monoidal-functors-0.3.0.0: src/Data/Bifunctor/Module.hs

module Data.Bifunctor.Module
  ( -- * LeftModule
    LeftModule (..),

    -- * RightModule
    RightModule (..),

    -- * Bimodule
    Bimodule,

    -- * LeftCoModule
    LeftCoModule (..),

    -- * RightCoModule
    RightCoModule (..),

    -- * CoBimodule
    CoBimodule,
  )
where

--------------------------------------------------------------------------------

import Control.Applicative (Applicative)
import Control.Arrow (Arrow, ArrowChoice, ArrowLoop, Kleisli (..))
import Control.Category.Tensor (GBifunctor (..))
import Control.Comonad (Cokleisli, Comonad)
import Control.Monad (Functor, Monad)
import Control.Monad.Fix (MonadFix)
import Data.Bifunctor (Bifunctor)
import Data.Bifunctor.Clown (Clown)
import Data.Bifunctor.Joker (Joker)
import Data.Bifunctor.Product (Product)
import Data.Bifunctor.Sum (Sum)
import Data.Bifunctor.Tannen (Tannen)
import Data.Either (Either (..))
import Data.Functor.Const (Const (..))
import Data.Functor.Contravariant (Contravariant, Op (..))
import Data.Kind (Type)
import Data.Monoid (Monoid)
import Data.Profunctor
import Data.Profunctor.Cayley (Cayley)
import Data.Profunctor.Choice (CopastroSum, CotambaraSum, PastroSum, TambaraSum)
import Data.Profunctor.Closed (Closure)
import Data.Profunctor.Composition (Procompose)
import Data.Profunctor.Mapping (CofreeMapping, FreeMapping)
import Data.Profunctor.Rep (Corepresentable)
import Data.Profunctor.Strong (Copastro, Pastro, Tambara)
import Data.Profunctor.Traversing (CofreeTraversing, FreeTraversing)
import Data.Profunctor.Yoneda (Coyoneda, Yoneda)
import Data.Semigroup (Arg)
import Data.Tagged (Tagged)
import Data.These (These (That, This))
import Data.Traversable (Traversable)
import Data.Tuple (fst, snd)
import GHC.Generics (K1 (..))

--------------------------------------------------------------------------------

-- $setup
-- >>> :set -dppr-cols=1000
-- >>> import Prelude

--------------------------------------------------------------------------------

-- | Boilerplate newtype to derive modules for any 'Profunctor'.
newtype FromProfunctor p a b = FromProfunctor (p a b)
  deriving newtype (Functor, Profunctor, Strong, Choice, Costrong, Cochoice)

-- | Boilerplate newtype to derive modules for any 'Bifunctor'.
newtype FromBifunctor p a b = FromBifunctor (p a b)
  deriving newtype (Functor, Bifunctor)

--------------------------------------------------------------------------------

-- | A 'Profunctor' \(P : \mathcal{C_1}^{op} \times \mathcal{C_2} \to Set\)
-- is a Tambara 'LeftModule' if it is equipped with a morphism \(s_{a,b,m} : P(a, b) \to P(a \odot m, b \odot m)\),
-- which we call 'lstrength'.
--
-- === Laws
--
-- @
-- 'Types.lmap' 'Control.Category.Cartesian.projl' ≡ 'Types.rmap' 'Control.Category.Cartesian.projl' 'Control.Category..' 'lstrength'
-- 'Data.Profunctor.Types.lmap' ('rstrength' @f@) 'Control.Category..' 'lstrength' ≡ 'Data.Profunctor.Types.rmap' ('rstrength' @f@) 'Control.Category..' 'lstrength'
-- 'lstrength' 'Control.Category..' 'lstrength' ≡ 'Types.dimap' ('Control.Category.Tensor.bwd' 'Control.Category.Tensor.assoc') ('Control.Category.Tensor.fwd' 'Control.Category.Tensor.assoc') 'Control.Category..' 'lstrength'
-- @
class LeftModule cat tC1 tC2 p where
  -- | ==== __Examples__
  --
  -- 'Data.Profiunctor.Strong.first'':
  --
  -- >>> :t lstrength @(->) @(,) @(,)
  -- lstrength @(->) @(,) @(,) :: LeftModule (->) (,) (,) p => p a b -> p (a, x) (b, x)
  --
  -- 'Data.Profiunctor.Choice.left'':
  --
  -- >>> :t lstrength @(->) @Either @Either
  -- lstrength @(->) @Either @Either :: LeftModule (->) Either Either p => p a b -> p (Either a x) (Either b x)
  lstrength :: cat (p a b) (p (tC1 a x) (tC2 b x))

instance (Strong p) => LeftModule (->) (,) (,) (FromProfunctor p) where
  lstrength :: FromProfunctor p a b -> FromProfunctor p (a, x) (b, x)
  lstrength = first'

instance (Choice p) => LeftModule (->) Either Either (FromProfunctor p) where
  lstrength :: FromProfunctor p a b -> FromProfunctor p (Either a x) (Either b x)
  lstrength = left'

instance (Bifunctor p) => LeftModule (->) Either Either (FromBifunctor p) where
  lstrength :: FromBifunctor p a b -> FromBifunctor p (Either a x) (Either b x)
  lstrength = gbimap Left Left

instance (Bifunctor p) => LeftModule (->) These These (FromBifunctor p) where
  lstrength :: FromBifunctor p a b -> FromBifunctor p (These a x) (These b x)
  lstrength = gbimap This This

instance (Bifunctor p) => LeftModule Op (,) (,) (FromBifunctor p) where
  lstrength :: Op (FromBifunctor p a b) (FromBifunctor p (a, x) (b, x))
  lstrength = Op (gbimap fst fst)

deriving via (FromProfunctor (Kleisli m)) instance (Monad m) => LeftModule (->) (,) (,) (Kleisli m)

deriving via (FromProfunctor (Pastro p)) instance LeftModule (->) (,) (,) (Pastro p)

deriving via (FromProfunctor (Tambara p)) instance (Profunctor p) => LeftModule (->) (,) (,) (Tambara p)

deriving via (FromProfunctor (Closure p)) instance (Strong p) => LeftModule (->) (,) (,) (Closure p)

deriving via (FromProfunctor (FreeTraversing p)) instance LeftModule (->) (,) (,) (FreeTraversing p)

deriving via (FromProfunctor (CofreeTraversing p)) instance (Profunctor p) => LeftModule (->) (,) (,) (CofreeTraversing p)

deriving via (FromProfunctor (FreeMapping p)) instance LeftModule (->) (,) (,) (FreeMapping p)

deriving via (FromProfunctor (CofreeMapping p)) instance (Profunctor p) => LeftModule (->) (,) (,) (CofreeMapping p)

deriving via (FromProfunctor (Coyoneda p)) instance (Strong p) => LeftModule (->) (,) (,) (Coyoneda p)

deriving via (FromProfunctor (Yoneda p)) instance (Strong p) => LeftModule (->) (,) (,) (Yoneda p)

deriving via (FromProfunctor (->)) instance LeftModule (->) (,) (,) (->)

deriving via (FromProfunctor (Forget r)) instance LeftModule (->) (,) (,) (Forget r)

deriving via (FromProfunctor (Star m)) instance (Functor m) => LeftModule (->) (,) (,) (Star m)

deriving via (FromProfunctor (Clown f)) instance (Contravariant f) => LeftModule (->) (,) (,) (Clown f)

deriving via (FromProfunctor (WrappedArrow p)) instance (Arrow p) => LeftModule (->) (,) (,) (WrappedArrow p)

deriving via (FromProfunctor (Sum p q)) instance (Strong p, Strong q) => LeftModule (->) (,) (,) (Sum p q)

deriving via (FromProfunctor (Product p q)) instance (Strong p, Strong q) => LeftModule (->) (,) (,) (Product p q)

deriving via (FromProfunctor (Tannen f q)) instance (Functor f, Strong q) => LeftModule (->) (,) (,) (Tannen f q)

deriving via (FromProfunctor (Procompose p q)) instance (Strong p, Strong q) => LeftModule (->) (,) (,) (Procompose p q)

deriving via (FromProfunctor (Cayley f q)) instance (Functor f, Strong q) => LeftModule (->) (,) (,) (Cayley f q)

deriving via (FromProfunctor (Kleisli m)) instance (Monad m) => LeftModule (->) Either Either (Kleisli m)

deriving via (FromProfunctor Tagged) instance LeftModule (->) Either Either Tagged

deriving via (FromProfunctor (Tambara p)) instance (Choice p) => LeftModule (->) Either Either (Tambara p)

deriving via (FromProfunctor (PastroSum p)) instance LeftModule (->) Either Either (PastroSum p)

deriving via (FromProfunctor (TambaraSum p)) instance (Profunctor p) => LeftModule (->) Either Either (TambaraSum p)

deriving via (FromProfunctor (FreeTraversing p)) instance LeftModule (->) Either Either (FreeTraversing p)

deriving via (FromProfunctor (CofreeTraversing p)) instance (Profunctor p) => LeftModule (->) Either Either (CofreeTraversing p)

deriving via (FromProfunctor (FreeMapping p)) instance LeftModule (->) Either Either (FreeMapping p)

deriving via (FromProfunctor (CofreeMapping p)) instance (Profunctor p) => LeftModule (->) Either Either (CofreeMapping p)

deriving via (FromProfunctor (Coyoneda p)) instance (Choice p) => LeftModule (->) Either Either (Coyoneda p)

deriving via (FromProfunctor (Yoneda p)) instance (Choice p) => LeftModule (->) Either Either (Yoneda p)

deriving via (FromProfunctor (->)) instance LeftModule (->) Either Either (->)

deriving via (FromProfunctor (Cokleisli w)) instance (Comonad w) => LeftModule (->) Either Either (Cokleisli w)

deriving via (FromProfunctor (Forget r)) instance (Monoid r) => LeftModule (->) Either Either (Forget r)

deriving via (FromProfunctor (Star f)) instance (Applicative f) => LeftModule (->) Either Either (Star f)

deriving via (FromProfunctor (Joker f)) instance (Functor f) => LeftModule (->) Either Either (Joker f)

deriving via (FromProfunctor (WrappedArrow p)) instance (ArrowChoice p) => LeftModule (->) Either Either (WrappedArrow p)

deriving via (FromProfunctor (Sum p q)) instance (Choice p, Choice q) => LeftModule (->) Either Either (Sum p q)

deriving via (FromProfunctor (Product p q)) instance (Choice p, Choice q) => LeftModule (->) Either Either (Product p q)

deriving via (FromProfunctor (Tannen f p)) instance (Functor f, Choice p) => LeftModule (->) Either Either (Tannen f p)

deriving via (FromProfunctor (Procompose p q)) instance (Choice p, Choice q) => LeftModule (->) Either Either (Procompose p q)

deriving via (FromProfunctor (Cayley f q)) instance (Functor f, Choice q) => LeftModule (->) Either Either (Cayley f q)

deriving via (FromBifunctor Arg) instance LeftModule (->) Either Either Arg

deriving via (FromBifunctor Const) instance LeftModule (->) Either Either Const

deriving via (FromBifunctor Either) instance LeftModule (->) Either Either Either

deriving via (FromBifunctor These) instance LeftModule (->) Either Either These

deriving via (FromBifunctor (K1 i)) instance LeftModule (->) Either Either (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance LeftModule (->) Either Either (,)

deriving via (FromBifunctor ((,,) x1)) instance LeftModule (->) Either Either ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance LeftModule (->) Either Either ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance LeftModule (->) Either Either ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance LeftModule (->) Either Either ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance LeftModule (->) Either Either ((,,,,,,) x1 x2 x3 x4 x5)

deriving via (FromBifunctor Arg) instance LeftModule (->) These These Arg

deriving via (FromBifunctor Const) instance LeftModule (->) These These Const

deriving via (FromBifunctor Either) instance LeftModule (->) These These Either

deriving via (FromBifunctor These) instance LeftModule (->) These These These

deriving via (FromBifunctor (K1 i)) instance LeftModule (->) These These (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance LeftModule (->) These These (,)

deriving via (FromBifunctor ((,,) x1)) instance LeftModule (->) These These ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance LeftModule (->) These These ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance LeftModule (->) These These ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance LeftModule (->) These These ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance LeftModule (->) These These ((,,,,,,) x1 x2 x3 x4 x5)

deriving via (FromBifunctor Arg) instance LeftModule Op (,) (,) Arg

deriving via (FromBifunctor Const) instance LeftModule Op (,) (,) Const

deriving via (FromBifunctor Either) instance LeftModule Op (,) (,) Either

deriving via (FromBifunctor These) instance LeftModule Op (,) (,) These

deriving via (FromBifunctor (K1 i)) instance LeftModule Op (,) (,) (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance LeftModule Op (,) (,) (,)

deriving via (FromBifunctor ((,,) x1)) instance LeftModule Op (,) (,) ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance LeftModule Op (,) (,) ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance LeftModule Op (,) (,) ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance LeftModule Op (,) (,) ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance LeftModule Op (,) (,) ((,,,,,,) x1 x2 x3 x4 x5)

--------------------------------------------------------------------------------

-- | A 'Profunctor' \(P : \mathcal{C_1}^{op} \times \mathcal{C_2} \to Set\)
-- is a Tambara 'RightModule' if it is equipped with a morphism \(s_{a,b,m} : P(a, b) \to P(m \odot a, m \odot b)\),
-- which we call 'rstrength'.
--
-- === Laws
--
-- @
-- 'Data.Profunctor.Types.lmap' 'Control.Category.Cartesian.projr' ≡ 'Data.Profunctor.Types.rmap' 'Control.Category.Cartesian.projr' 'Control.Category..' 'rstrength'
-- 'Data.Profunctor.Types.lmap' ('lstrength' @f@) 'Control.Category..' 'rstrength' ≡ 'Data.Profunctor.Types.rmap' ('lstrength' @f@) 'Control.Category..' 'rstrength'
-- 'rstrength' 'Control.Category..' 'rstrength' ≡  'Data.Profunctor.Types.dimap' ('Control.Category.Tensor.fwd' 'Control.Category.Tensor.assoc') ('Control.Category.Tensor.bwd' 'Control.Category.Tensor.assoc') 'Control.Category..' 'rstrength'
-- @
class RightModule cat tC1 tC2 f where
  -- | ==== __Examples__
  --
  -- 'Data.Profunctor.Strong.second'':
  --
  -- >>>  :t rstrength @(->) @(,) @(,)
  -- rstrength @(->) @(,) @(,) :: RightModule (->) (,) (,) f => f a b -> f (x, a) (x, b)
  --
  -- 'Data.Profunctor.Choice.right'':
  --
  -- >>> :t rstrength @(->) @Either @Either
  -- rstrength @(->) @Either @Either :: RightModule (->) Either Either f => f a b -> f (Either x a) (Either x b)
  rstrength :: cat (f a b) (f (x `tC1` a) (x `tC2` b))

instance (Strong p) => RightModule (->) (,) (,) (FromProfunctor p) where
  rstrength :: FromProfunctor p a b -> FromProfunctor p (c, a) (c, b)
  rstrength = second'

instance (Choice p) => RightModule (->) Either Either (FromProfunctor p) where
  rstrength :: FromProfunctor p a b -> FromProfunctor p (Either c a) (Either c b)
  rstrength = right'

instance (Bifunctor p) => RightModule (->) Either Either (FromBifunctor p) where
  rstrength :: FromBifunctor p a b -> FromBifunctor p (Either x a) (Either x b)
  rstrength = gbimap Right Right

instance (Bifunctor p) => RightModule (->) These These (FromBifunctor p) where
  rstrength :: FromBifunctor p a b -> FromBifunctor p (These x a) (These x b)
  rstrength = gbimap That That

instance (Bifunctor p) => RightModule Op (,) (,) (FromBifunctor p) where
  rstrength :: Op (FromBifunctor p a b) (FromBifunctor p (x, a) (x, b))
  rstrength = Op (gbimap snd snd)

deriving via (FromProfunctor (Kleisli m)) instance (Monad m) => RightModule (->) (,) (,) (Kleisli m)

deriving via (FromProfunctor (Pastro p)) instance RightModule (->) (,) (,) (Pastro p)

deriving via (FromProfunctor (Tambara p)) instance (Profunctor p) => RightModule (->) (,) (,) (Tambara p)

deriving via (FromProfunctor (Closure p)) instance (Strong p) => RightModule (->) (,) (,) (Closure p)

deriving via (FromProfunctor (FreeTraversing p)) instance RightModule (->) (,) (,) (FreeTraversing p)

deriving via (FromProfunctor (CofreeTraversing p)) instance (Profunctor p) => RightModule (->) (,) (,) (CofreeTraversing p)

deriving via (FromProfunctor (FreeMapping p)) instance RightModule (->) (,) (,) (FreeMapping p)

deriving via (FromProfunctor (CofreeMapping p)) instance (Profunctor p) => RightModule (->) (,) (,) (CofreeMapping p)

deriving via (FromProfunctor (Coyoneda p)) instance (Strong p) => RightModule (->) (,) (,) (Coyoneda p)

deriving via (FromProfunctor (Yoneda p)) instance (Strong p) => RightModule (->) (,) (,) (Yoneda p)

deriving via (FromProfunctor (->)) instance RightModule (->) (,) (,) (->)

deriving via (FromProfunctor (Forget r)) instance RightModule (->) (,) (,) (Forget r)

deriving via (FromProfunctor (Star m)) instance (Functor m) => RightModule (->) (,) (,) (Star m)

deriving via (FromProfunctor (Clown f)) instance (Contravariant f) => RightModule (->) (,) (,) (Clown f)

deriving via (FromProfunctor (WrappedArrow p)) instance (Arrow p) => RightModule (->) (,) (,) (WrappedArrow p)

deriving via (FromProfunctor (Sum p q)) instance (Strong p, Strong q) => RightModule (->) (,) (,) (Sum p q)

deriving via (FromProfunctor (Product p q)) instance (Strong p, Strong q) => RightModule (->) (,) (,) (Product p q)

deriving via (FromProfunctor (Tannen f q)) instance (Functor f, Strong q) => RightModule (->) (,) (,) (Tannen f q)

deriving via (FromProfunctor (Procompose p q)) instance (Strong p, Strong q) => RightModule (->) (,) (,) (Procompose p q)

deriving via (FromProfunctor (Cayley f q)) instance (Functor f, Strong q) => RightModule (->) (,) (,) (Cayley f q)

deriving via (FromProfunctor (Kleisli m)) instance (Monad m) => RightModule (->) Either Either (Kleisli m)

deriving via (FromProfunctor Tagged) instance RightModule (->) Either Either Tagged

deriving via (FromProfunctor (Tambara p)) instance (Choice p) => RightModule (->) Either Either (Tambara p)

deriving via (FromProfunctor (PastroSum p)) instance RightModule (->) Either Either (PastroSum p)

deriving via (FromProfunctor (TambaraSum p)) instance (Profunctor p) => RightModule (->) Either Either (TambaraSum p)

deriving via (FromProfunctor (FreeTraversing p)) instance RightModule (->) Either Either (FreeTraversing p)

deriving via (FromProfunctor (CofreeTraversing p)) instance (Profunctor p) => RightModule (->) Either Either (CofreeTraversing p)

deriving via (FromProfunctor (FreeMapping p)) instance RightModule (->) Either Either (FreeMapping p)

deriving via (FromProfunctor (CofreeMapping p)) instance (Profunctor p) => RightModule (->) Either Either (CofreeMapping p)

deriving via (FromProfunctor (Coyoneda p)) instance (Choice p) => RightModule (->) Either Either (Coyoneda p)

deriving via (FromProfunctor (Yoneda p)) instance (Choice p) => RightModule (->) Either Either (Yoneda p)

deriving via (FromProfunctor (->)) instance RightModule (->) Either Either (->)

deriving via (FromProfunctor (Cokleisli w)) instance (Comonad w) => RightModule (->) Either Either (Cokleisli w)

deriving via (FromProfunctor (Forget r)) instance (Monoid r) => RightModule (->) Either Either (Forget r)

deriving via (FromProfunctor (Star f)) instance (Applicative f) => RightModule (->) Either Either (Star f)

deriving via (FromProfunctor (Joker f)) instance (Functor f) => RightModule (->) Either Either (Joker f)

deriving via (FromProfunctor (WrappedArrow p)) instance (ArrowChoice p) => RightModule (->) Either Either (WrappedArrow p)

deriving via (FromProfunctor (Sum p q)) instance (Choice p, Choice q) => RightModule (->) Either Either (Sum p q)

deriving via (FromProfunctor (Product p q)) instance (Choice p, Choice q) => RightModule (->) Either Either (Product p q)

deriving via (FromProfunctor (Tannen f p)) instance (Functor f, Choice p) => RightModule (->) Either Either (Tannen f p)

deriving via (FromProfunctor (Procompose p q)) instance (Choice p, Choice q) => RightModule (->) Either Either (Procompose p q)

deriving via (FromProfunctor (Cayley f q)) instance (Functor f, Choice q) => RightModule (->) Either Either (Cayley f q)

deriving via (FromBifunctor Arg) instance RightModule (->) Either Either Arg

deriving via (FromBifunctor Const) instance RightModule (->) Either Either Const

deriving via (FromBifunctor Either) instance RightModule (->) Either Either Either

deriving via (FromBifunctor These) instance RightModule (->) Either Either These

deriving via (FromBifunctor (K1 i)) instance RightModule (->) Either Either (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance RightModule (->) Either Either (,)

deriving via (FromBifunctor ((,,) x1)) instance RightModule (->) Either Either ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance RightModule (->) Either Either ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance RightModule (->) Either Either ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance RightModule (->) Either Either ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance RightModule (->) Either Either ((,,,,,,) x1 x2 x3 x4 x5)

deriving via (FromBifunctor Arg) instance RightModule (->) These These Arg

deriving via (FromBifunctor Const) instance RightModule (->) These These Const

deriving via (FromBifunctor Either) instance RightModule (->) These These Either

deriving via (FromBifunctor These) instance RightModule (->) These These These

deriving via (FromBifunctor (K1 i)) instance RightModule (->) These These (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance RightModule (->) These These (,)

deriving via (FromBifunctor ((,,) x1)) instance RightModule (->) These These ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance RightModule (->) These These ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance RightModule (->) These These ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance RightModule (->) These These ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance RightModule (->) These These ((,,,,,,) x1 x2 x3 x4 x5)

deriving via (FromBifunctor Arg) instance RightModule Op (,) (,) Arg

deriving via (FromBifunctor Const) instance RightModule Op (,) (,) Const

deriving via (FromBifunctor Either) instance RightModule Op (,) (,) Either

deriving via (FromBifunctor These) instance RightModule Op (,) (,) These

deriving via (FromBifunctor (K1 i)) instance RightModule Op (,) (,) (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance RightModule Op (,) (,) (,)

deriving via (FromBifunctor ((,,) x1)) instance RightModule Op (,) (,) ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance RightModule Op (,) (,) ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance RightModule Op (,) (,) ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance RightModule Op (,) (,) ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance RightModule Op (,) (,) ((,,,,,,) x1 x2 x3 x4 x5)

--------------------------------------------------------------------------------

-- | A 'Profunctor' equipped with both a Tambara 'LeftModule' and
-- Tambara 'RightModule' is a 'Bimodule'.
--
-- === Laws
--
-- @
-- 'rstrength' ≡ 'Data.Profunctor.Types.dimap' 'Control.Category.Tensor.swap' 'Control.Category.Tensor.swap' 'Control.Category..' 'lstrength'
-- 'lstrength' ≡ 'Data.Profunctor.Types.dimap' 'Control.Category.Tensor.swap' 'Control.Category.Tensor.swap' 'Control.Category..' 'rstrength'
-- @
class (LeftModule cat tC1 tC2 f, RightModule cat tC1 tC2 f) => Bimodule cat tC1 tC2 f

instance (Strong p) => Bimodule (->) (,) (,) (FromProfunctor p)

instance (Choice p) => Bimodule (->) Either Either (FromProfunctor p)

instance (Bifunctor p) => Bimodule (->) Either Either (FromBifunctor p)

instance (Bifunctor p) => Bimodule (->) These These (FromBifunctor p)

instance (Bifunctor p) => Bimodule Op (,) (,) (FromBifunctor p)

deriving via (FromProfunctor (Kleisli m)) instance (Monad m) => Bimodule (->) (,) (,) (Kleisli m)

deriving via (FromProfunctor (Pastro p)) instance Bimodule (->) (,) (,) (Pastro p)

deriving via (FromProfunctor (Tambara p)) instance (Profunctor p) => Bimodule (->) (,) (,) (Tambara p)

deriving via (FromProfunctor (Closure p)) instance (Strong p) => Bimodule (->) (,) (,) (Closure p)

deriving via (FromProfunctor (FreeTraversing p)) instance Bimodule (->) (,) (,) (FreeTraversing p)

deriving via (FromProfunctor (CofreeTraversing p)) instance (Profunctor p) => Bimodule (->) (,) (,) (CofreeTraversing p)

deriving via (FromProfunctor (FreeMapping p)) instance Bimodule (->) (,) (,) (FreeMapping p)

deriving via (FromProfunctor (CofreeMapping p)) instance (Profunctor p) => Bimodule (->) (,) (,) (CofreeMapping p)

deriving via (FromProfunctor (Coyoneda p)) instance (Strong p) => Bimodule (->) (,) (,) (Coyoneda p)

deriving via (FromProfunctor (Yoneda p)) instance (Strong p) => Bimodule (->) (,) (,) (Yoneda p)

deriving via (FromProfunctor (->)) instance Bimodule (->) (,) (,) (->)

deriving via (FromProfunctor (Forget r)) instance Bimodule (->) (,) (,) (Forget r)

deriving via (FromProfunctor (Star m)) instance (Functor m) => Bimodule (->) (,) (,) (Star m)

deriving via (FromProfunctor (Clown f)) instance (Contravariant f) => Bimodule (->) (,) (,) (Clown f)

deriving via (FromProfunctor (WrappedArrow p)) instance (Arrow p) => Bimodule (->) (,) (,) (WrappedArrow p)

deriving via (FromProfunctor (Sum p q)) instance (Strong p, Strong q) => Bimodule (->) (,) (,) (Sum p q)

deriving via (FromProfunctor (Product p q)) instance (Strong p, Strong q) => Bimodule (->) (,) (,) (Product p q)

deriving via (FromProfunctor (Tannen f q)) instance (Functor f, Strong q) => Bimodule (->) (,) (,) (Tannen f q)

deriving via (FromProfunctor (Procompose p q)) instance (Strong p, Strong q) => Bimodule (->) (,) (,) (Procompose p q)

deriving via (FromProfunctor (Cayley f q)) instance (Functor f, Strong q) => Bimodule (->) (,) (,) (Cayley f q)

deriving via (FromProfunctor (Kleisli m)) instance (Monad m) => Bimodule (->) Either Either (Kleisli m)

deriving via (FromProfunctor Tagged) instance Bimodule (->) Either Either Tagged

deriving via (FromProfunctor (Tambara p)) instance (Choice p) => Bimodule (->) Either Either (Tambara p)

deriving via (FromProfunctor (PastroSum p)) instance Bimodule (->) Either Either (PastroSum p)

deriving via (FromProfunctor (TambaraSum p)) instance (Profunctor p) => Bimodule (->) Either Either (TambaraSum p)

deriving via (FromProfunctor (FreeTraversing p)) instance Bimodule (->) Either Either (FreeTraversing p)

deriving via (FromProfunctor (CofreeTraversing p)) instance (Profunctor p) => Bimodule (->) Either Either (CofreeTraversing p)

deriving via (FromProfunctor (FreeMapping p)) instance Bimodule (->) Either Either (FreeMapping p)

deriving via (FromProfunctor (CofreeMapping p)) instance (Profunctor p) => Bimodule (->) Either Either (CofreeMapping p)

deriving via (FromProfunctor (Coyoneda p)) instance (Choice p) => Bimodule (->) Either Either (Coyoneda p)

deriving via (FromProfunctor (Yoneda p)) instance (Choice p) => Bimodule (->) Either Either (Yoneda p)

deriving via (FromProfunctor (->)) instance Bimodule (->) Either Either (->)

deriving via (FromProfunctor (Cokleisli w)) instance (Comonad w) => Bimodule (->) Either Either (Cokleisli w)

deriving via (FromProfunctor (Forget r)) instance (Monoid r) => Bimodule (->) Either Either (Forget r)

deriving via (FromProfunctor (Star f)) instance (Applicative f) => Bimodule (->) Either Either (Star f)

deriving via (FromProfunctor (Joker f)) instance (Functor f) => Bimodule (->) Either Either (Joker f)

deriving via (FromProfunctor (WrappedArrow p)) instance (ArrowChoice p) => Bimodule (->) Either Either (WrappedArrow p)

deriving via (FromProfunctor (Sum p q)) instance (Choice p, Choice q) => Bimodule (->) Either Either (Sum p q)

deriving via (FromProfunctor (Product p q)) instance (Choice p, Choice q) => Bimodule (->) Either Either (Product p q)

deriving via (FromProfunctor (Tannen f p)) instance (Functor f, Choice p) => Bimodule (->) Either Either (Tannen f p)

deriving via (FromProfunctor (Procompose p q)) instance (Choice p, Choice q) => Bimodule (->) Either Either (Procompose p q)

deriving via (FromProfunctor (Cayley f q)) instance (Functor f, Choice q) => Bimodule (->) Either Either (Cayley f q)

deriving via (FromBifunctor Arg) instance Bimodule (->) Either Either Arg

deriving via (FromBifunctor Const) instance Bimodule (->) Either Either Const

deriving via (FromBifunctor Either) instance Bimodule (->) Either Either Either

deriving via (FromBifunctor These) instance Bimodule (->) Either Either These

deriving via (FromBifunctor (K1 i)) instance Bimodule (->) Either Either (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance Bimodule (->) Either Either (,)

deriving via (FromBifunctor ((,,) x1)) instance Bimodule (->) Either Either ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance Bimodule (->) Either Either ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance Bimodule (->) Either Either ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance Bimodule (->) Either Either ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance Bimodule (->) Either Either ((,,,,,,) x1 x2 x3 x4 x5)

deriving via (FromBifunctor Arg) instance Bimodule (->) These These Arg

deriving via (FromBifunctor Const) instance Bimodule (->) These These Const

deriving via (FromBifunctor Either) instance Bimodule (->) These These Either

deriving via (FromBifunctor These) instance Bimodule (->) These These These

deriving via (FromBifunctor (K1 i)) instance Bimodule (->) These These (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance Bimodule (->) These These (,)

deriving via (FromBifunctor ((,,) x1)) instance Bimodule (->) These These ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance Bimodule (->) These These ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance Bimodule (->) These These ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance Bimodule (->) These These ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance Bimodule (->) These These ((,,,,,,) x1 x2 x3 x4 x5)

deriving via (FromBifunctor Arg) instance Bimodule Op (,) (,) Arg

deriving via (FromBifunctor Const) instance Bimodule Op (,) (,) Const

deriving via (FromBifunctor Either) instance Bimodule Op (,) (,) Either

deriving via (FromBifunctor These) instance Bimodule Op (,) (,) These

deriving via (FromBifunctor (K1 i)) instance Bimodule Op (,) (,) (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance Bimodule Op (,) (,) (,)

deriving via (FromBifunctor ((,,) x1)) instance Bimodule Op (,) (,) ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance Bimodule Op (,) (,) ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance Bimodule Op (,) (,) ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance Bimodule Op (,) (,) ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance Bimodule Op (,) (,) ((,,,,,,) x1 x2 x3 x4 x5)

--------------------------------------------------------------------------------

-- | A 'Profunctor' \(P : \mathcal{C_1}^{op} \times \mathcal{C_2} \to Set\)
-- is a Tambara 'LeftCoModule' if it is equipped with a morphism \(s^{-1}_{a,b,m} : P(a \odot m, a \odot m) \to P(a, b) \),
-- which we call 'lcostrength'.
--
-- === Laws
--
-- @
-- 'Data.Profunctor.Types.Data.Profunctor.Types.lmap' 'Control.Category.Cartesian.incll' ≡ 'lcostrength' 'Control.Category..' 'Data.Profunctor.Types.rmap' 'Control.Category.Cartesian.incll'
-- 'lcostrength' 'Control.Category..' 'Data.Profunctor.Types.lmap' ('rstrength' f) ≡ 'lcostrength' 'Control.Category..' 'Data.Profunctor.Types.rmap' ('rstrength' f)
-- 'lcostrength' 'Control.Category..' 'lcostrength' ≡  'lcostrength' 'Control.Category..' 'Data.Profunctor.Types.dimap' ('Control.Category.Tensor.fwd' 'Control.Category.Tensor.assoc') ('Control.Category.Tensor.bwd' 'Control.Category.Tensor.assoc')
-- @
class LeftCoModule cat tC1 tC2 f where
  -- | ==== __Examples__
  --
  -- 'Data.Profunctor.Strong.unfirst':
  --
  -- >>> :t lcostrength @(->) @(,) @(,)
  -- lcostrength @(->) @(,) @(,) :: LeftCoModule (->) (,) (,) f => f (a, x) (b, x) -> f a b
  --
  -- 'Data.Profunctor.Choice.unleft':
  --
  -- >>> :t lcostrength @(->) @Either @Either
  -- lcostrength @(->) @Either @Either :: LeftCoModule (->) Either Either f => f (Either a x) (Either b x) -> f a b
  lcostrength :: cat (f (tC1 a x) (tC2 b x)) (f a b)

instance (Costrong p) => LeftCoModule (->) (,) (,) (FromProfunctor p) where
  lcostrength :: FromProfunctor p (a, x) (b, x) -> FromProfunctor p a b
  lcostrength = unfirst

instance (Cochoice p) => LeftCoModule (->) Either Either (FromProfunctor p) where
  lcostrength :: (Cochoice p) => FromProfunctor p (Either a x) (Either b x) -> FromProfunctor p a b
  lcostrength = unleft

instance (Bifunctor p) => LeftCoModule (->) (,) (,) (FromBifunctor p) where
  lcostrength :: (Bifunctor p) => FromBifunctor p (a, x) (b, x) -> FromBifunctor p a b
  lcostrength = gbimap fst fst

instance (Bifunctor p) => LeftCoModule Op Either Either (FromBifunctor p) where
  lcostrength :: (Bifunctor p) => Op (FromBifunctor p (Either a x) (Either b x)) (FromBifunctor p a b)
  lcostrength = Op (gbimap Left Left)

instance (Bifunctor p) => LeftCoModule Op These These (FromBifunctor p) where
  lcostrength :: (Bifunctor p) => Op (FromBifunctor p (These a x) (These b x)) (FromBifunctor p a b)
  lcostrength = Op (gbimap This This)

deriving via (FromProfunctor (Kleisli m)) instance (MonadFix m) => LeftCoModule (->) (,) (,) (Kleisli m)

deriving via (FromProfunctor Tagged) instance LeftCoModule (->) (,) (,) Tagged

deriving via (FromProfunctor (Coyoneda p)) instance (Costrong p) => LeftCoModule (->) (,) (,) (Coyoneda p)

deriving via (FromProfunctor (Copastro p)) instance (Cochoice p) => LeftCoModule (->) (,) (,) (Copastro p)

deriving via (FromProfunctor (Yoneda p)) instance (Costrong p) => LeftCoModule (->) (,) (,) (Yoneda p)

deriving via (FromProfunctor (->)) instance LeftCoModule (->) (,) (,) (->)

deriving via (FromProfunctor (Cokleisli f)) instance (Functor f) => LeftCoModule (->) (,) (,) (Cokleisli f)

deriving via (FromProfunctor (Costar f)) instance (Functor f) => LeftCoModule (->) (,) (,) (Costar f)

deriving via (FromProfunctor (WrappedArrow p)) instance (ArrowLoop p) => LeftCoModule (->) (,) (,) (WrappedArrow p)

deriving via (FromProfunctor (Sum p q)) instance (Costrong p, Costrong q) => LeftCoModule (->) (,) (,) (Sum p q)

deriving via (FromProfunctor (Product p q)) instance (Costrong p, Costrong q) => LeftCoModule (->) (,) (,) (Product p q)

deriving via (FromProfunctor (Tannen f p)) instance (Functor f, Costrong p) => LeftCoModule (->) (,) (,) (Tannen f p)

deriving via (FromProfunctor (Procompose p q)) instance (Corepresentable p, Corepresentable q) => LeftCoModule (->) (,) (,) (Procompose p q)

deriving via (FromProfunctor (Cayley f p)) instance (Functor f, Costrong p) => LeftCoModule (->) (,) (,) (Cayley f p)

deriving via (FromProfunctor (CopastroSum p)) instance LeftCoModule (->) Either Either (CopastroSum p)

deriving via (FromProfunctor (CotambaraSum p)) instance LeftCoModule (->) Either Either (CotambaraSum p)

deriving via (FromProfunctor (Coyoneda p)) instance (Cochoice p) => LeftCoModule (->) Either Either (Coyoneda p)

deriving via (FromProfunctor (Yoneda p)) instance (Cochoice p) => LeftCoModule (->) Either Either (Yoneda p)

deriving via (FromProfunctor (->)) instance LeftCoModule (->) Either Either (->)

deriving via (FromProfunctor (Forget r)) instance LeftCoModule (->) Either Either (Forget r)

deriving via (FromProfunctor (Costar f)) instance (Applicative f) => LeftCoModule (->) Either Either (Costar f)

deriving via (FromProfunctor (Star f)) instance (Traversable f) => LeftCoModule (->) Either Either (Star f)

deriving via (FromProfunctor (Sum p q)) instance (Cochoice p, Cochoice q) => LeftCoModule (->) Either Either (Sum p q)

deriving via (FromProfunctor (Product p q)) instance (Cochoice p, Cochoice q) => LeftCoModule (->) Either Either (Product p q)

deriving via (FromProfunctor (Tannen f p)) instance (Functor f, Cochoice p) => LeftCoModule (->) Either Either (Tannen f p)

deriving via (FromProfunctor (Cayley f p)) instance (Functor f, Cochoice p) => LeftCoModule (->) Either Either (Cayley f p)

deriving via (FromBifunctor Arg) instance LeftCoModule (->) (,) (,) Arg

deriving via (FromBifunctor Const) instance LeftCoModule (->) (,) (,) Const

deriving via (FromBifunctor Either) instance LeftCoModule (->) (,) (,) Either

deriving via (FromBifunctor These) instance LeftCoModule (->) (,) (,) These

deriving via (FromBifunctor (K1 i)) instance LeftCoModule (->) (,) (,) (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance LeftCoModule (->) (,) (,) (,)

deriving via (FromBifunctor ((,,) x1)) instance LeftCoModule (->) (,) (,) ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance LeftCoModule (->) (,) (,) ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance LeftCoModule (->) (,) (,) ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance LeftCoModule (->) (,) (,) ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance LeftCoModule (->) (,) (,) ((,,,,,,) x1 x2 x3 x4 x5)

deriving via (FromBifunctor Arg) instance LeftCoModule Op Either Either Arg

deriving via (FromBifunctor Const) instance LeftCoModule Op Either Either Const

deriving via (FromBifunctor Either) instance LeftCoModule Op Either Either Either

deriving via (FromBifunctor These) instance LeftCoModule Op Either Either These

deriving via (FromBifunctor (K1 i)) instance LeftCoModule Op Either Either (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance LeftCoModule Op Either Either (,)

deriving via (FromBifunctor ((,,) x1)) instance LeftCoModule Op Either Either ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance LeftCoModule Op Either Either ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance LeftCoModule Op Either Either ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance LeftCoModule Op Either Either ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance LeftCoModule Op Either Either ((,,,,,,) x1 x2 x3 x4 x5)

deriving via (FromBifunctor Arg) instance LeftCoModule Op These These Arg

deriving via (FromBifunctor Const) instance LeftCoModule Op These These Const

deriving via (FromBifunctor Either) instance LeftCoModule Op These These Either

deriving via (FromBifunctor These) instance LeftCoModule Op These These These

deriving via (FromBifunctor (K1 i)) instance LeftCoModule Op These These (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance LeftCoModule Op These These (,)

deriving via (FromBifunctor ((,,) x1)) instance LeftCoModule Op These These ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance LeftCoModule Op These These ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance LeftCoModule Op These These ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance LeftCoModule Op These These ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance LeftCoModule Op These These ((,,,,,,) x1 x2 x3 x4 x5)

--------------------------------------------------------------------------------

-- | A 'Profunctor' \(P : \mathcal{C_1}^{op} \times \mathcal{C_2} \to Set\)
-- is a Tambara 'RightCoModule' if it is equipped with a morphism \(s^{-1}_{a,b,m} : P(m \odot a, m \odot a) \to P(a, b) \),
-- which we call 'rcostrength'.
--
-- === Laws
--
-- @
-- 'Data.Profunctor.Types.Data.Profunctor.Types.lmap' 'Control.Category.Cartesian.inclr' ≡ 'rcostrength' 'Control.Category..' 'Data.Profunctor.Types.rmap' 'Control.Category.Cartesian.inclr'
-- 'rcostrength' 'Control.Category..' 'Data.Profunctor.Types.lmap' ('lstrength' f) ≡ 'rcostrength' 'Control.Category..' 'Data.Profunctor.Types.rmap' ('lstrength' f)
-- 'rcostrength' 'Control.Category..' 'rcostrength' ≡  'rcostrength' 'Control.Category..' 'Data.Profunctor.Types.dimap' ('Control.Category.Tensor.bwd' 'Control.Category.Tensor.assoc') ('Control.Category.Tensor.fwd' 'Control.Category.Tensor.assoc')
-- @
class RightCoModule cat tC1 tC2 f where
  -- | ==== __Examples__
  --
  -- 'Data.Profunctor.Strong.unsecond':
  --
  -- >>> :t rcostrength @(->) @(,) @(,)
  -- rcostrength @(->) @(,) @(,) :: RightCoModule (->) (,) (,) f => f (x, a) (x, b) -> f a b
  --
  -- 'Data.Profunctor.Choice.unright':
  --
  -- >>> :t rcostrength @(->) @Either @Either
  -- rcostrength @(->) @Either @Either :: RightCoModule (->) Either Either f => f (Either x a) (Either x b) -> f a b
  rcostrength :: cat (f (x `tC1` a) (x `tC2` b)) (f a b)

instance (Costrong p) => RightCoModule (->) (,) (,) (FromProfunctor p) where
  rcostrength :: FromProfunctor p (x, a) (x, b) -> FromProfunctor p a b
  rcostrength = unsecond

instance (Cochoice p) => RightCoModule (->) Either Either (FromProfunctor p) where
  rcostrength :: FromProfunctor p (Either x a) (Either x b) -> FromProfunctor p a b
  rcostrength = unright

instance (Bifunctor p) => RightCoModule (->) (,) (,) (FromBifunctor p) where
  rcostrength :: FromBifunctor p (x, a) (x, b) -> FromBifunctor p a b
  rcostrength = gbimap snd snd

instance (Bifunctor p) => RightCoModule Op Either Either (FromBifunctor p) where
  rcostrength :: Op (FromBifunctor p (Either x a) (Either x b)) (FromBifunctor p a b)
  rcostrength = Op (gbimap Right Right)

instance (Bifunctor p) => RightCoModule Op These These (FromBifunctor p) where
  rcostrength :: Op (FromBifunctor p (These x a) (These x b)) (FromBifunctor p a b)
  rcostrength = Op (gbimap That That)

deriving via (FromProfunctor (Kleisli m)) instance (MonadFix m) => RightCoModule (->) (,) (,) (Kleisli m)

deriving via (FromProfunctor Tagged) instance RightCoModule (->) (,) (,) Tagged

deriving via (FromProfunctor (Coyoneda p)) instance (Costrong p) => RightCoModule (->) (,) (,) (Coyoneda p)

deriving via (FromProfunctor (Copastro p)) instance (Cochoice p) => RightCoModule (->) (,) (,) (Copastro p)

deriving via (FromProfunctor (Yoneda p)) instance (Costrong p) => RightCoModule (->) (,) (,) (Yoneda p)

deriving via (FromProfunctor (->)) instance RightCoModule (->) (,) (,) (->)

deriving via (FromProfunctor (Cokleisli f)) instance (Functor f) => RightCoModule (->) (,) (,) (Cokleisli f)

deriving via (FromProfunctor (Costar f)) instance (Functor f) => RightCoModule (->) (,) (,) (Costar f)

deriving via (FromProfunctor (WrappedArrow p)) instance (ArrowLoop p) => RightCoModule (->) (,) (,) (WrappedArrow p)

deriving via (FromProfunctor (Sum p q)) instance (Costrong p, Costrong q) => RightCoModule (->) (,) (,) (Sum p q)

deriving via (FromProfunctor (Product p q)) instance (Costrong p, Costrong q) => RightCoModule (->) (,) (,) (Product p q)

deriving via (FromProfunctor (Tannen f p)) instance (Functor f, Costrong p) => RightCoModule (->) (,) (,) (Tannen f p)

deriving via (FromProfunctor (Procompose p q)) instance (Corepresentable p, Corepresentable q) => RightCoModule (->) (,) (,) (Procompose p q)

deriving via (FromProfunctor (Cayley f p)) instance (Functor f, Costrong p) => RightCoModule (->) (,) (,) (Cayley f p)

deriving via (FromProfunctor (CopastroSum p)) instance RightCoModule (->) Either Either (CopastroSum p)

deriving via (FromProfunctor (CotambaraSum p)) instance RightCoModule (->) Either Either (CotambaraSum p)

deriving via (FromProfunctor (Coyoneda p)) instance (Cochoice p) => RightCoModule (->) Either Either (Coyoneda p)

deriving via (FromProfunctor (Yoneda p)) instance (Cochoice p) => RightCoModule (->) Either Either (Yoneda p)

deriving via (FromProfunctor (->)) instance RightCoModule (->) Either Either (->)

deriving via (FromProfunctor (Forget r)) instance RightCoModule (->) Either Either (Forget r)

deriving via (FromProfunctor (Costar f)) instance (Applicative f) => RightCoModule (->) Either Either (Costar f)

deriving via (FromProfunctor (Star f)) instance (Traversable f) => RightCoModule (->) Either Either (Star f)

deriving via (FromProfunctor (Sum p q)) instance (Cochoice p, Cochoice q) => RightCoModule (->) Either Either (Sum p q)

deriving via (FromProfunctor (Product p q)) instance (Cochoice p, Cochoice q) => RightCoModule (->) Either Either (Product p q)

deriving via (FromProfunctor (Tannen f p)) instance (Functor f, Cochoice p) => RightCoModule (->) Either Either (Tannen f p)

deriving via (FromProfunctor (Cayley f p)) instance (Functor f, Cochoice p) => RightCoModule (->) Either Either (Cayley f p)

deriving via (FromBifunctor Arg) instance RightCoModule (->) (,) (,) Arg

deriving via (FromBifunctor Const) instance RightCoModule (->) (,) (,) Const

deriving via (FromBifunctor Either) instance RightCoModule (->) (,) (,) Either

deriving via (FromBifunctor These) instance RightCoModule (->) (,) (,) These

deriving via (FromBifunctor (K1 i)) instance RightCoModule (->) (,) (,) (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance RightCoModule (->) (,) (,) (,)

deriving via (FromBifunctor ((,,) x1)) instance RightCoModule (->) (,) (,) ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance RightCoModule (->) (,) (,) ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance RightCoModule (->) (,) (,) ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance RightCoModule (->) (,) (,) ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance RightCoModule (->) (,) (,) ((,,,,,,) x1 x2 x3 x4 x5)

deriving via (FromBifunctor Arg) instance RightCoModule Op Either Either Arg

deriving via (FromBifunctor Const) instance RightCoModule Op Either Either Const

deriving via (FromBifunctor Either) instance RightCoModule Op Either Either Either

deriving via (FromBifunctor These) instance RightCoModule Op Either Either These

deriving via (FromBifunctor (K1 i)) instance RightCoModule Op Either Either (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance RightCoModule Op Either Either (,)

deriving via (FromBifunctor ((,,) x1)) instance RightCoModule Op Either Either ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance RightCoModule Op Either Either ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance RightCoModule Op Either Either ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance RightCoModule Op Either Either ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance RightCoModule Op Either Either ((,,,,,,) x1 x2 x3 x4 x5)

deriving via (FromBifunctor Arg) instance RightCoModule Op These These Arg

deriving via (FromBifunctor Const) instance RightCoModule Op These These Const

deriving via (FromBifunctor Either) instance RightCoModule Op These These Either

deriving via (FromBifunctor These) instance RightCoModule Op These These These

deriving via (FromBifunctor (K1 i)) instance RightCoModule Op These These (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance RightCoModule Op These These (,)

deriving via (FromBifunctor ((,,) x1)) instance RightCoModule Op These These ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance RightCoModule Op These These ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance RightCoModule Op These These ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance RightCoModule Op These These ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance RightCoModule Op These These ((,,,,,,) x1 x2 x3 x4 x5)

--------------------------------------------------------------------------------

-- | A 'Profunctor' equipped with both a Tambara 'LeftCoModule' and
-- Tambara 'RightCoModule' is a 'CoBimodule'.
--
-- === Laws
--
-- @
-- 'rcostrength' ≡ 'lcostrength' 'Control.Category..' 'Data.Profunctor.Types.dimap' 'Control.Category.Tensor.swap' 'Control.Category.Tensor.swap'
-- 'lcostrength' ≡ 'rcostrength' 'Control.Category..' 'Data.Profunctor.Types.dimap' 'Control.Category.Tensor.swap' 'Control.Category.Tensor.swap'
-- @
class (LeftCoModule cat tC1 tC2 f, RightCoModule cat tC1 tC2 f) => CoBimodule cat tC1 tC2 f

instance (Costrong p) => CoBimodule (->) (,) (,) (FromProfunctor p)

instance (Cochoice p) => CoBimodule (->) Either Either (FromProfunctor p)

instance (Bifunctor p) => CoBimodule (->) (,) (,) (FromBifunctor p)

instance (Bifunctor p) => CoBimodule Op Either Either (FromBifunctor p)

instance (Bifunctor p) => CoBimodule Op These These (FromBifunctor p)

deriving via (FromProfunctor (Kleisli m)) instance (MonadFix m) => CoBimodule (->) (,) (,) (Kleisli m)

deriving via (FromProfunctor Tagged) instance CoBimodule (->) (,) (,) Tagged

deriving via (FromProfunctor (Coyoneda p)) instance (Costrong p) => CoBimodule (->) (,) (,) (Coyoneda p)

deriving via (FromProfunctor (Copastro p)) instance (Cochoice p) => CoBimodule (->) (,) (,) (Copastro p)

deriving via (FromProfunctor (Yoneda p)) instance (Costrong p) => CoBimodule (->) (,) (,) (Yoneda p)

deriving via (FromProfunctor (->)) instance CoBimodule (->) (,) (,) (->)

deriving via (FromProfunctor (Cokleisli f)) instance (Functor f) => CoBimodule (->) (,) (,) (Cokleisli f)

deriving via (FromProfunctor (Costar f)) instance (Functor f) => CoBimodule (->) (,) (,) (Costar f)

deriving via (FromProfunctor (WrappedArrow p)) instance (ArrowLoop p) => CoBimodule (->) (,) (,) (WrappedArrow p)

deriving via (FromProfunctor (Sum p q)) instance (Costrong p, Costrong q) => CoBimodule (->) (,) (,) (Sum p q)

deriving via (FromProfunctor (Product p q)) instance (Costrong p, Costrong q) => CoBimodule (->) (,) (,) (Product p q)

deriving via (FromProfunctor (Tannen f p)) instance (Functor f, Costrong p) => CoBimodule (->) (,) (,) (Tannen f p)

deriving via (FromProfunctor (Procompose p q)) instance (Corepresentable p, Corepresentable q) => CoBimodule (->) (,) (,) (Procompose p q)

deriving via (FromProfunctor (Cayley f p)) instance (Functor f, Costrong p) => CoBimodule (->) (,) (,) (Cayley f p)

deriving via (FromProfunctor (CopastroSum p)) instance CoBimodule (->) Either Either (CopastroSum p)

deriving via (FromProfunctor (CotambaraSum p)) instance CoBimodule (->) Either Either (CotambaraSum p)

deriving via (FromProfunctor (Coyoneda p)) instance (Cochoice p) => CoBimodule (->) Either Either (Coyoneda p)

deriving via (FromProfunctor (Yoneda p)) instance (Cochoice p) => CoBimodule (->) Either Either (Yoneda p)

deriving via (FromProfunctor (->)) instance CoBimodule (->) Either Either (->)

deriving via (FromProfunctor (Forget r)) instance CoBimodule (->) Either Either (Forget r)

deriving via (FromProfunctor (Costar f)) instance (Applicative f) => CoBimodule (->) Either Either (Costar f)

deriving via (FromProfunctor (Star f)) instance (Traversable f) => CoBimodule (->) Either Either (Star f)

deriving via (FromProfunctor (Sum p q)) instance (Cochoice p, Cochoice q) => CoBimodule (->) Either Either (Sum p q)

deriving via (FromProfunctor (Product p q)) instance (Cochoice p, Cochoice q) => CoBimodule (->) Either Either (Product p q)

deriving via (FromProfunctor (Tannen f p)) instance (Functor f, Cochoice p) => CoBimodule (->) Either Either (Tannen f p)

deriving via (FromProfunctor (Cayley f p)) instance (Functor f, Cochoice p) => CoBimodule (->) Either Either (Cayley f p)

deriving via (FromBifunctor Arg) instance CoBimodule (->) (,) (,) Arg

deriving via (FromBifunctor Const) instance CoBimodule (->) (,) (,) Const

deriving via (FromBifunctor Either) instance CoBimodule (->) (,) (,) Either

deriving via (FromBifunctor These) instance CoBimodule (->) (,) (,) These

deriving via (FromBifunctor (K1 i)) instance CoBimodule (->) (,) (,) (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance CoBimodule (->) (,) (,) (,)

deriving via (FromBifunctor ((,,) x1)) instance CoBimodule (->) (,) (,) ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance CoBimodule (->) (,) (,) ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance CoBimodule (->) (,) (,) ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance CoBimodule (->) (,) (,) ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance CoBimodule (->) (,) (,) ((,,,,,,) x1 x2 x3 x4 x5)

deriving via (FromBifunctor Arg) instance CoBimodule Op Either Either Arg

deriving via (FromBifunctor Const) instance CoBimodule Op Either Either Const

deriving via (FromBifunctor Either) instance CoBimodule Op Either Either Either

deriving via (FromBifunctor These) instance CoBimodule Op Either Either These

deriving via (FromBifunctor (K1 i)) instance CoBimodule Op Either Either (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance CoBimodule Op Either Either (,)

deriving via (FromBifunctor ((,,) x1)) instance CoBimodule Op Either Either ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance CoBimodule Op Either Either ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance CoBimodule Op Either Either ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance CoBimodule Op Either Either ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance CoBimodule Op Either Either ((,,,,,,) x1 x2 x3 x4 x5)

deriving via (FromBifunctor Arg) instance CoBimodule Op These These Arg

deriving via (FromBifunctor Const) instance CoBimodule Op These These Const

deriving via (FromBifunctor Either) instance CoBimodule Op These These Either

deriving via (FromBifunctor These) instance CoBimodule Op These These These

deriving via (FromBifunctor (K1 i)) instance CoBimodule Op These These (K1 i :: Type -> Type -> Type)

deriving via (FromBifunctor (,)) instance CoBimodule Op These These (,)

deriving via (FromBifunctor ((,,) x1)) instance CoBimodule Op These These ((,,) x1)

deriving via (FromBifunctor ((,,,) x1 x2)) instance CoBimodule Op These These ((,,,) x1 x2)

deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance CoBimodule Op These These ((,,,,) x1 x2 x3)

deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance CoBimodule Op These These ((,,,,,) x1 x2 x3 x4)

deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance CoBimodule Op These These ((,,,,,,) x1 x2 x3 x4 x5)