct.
class Profunctor p => Choice p where left' = dimap (either Right Left) (either Right Left) . right' right' = dimap (either Right Left) (either Right Left) . left'
left' :: Choice p => p a b -> p (Either a c) (Either b c)
right' :: Choice p => p a b -> p (Either c a) (Either c b)

-- | Analogous to <a>ArrowLoop</a>, <a>loop</a> = <a>unfirst</a>
class Profunctor p => Costrong p where unfirst = unsecond . dimap swap swap unsecond = unfirst . dimap swap swap
unfirst :: Costrong p => p (a, d) (b, d) -> p a b
unsecond :: Costrong p => p (d, a) (d, b) -> p a b
class Profunctor p => Cochoice p where unleft = unright . dimap (either Right Left) (either Right Left) unright = unleft . dimap (either Right Left) (either Right Left)
unleft :: Cochoice p => p (Either a d) (Either b d) -> p a b
unright :: Cochoice p => p (Either d a) (Either d b) -> p a b

-- | Lift a <a>Functor</a> into a <a>Profunctor</a> (forwards).
newtype Star f d c
Star :: (d -> f c) -> Star f d c
[runStar] :: Star f d c -> d -> f c

-- | Lift a <a>Functor</a> into a <a>Profunctor</a> (backwards).
newtype Costar f d c
Costar :: (f d -> c) -> Costar f d c
[runCostar] :: Costar f d c -> f d -> c

-- | Wrap an arrow for use as a <a>Profunctor</a>.
newtype WrappedArrow p a b
WrapArrow :: p a b -> WrappedArrow p a b
[unwrapArrow] :: WrappedArrow p a b -> p a b
newtype Forget r a b
Forget :: (a -> r) -> Forget r a b
[runForget] :: Forget r a b -> a -> r
type (:->) p q = forall a b. p a b -> q a b
instance GHC.Base.Functor f => Data.Profunctor.Unsafe.Profunctor (Data.Profunctor.Star f)
instance GHC.Base.Functor f => GHC.Base.Functor (Data.Profunctor.Star f a)
instance GHC.Base.Applicative f => GHC.Base.Applicative (Data.Profunctor.Star f a)
instance GHC.Base.Alternative f => GHC.Base.Alternative (Data.Profunctor.Star f a)
instance GHC.Base.Monad f => GHC.Base.Monad (Data.Profunctor.Star f a)
instance GHC.Base.MonadPlus f => GHC.Base.MonadPlus (Data.Profunctor.Star f a)
instance Data.Distributive.Distributive f => Data.Distributive.Distributive (Data.Profunctor.Star f a)
instance GHC.Base.Functor f => Data.Profunctor.Unsafe.Profunctor (Data.Profunctor.Costar f)
instance Data.Distributive.Distributive (Data.Profunctor.Costar f d)
instance GHC.Base.Functor (Data.Profunctor.Costar f a)
instance GHC.Base.Applicative (Data.Profunctor.Costar f a)
instance GHC.Base.Monad (Data.Profunctor.Costar f a)
instance Control.Category.Category p => Control.Category.Category (Data.Profunctor.WrappedArrow p)
instance Control.Arrow.Arrow p => Control.Arrow.Arrow (Data.Profunctor.WrappedArrow p)
instance Control.Arrow.ArrowZero p => Control.Arrow.ArrowZero (Data.Profunctor.WrappedArrow p)
instance Control.Arrow.ArrowChoice p => Control.Arrow.ArrowChoice (Data.Profunctor.WrappedArrow p)
instance Control.Arrow.ArrowApply p => Control.Arrow.ArrowApply (Data.Profunctor.WrappedArrow p)
instance Control.Arrow.ArrowLoop p => Control.Arrow.ArrowLoop (Data.Profunctor.WrappedArrow p)
instance Control.Arrow.Arrow p => Data.Profunctor.Unsafe.Profunctor (Data.Profunctor.WrappedArrow p)
instance Data.Profunctor.Unsafe.Profunctor (Data.Profunctor.Forget r)
instance GHC.Base.Functor (Data.Profunctor.Forget r a)
instance Data.Foldable.Foldable (Data.Profunctor.Forget r a)
instance Data.Traversable.Traversable (Data.Profunctor.Forget r a)
instance Data.Profunctor.Strong (->)
instance GHC.Base.Monad m => Data.Profunctor.Strong (Control.Arrow.Kleisli m)
instance GHC.Base.Functor m => Data.Profunctor.Strong (Data.Profunctor.Star m)
instance Control.Arrow.Arrow p => Data.Profunctor.Strong (Data.Profunctor.WrappedArrow p)
instance Data.Profunctor.Strong (Data.Profunctor.Forget r)
instance Data.Profunctor.Choice (->)
instance GHC.Base.Monad m => Data.Profunctor.Choice (Control.Arrow.Kleisli m)
instance GHC.Base.Applicative f => Data.Profunctor.Choice (Data.Profunctor.Star f)
instance Control.Comonad.Comonad w => Data.Profunctor.Choice (Control.Comonad.Cokleisli w)
instance Data.Traversable.Traversable w => Data.Profunctor.Choice (Data.Profunctor.Costar w)
instance Data.Profunctor.Choice Data.Tagged.Tagged
instance Control.Arrow.ArrowChoice p => Data.Profunctor.Choice (Data.Profunctor.WrappedArrow p)
instance GHC.Base.Monoid r => Data.Profunctor.Choice (Data.Profunctor.Forget r)
instance Data.Profunctor.Costrong (->)
instance GHC.Base.Functor f => Data.Profunctor.Costrong (Data.Profunctor.Costar f)
instance Data.Profunctor.Costrong Data.Tagged.Tagged
instance Control.Arrow.ArrowLoop p => Data.Profunctor.Costrong (Data.Profunctor.WrappedArrow p)
instance Control.Monad.Fix.MonadFix m => Data.Profunctor.Costrong (Control.Arrow.Kleisli m)
instance GHC.Base.Functor f => Data.Profunctor.Costrong (Control.Comonad.Cokleisli f)
instance Data.Profunctor.Cochoice (->)
instance GHC.Base.Applicative f => Data.Profunctor.Cochoice (Data.Profunctor.Costar f)
instance Data.Traversable.Traversable f => Data.Profunctor.Cochoice (Data.Profunctor.Star f)

module Data.Profunctor.Monad
class ProfunctorFunctor t
promap :: (ProfunctorFunctor t, Profunctor p) => (p :-> q) -> t p :-> t q
class ProfunctorFunctor t => ProfunctorMonad t
proreturn :: (ProfunctorMonad t, Profunctor p) => p :-> t p
projoin :: (ProfunctorMonad t, Profunctor p) => t (t p) :-> t p
class ProfunctorFunctor t => ProfunctorComonad t
proextract :: (ProfunctorComonad t, Profunctor p) => t p :-> p
produplicate :: (ProfunctorComonad t, Profunctor p) => t p :-> t (t p)

module Data.Profunctor.Adjunction
class (ProfunctorFunctor f, ProfunctorFunctor u) => ProfunctorAdjunction f u | f -> u, u -> f
unit :: (ProfunctorAdjunction f u, Profunctor p) => p :-> u (f p)
counit :: (ProfunctorAdjunction f u, Profunctor p) => f (u p) :-> p


module Data.Profunctor.Cayley
newtype Cayley f p a b
Cayley :: f (p a b) -> Cayley f p a b
[runCayley] :: Cayley f p a b -> f (p a b)

-- | Cayley transforms Monads in <tt>Hask</tt> into monads on <tt>Prof</tt>

-- | Cayley transforms Comonads in <tt>Hask</tt> into comonads on
--   <tt>Prof</tt>
instance GHC.Base.Functor f => Data.Profunctor.Monad.ProfunctorFunctor (Data.Profunctor.Cayley.Cayley f)
instance (GHC.Base.Functor f, GHC.Base.Monad f) => Data.Profunctor.Monad.ProfunctorMonad (Data.Profunctor.Cayley.Cayley f)
instance Control.Comonad.Comonad f => Data.Profunctor.Monad.ProfunctorComonad (Data.Profunctor.Cayley.Cayley f)
instance (GHC.Base.Functor f, Data.Profunctor.Unsafe.Profunctor p) => Data.Profunctor.Unsafe.Profunctor (Data.Profunctor.Cayley.Cayley f p)
instance (GHC.Base.Functor f, Data.Profunctor.Strong p) => Data.Profunctor.Strong (Data.Profunctor.Cayley.Cayley f p)
instance (GHC.Base.Functor f, Data.Profunctor.Choice p) => Data.Profunctor.Choice (Data.Profunctor.Cayley.Cayley f p)
instance (GHC.Base.Applicative f, Control.Category.Category p) => Control.Category.Category (Data.Profunctor.Cayley.Cayley f p)
instance (GHC.Base.Applicative f, Control.Arrow.Arrow p) => Control.Arrow.Arrow (Data.Profunctor.Cayley.Cayley f p)
instance (GHC.Base.Applicative f, Control.Arrow.ArrowChoice p) => Control.Arrow.ArrowChoice (Data.Profunctor.Cayley.Cayley f p)
instance (GHC.Base.Applicative f, Control.Arrow.ArrowLoop p) => Control.Arrow.ArrowLoop (Data.Profunctor.Cayley.Cayley f p)
instance (GHC.Base.Applicative f, Control.Arrow.ArrowZero p) => Control.Arrow.ArrowZero (Data.Profunctor.Cayley.Cayley f p)
instance (GHC.Base.Applicative f, Control.Arrow.ArrowPlus p) => Control.Arrow.ArrowPlus (Data.Profunctor.Cayley.Cayley f p)

module Data.Profunctor.Closed

-- | A strong profunctor allows the monoidal structure to pass through.
--   
--   A closed profunctor allows the closed structure to pass through.
class Profunctor p => Closed p
closed :: Closed p => p a b -> p (x -> a) (x -> b)

-- | <a>Closure</a> adjoins a <a>Closed</a> structure to any
--   <a>Profunctor</a>.
--   
--   Analogous to <a>Tambara</a> for <a>Strong</a>.
newtype Closure p a b
Closure :: (forall x. p (x -> a) (x -> b)) -> Closure p a b
[runClosure] :: Closure p a b -> forall x. p (x -> a) (x -> b)

-- | <pre>
--   <a>close</a> <a>.</a> <a>unclose</a> ≡ <a>id</a>
--   <a>unclose</a> <a>.</a> <a>close</a> ≡ <a>id</a>
--   </pre>
close :: Closed p => (p :-> q) -> p :-> Closure q

-- | <pre>
--   <a>close</a> <a>.</a> <a>unclose</a> ≡ <a>id</a>
--   <a>unclose</a> <a>.</a> <a>close</a> ≡ <a>id</a>
--   </pre>
unclose :: Profunctor q => (p :-> Closure q) -> p :-> q
data Environment p a b
Environment :: ((z -> y) -> b) -> p x y -> (a -> z -> x) -> Environment p a b
instance Data.Profunctor.Closed.Closed Data.Tagged.Tagged
instance Data.Profunctor.Closed.Closed (->)
instance GHC.Base.Functor f => Data.Profunctor.Closed.Closed (Data.Profunctor.Costar f)
instance GHC.Base.Functor f => Data.Profunctor.Closed.Closed (Control.Comonad.Cokleisli f)
instance Data.Distributive.Distributive f => Data.Profunctor.Closed.Closed (Data.Profunctor.Star f)
instance (Data.Distributive.Distributive f, GHC.Base.Monad f) => Data.Profunctor.Closed.Closed (Control.Arrow.Kleisli f)
instance Data.Profunctor.Unsafe.Profunctor p => Data.Profunctor.Unsafe.Profunctor (Data.Profunctor.Closed.Closure p)
instance Data.Profunctor.Monad.ProfunctorFunctor Data.Profunctor.Closed.Closure
instance Data.Profunctor.Monad.ProfunctorComonad Data.Profunctor.Closed.Closure
instance Data.Profunctor.Unsafe.Profunctor p => Data.Profunctor.Closed.Closed (Data.Profunctor.Closed.Closure p)
instance Data.Profunctor.Strong p => Data.Profunctor.Strong (Data.Profunctor.Closed.Closure p)
instance Control.Category.Category p => Control.Category.Category (Data.Profunctor.Closed.Closure p)
instance Control.Arrow.Arrow p => Control.Arrow.Arrow (Data.Profunctor.Closed.Closure p)
instance Control.Arrow.ArrowLoop p => Control.Arrow.ArrowLoop (Data.Profunctor.Closed.Closure p)
instance Control.Arrow.ArrowZero p => Control.Arrow.ArrowZero (Data.Profunctor.Closed.Closure p)
instance Control.Arrow.ArrowPlus p => Control.Arrow.ArrowPlus (Data.Profunctor.Closed.Closure p)
instance Data.Profunctor.Unsafe.Profunctor p => GHC.Base.Functor (Data.Profunctor.Closed.Closure p a)
instance (Data.Profunctor.Unsafe.Profunctor p, Control.Arrow.Arrow p) => GHC.Base.Applicative (Data.Profunctor.Closed.Closure p a)
instance (Data.Profunctor.Unsafe.Profunctor p, Control.Arrow.ArrowPlus p) => GHC.Base.Alternative (Data.Profunctor.Closed.Closure p a)
instance (Data.Profunctor.Unsafe.Profunctor p, Control.Arrow.Arrow p, GHC.Base.Monoid b) => GHC.Base.Monoid (Data.Profunctor.Closed.Closure p a b)
instance Data.Profunctor.Unsafe.Profunctor p => Data.Profunctor.Unsafe.Profunctor (Data.Profunctor.Closed.Environment p)
instance Data.Profunctor.Monad.ProfunctorFunctor Data.Profunctor.Closed.Environment
instance Data.Profunctor.Monad.ProfunctorMonad Data.Profunctor.Closed.Environment
instance Data.Profunctor.Adjunction.ProfunctorAdjunction Data.Profunctor.Closed.Environment Data.Profunctor.Closed.Closure


module Data.Profunctor.Sieve

-- | A <a>Profunctor</a> <tt>p</tt> is a <a>Sieve</a> <b>on</b> <tt>f</tt>
--   if it is a subprofunctor of <tt><a>Star</a> f</tt>.
--   
--   That is to say it is a subset of <tt>Hom(-,f=)</tt> closed under
--   <a>lmap</a> and <a>rmap</a>.
--   
--   Alternately, you can view it as a sieve <b>in</b> the comma category
--   <tt>Hask/f</tt>.
class (Profunctor p, Functor f) => Sieve p f | p -> f
sieve :: Sieve p f => p a b -> a -> f b

-- | A <a>Profunctor</a> <tt>p</tt> is a <a>Cosieve</a> <b>on</b>
--   <tt>f</tt> if it is a subprofunctor of <tt><a>Costar</a> f</tt>.
--   
--   That is to say it is a subset of <tt>Hom(f-,=)</tt> closed under
--   <a>lmap</a> and <a>rmap</a>.
--   
--   Alternately, you can view it as a cosieve <b>in</b> the comma category
--   <tt>f/Hask</tt>.
class (Profunctor p, Functor f) => Cosieve p f | p -> f
cosieve :: Cosieve p f => p a b -> f a -> b
instance Data.Profunctor.Sieve.Sieve (->) Data.Functor.Identity.Identity
instance (GHC.Base.Monad m, GHC.Base.Functor m) => Data.Profunctor.Sieve.Sieve (Control.Arrow.Kleisli m) m
instance GHC.Base.Functor f => Data.Profunctor.Sieve.Sieve (Data.Profunctor.Star f) f
instance Data.Profunctor.Sieve.Sieve (Data.Profunctor.Forget r) (Control.Applicative.Const r)
instance Data.Profunctor.Sieve.Cosieve (->) Data.Functor.Identity.Identity
instance GHC.Base.Functor w => Data.Profunctor.Sieve.Cosieve (Control.Comonad.Cokleisli w) w
instance Data.Profunctor.Sieve.Cosieve Data.Tagged.Tagged Data.Proxy.Proxy
instance GHC.Base.Functor f => Data.Profunctor.Sieve.Cosieve (Data.Profunctor.Costar f) f


module Data.Profunctor.Rep

-- | A <a>Profunctor</a> <tt>p</tt> is <a>Representable</a> if there exists
--   a <a>Functor</a> <tt>f</tt> such that <tt>p d c</tt> is isomorphic to
--   <tt>d -&gt; f c</tt>.
class (Sieve p (Rep p), Strong p) => Representable p where type family Rep p :: * -> *
tabulate :: Representable p => (d -> Rep p c) -> p d c

-- | <a>tabulate</a> and <a>sieve</a> form two halves of an isomorphism.
--   
--   This can be used with the combinators from the <tt>lens</tt> package.
--   
--   <pre>
--   <a>tabulated</a> :: <a>Representable</a> p =&gt; <tt>Iso'</tt> (d -&gt; <a>Rep</a> p c) (p d c)
--   </pre>
tabulated :: (Representable p, Representable q) => Iso (d -> Rep p c) (d' -> Rep q c') (p d c) (q d' c')

-- | Default definition for <a>first'</a> given that p is
--   <a>Representable</a>.
firstRep :: Representable p => p a b -> p (a, c) (b, c)

-- | Default definition for <a>second'</a> given that p is
--   <a>Representable</a>.
secondRep :: Representable p => p a b -> p (c, a) (c, b)

-- | A <a>Profunctor</a> <tt>p</tt> is <a>Corepresentable</a> if there
--   exists a <a>Functor</a> <tt>f</tt> such that <tt>p d c</tt> is
--   isomorphic to <tt>f d -&gt; c</tt>.
class (Cosieve p (Corep p), Costrong p) => Corepresentable p where type family Corep p :: * -> *
cotabulate :: Corepresentable p => (Corep p d -> c) -> p d c

-- | <a>cotabulate</a> and <a>cosieve</a> form two halves of an
--   isomorphism.
--   
--   This can be used with the combinators from the <tt>lens</tt> package.
--   
--   <pre>
--   <a>cotabulated</a> :: <a>Corep</a> f p =&gt; <tt>Iso'</tt> (f d -&gt; c) (p d c)
--   </pre>
cotabulated :: (Corepresentable p, Corepresentable q) => Iso (Corep p d -> c) (Corep q d' -> c') (p d c) (q d' c')

-- | Default definition for <a>unfirst</a> given that p is
--   <a>Corepresentable</a>.
unfirstCorep :: Corepresentable p => p (a, d) (b, d) -> p a b

-- | Default definition for <a>unsecond</a> given that p is
--   <a>Corepresentable</a>.
unsecondCorep :: Corepresentable p => p (d, a) (d, b) -> p a b

-- | <pre>
--   <a>Prep</a> -| <a>Star</a> :: [Hask, Hask] -&gt; Prof
--   </pre>
--   
--   This gives rise to a monad in <tt>Prof</tt>, <tt>('Star'.'Prep')</tt>,
--   and a comonad in <tt>[Hask,Hask]</tt> <tt>('Prep'.'Star')</tt>
data Prep p a
Prep :: x -> p x a -> Prep p a
prepAdj :: (forall a. Prep p a -> g a) -> p :-> Star g
unprepAdj :: (p :-> Star g) -> Prep p a -> g a
prepUnit :: p :-> Star (Prep p)
prepCounit :: Prep (Star f) a -> f a
newtype Coprep p a
Coprep :: (forall r. p a r -> r) -> Coprep p a
[runCoprep] :: Coprep p a -> forall r. p a r -> r

-- | <pre>
--   <a>Coprep</a> -| <a>Costar</a> :: [Hask, Hask]^op -&gt; Prof
--   </pre>
--   
--   Like all adjunctions this gives rise to a monad and a comonad.
--   
--   This gives rise to a monad on Prof <tt>('Costar'.'Coprep')</tt> and a
--   comonad on <tt>[Hask, Hask]^op</tt> given by
--   <tt>('Coprep'.'Costar')</tt> which is a monad in <tt>[Hask,Hask]</tt>
coprepAdj :: (forall a. f a -> Coprep p a) -> p :-> Costar f
uncoprepAdj :: (p :-> Costar f) -> f a -> Coprep p a
coprepUnit :: p :-> Costar (Coprep p)
coprepCounit :: f a -> Coprep (Costar f) a
instance Data.Profunctor.Rep.Representable (->)
instance (GHC.Base.Monad m, GHC.Base.Functor m) => Data.Profunctor.Rep.Representable (Control.Arrow.Kleisli m)
instance GHC.Base.Functor f => Data.Profunctor.Rep.Representable (Data.Profunctor.Star f)
instance Data.Profunctor.Rep.Representable (Data.Profunctor.Forget r)
instance Data.Profunctor.Rep.Corepresentable (->)
instance GHC.Base.Functor w => Data.Profunctor.Rep.Corepresentable (Control.Comonad.Cokleisli w)
instance Data.Profunctor.Rep.Corepresentable Data.Tagged.Tagged
instance GHC.Base.Functor f => Data.Profunctor.Rep.Corepresentable (Data.Profunctor.Costar f)
instance Data.Profunctor.Unsafe.Profunctor p => GHC.Base.Functor (Data.Profunctor.Rep.Prep p)
instance (GHC.Base.Applicative (Data.Profunctor.Rep.Rep p), Data.Profunctor.Rep.Representable p) => GHC.Base.Applicative (Data.Profunctor.Rep.Prep p)
instance (GHC.Base.Monad (Data.Profunctor.Rep.Rep p), Data.Profunctor.Rep.Representable p) => GHC.Base.Monad (Data.Profunctor.Rep.Prep p)
instance Data.Profunctor.Unsafe.Profunctor p => GHC.Base.Functor (Data.Profunctor.Rep.Coprep p)


module Data.Profunctor.Composition

-- | <tt><a>Procompose</a> p q</tt> is the <a>Profunctor</a> composition of
--   the <a>Profunctor</a>s <tt>p</tt> and <tt>q</tt>.
--   
--   For a good explanation of <a>Profunctor</a> composition in Haskell see
--   Dan Piponi's article:
--   
--   <a>http://blog.sigfpe.com/2011/07/profunctors-in-haskell.html</a>
data Procompose p q d c
Procompose :: p x c -> q d x -> Procompose p q d c
procomposed :: Category p => Procompose p p a b -> p a b

-- | <tt>(-&gt;)</tt> functions as a lax identity for <a>Profunctor</a>
--   composition.
--   
--   This provides an <a>Iso</a> for the <tt>lens</tt> package that
--   witnesses the isomorphism between <tt><a>Procompose</a> (-&gt;) q d
--   c</tt> and <tt>q d c</tt>, which is the left identity law.
--   
--   <pre>
--   <a>idl</a> :: <a>Profunctor</a> q =&gt; Iso' (<a>Procompose</a> (-&gt;) q d c) (q d c)
--   </pre>
idl :: Profunctor q => Iso (Procompose (->) q d c) (Procompose (->) r d' c') (q d c) (r d' c')

-- | <tt>(-&gt;)</tt> functions as a lax identity for <a>Profunctor</a>
--   composition.
--   
--   This provides an <a>Iso</a> for the <tt>lens</tt> package that
--   witnesses the isomorphism between <tt><a>Procompose</a> q (-&gt;) d
--   c</tt> and <tt>q d c</tt>, which is the right identity law.
--   
--   <pre>
--   <a>idr</a> :: <a>Profunctor</a> q =&gt; Iso' (<a>Procompose</a> q (-&gt;) d c) (q d c)
--   </pre>
idr :: Profunctor q => Iso (Procompose q (->) d c) (Procompose r (->) d' c') (q d c) (r d' c')

-- | The associator for <a>Profunctor</a> composition.
--   
--   This provides an <a>Iso</a> for the <tt>lens</tt> package that
--   witnesses the isomorphism between <tt><a>Procompose</a> p
--   (<a>Procompose</a> q r) a b</tt> and <tt><a>Procompose</a>
--   (<a>Procompose</a> p q) r a b</tt>, which arises because <tt>Prof</tt>
--   is only a bicategory, rather than a strict 2-category.
assoc :: Iso (Procompose p (Procompose q r) a b) (Procompose x (Procompose y z) a b) (Procompose (Procompose p q) r a b) (Procompose (Procompose x y) z a b)

-- | <a>Profunctor</a> composition generalizes <a>Functor</a> composition
--   in two ways.
--   
--   This is the first, which shows that <tt>exists b. (a -&gt; f b, b
--   -&gt; g c)</tt> is isomorphic to <tt>a -&gt; f (g c)</tt>.
--   
--   <pre>
--   <a>stars</a> :: <a>Functor</a> f =&gt; Iso' (<a>Procompose</a> (<a>Star</a> f) (<a>Star</a> g) d c) (<a>Star</a> (<a>Compose</a> f g) d c)
--   </pre>
stars :: Functor g => Iso (Procompose (Star f) (Star g) d c) (Procompose (Star f') (Star g') d' c') (Star (Compose g f) d c) (Star (Compose g' f') d' c')

-- | This is a variant on <a>stars</a> that uses <a>Kleisli</a> instead of
--   <a>Star</a>.
--   
--   <pre>
--   <a>kleislis</a> :: <a>Monad</a> f =&gt; Iso' (<a>Procompose</a> (<a>Kleisli</a> f) (<a>Kleisli</a> g) d c) (<a>Kleisli</a> (<a>Compose</a> f g) d c)
--   </pre>
kleislis :: Monad g => Iso (Procompose (Kleisli f) (Kleisli g) d c) (Procompose (Kleisli f') (Kleisli g') d' c') (Kleisli (Compose g f) d c) (Kleisli (Compose g' f') d' c')

-- | <a>Profunctor</a> composition generalizes <a>Functor</a> composition
--   in two ways.
--   
--   This is the second, which shows that <tt>exists b. (f a -&gt; b, g b
--   -&gt; c)</tt> is isomorphic to <tt>g (f a) -&gt; c</tt>.
--   
--   <pre>
--   <a>costars</a> :: <a>Functor</a> f =&gt; Iso' (<a>Procompose</a> (<a>Costar</a> f) (<a>Costar</a> g) d c) (<a>Costar</a> (<a>Compose</a> g f) d c)
--   </pre>
costars :: Functor f => Iso (Procompose (Costar f) (Costar g) d c) (Procompose (Costar f') (Costar g') d' c') (Costar (Compose f g) d c) (Costar (Compose f' g') d' c')

-- | This is a variant on <a>costars</a> that uses <a>Cokleisli</a> instead
--   of <a>Costar</a>.
--   
--   <pre>
--   <a>cokleislis</a> :: <a>Functor</a> f =&gt; Iso' (<a>Procompose</a> (<a>Cokleisli</a> f) (<a>Cokleisli</a> g) d c) (<a>Cokleisli</a> (<a>Compose</a> g f) d c)
--   </pre>
cokleislis :: Functor f => Iso (Procompose (Cokleisli f) (Cokleisli g) d c) (Procompose (Cokleisli f') (Cokleisli g') d' c') (Cokleisli (Compose f g) d c) (Cokleisli (Compose f' g') d' c')

-- | This represents the right Kan lift of a <a>Profunctor</a> <tt>q</tt>
--   along a <a>Profunctor</a> <tt>p</tt> in a limited version of the
--   2-category of Profunctors where the only object is the category Hask,
--   1-morphisms are profunctors composed and compose with Profunctor
--   composition, and 2-morphisms are just natural transformations.
newtype Rift p q a b
Rift :: (forall x. p b x -> q a x) -> Rift p q a b
[runRift] :: Rift p q a b -> forall x. p b x -> q a x

-- | The 2-morphism that defines a left Kan lift.
--   
--   Note: When <tt>p</tt> is right adjoint to <tt><a>Rift</a> p
--   (-&gt;)</tt> then <a>decomposeRift</a> is the <a>counit</a> of the
--   adjunction.
decomposeRift :: Procompose p (Rift p q) :-> q
instance Data.Profunctor.Monad.ProfunctorFunctor (Data.Profunctor.Composition.Procompose p)
instance Control.Category.Category p => Data.Profunctor.Monad.ProfunctorMonad (Data.Profunctor.Composition.Procompose p)
instance (Data.Profunctor.Unsafe.Profunctor p, Data.Profunctor.Unsafe.Profunctor q) => Data.Profunctor.Unsafe.Profunctor (Data.Profunctor.Composition.Procompose p q)
instance Data.Profunctor.Unsafe.Profunctor p => GHC.Base.Functor (Data.Profunctor.Composition.Procompose p q a)
instance (Data.Profunctor.Sieve.Sieve p f, Data.Profunctor.Sieve.Sieve q g) => Data.Profunctor.Sieve.Sieve (Data.Profunctor.Composition.Procompose p q) (Data.Functor.Compose.Compose g f)
instance (Data.Profunctor.Rep.Representable p, Data.Profunctor.Rep.Representable q) => Data.Profunctor.Rep.Representable (Data.Profunctor.Composition.Procompose p q)
instance (Data.Profunctor.Sieve.Cosieve p f, Data.Profunctor.Sieve.Cosieve q g) => Data.Profunctor.Sieve.Cosieve (Data.Profunctor.Composition.Procompose p q) (Data.Functor.Compose.Compose f g)
instance (Data.Profunctor.Rep.Corepresentable p, Data.Profunctor.Rep.Corepresentable q) => Data.Profunctor.Rep.Corepresentable (Data.Profunctor.Composition.Procompose p q)
instance (Data.Profunctor.Strong p, Data.Profunctor.Strong q) => Data.Profunctor.Strong (Data.Profunctor.Composition.Procompose p q)
instance (Data.Profunctor.Choice p, Data.Profunctor.Choice q) => Data.Profunctor.Choice (Data.Profunctor.Composition.Procompose p q)
instance (Data.Profunctor.Closed.Closed p, Data.Profunctor.Closed.Closed q) => Data.Profunctor.Closed.Closed (Data.Profunctor.Composition.Procompose p q)
instance (Data.Profunctor.Rep.Corepresentable p, Data.Profunctor.Rep.Corepresentable q) => Data.Profunctor.Costrong (Data.Profunctor.Composition.Procompose p q)
instance Data.Profunctor.Monad.ProfunctorFunctor (Data.Profunctor.Composition.Rift p)
instance Control.Category.Category p => Data.Profunctor.Monad.ProfunctorComonad (Data.Profunctor.Composition.Rift p)
instance (Data.Profunctor.Unsafe.Profunctor p, Data.Profunctor.Unsafe.Profunctor q) => Data.Profunctor.Unsafe.Profunctor (Data.Profunctor.Composition.Rift p q)
instance Data.Profunctor.Unsafe.Profunctor p => GHC.Base.Functor (Data.Profunctor.Composition.Rift p q a)
instance (p ~ q) => Control.Category.Category (Data.Profunctor.Composition.Rift p q)
instance Data.Profunctor.Adjunction.ProfunctorAdjunction (Data.Profunctor.Composition.Procompose p) (Data.Profunctor.Composition.Rift p)


module Data.Profunctor.Codensity

-- | This represents the right Kan extension of a <a>Profunctor</a>
--   <tt>p</tt> along itself. This provides a generalization of the
--   "difference list" trick to profunctors.
newtype Codensity p a b
Codensity :: (forall x. p x a -> p x b) -> Codensity p a b
[runCodensity] :: Codensity p a b -> forall x. p x a -> p x b
decomposeCodensity :: Procompose (Codensity p) p a b -> p a b
instance Data.Profunctor.Unsafe.Profunctor p => Data.Profunctor.Unsafe.Profunctor (Data.Profunctor.Codensity.Codensity p)
instance Data.Profunctor.Unsafe.Profunctor p => GHC.Base.Functor (Data.Profunctor.Codensity.Codensity p a)
instance Control.Category.Category (Data.Profunctor.Codensity.Codensity p)

module Data.Profunctor.Monoid

-- | a <a>Category</a> that is also a <a>Profunctor</a> is a
--   <tt>Monoid</tt> in <tt>Prof</tt>
eta :: (Profunctor p, Category p) => (->) :-> p
mu :: Category p => Procompose p p :-> p


module Data.Profunctor.Ran

-- | This represents the right Kan extension of a <a>Profunctor</a>
--   <tt>q</tt> along a <a>Profunctor</a> <tt>p</tt> in a limited version
--   of the 2-category of Profunctors where the only object is the category
--   Hask, 1-morphisms are profunctors composed and compose with Profunctor
--   composition, and 2-morphisms are just natural transformations.
newtype Ran p q a b
Ran :: (forall x. p x a -> q x b) -> Ran p q a b
[runRan] :: Ran p q a b -> forall x. p x a -> q x b

-- | The 2-morphism that defines a right Kan extension.
--   
--   Note: When <tt>q</tt> is left adjoint to <tt><a>Ran</a> q (-&gt;)</tt>
--   then <a>decomposeRan</a> is the <tt>counit</tt> of the adjunction.
decomposeRan :: Procompose (Ran q p) q :-> p
precomposeRan :: Profunctor q => Procompose q (Ran p (->)) :-> Ran p q
curryRan :: (Procompose p q :-> r) -> p :-> Ran q r
uncurryRan :: (p :-> Ran q r) -> Procompose p q :-> r
instance Data.Profunctor.Monad.ProfunctorFunctor (Data.Profunctor.Ran.Ran p)
instance Control.Category.Category p => Data.Profunctor.Monad.ProfunctorComonad (Data.Profunctor.Ran.Ran p)
instance (Data.Profunctor.Unsafe.Profunctor p, Data.Profunctor.Unsafe.Profunctor q) => Data.Profunctor.Unsafe.Profunctor (Data.Profunctor.Ran.Ran p q)
instance Data.Profunctor.Unsafe.Profunctor q => GHC.Base.Functor (Data.Profunctor.Ran.Ran p q a)
instance (p ~ q) => Control.Category.Category (Data.Profunctor.Ran.Ran p q)


module Data.Profunctor.Tambara
newtype Tambara p a b
Tambara :: (forall c. p (a, c) (b, c)) -> Tambara p a b
[runTambara] :: Tambara p a b -> forall c. p (a, c) (b, c)

-- | <pre>
--   <a>tambara</a> <a>.</a> <a>untambara</a> ≡ <a>id</a>
--   <a>untambara</a> <a>.</a> <a>tambara</a> ≡ <a>id</a>
--   </pre>
tambara :: Strong p => (p :-> q) -> p :-> Tambara q

-- | <pre>
--   <a>tambara</a> <a>.</a> <a>untambara</a> ≡ <a>id</a>
--   <a>untambara</a> <a>.</a> <a>tambara</a> ≡ <a>id</a>
--   </pre>
untambara :: Profunctor q => (p :-> Tambara q) -> p :-> q

-- | Pastro -| Tambara
--   
--   <pre>
--   Pastro p ~ exists z. Costar ((,)z) <tt>Procompose</tt> p <tt>Procompose</tt> Star ((,)z)
--   </pre>
data Pastro p a b
Pastro :: ((y, z) -> b) -> p x y -> (a -> (x, z)) -> Pastro p a b

-- | Cotambara is freely adjoins respect for cocartesian structure to a
--   profunctor
--   
--   Note: this is not dual to <a>Tambara</a>. It is <a>Tambara</a> with
--   respect to a different tensor.
newtype Cotambara p a b
Cotambara :: (forall c. p (Either a c) (Either b c)) -> Cotambara p a b
[runCotambara] :: Cotambara p a b -> forall c. p (Either a c) (Either b c)

-- | <pre>
--   <a>cotambara</a> <a>.</a> <a>uncotambara</a> ≡ <a>id</a>
--   <a>uncotambara</a> <a>.</a> <a>cotambara</a> ≡ <a>id</a>
--   </pre>
cotambara :: Choice p => (p :-> q) -> p :-> Cotambara q

-- | <pre>
--   <a>cotambara</a> <a>.</a> <a>uncotambara</a> ≡ <a>id</a>
--   <a>uncotambara</a> <a>.</a> <a>cotambara</a> ≡ <a>id</a>
--   </pre>
uncotambara :: Profunctor q => (p :-> Cotambara q) -> p :-> q

-- | Copastro -| Cotambara
data Copastro p a b
Copastro :: (Either y z -> b) -> p x y -> (a -> Either x z) -> Copastro p a b
instance Data.Profunctor.Unsafe.Profunctor p => Data.Profunctor.Unsafe.Profunctor (Data.Profunctor.Tambara.Tambara p)
instance Data.Profunctor.Monad.ProfunctorFunctor Data.Profunctor.Tambara.Tambara
instance Data.Profunctor.Monad.ProfunctorComonad Data.Profunctor.Tambara.Tambara
instance Data.Profunctor.Unsafe.Profunctor p => Data.Profunctor.Strong (Data.Profunctor.Tambara.Tambara p)
instance Data.Profunctor.Choice p => Data.Profunctor.Choice (Data.Profunctor.Tambara.Tambara p)
instance Control.Category.Category p => Control.Category.Category (Data.Profunctor.Tambara.Tambara p)
instance Control.Arrow.Arrow p => Control.Arrow.Arrow (Data.Profunctor.Tambara.Tambara p)
instance Control.Arrow.ArrowChoice p => Control.Arrow.ArrowChoice (Data.Profunctor.Tambara.Tambara p)
instance Control.Arrow.ArrowApply p => Control.Arrow.ArrowApply (Data.Profunctor.Tambara.Tambara p)
instance Control.Arrow.ArrowLoop p => Control.Arrow.ArrowLoop (Data.Profunctor.Tambara.Tambara p)
instance Control.Arrow.ArrowZero p => Control.Arrow.ArrowZero (Data.Profunctor.Tambara.Tambara p)
instance Control.Arrow.ArrowPlus p => Control.Arrow.ArrowPlus (Data.Profunctor.Tambara.Tambara p)
instance Data.Profunctor.Unsafe.Profunctor p => GHC.Base.Functor (Data.Profunctor.Tambara.Tambara p a)
instance (Data.Profunctor.Unsafe.Profunctor p, Control.Arrow.Arrow p) => GHC.Base.Applicative (Data.Profunctor.Tambara.Tambara p a)
instance (Data.Profunctor.Unsafe.Profunctor p, Control.Arrow.ArrowPlus p) => GHC.Base.Alternative (Data.Profunctor.Tambara.Tambara p a)
instance (Data.Profunctor.Unsafe.Profunctor p, Control.Arrow.ArrowPlus p) => GHC.Base.Monoid (Data.Profunctor.Tambara.Tambara p a b)
instance Data.Profunctor.Unsafe.Profunctor p => Data.Profunctor.Unsafe.Profunctor (Data.Profunctor.Tambara.Pastro p)
instance Data.Profunctor.Monad.ProfunctorFunctor Data.Profunctor.Tambara.Pastro
instance Data.Profunctor.Monad.ProfunctorMonad Data.Profunctor.Tambara.Pastro
instance Data.Profunctor.Adjunction.ProfunctorAdjunction Data.Profunctor.Tambara.Pastro Data.Profunctor.Tambara.Tambara
instance Data.Profunctor.Monad.ProfunctorFunctor Data.Profunctor.Tambara.Cotambara
instance Data.Profunctor.Monad.ProfunctorComonad Data.Profunctor.Tambara.Cotambara
instance Data.Profunctor.Unsafe.Profunctor p => Data.Profunctor.Unsafe.Profunctor (Data.Profunctor.Tambara.Cotambara p)
instance Data.Profunctor.Unsafe.Profunctor p => Data.Profunctor.Choice (Data.Profunctor.Tambara.Cotambara p)
instance Control.Category.Category p => Control.Category.Category (Data.Profunctor.Tambara.Cotambara p)
instance Data.Profunctor.Unsafe.Profunctor p => GHC.Base.Functor (Data.Profunctor.Tambara.Cotambara p a)
instance Data.Profunctor.Unsafe.Profunctor p => Data.Profunctor.Unsafe.Profunctor (Data.Profunctor.Tambara.Copastro p)
instance Data.Profunctor.Adjunction.ProfunctorAdjunction Data.Profunctor.Tambara.Copastro Data.Profunctor.Tambara.Cotambara
instance Data.Profunctor.Monad.ProfunctorFunctor Data.Profunctor.Tambara.Copastro
instance Data.Profunctor.Monad.ProfunctorMonad Data.Profunctor.Tambara.Copastro