monoidal-functors 0.2.1.0 → 0.2.2.0

raw patch · 14 files changed

+2747/−1243 lines, 14 filesdep +monoidal-functorsdep +mtldep +transformersdep ~basedep ~bifunctorsdep ~contravariantsetup-changednew-component:exe:co-logPVP ok

version bump matches the API change (PVP)

Dependencies added: monoidal-functors, mtl, transformers

Dependency ranges changed: base, bifunctors, contravariant, distributive, semialign, semigroupoids, tagged, these

API changes (from Hackage documentation)

Files

• CHANGELOG.md +8/−0
• Setup.hs +1/−0
• examples/co-log/Main.hs +188/−0
• monoidal-functors.cabal +53/−32
• src/Control/Category/Tensor.hs +124/−69
• src/Control/Category/Tensor/Expr.hs +15/−16
• src/Data/Bifunctor/BiInvariant.hs +111/−55
• src/Data/Bifunctor/Module.hs +1051/−671
• src/Data/Bifunctor/Monoidal.hs +119/−29
• src/Data/Bifunctor/Monoidal/Specialized.hs +12/−11
• src/Data/Functor/Invariant.hs +28/−15
• src/Data/Functor/Module.hs +437/−217
• src/Data/Functor/Monoidal.hs +581/−112
• src/Data/Trifunctor/Monoidal.hs +19/−16

@@ -2,6 +2,14 @@  ## Upcoming +## 0.2.2.0 -- 2023-06-26++* Adds `co-log` example.+* Switch to Ormolu formatting and a `Makefile` to manage local development.+* Remove Arrow terminology from haddocks.+* Adds missing `Star` and `Kleisli` instances.+* Adds `Unital` and `Monoidal` instances for `Divisible` and `Decidable`.+ ## 0.2.1.0 -- 2023-01-29  * Rewrite `Semigroupal`, `Unital`, and `Monoidal` `Functor` instances

@@ -1,2 +1,3 @@ import Distribution.Simple+ main = defaultMain

@@ -0,0 +1,188 @@+module Main where++--------------------------------------------------------------------------------++import Control.Category+import Control.Category.Cartesian+import Control.Category.Tensor+import Control.Monad.IO.Class+import Control.Monad.Reader+import Control.Monad.Trans+import Data.Coerce+import Data.Functor.Contravariant hiding ((>$<))+import Data.Functor.Contravariant.Divisible hiding (divide)+import Data.Functor.Monoidal+import Data.Kind+import Data.Void+import Prelude hiding (id, (.))++--------------------------------------------------------------------------------++main :: IO ()+main = runCarExample++--------------------------------------------------------------------------------+-- Car Example from co-log blog post+-- https://kowainik.github.io/posts/2018-09-25-co-log#combinators++data Engine = Pistons Int | Rocket++data Car = Car+  { carMake :: String,+    carModel :: String,+    carEngine :: Engine+  }++engineToEither :: Engine -> Either Int ()+engineToEither e = case e of+  Pistons i -> Left i+  Rocket -> Right ()++carToTuple :: Car -> (String, (String, Engine))+carToTuple (Car make model engine) = (make, (model, engine))++carL :: LogAction IO Car+carL =+  carToTuple+    >$< (constL "Logging make..." *< showL >* constL "Finished logging make...")+      >*< (constL "Logging model.." *< showL >* constL "Finished logging model...")+      >*< ( engineToEither+              >$< constL "Logging pistons..."+              *< intL+              >|< constL "Logging rocket..."+          )++runCarExample :: IO ()+runCarExample = usingLoggerT carL $ logMsg $ Car "Toyota" "Corolla" (Pistons 4)++--------------------------------------------------------------------------------++newtype LogAction m msg = LogAction {unLogAction :: msg -> m ()}++instance Contravariant (LogAction m) where+  contramap :: (a -> b) -> LogAction m b -> LogAction m a+  contramap f (LogAction act) = LogAction $ \a -> act (f a)++instance Applicative m => Semigroupal (->) (,) (,) (LogAction m) where+  combine :: (LogAction m a, LogAction m b) -> LogAction m (a, b)+  combine (act1, act2) = LogAction $ \(a, b) ->+    unLogAction act1 a+      *> unLogAction act2 b+      *> pure ()++instance Applicative m => Unital (->) () () (LogAction m) where+  introduce :: () -> LogAction m ()+  introduce () = LogAction $ \_ -> pure ()++instance Applicative m => Semigroupal (->) Either (,) (LogAction m) where+  combine :: (LogAction m a, LogAction m b) -> LogAction m (Either a b)+  combine (act1, act2) = LogAction $ \case+    Left a -> coerce act1 a+    Right b -> coerce act2 b++instance Applicative m => Unital (->) Void () (LogAction m) where+  introduce :: () -> LogAction m Void+  introduce () = LogAction $ \_ -> pure ()++-- NOTE: We don't actually need these instances but include them to demonstrate the equivalence:+-- instance Applicative m => Semigroup (LogAction m a) where+--   act1 <> act2 = contramap (split @_ @(,)) $ combine (act1, act2)+--+-- instance Applicative m => Monoid (LogAction m a) where+--   mempty = contramap (\_ -> ()) $ introduce ()+--+-- instance Applicative m => Divisible (LogAction m) where+--   conquer :: LogAction m a+--   conquer = mempty+--+--   divide :: (a -> (b, c)) -> LogAction m b -> LogAction m c -> LogAction m a+--   divide f act1 act2 = contramap f $ combine (act1, act2)+--+-- instance Applicative m => Decidable (LogAction m) where+--     lose :: (a -> Void) -> LogAction m a+--     lose f = contramap f $ introduce @_ @Void ()+--+--     choose :: (a -> Either b c) -> LogAction m b -> LogAction m c -> LogAction m a+--     choose f act1 act2 = contramap f $ combine @_ @Either (act1, act2)++--------------------------------------------------------------------------------+-- Combinators++divide :: (Contravariant f, Semigroupal (->) (,) (,) f) => (a -> (b, c)) -> f b -> f c -> f a+divide f fb fc = curry (contramap f . combine) fb fc++infixr 3 >$<++(>$<) :: (a -> b) -> LogAction m b -> LogAction m a+(>$<) = contramap++infixr 4 >*<++(>*<) :: Semigroupal (->) (,) (,) f => f a -> f b -> f (a, b)+(>*<) = (|?|)++infixr 3 >|<++(>|<) :: Semigroupal (->) Either (,) f => f a -> f b -> f (Either a b)+(>|<) = (|?|)++infixr 4 >*++(>*) :: (Contravariant f, (Semigroupal (->) (,) (,) f)) => f a -> f () -> f a+(>*) = divide (,())++infixr 4 *<++(*<) :: (Contravariant f, (Semigroupal (->) (,) (,) f)) => f () -> f a -> f a+(*<) = divide ((),)++--------------------------------------------------------------------------------+-- Log Actions++hoistLogAction :: (forall x. m x -> n x) -> LogAction m a -> LogAction n a+hoistLogAction nat (LogAction act) = LogAction $ nat . act++liftLogAction :: (Monad m, MonadTrans t) => LogAction m msg -> LogAction (t m) msg+liftLogAction = hoistLogAction lift++logStringStdout :: LogAction IO String+logStringStdout = LogAction putStrLn++-- Combinator that allows to log any showable value+showL :: Show a => LogAction IO a+showL = contramap show logStringStdout++-- Returns a log action that logs a given string ignoring its input.+constL :: String -> LogAction IO a+constL s = s >$ logStringStdout++intL :: LogAction IO Int+intL = showL++--------------------------------------------------------------------------------++class HasLog env msg (m :: Type -> Type) where+  getLogAction :: env -> LogAction m msg+  setLogAction :: LogAction m msg -> env -> env++instance HasLog (LogAction m msg) msg m where+  getLogAction :: LogAction m msg -> LogAction m msg+  getLogAction = id++  setLogAction :: LogAction m msg -> LogAction m msg -> LogAction m msg+  setLogAction = const++logMsg :: (MonadReader env m, HasLog env msg m) => msg -> m ()+logMsg msg = do+  LogAction logger <- asks getLogAction+  logger msg++usingLoggerT :: Monad m => LogAction m msg -> LoggerT msg m a -> m a+usingLoggerT action = flip runReaderT (liftLogAction action) . runLoggerT++newtype LoggerT msg m a = LoggerT {runLoggerT :: ReaderT (LogAction (LoggerT msg m) msg) m a}+  deriving newtype (Functor, Applicative, Monad, MonadIO, MonadReader (LogAction (LoggerT msg m) msg))++instance MonadTrans (LoggerT msg) where+  lift :: Monad m => m a -> LoggerT msg m a+  lift = LoggerT . lift

@@ -1,7 +1,7 @@ cabal-version:       2.4 name:                monoidal-functors category:            Control, Categories-version:             0.2.1.0+version:             0.2.2.0 license:             MIT license-file:        LICENSE author:              Solomon Bothwell & Asad Saeeduddin@@ -18,18 +18,47 @@  -------------------------------------------------------------------------------- +common common-extensions+  default-extensions:+    ConstraintKinds+    DeriveFunctor+    DerivingVia+    FunctionalDependencies+    FlexibleInstances+    FlexibleContexts+    GeneralizedNewtypeDeriving+    ImportQualifiedPost+    InstanceSigs+    KindSignatures+    LambdaCase+    MultiParamTypeClasses+    NoImplicitPrelude+    QuantifiedConstraints+    RankNTypes+    ScopedTypeVariables+    StandaloneDeriving+    TupleSections+    TypeApplications+    TypeOperators+    UndecidableInstances++--------------------------------------------------------------------------------+ library+  import: common-extensions   build-depends:-    base          >= 4.12   && < 5,-    bifunctors    >= 5.5.11 && < 5.6,-    comonad       >= 5.0.8  && < 5.1,-    distributive  >= 0.6.2  && < 0.7,-    tagged        >= 0.8.6  && < 0.9,-    contravariant >= 1.5.5  && < 1.6,-    profunctors   >= 5.6.2  && < 5.7,-    semialign     >= 1.2.0  && < 1.3,-    semigroupoids >= 5.3.6  && < 5.4,-    these         >= 1.1.1  && < 1.2,+    base                          >= 4.12 && < 4.18,+    bifunctors                    >= 5.6.1 && < 5.7,+    tagged                        >= 0.8.7 && < 0.9,+    transformers                  >= 0.5.6 && <= 0.6.1.0,+    comonad                       >= 5.0.8 && < 5.1,+    distributive                  >= 0.6.2 && < 0.7,+    contravariant                 >= 1.5.5 && < 1.6,+    profunctors                   >= 5.6.2 && < 5.7,+    semialign                     >= 1.3 && < 1.4,+    semigroupoids                 >= 6.0.0 && < 6.1,+    these                         >= 1.2 && < 1.3,+    mtl                           >= 2.2.2 && <= 2.3.1,    exposed-modules:     Control.Category.Tensor@@ -58,25 +87,17 @@   hs-source-dirs: src    default-language: Haskell2010--  default-extensions:-    ConstraintKinds-    DeriveFunctor-    DerivingVia-    FunctionalDependencies-    FlexibleInstances-    FlexibleContexts-    GeneralizedNewtypeDeriving-    InstanceSigs-    KindSignatures-    LambdaCase-    MultiParamTypeClasses-    NoImplicitPrelude-    QuantifiedConstraints-    RankNTypes-    ScopedTypeVariables-    StandaloneDeriving-    TypeApplications-    TypeOperators-    UndecidableInstances   +--------------------------------------------------------------------------------++executable co-log+  import: common-extensions+  hs-source-dirs:    examples/co-log+  main-is:           Main.hs+  build-depends:     base+                   , bifunctors+                   , contravariant+                   , distributive+                   , monoidal-functors+                   , mtl+  default-language: Haskell2010

@@ -1,4 +1,5 @@ {-# LANGUAGE MonoLocalBinds #-}+ module Control.Category.Tensor   ( -- * Iso     Iso (..),@@ -8,6 +9,7 @@     (#),     grmap,     glmap,+     -- * Associative     Associative (..), @@ -22,6 +24,7 @@ --------------------------------------------------------------------------------  import Control.Applicative (Applicative (..))+import Control.Arrow (Kleisli (..)) import Control.Category (Category (..)) import Data.Biapplicative (Biapplicative (..), Bifunctor (..)) import Data.Functor.Contravariant (Op (..))@@ -40,7 +43,7 @@ -- 'fwd' '.' 'bwd' ≡ 'id' -- 'bwd' '.' 'fwd' ≡ 'id' -- @-data Iso cat a b = Iso { fwd :: cat a b, bwd :: cat b a }+data Iso cat a b = Iso {fwd :: cat a b, bwd :: cat b a}  instance Category cat => Category (Iso cat) where   id :: Iso cat a a@@ -82,11 +85,12 @@   --   -- >>> getOp (gbimap @Op @Op @Op @Either (Op (+ 1)) (Op show)) (Right True)   -- Right "True"-  gbimap :: cat1 a b -> cat2 c d -> cat3 (a `t` c)  (b `t` d)+  gbimap :: cat1 a b -> cat2 c d -> cat3 (a `t` c) (b `t` d)  -- | Infix operator for 'gbimap'. infixr 9 #-(#) :: GBifunctor cat1 cat2 cat3 t => cat1 a b -> cat2 c d -> cat3 (a `t` c)  (b `t` d)++(#) :: GBifunctor cat1 cat2 cat3 t => cat1 a b -> cat2 c d -> cat3 (a `t` c) (b `t` d) (#) = gbimap  -- | Covariantally map over the right variable.@@ -108,10 +112,18 @@   gbimap :: Star Maybe a b -> Star Maybe c d -> Star Maybe (These a c) (These b d)   gbimap (Star f) (Star g) =     Star $ \case-      This a    -> This <$> f a-      That c    -> That <$> g c+      This a -> This <$> f a+      That c -> That <$> g c       These a c -> liftA2 These (f a) (g c) +instance GBifunctor (Kleisli Maybe) (Kleisli Maybe) (Kleisli Maybe) These where+  gbimap :: Kleisli Maybe a b -> Kleisli Maybe c d -> Kleisli Maybe (These a c) (These b d)+  gbimap (Kleisli f) (Kleisli g) =+    Kleisli $ \case+      This a -> This <$> f a+      That c -> That <$> g c+      These a c -> liftA2 These (f a) (g c)+ instance GBifunctor cat cat cat t => GBifunctor (Iso cat) (Iso cat) (Iso cat) t where   gbimap :: Iso cat a b -> Iso cat c d -> Iso cat (t a c) (t b d)   gbimap iso1 iso2 = Iso (gbimap (fwd iso1) (fwd iso2)) (gbimap (bwd iso1) (bwd iso2))@@ -136,7 +148,7 @@   --   -- ==== __Examples__   ---  -- >>> :t assoc @(->) @(,) +  -- >>> :t assoc @(->) @(,)   -- assoc @(->) @(,) :: Iso (->) (a, (b, c)) ((a, b), c)   --   -- >>> fwd (assoc @(->) @(,)) (1, ("hello", True))@@ -145,39 +157,52 @@  instance Associative (->) t => Associative Op t where   assoc :: Iso Op (a `t` (b `t` c)) ((a `t` b) `t` c)-  assoc = Iso-    { fwd = Op $ bwd assoc-    , bwd = Op $ fwd assoc-    }+  assoc =+    Iso+      { fwd = Op $ bwd assoc,+        bwd = Op $ fwd assoc+      }  instance Associative (->) (,) where   assoc :: Iso (->) (a, (b, c)) ((a, b), c)-  assoc = Iso-    { fwd = \(a, (b, c)) -> ((a, b), c)-    , bwd = \((a, b), c) -> (a, (b, c))-    }+  assoc =+    Iso+      { fwd = \(a, (b, c)) -> ((a, b), c),+        bwd = \((a, b), c) -> (a, (b, c))+      }  instance Associative (->) Either where   assoc :: Iso (->) (Either a (Either b c)) (Either (Either a b) c)-  assoc = Iso-    { fwd = either (Left . Left) (either (Left . Right) Right)-    , bwd = either (fmap Left) (Right . Right)-    }+  assoc =+    Iso+      { fwd = either (Left . Left) (either (Left . Right) Right),+        bwd = either (fmap Left) (Right . Right)+      }  instance Associative (->) These where   assoc :: Iso (->) (These a (These b c)) (These (These a b) c)-  assoc = Iso-    { fwd = these (This . This) (glmap That) (glmap . These)-    , bwd = these (grmap This) (That . That) (flip $ grmap . flip These)-    }+  assoc =+    Iso+      { fwd = these (This . This) (glmap That) (glmap . These),+        bwd = these (grmap This) (That . That) (flip $ grmap . flip These)+      }  instance (Monad m, Associative (->) t, GBifunctor (Star m) (Star m) (Star m) t) => Associative (Star m) t where   assoc :: Iso (Star m) (a `t` (b `t` c)) ((a `t` b) `t` c)-  assoc = Iso-    { fwd = (`rmap` id) (fwd assoc)-    , bwd = (`rmap` id) (bwd assoc)-    }+  assoc =+    Iso+      { fwd = (`rmap` id) (fwd assoc),+        bwd = (`rmap` id) (bwd assoc)+      } +instance (Monad m, Associative (->) t, GBifunctor (Kleisli m) (Kleisli m) (Kleisli m) t) => Associative (Kleisli m) t where+  assoc :: Iso (Kleisli m) (a `t` (b `t` c)) ((a `t` b) `t` c)+  assoc =+    Iso+      { fwd = (`rmap` id) (fwd assoc),+        bwd = (`rmap` id) (bwd assoc)+      }+ --------------------------------------------------------------------------------  -- | A bifunctor \(\_ \otimes\_ \ : \mathcal{C} \times \mathcal{C} \to \mathcal{C}\)@@ -194,7 +219,7 @@ -- 'fwd' 'unitr' (a ⊗ i) ≡ a -- 'bwd' 'unitr' a ≡ (a ⊗ i) ----- 'fwd' 'unitl' (i ⊗ a) ≡ a +-- 'fwd' 'unitl' (i ⊗ a) ≡ a -- 'bwd' 'unitl' a ≡ (i ⊗ a) -- @ class Associative cat t => Tensor cat t i | t -> i where@@ -204,7 +229,7 @@   --   -- >>> fwd (unitl @_ @(,)) ((), True)   -- True-  -- +  --   -- >>> bwd (unitl @_ @(,)) True   -- ((),True)   --@@ -214,13 +239,14 @@   -- >>> :t bwd (unitl @_ @Either) True   -- bwd (unitl @_ @Either) True :: Either Void Bool   unitl :: Iso cat (i `t` a) a+   -- | The <https://ncatlab.org/nlab/show/natural+isomorphism natural isomorphism> between @(a \`t\` i)@ and @a@.   --   -- ==== __Examples__   --   -- >>> fwd (unitr @_ @(,)) (True, ())   -- True-  -- +  --   -- >>> bwd (unitr @_ @(,)) True   -- (True,())   --@@ -233,69 +259,94 @@  instance (Tensor (->) t i) => Tensor Op t i where   unitl :: Iso Op (i `t` a) a-  unitl = Iso-    { fwd = Op $ bwd unitl-    , bwd = Op $ fwd unitl-    }+  unitl =+    Iso+      { fwd = Op $ bwd unitl,+        bwd = Op $ fwd unitl+      }    unitr :: Iso Op (a `t` i) a-  unitr = Iso-    { fwd = Op $ bwd unitr-    , bwd = Op $ fwd unitr-    }+  unitr =+    Iso+      { fwd = Op $ bwd unitr,+        bwd = Op $ fwd unitr+      }  instance Tensor (->) (,) () where   unitl :: Iso (->) ((), a) a-  unitl = Iso-    { fwd = snd-    , bwd = bipure ()-    }+  unitl =+    Iso+      { fwd = snd,+        bwd = bipure ()+      }    unitr :: Iso (->) (a, ()) a-  unitr = Iso-    { fwd = fst-    , bwd = (`bipure` ())-    }+  unitr =+    Iso+      { fwd = fst,+        bwd = (`bipure` ())+      }  instance Tensor (->) Either Void where   unitl :: Iso (->) (Either Void a) a-  unitl = Iso-     { fwd = either absurd id-     , bwd = pure-     }+  unitl =+    Iso+      { fwd = either absurd id,+        bwd = pure+      }    unitr :: Iso (->) (Either a Void) a-  unitr = Iso-    { fwd = either id absurd-    , bwd = Left-    }+  unitr =+    Iso+      { fwd = either id absurd,+        bwd = Left+      }  instance Tensor (->) These Void where   unitl :: Iso (->) (These Void a) a-  unitl = Iso-    { fwd = these absurd id (\ _ x -> x)-    , bwd = That-    }+  unitl =+    Iso+      { fwd = these absurd id (\_ x -> x),+        bwd = That+      }    unitr :: Iso (->) (These a Void) a-  unitr = Iso-    { fwd = these id absurd const-    , bwd = This-    }+  unitr =+    Iso+      { fwd = these id absurd const,+        bwd = This+      }  instance (Monad m, Tensor (->) t i, Associative (Star m) t) => Tensor (Star m) t i where   unitl :: Iso (Star m) (i `t` a) a-  unitl = Iso-    { fwd = (`rmap` id) (fwd unitl)-    , bwd = (`rmap` id) (bwd unitl)-    }+  unitl =+    Iso+      { fwd = (`rmap` id) (fwd unitl),+        bwd = (`rmap` id) (bwd unitl)+      }    unitr :: Iso (Star m) (a `t` i) a-  unitr = Iso-    { fwd = (`rmap` id) (fwd unitr)-    , bwd = (`rmap` id) (bwd unitr)-    }+  unitr =+    Iso+      { fwd = (`rmap` id) (fwd unitr),+        bwd = (`rmap` id) (bwd unitr)+      } +instance (Monad m, Tensor (->) t i, Associative (Kleisli m) t) => Tensor (Kleisli m) t i where+  unitl :: Iso (Kleisli m) (i `t` a) a+  unitl =+    Iso+      { fwd = (`rmap` id) (fwd unitl),+        bwd = (`rmap` id) (bwd unitl)+      }++  unitr :: Iso (Kleisli m) (a `t` i) a+  unitr =+    Iso+      { fwd = (`rmap` id) (fwd unitr),+        bwd = (`rmap` id) (bwd unitr)+      }+ --------------------------------------------------------------------------------  -- | A bifunctor \(\_ \otimes\_ \ : \mathcal{C} \times \mathcal{C} \to \mathcal{C}\)@@ -344,3 +395,7 @@ instance (Monad m, Symmetric (->) t, Associative (Star m) t) => Symmetric (Star m) t where   swap :: Star m (a `t` b) (b `t` a)   swap = Star $ pure . swap++instance (Monad m, Symmetric (->) t, Associative (Kleisli m) t) => Symmetric (Kleisli m) t where+  swap :: Kleisli m (a `t` b) (b `t` a)+  swap = Kleisli $ pure . swap

@@ -1,11 +1,12 @@-{-# LANGUAGE AllowAmbiguousTypes      #-}-{-# LANGUAGE DataKinds                #-}-{-# LANGUAGE GADTs                    #-}-{-# LANGUAGE PolyKinds                #-}-{-# LANGUAGE ScopedTypeVariables      #-}+{-# LANGUAGE AllowAmbiguousTypes #-}+{-# LANGUAGE DataKinds #-}+{-# LANGUAGE GADTs #-}+{-# LANGUAGE PolyKinds #-}+{-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE StandaloneKindSignatures #-}-{-# LANGUAGE TypeApplications         #-}-{-# LANGUAGE TypeFamilies             #-}+{-# LANGUAGE TypeApplications #-}+{-# LANGUAGE TypeFamilies #-}+ module Control.Category.Tensor.Expr   ( -- * Type Families     MConcat,@@ -37,7 +38,7 @@ -- let bar :: Tensored Either Void '[Bool, Int] --     bar = Tensored $ Right $ Left 8 -- :}--- +-- -- >>> :{ -- let baz :: Tensored These Void '[Bool, Int] --     baz = Tensored $ These True $ This 8@@ -47,28 +48,26 @@   MConcat mappend mempty '[] = mempty   MConcat mappend mempty (x ': xs) = mappend x (MConcat mappend mempty xs) -newtype Tensored t i xs = Tensored { getTensored :: MConcat t i xs }+newtype Tensored t i xs = Tensored {getTensored :: MConcat t i xs}  deriving newtype instance Show (MConcat t i xs) => Show (Tensored t i xs)+ deriving newtype instance Eq (MConcat t i xs) => Eq (Tensored t i xs)+ deriving newtype instance Ord (MConcat t i xs) => Ord (Tensored t i xs)  --------------------------------------------------------------------------------  type (++) :: [k] -> [k] -> [k]-type family xs ++ ys-  where+type family xs ++ ys where   '[] ++ xs = xs   (x ': xs) ++ ys = x ': (xs ++ ys)  class AppendTensored xs where   appendTensored :: Tensor (->) t i => Tensored t i xs `t` Tensored t i ys -> Tensored t i (xs ++ ys) -instance AppendTensored '[]-  where+instance AppendTensored '[] where   appendTensored = fwd unitl . glmap getTensored -instance AppendTensored xs => AppendTensored (x ': xs)-  where+instance AppendTensored xs => AppendTensored (x ': xs) where   appendTensored = Tensored . grmap (getTensored . appendTensored @xs . glmap Tensored) . bwd assoc . glmap getTensored-

@@ -78,85 +78,141 @@ biinvIso (Iso f f') (Iso g g') = Iso (biinvmap f' f g' g) (biinvmap f f' g g')  -- | Boilerplate newtype to derive 'BiInvariant' for any 'Profunctor'.-newtype FromProfunctor p a b = FromProfunctor { runPro :: p a b}+newtype FromProfunctor p a b = FromProfunctor {runPro :: p a b}  instance Profunctor p => BiInvariant (FromProfunctor p) where   biinvmap :: (a' -> a) -> (a -> a') -> (b' -> b) -> (b -> b') -> FromProfunctor p a b -> FromProfunctor p a' b'   biinvmap f _ _ g = FromProfunctor . dimap f g . runPro  -- | Boilerplate newtype to derive 'BiInvariant' for any 'Bifunctor'.-newtype FromBifunctor p a b = FromBifunctor { runBi :: p a b }+newtype FromBifunctor p a b = FromBifunctor {runBi :: p a b}  instance Bifunctor p => BiInvariant (FromBifunctor p) where   biinvmap :: (a' -> a) -> (a -> a') -> (b' -> b) -> (b -> b') -> FromBifunctor p a b -> FromBifunctor p a' b'   biinvmap _ f _ g = FromBifunctor . bimap f g . runBi  -- | Boilerplate newtype to derive 'BiInvariant' for any 'Contravariant'.-newtype FromContra f a = FromContra { runContra :: f a }+newtype FromContra f a = FromContra {runContra :: f a}  instance Contravariant f => Contravariant (FromContra f) where   contramap :: Contravariant f => (a' -> a) -> FromContra f a -> FromContra f a'   contramap f = FromContra . contramap f . runContra  newtype FromFunctor f a = FromFunctor (f a)-  deriving Functor+  deriving (Functor)  type Coercible1 f = ((forall a b. Coercible a b => Coercible (f a) (f b)) :: Constraint)+ type Coercible2 f = (forall a b c d. (Coercible a b, Coercible c d) => Coercible (f a c) (f b d) :: Constraint) -deriving via (FromProfunctor (->))                   instance BiInvariant (->)-deriving via (FromProfunctor (Biff p f g))           instance (Profunctor p, Functor f, Functor g) => BiInvariant (Biff (FromProfunctor p) f g)-deriving via (FromProfunctor (Cayley f q))           instance (Functor f, Profunctor q) => BiInvariant (Cayley f q)-deriving via (FromProfunctor (Closure p))            instance Profunctor p => BiInvariant (Closure p)+deriving via (FromProfunctor (->)) instance BiInvariant (->)++deriving via (FromProfunctor (Biff p f g)) instance (Profunctor p, Functor f, Functor g) => BiInvariant (Biff (FromProfunctor p) f g)++deriving via (FromProfunctor (Cayley f q)) instance (Functor f, Profunctor q) => BiInvariant (Cayley f q)++deriving via (FromProfunctor (Closure p)) instance Profunctor p => BiInvariant (Closure p)+ deriving via (FromProfunctor (Clown f :: * -> * -> *)) instance Contravariant f => BiInvariant (Clown (FromContra f) :: * -> * -> *)-deriving via (FromProfunctor (Codensity p))          instance Profunctor p => BiInvariant (Codensity p)-deriving via (FromProfunctor (CofreeMapping p))      instance Profunctor p => BiInvariant (CofreeMapping p)-deriving via (FromProfunctor (CofreeTraversing p))   instance Profunctor p => BiInvariant (CofreeTraversing p)-deriving via (FromProfunctor (Cokleisli w))          instance Functor w => BiInvariant (Cokleisli w)-deriving via (FromProfunctor (Copastro p))           instance BiInvariant (Copastro p)-deriving via (FromProfunctor (CopastroSum p))        instance BiInvariant (CopastroSum p)-deriving via (FromProfunctor (Costar f))             instance Functor f => BiInvariant (Costar f)-deriving via (FromProfunctor (Cotambara p))          instance BiInvariant (Cotambara p)-deriving via (FromProfunctor (CotambaraSum p))       instance BiInvariant (CotambaraSum p)-deriving via (FromProfunctor (Coyoneda p))           instance BiInvariant (Coyoneda p)-deriving via (FromProfunctor (Environment p))        instance BiInvariant (Environment p)++deriving via (FromProfunctor (Codensity p)) instance Profunctor p => BiInvariant (Codensity p)++deriving via (FromProfunctor (CofreeMapping p)) instance Profunctor p => BiInvariant (CofreeMapping p)++deriving via (FromProfunctor (CofreeTraversing p)) instance Profunctor p => BiInvariant (CofreeTraversing p)++deriving via (FromProfunctor (Cokleisli w)) instance Functor w => BiInvariant (Cokleisli w)++deriving via (FromProfunctor (Copastro p)) instance BiInvariant (Copastro p)++deriving via (FromProfunctor (CopastroSum p)) instance BiInvariant (CopastroSum p)++deriving via (FromProfunctor (Costar f)) instance Functor f => BiInvariant (Costar f)++deriving via (FromProfunctor (Cotambara p)) instance BiInvariant (Cotambara p)++deriving via (FromProfunctor (CotambaraSum p)) instance BiInvariant (CotambaraSum p)++deriving via (FromProfunctor (Coyoneda p)) instance BiInvariant (Coyoneda p)++deriving via (FromProfunctor (Environment p)) instance BiInvariant (Environment p)+ deriving via (FromProfunctor (Forget r :: * -> * -> *)) instance BiInvariant (Forget r :: * -> * -> *)-deriving via (FromProfunctor (FreeMapping p))        instance BiInvariant (FreeMapping p)-deriving via (FromProfunctor (FreeTraversing p))     instance BiInvariant (FreeTraversing p)-deriving via (FromProfunctor (Joker f :: * -> * -> *))  instance Functor f => BiInvariant (Joker (FromContra f) :: * -> * -> *)-deriving via (FromProfunctor (Kleisli m))            instance Monad m => BiInvariant (Kleisli m)-deriving via (FromProfunctor (Pastro p))             instance BiInvariant (Pastro p)-deriving via (FromProfunctor (PastroSum p))          instance BiInvariant (PastroSum p)-deriving via (FromProfunctor (Procompose p q))       instance (Profunctor p, Profunctor q) => BiInvariant (Procompose p q)-deriving via (FromProfunctor (Product p q))          instance (Profunctor p, Profunctor q) => BiInvariant (Product (FromProfunctor p) (FromProfunctor q))-deriving via (FromProfunctor (Ran p q))              instance (Profunctor p, Profunctor q) => BiInvariant (Ran p q)-deriving via (FromProfunctor (Rift p q))             instance (Profunctor p, Profunctor q) => BiInvariant (Rift p q)-deriving via (FromProfunctor (Star f))               instance Functor f => BiInvariant (Star (FromFunctor f))-deriving via (FromProfunctor (Sum p q))              instance (Profunctor p, Profunctor q) => BiInvariant (Sum (FromProfunctor p) (FromProfunctor q))++deriving via (FromProfunctor (FreeMapping p)) instance BiInvariant (FreeMapping p)++deriving via (FromProfunctor (FreeTraversing p)) instance BiInvariant (FreeTraversing p)++deriving via (FromProfunctor (Joker f :: * -> * -> *)) instance Functor f => BiInvariant (Joker (FromContra f) :: * -> * -> *)++deriving via (FromProfunctor (Kleisli m)) instance Monad m => BiInvariant (Kleisli m)++deriving via (FromProfunctor (Pastro p)) instance BiInvariant (Pastro p)++deriving via (FromProfunctor (PastroSum p)) instance BiInvariant (PastroSum p)++deriving via (FromProfunctor (Procompose p q)) instance (Profunctor p, Profunctor q) => BiInvariant (Procompose p q)++deriving via (FromProfunctor (Product p q)) instance (Profunctor p, Profunctor q) => BiInvariant (Product (FromProfunctor p) (FromProfunctor q))++deriving via (FromProfunctor (Ran p q)) instance (Profunctor p, Profunctor q) => BiInvariant (Ran p q)++deriving via (FromProfunctor (Rift p q)) instance (Profunctor p, Profunctor q) => BiInvariant (Rift p q)++deriving via (FromProfunctor (Star f)) instance Functor f => BiInvariant (Star (FromFunctor f))++deriving via (FromProfunctor (Star f)) instance Functor f => BiInvariant (Star (FromContra f))++deriving via (FromProfunctor (Sum p q)) instance (Profunctor p, Profunctor q) => BiInvariant (Sum (FromProfunctor p) (FromProfunctor q))+ deriving via (FromProfunctor (Tagged :: * -> * -> *)) instance BiInvariant (Tagged :: * -> * -> *)-deriving via (FromProfunctor (Tambara p))            instance Profunctor p => BiInvariant (Tambara p)-deriving via (FromProfunctor (TambaraSum p))         instance Profunctor p => BiInvariant (TambaraSum p)-deriving via (FromProfunctor (Tannen f q))           instance (Functor f, Profunctor q) => BiInvariant (Tannen f q)-deriving via (FromProfunctor (WrappedArrow p))       instance Arrow p => BiInvariant (WrappedArrow p)-deriving via (FromProfunctor (Yoneda p))             instance BiInvariant (Yoneda p) -deriving via (FromBifunctor ((,,) x1))                 instance BiInvariant ((,,) x1)-deriving via (FromBifunctor ((,,,) x1 x2))             instance BiInvariant ((,,,) x1 x2)-deriving via (FromBifunctor ((,,,,) x1 x2 x3))         instance BiInvariant ((,,,,) x1 x2 x3)-deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4))     instance BiInvariant ((,,,,,) x1 x2 x3 x4)+deriving via (FromProfunctor (Tambara p)) instance Profunctor p => BiInvariant (Tambara p)++deriving via (FromProfunctor (TambaraSum p)) instance Profunctor p => BiInvariant (TambaraSum p)++deriving via (FromProfunctor (Tannen f q)) instance (Functor f, Profunctor q) => BiInvariant (Tannen f q)++deriving via (FromProfunctor (WrappedArrow p)) instance Arrow p => BiInvariant (WrappedArrow p)++deriving via (FromProfunctor (Yoneda p)) instance BiInvariant (Yoneda p)++deriving via (FromBifunctor ((,,) x1)) instance BiInvariant ((,,) x1)++deriving via (FromBifunctor ((,,,) x1 x2)) instance BiInvariant ((,,,) x1 x2)++deriving via (FromBifunctor ((,,,,) x1 x2 x3)) instance BiInvariant ((,,,,) x1 x2 x3)++deriving via (FromBifunctor ((,,,,,) x1 x2 x3 x4)) instance BiInvariant ((,,,,,) x1 x2 x3 x4)+ deriving via (FromBifunctor ((,,,,,,) x1 x2 x3 x4 x5)) instance BiInvariant ((,,,,,,) x1 x2 x3 x4 x5)-deriving via (FromBifunctor (,))                       instance BiInvariant (,)-deriving via (FromBifunctor Arg)                       instance BiInvariant Arg-deriving via (FromBifunctor (Biap bi))                 instance Bifunctor bi => BiInvariant (Biap bi)-deriving via (FromBifunctor (Biff p f g))              instance (Bifunctor p, Functor f, Functor g) => BiInvariant (Biff (FromBifunctor p) f g)-deriving via (FromBifunctor (Clown f :: * -> * -> *))  instance Functor f => BiInvariant (Clown (FromFunctor f) :: * -> * -> *)-deriving via (FromBifunctor (Const :: * -> * -> *))    instance BiInvariant (Const :: * -> * -> *)-deriving via (FromBifunctor Either)                    instance BiInvariant Either-deriving via (FromBifunctor (Flip p))                  instance Bifunctor p => BiInvariant (Flip p)-deriving via (FromBifunctor (Joker f :: * -> * -> *))  instance Functor f => BiInvariant (Joker (FromFunctor f) :: * -> * -> *)-deriving via (FromBifunctor (K1 i :: * -> * -> *))     instance BiInvariant (K1 i :: * -> * -> *)-deriving via (FromBifunctor (Product p q))             instance (Bifunctor p, Bifunctor q) => BiInvariant (Product (FromBifunctor p) (FromBifunctor q))-deriving via (FromBifunctor (Sum p q))                 instance (Bifunctor p, Bifunctor q) => BiInvariant (Sum (FromBifunctor p) (FromBifunctor q))-deriving via (FromBifunctor (Tannen f q))              instance (Functor f, Coercible1 f, Bifunctor q) => BiInvariant (Tannen (FromFunctor f) (FromBifunctor q))-deriving via (FromBifunctor These)                     instance BiInvariant These-deriving via (FromBifunctor (WrappedBifunctor p))      instance Bifunctor p => BiInvariant (WrappedBifunctor p)++deriving via (FromBifunctor (,)) instance BiInvariant (,)++deriving via (FromBifunctor Arg) instance BiInvariant Arg++deriving via (FromBifunctor (Biap bi)) instance Bifunctor bi => BiInvariant (Biap bi)++deriving via (FromBifunctor (Biff p f g)) instance (Bifunctor p, Functor f, Functor g) => BiInvariant (Biff (FromBifunctor p) f g)++deriving via (FromBifunctor (Clown f :: * -> * -> *)) instance Functor f => BiInvariant (Clown (FromFunctor f) :: * -> * -> *)++deriving via (FromBifunctor (Const :: * -> * -> *)) instance BiInvariant (Const :: * -> * -> *)++deriving via (FromBifunctor Either) instance BiInvariant Either++deriving via (FromBifunctor (Flip p)) instance Bifunctor p => BiInvariant (Flip p)++deriving via (FromBifunctor (Joker f :: * -> * -> *)) instance Functor f => BiInvariant (Joker (FromFunctor f) :: * -> * -> *)++deriving via (FromBifunctor (K1 i :: * -> * -> *)) instance BiInvariant (K1 i :: * -> * -> *)++deriving via (FromBifunctor (Product p q)) instance (Bifunctor p, Bifunctor q) => BiInvariant (Product (FromBifunctor p) (FromBifunctor q))++deriving via (FromBifunctor (Sum p q)) instance (Bifunctor p, Bifunctor q) => BiInvariant (Sum (FromBifunctor p) (FromBifunctor q))++deriving via (FromBifunctor (Tannen f q)) instance (Functor f, Coercible1 f, Bifunctor q) => BiInvariant (Tannen (FromFunctor f) (FromBifunctor q))++deriving via (FromBifunctor These) instance BiInvariant These++deriving via (FromBifunctor (WrappedBifunctor p)) instance Bifunctor p => BiInvariant (WrappedBifunctor p)

@@ -50,675 +50,1055 @@ import Data.Profunctor.Yoneda (Coyoneda, Yoneda) import Data.Semigroup (Arg) import Data.Tagged (Tagged)-import Data.These (These (This, That))-import Data.Traversable (Traversable)-import Data.Tuple (fst, snd)-import GHC.Generics (K1 (..))-------------------------------------------------------------------------------------- | 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' \(P : \mathcal{C}^{op} \times \mathcal{D} \to Set\)--- 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 t1 t2 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 (t1 a x) (t2 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' \(P : \mathcal{C}^{op} \times \mathcal{D} \to Set\)--- 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 t1 t2 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 `t1` a) (x `t2` 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 t1 t2 f, RightModule cat t1 t2 f) => Bimodule cat t1 t2 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' \(P : \mathcal{C}^{op} \times \mathcal{D} \to Set\)--- 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 t1 t2 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 (t1 a x) (t2 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' \(P : \mathcal{C}^{op} \times \mathcal{D} \to Set\)--- 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 t1 t2 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 `t1` a) (x `t2` 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 t1 t2 f, RightCoModule cat t1 t2 f) => CoBimodule cat t1 t2 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)+import Data.These (These (That, This))+import Data.Traversable (Traversable)+import Data.Tuple (fst, snd)+import GHC.Generics (K1 (..))++--------------------------------------------------------------------------------++-- | 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' \(P : \mathcal{C}^{op} \times \mathcal{D} \to Set\)+-- 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 t1 t2 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 (t1 a x) (t2 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' \(P : \mathcal{C}^{op} \times \mathcal{D} \to Set\)+-- 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 t1 t2 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 `t1` a) (x `t2` 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 t1 t2 f, RightModule cat t1 t2 f) => Bimodule cat t1 t2 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' \(P : \mathcal{C}^{op} \times \mathcal{D} \to Set\)+-- 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 t1 t2 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 (t1 a x) (t2 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' \(P : \mathcal{C}^{op} \times \mathcal{D} \to Set\)+-- 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 t1 t2 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 `t1` a) (x `t2` 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 t1 t2 f, RightCoModule cat t1 t2 f) => CoBimodule cat t1 t2 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)

@@ -13,10 +13,11 @@ --------------------------------------------------------------------------------  import Control.Applicative (Alternative (..), Applicative (..), pure, (<$>))+import Control.Arrow (Kleisli (..)) import Control.Category (Category (..)) import Control.Category.Cartesian (Cocartesian (..), Semicartesian (..)) import Control.Category.Tensor (Associative, Iso (..), Tensor (..))-import Control.Monad (Functor(..), Monad)+import Control.Monad (Functor (..), Monad) import Data.Biapplicative (Biapplicative (..), Bifunctor (..)) import Data.Bifunctor.Clown (Clown) import Data.Bifunctor.Joker (Joker (..))@@ -24,7 +25,7 @@ import Data.Function (const, ($)) import Data.Profunctor (Forget (..), Profunctor (..), Star (..), Strong (..)) import Data.Semigroupoid (Semigroupoid (..))-import Data.These (These (..))+import Data.These (These (..), these) import Data.Tuple (fst, snd, uncurry) import Data.Void (Void, absurd) import Prelude (Either (..))@@ -39,7 +40,7 @@ -- -- __Associativity:__ ----- \[ +-- \[ -- \require{AMScd} -- \begin{CD} -- (F A B \bullet F C D) \bullet F X Y                      @>>{\alpha_{\mathcal{D}}}>                              F A B \bullet (F C D \bullet F X Y) \\@@ -54,7 +55,7 @@ -- 'combine' 'Control.Category..' 'Control.Category.Tensor.grmap' 'combine' 'Control.Category..' 'bwd' 'Control.Category.Tensor.assoc' ≡ 'fmap' ('bwd' 'Control.Category.Tensor.assoc') 'Control.Category..' 'combine' 'Control.Category..' 'Control.Category.Tensor.glmap' 'combine' -- @ class (Associative cat t1, Associative cat t2, Associative cat to) => Semigroupal cat t1 t2 to f where-  -- | A natural transformation \(\phi_{AB,CD} : F\ A\ B \bullet F\ C\ D \to F\ (A \otimes C)\ (B \otimes D)\). +  -- | A natural transformation \(\phi_{AB,CD} : F\ A\ B \bullet F\ C\ D \to F\ (A \otimes C)\ (B \otimes D)\).   --   -- ==== __Examples__   --@@ -75,13 +76,14 @@ instance Semigroupal (->) (,) (,) (,) (,) where   combine :: ((x, y), (x', y')) -> ((x, x'), (y, y'))   combine ((x, y), (x', y')) = ((x, x'), (y, y'))-  -- NOTE: This version could be used for a more general abstraction-  -- of products in a category:-  -- combine =-  --   let fwd' = fwd assoc-  --       bwd' = bwd assoc-  --   in second swap . swap . fwd' . swap . first (bwd' . first swap) . fwd' +-- NOTE: This version could be used for a more general abstraction+-- of products in a category:+-- combine =+--   let fwd' = fwd assoc+--       bwd' = bwd assoc+--   in second swap . swap . fwd' . swap . first (bwd' . first swap) . fwd'+ instance Semigroupal (->) Either Either Either (,) where   combine :: Either (x, y) (x', y') -> (Either x x', Either y y')   combine = either (bimap Left Left) (bimap Right Right)@@ -93,17 +95,17 @@ instance Semigroupal (->) Either (,) (,) Either where   combine :: (Either x y, Either x' y') -> Either (Either x x') (y, y')   combine = \case-    (Left x, Left _)    -> Left $ Left x-    (Left x, Right _)   -> Left $ Left x-    (Right _, Left x')  -> Left $ Right x'+    (Left x, Left _) -> Left $ Left x+    (Left x, Right _) -> Left $ Left x+    (Right _, Left x') -> Left $ Right x'     (Right y, Right y') -> Right (y, y')  instance Semigroupal (->) These (,) (,) Either where   combine :: (Either x y, Either x' y') -> Either (These x x') (y, y')   combine = \case-    (Left x, Left x')   -> Left $ These x x'-    (Left x, Right _)   -> Left $ This x-    (Right _, Left x')  -> Left $ That x'+    (Left x, Left x') -> Left $ These x x'+    (Left x, Right _) -> Left $ This x+    (Right _, Left x') -> Left $ That x'     (Right y, Right y') -> Right (y, y')  instance Semigroupal (->) (,) (,) (,) (->) where@@ -120,11 +122,11 @@  instance Alternative f => Semigroupal (->) Either Either (,) (Joker f) where   combine :: (Joker f x y, Joker f x' y') -> Joker f (Either x x') (Either y y')-  combine  = uncurry $ biliftA2 (\_ x' -> Right x') (\_ y' -> Right y')+  combine = uncurry $ biliftA2 (\_ x' -> Right x') (\_ y' -> Right y')  instance Functor f => Semigroupal (->) Either Either Either (Joker f) where   combine :: Either (Joker f x y) (Joker f x' y') -> Joker f (Either x x') (Either y y')-  combine = either (Joker . fmap Left . runJoker ) (Joker . fmap Right . runJoker)+  combine = either (Joker . fmap Left . runJoker) (Joker . fmap Right . runJoker)  instance Applicative f => Semigroupal (->) (,) (,) (,) (Clown f) where   combine :: (Clown f x y, Clown f x' y') -> Clown f (x, x') (y, y')@@ -142,16 +144,56 @@   combine :: (Star f x y, Star f x' y') -> Star f (Either x x') (Either y y')   combine (Star fxy, Star fxy') = Star $ either (fmap Left . fxy) (fmap Right . fxy') +instance Applicative f => Semigroupal (->) These These (,) (Star f) where+  combine :: (Star f x y, Star f x' y') -> Star f (These x x') (These y y')+  combine (Star fxy, Star fxy') = Star $ these (fmap This . fxy) (fmap That . fxy') (\x x' -> liftA2 These (fxy x) (fxy' x'))++instance Alternative f => Semigroupal (->) These These These (Star f) where+  combine :: Applicative f => These (Star f x y) (Star f x' y') -> Star f (These x x') (These y y')+  combine = \case+    This (Star fxy) -> Star $ these (fmap This . fxy) (const empty) (\x _ -> This <$> fxy x)+    That (Star fxy') -> Star $ these (const empty) (fmap That . fxy') (\_ x' -> That <$> fxy' x')+    These (Star fxy) (Star fxy') -> Star $ these (fmap This . fxy) (fmap That . fxy') (\x x' -> liftA2 These (fxy x) (fxy' x'))+ instance Alternative f => Semigroupal (->) Either Either Either (Star f) where   combine :: Either (Star f x y) (Star f x' y') -> Star f (Either x x') (Either y y')   combine = \case-    Left (Star fxy)   -> Star $ either (fmap Left . fxy) (const empty)+    Left (Star fxy) -> Star $ either (fmap Left . fxy) (const empty)     Right (Star fxy') -> Star $ either (const empty) (fmap Right . fxy')  instance Alternative f => Semigroupal (->) (,) Either (,) (Star f) where   combine :: (Star f x y, Star f x' y') -> Star f (x, x') (Either y y')   combine (Star f, Star g) = Star $ \(x, x') -> (Left <$> f x) <|> (Right <$> g x') +instance Applicative f => Semigroupal (->) (,) (,) (,) (Kleisli f) where+  combine :: (Kleisli f x y, Kleisli f x' y') -> Kleisli f (x, x') (y, y')+  combine (Kleisli fxy, Kleisli fxy') = Kleisli $ \(x, x') -> liftA2 (,) (fxy x) (fxy' x')++instance Functor f => Semigroupal (->) Either Either (,) (Kleisli f) where+  combine :: (Kleisli f x y, Kleisli f x' y') -> Kleisli f (Either x x') (Either y y')+  combine (Kleisli fxy, Kleisli fxy') = Kleisli $ either (fmap Left . fxy) (fmap Right . fxy')++instance Applicative f => Semigroupal (->) These These (,) (Kleisli f) where+  combine :: (Kleisli f x y, Kleisli f x' y') -> Kleisli f (These x x') (These y y')+  combine (Kleisli fxy, Kleisli fxy') = Kleisli $ these (fmap This . fxy) (fmap That . fxy') (\x x' -> liftA2 These (fxy x) (fxy' x'))++instance Alternative f => Semigroupal (->) These These These (Kleisli f) where+  combine :: Applicative f => These (Kleisli f x y) (Kleisli f x' y') -> Kleisli f (These x x') (These y y')+  combine = \case+    This (Kleisli fxy) -> Kleisli $ these (fmap This . fxy) (const empty) (\x _ -> This <$> fxy x)+    That (Kleisli fxy') -> Kleisli $ these (const empty) (fmap That . fxy') (\_ x' -> That <$> fxy' x')+    These (Kleisli fxy) (Kleisli fxy') -> Kleisli $ these (fmap This . fxy) (fmap That . fxy') (\x x' -> liftA2 These (fxy x) (fxy' x'))++instance Alternative f => Semigroupal (->) Either Either Either (Kleisli f) where+  combine :: Either (Kleisli f x y) (Kleisli f x' y') -> Kleisli f (Either x x') (Either y y')+  combine = \case+    Left (Kleisli fxy) -> Kleisli $ either (fmap Left . fxy) (const empty)+    Right (Kleisli fxy') -> Kleisli $ either (const empty) (fmap Right . fxy')++instance Alternative f => Semigroupal (->) (,) Either (,) (Kleisli f) where+  combine :: (Kleisli f x y, Kleisli f x' y') -> Kleisli f (x, x') (Either y y')+  combine (Kleisli f, Kleisli g) = Kleisli $ \(x, x') -> (Left <$> f x) <|> (Right <$> g x')+ instance Alternative f => Semigroupal (->) (,) (,) (,) (Forget (f r)) where   combine :: (Forget (f r) x y, Forget (f r) x' y') -> Forget (f r) (x, x') (y, y')   combine (Forget f, Forget g) = Forget $ \(x, x') -> f x <|> g x'@@ -163,7 +205,7 @@ instance Alternative f => Semigroupal (->) Either Either Either (Forget (f r)) where   combine :: Either (Forget (f r) x y) (Forget (f r) x' y') -> Forget (f r) (Either x x') (Either y y')   combine = \case-    Left (Forget f)  -> Forget $ either f (const empty)+    Left (Forget f) -> Forget $ either f (const empty)     Right (Forget g) -> Forget $ either (const empty) g  instance Alternative f => Semigroupal (->) (,) Either (,) (Forget (f r)) where@@ -186,7 +228,7 @@   --   -- >>> :t introduce @(->) @Void @() @() @Either   -- introduce @(->) @Void @() @() @Either :: () -> Either Void ()-  -- +  --   -- >>> introduce @(->) @Void @() @() @Either ()   -- Right ()   introduce :: cat io (f i1 i2)@@ -251,6 +293,22 @@   introduce :: () -> Star f () Void   introduce () = Star $ const empty +instance Applicative f => Unital (->) () () () (Kleisli f) where+  introduce :: () -> Kleisli f () ()+  introduce () = Kleisli pure++instance Unital (->) Void Void () (Kleisli f) where+  introduce :: () -> Kleisli f Void Void+  introduce () = Kleisli absurd++instance Alternative f => Unital (->) Void Void Void (Kleisli f) where+  introduce :: Void -> Kleisli f Void Void+  introduce = absurd++instance Alternative f => Unital (->) () Void () (Kleisli f) where+  introduce :: () -> Kleisli f () Void+  introduce () = Kleisli $ const empty+ -------------------------------------------------------------------------------- -- Monoidal @@ -264,7 +322,7 @@ -- -- __Right Unitality:__ ----- \[ +-- \[ -- \require{AMScd} -- \begin{CD} -- F A B \bullet I_{\mathcal{D}}   @>{1 \bullet \phi}>>                                     F A B \bullet F I_{\mathcal{C_{1}}} I_{\mathcal{C_{2}}}\\@@ -279,7 +337,7 @@ -- -- __ Left Unitality__: ----- \[ +-- \[ -- \begin{CD} -- I_{\mathcal{D}} \bullet F A B   @>{\phi \bullet 1}>>                                          F I_{\mathcal{C_{1}}} I_{\mathcal{C_{2}}} \bullet F A B\\ -- @VV{\lambda_{\mathcal{D}}}V                                                                   @VV{I_{\mathcal{C_{1}}}I_{\mathcal{C_{2}}},\phi AB}V \\@@ -290,28 +348,60 @@ -- @ -- 'combine' 'Control.Category..' 'Control.Category.Tensor.glmap' 'introduce' ≡ 'fmap' ('bwd' 'unitl') 'Control.Category..' 'fwd' 'unitl' -- @-class ( Tensor cat t1 i1-      , Tensor cat t2 i2-      , Tensor cat to io-      , Semigroupal cat t1 t2 to f-      , Unital cat i1 i2 io f-      ) => Monoidal cat t1 i1 t2 i2 to io f+class+  ( Tensor cat t1 i1,+    Tensor cat t2 i2,+    Tensor cat to io,+    Semigroupal cat t1 t2 to f,+    Unital cat i1 i2 io f+  ) =>+  Monoidal cat t1 i1 t2 i2 to io f  instance (Strong p, Semigroupoid p, Category p) => Monoidal (->) (,) () (,) () (,) () (StrongCategory p)+ instance Monoidal (->) (,) () (,) () (,) () (,)+ instance Monoidal (->) Either Void Either Void Either Void (,)+ instance Monoidal (->) Either Void Either Void Either Void Either+ instance Monoidal (->) Either Void (,) () (,) () Either+ instance Monoidal (->) These Void (,) () (,) () Either+ instance Monoidal (->) (,) () (,) () (,) () (->)+ instance Monoidal (->) Either Void Either Void (,) () (->)+ instance Applicative f => Monoidal (->) (,) () (,) () (,) () (Joker f)+ instance Alternative f => Monoidal (->) Either Void Either Void (,) () (Joker f)+ instance Functor f => Monoidal (->) Either Void Either Void Either Void (Joker f)+ instance Applicative f => Monoidal (->) (,) () (,) () (,) () (Star f)+ instance Functor f => Monoidal (->) Either Void Either Void (,) () (Star f)++instance Applicative f => Monoidal (->) These Void These Void (,) () (Star f)+ instance Alternative f => Monoidal (->) Either Void Either Void Either Void (Star f)++instance Alternative f => Monoidal (->) These Void These Void These Void (Star f)+ instance Alternative f => Monoidal (->) (,) () Either Void (,) () (Star f)++instance Applicative f => Monoidal (->) (,) () (,) () (,) () (Kleisli f)++instance Functor f => Monoidal (->) Either Void Either Void (,) () (Kleisli f)++instance Applicative f => Monoidal (->) These Void These Void (,) () (Kleisli f)++instance Alternative f => Monoidal (->) Either Void Either Void Either Void (Kleisli f)++instance Alternative f => Monoidal (->) These Void These Void These Void (Kleisli f)++instance Alternative f => Monoidal (->) (,) () Either Void (,) () (Kleisli f)  newtype StrongCategory p a b = StrongCategory (p a b)   deriving (Functor, Applicative, Monad, Profunctor, Category)

@@ -1,16 +1,17 @@ {-# LANGUAGE TupleSections #-}-module Data.Bifunctor.Monoidal.Specialized where -import Prelude hiding ((&&), (||))+module Data.Bifunctor.Monoidal.Specialized where  import Control.Category.Cartesian import Control.Category.Tensor () import Data.Bifunctor.Monoidal import Data.Functor.Contravariant import Data.Profunctor+import Data.These import Data.Void+import Prelude hiding ((&&), (||)) --- | Split the input between the two argument arrows and multiply their outputs.+-- | Split the input between the two arguments and multiply their outputs. mux :: Semigroupal (->) (,) (,) (,) p => p a b -> p c d -> p (a, c) (b, d) mux = curry combine @@ -20,7 +21,7 @@ (***) :: Semigroupal (->) (,) (,) (,) p => p a b -> p c d -> p (a, c) (b, d) (***) = mux --- | Split the input between the two argument arrows and sum their outputs.+-- | Split the input between the two arguments and sum their outputs. demux :: Semigroupal (->) Either Either (,) p => p a b -> p c d -> p (Either a c) (Either b d) demux = curry combine @@ -30,7 +31,7 @@ (+++) :: Semigroupal (->) Either Either (,) p => p a b -> p c d -> p (Either a c) (Either b d) (+++) = demux --- | Send the whole input to the two argument arrows and multiply their outputs.+-- | Send the whole input to the two arguments and multiply their outputs. fanout :: (Profunctor p, Semigroupal (->) (,) (,) (,) p) => p x a -> p x b -> p x (a, b) fanout pxa pxb = lmap split' $ pxa *** pxb @@ -40,7 +41,7 @@ (&&&) :: (Profunctor p, Semigroupal (->) (,) (,) (,) p) => p x a -> p x b -> p x (a, b) (&&&) = fanout --- | Split the input between the two argument arrows and merge their outputs.+-- | Split the input between the two arguments and merge their outputs. fanin :: (Profunctor p, Semigroupal (->) Either Either (,) p) => p a x -> p b x -> p (Either a b) x fanin pax pbx = rmap merge' $ pax +++ pbx @@ -49,8 +50,8 @@ -- | Infix operator for 'fanin'. (|||) :: (Profunctor p, Semigroupal (->) Either Either (,) p) => p a x -> p b x -> p (Either a b) x (|||) = fanin-    --- | Split the input between the two argument arrows and and sum their outputs.++-- | Split the input between the two arguments and and sum their outputs. switch :: Semigroupal (->) (,) Either (,) p => p a b -> p c d -> p (a, c) (Either b d) switch = curry combine @@ -60,15 +61,15 @@ (&|) :: Semigroupal (->) (,) Either (,) p => p a b -> p c d -> p (a, c) (Either b d) (&|) = switch --- | Send the whole input to the two argument arrows and sum their outputs.+-- | Send the whole input to the two arguments and sum their outputs. union :: Profunctor p => Semigroupal (->) (,) Either (,) p => p x a -> p x b -> p x (Either a b) union pxa pxb = lmap split' $ pxa &| pxb --- | Split the input between the two argument arrows then merge their outputs.+-- | Split the input between the two arguments then merge their outputs. divide :: (Profunctor p, Semigroupal (->) (,) Either (,) p) => p a x -> p b x -> p (a, b) x divide pxa pxb = rmap merge' $ pxa &| pxb --- | Split the input between the two argument arrows then multiply their outputs.+-- | Split the input between the two arguments then multiply their outputs. splice :: Semigroupal (->) Either (,) (,) p => p a b -> p c d -> p (Either a c) (b, d) splice = curry combine 

@@ -1,4 +1,5 @@ {-# LANGUAGE DefaultSignatures #-}+ module Data.Functor.Invariant   ( -- * Invariant     Invariant (..),@@ -45,9 +46,9 @@   invmap = invmapFunctor  invIso :: Invariant f => Iso (->) a a' -> Iso (->) (f a) (f a')-invIso (Iso f g)  = Iso (invmap f g) (invmap g f)+invIso (Iso f g) = Iso (invmap f g) (invmap g f) -newtype FromFunctor f a = FromFunctor { runBi :: f a }+newtype FromFunctor f a = FromFunctor {runBi :: f a}  -- | Every 'Functor' is also an 'Invariant' functor. invmapFunctor :: Functor f => (a -> b) -> (b -> a) -> f a -> f b@@ -57,22 +58,34 @@   invmap :: (a -> a') -> (a' -> a) -> FromFunctor f a -> FromFunctor f a'   invmap f _ = FromFunctor . fmap f . runBi -newtype FromContra f a = FromContra { runContra :: f a }+newtype FromContra f a = FromContra {runContra :: f a}  instance Contravariant f => Invariant (FromContra f) where   invmap :: (a -> a') -> (a' -> a) -> FromContra f a -> FromContra f a'   invmap _ g = FromContra . contramap g . runContra -deriving via FromFunctor Identity           instance Invariant Identity-deriving via FromFunctor (Compose f g)      instance (Functor f, Functor g) => Invariant (Compose f g)-deriving via FromFunctor []                 instance Invariant []-deriving via FromFunctor ZipList            instance Invariant ZipList-deriving via FromFunctor NonEmpty           instance Invariant NonEmpty-deriving via FromFunctor Maybe              instance Invariant Maybe-deriving via FromFunctor (Either e)         instance Invariant (Either e)-deriving via FromFunctor IO                 instance Invariant IO-deriving via FromFunctor (Sum f g)          instance (Functor f, Functor g) => Invariant (Sum f g)-deriving via FromFunctor (Product f g)      instance (Functor f, Functor g) => Invariant (Product f g)-deriving via (FromFunctor ((,) x1))         instance Invariant ((,) x1)-deriving via (FromFunctor ((,,) x1 x2))     instance Invariant ((,,) x1 x2)+deriving via FromFunctor Identity instance Invariant Identity++deriving via FromFunctor (Compose f g) instance (Functor f, Functor g) => Invariant (Compose f g)++deriving via FromFunctor [] instance Invariant []++deriving via FromFunctor ZipList instance Invariant ZipList++deriving via FromFunctor NonEmpty instance Invariant NonEmpty++deriving via FromFunctor Maybe instance Invariant Maybe++deriving via FromFunctor (Either e) instance Invariant (Either e)++deriving via FromFunctor IO instance Invariant IO++deriving via FromFunctor (Sum f g) instance (Functor f, Functor g) => Invariant (Sum f g)++deriving via FromFunctor (Product f g) instance (Functor f, Functor g) => Invariant (Product f g)++deriving via (FromFunctor ((,) x1)) instance Invariant ((,) x1)++deriving via (FromFunctor ((,,) x1 x2)) instance Invariant ((,,) x1 x2)+ deriving via (FromFunctor ((,,,) x1 x2 x3)) instance Invariant ((,,,) x1 x2 x3)

@@ -46,7 +46,7 @@   -- >>> :t lstrength @(->) @(,) @Predicate (Predicate @Int (> 10))   -- lstrength @(->) @(,) @Predicate (Predicate @Int (> 10)) :: Predicate (Int, x)   ---  -- >>> :t lstrength @(->) @Either @[] +  -- >>> :t lstrength @(->) @Either @[]   -- lstrength @(->) @Either @[] :: a -> [Either a x]   --   -- >>> lstrength @(->) @Either @[] [True, False]@@ -71,86 +71,158 @@ instance Functor f => LeftModule Op (,) (FromFunctor f) where   lstrength = Op (fmap fst) -deriving via (FromContra Comparison)    instance LeftModule (->) (,) Comparison-deriving via (FromContra Equivalence)   instance LeftModule (->) (,) Equivalence-deriving via (FromContra Predicate)     instance LeftModule (->) (,) Predicate-deriving via (FromContra (Op a))        instance LeftModule (->) (,) (Op a)-deriving via (FromContra Proxy)         instance LeftModule (->) (,) Proxy-deriving via (FromContra U1)            instance LeftModule (->) (,) U1-deriving via (FromContra V1)            instance LeftModule (->) (,) V1-deriving via (FromContra (Const a))     instance LeftModule (->) (,) (Const a)-deriving via (FromContra (Alt f))       instance Contravariant f => LeftModule (->) (,) (Alt f)-deriving via (FromContra (Rec1 f))      instance Contravariant f => LeftModule (->) (,) (Rec1 f)+deriving via (FromContra Comparison) instance LeftModule (->) (,) Comparison++deriving via (FromContra Equivalence) instance LeftModule (->) (,) Equivalence++deriving via (FromContra Predicate) instance LeftModule (->) (,) Predicate++deriving via (FromContra (Op a)) instance LeftModule (->) (,) (Op a)++deriving via (FromContra Proxy) instance LeftModule (->) (,) Proxy++deriving via (FromContra U1) instance LeftModule (->) (,) U1++deriving via (FromContra V1) instance LeftModule (->) (,) V1++deriving via (FromContra (Const a)) instance LeftModule (->) (,) (Const a)++deriving via (FromContra (Alt f)) instance Contravariant f => LeftModule (->) (,) (Alt f)++deriving via (FromContra (Rec1 f)) instance Contravariant f => LeftModule (->) (,) (Rec1 f)+ deriving via (FromContra (Product f g)) instance (Contravariant f, Contravariant g) => LeftModule (->) (,) (Product f g)-deriving via (FromContra (Sum f g))     instance (Contravariant f, Contravariant g) => LeftModule (->) (,) (Sum f g)-deriving via (FromContra (f :+: g))     instance (Contravariant f, Contravariant g) => LeftModule (->) (,) (f :+: g)-deriving via (FromContra (f :*: g))     instance (Contravariant f, Contravariant g) => LeftModule (->) (,) (f :*: g)-deriving via (FromContra (K1 i c))      instance LeftModule (->) (,) (K1 i c)++deriving via (FromContra (Sum f g)) instance (Contravariant f, Contravariant g) => LeftModule (->) (,) (Sum f g)++deriving via (FromContra (f :+: g)) instance (Contravariant f, Contravariant g) => LeftModule (->) (,) (f :+: g)++deriving via (FromContra (f :*: g)) instance (Contravariant f, Contravariant g) => LeftModule (->) (,) (f :*: g)++deriving via (FromContra (K1 i c)) instance LeftModule (->) (,) (K1 i c)+ deriving via (FromContra (Compose f g)) instance (Functor f, Contravariant g) => LeftModule (->) (,) (Compose f g)-deriving via (FromContra (f :.: g))     instance (Functor f, Contravariant g) => LeftModule (->) (,) (f :.: g)-deriving via (FromContra (M1 i c f))    instance Contravariant f => LeftModule (->) (,) (M1 i c f) -deriving via (FromContra Comparison)    instance LeftModule Op Either Comparison-deriving via (FromContra Equivalence)   instance LeftModule Op Either Equivalence-deriving via (FromContra Predicate)     instance LeftModule Op Either Predicate-deriving via (FromContra (Op a))        instance LeftModule Op Either (Op a)-deriving via (FromContra Proxy)         instance LeftModule Op Either Proxy-deriving via (FromContra U1)            instance LeftModule Op Either U1-deriving via (FromContra V1)            instance LeftModule Op Either V1-deriving via (FromContra (Const a))     instance LeftModule Op Either (Const a)-deriving via (FromContra (Alt f))       instance Contravariant f => LeftModule Op Either (Alt f)-deriving via (FromContra (Rec1 f))      instance Contravariant f => LeftModule Op Either (Rec1 f)+deriving via (FromContra (f :.: g)) instance (Functor f, Contravariant g) => LeftModule (->) (,) (f :.: g)++deriving via (FromContra (M1 i c f)) instance Contravariant f => LeftModule (->) (,) (M1 i c f)++deriving via (FromContra Comparison) instance LeftModule Op Either Comparison++deriving via (FromContra Equivalence) instance LeftModule Op Either Equivalence++deriving via (FromContra Predicate) instance LeftModule Op Either Predicate++deriving via (FromContra (Op a)) instance LeftModule Op Either (Op a)++deriving via (FromContra Proxy) instance LeftModule Op Either Proxy++deriving via (FromContra U1) instance LeftModule Op Either U1++deriving via (FromContra V1) instance LeftModule Op Either V1++deriving via (FromContra (Const a)) instance LeftModule Op Either (Const a)++deriving via (FromContra (Alt f)) instance Contravariant f => LeftModule Op Either (Alt f)++deriving via (FromContra (Rec1 f)) instance Contravariant f => LeftModule Op Either (Rec1 f)+ deriving via (FromContra (Product f g)) instance (Contravariant f, Contravariant g) => LeftModule Op Either (Product f g)-deriving via (FromContra (Sum f g))     instance (Contravariant f, Contravariant g) => LeftModule Op Either (Sum f g)-deriving via (FromContra (f :+: g))     instance (Contravariant f, Contravariant g) => LeftModule Op Either (f :+: g)-deriving via (FromContra (f :*: g))     instance (Contravariant f, Contravariant g) => LeftModule Op Either (f :*: g)-deriving via (FromContra (K1 i c))      instance LeftModule Op Either (K1 i c)++deriving via (FromContra (Sum f g)) instance (Contravariant f, Contravariant g) => LeftModule Op Either (Sum f g)++deriving via (FromContra (f :+: g)) instance (Contravariant f, Contravariant g) => LeftModule Op Either (f :+: g)++deriving via (FromContra (f :*: g)) instance (Contravariant f, Contravariant g) => LeftModule Op Either (f :*: g)++deriving via (FromContra (K1 i c)) instance LeftModule Op Either (K1 i c)+ deriving via (FromContra (Compose f g)) instance (Functor f, Contravariant g) => LeftModule Op Either (Compose f g)-deriving via (FromContra (f :.: g))     instance (Functor f, Contravariant g) => LeftModule Op Either (f :.: g)-deriving via (FromContra (M1 i c f))    instance Contravariant f => LeftModule Op Either (M1 i c f) -deriving via FromFunctor Identity           instance LeftModule (->) Either Identity-deriving via FromFunctor (Compose f g)      instance (Functor f, Functor g) => LeftModule (->) Either (Compose f g)-deriving via FromFunctor []                 instance LeftModule (->) Either []-deriving via FromFunctor ZipList            instance LeftModule (->) Either ZipList-deriving via FromFunctor NonEmpty           instance LeftModule (->) Either NonEmpty-deriving via FromFunctor Maybe              instance LeftModule (->) Either Maybe-deriving via FromFunctor (Either e)         instance LeftModule (->) Either (Either e)-deriving via FromFunctor (These a)          instance LeftModule (->) Either (These a)-deriving via FromFunctor IO                 instance LeftModule (->) Either IO-deriving via FromFunctor (Sum f g)          instance (Functor f, Functor g) => LeftModule (->) Either (Sum f g)-deriving via FromFunctor (Product f g)      instance (Functor f, Functor g) => LeftModule (->) Either (Product f g)-deriving via (FromFunctor ((,) x1))         instance LeftModule (->) Either ((,) x1)-deriving via (FromFunctor ((,,) x1 x2))     instance LeftModule (->) Either ((,,) x1 x2)+deriving via (FromContra (f :.: g)) instance (Functor f, Contravariant g) => LeftModule Op Either (f :.: g)++deriving via (FromContra (M1 i c f)) instance Contravariant f => LeftModule Op Either (M1 i c f)++deriving via FromFunctor Identity instance LeftModule (->) Either Identity++deriving via FromFunctor (Compose f g) instance (Functor f, Functor g) => LeftModule (->) Either (Compose f g)++deriving via FromFunctor [] instance LeftModule (->) Either []++deriving via FromFunctor ZipList instance LeftModule (->) Either ZipList++deriving via FromFunctor NonEmpty instance LeftModule (->) Either NonEmpty++deriving via FromFunctor Maybe instance LeftModule (->) Either Maybe++deriving via FromFunctor (Either e) instance LeftModule (->) Either (Either e)++deriving via FromFunctor (These a) instance LeftModule (->) Either (These a)++deriving via FromFunctor IO instance LeftModule (->) Either IO++deriving via FromFunctor (Sum f g) instance (Functor f, Functor g) => LeftModule (->) Either (Sum f g)++deriving via FromFunctor (Product f g) instance (Functor f, Functor g) => LeftModule (->) Either (Product f g)++deriving via (FromFunctor ((,) x1)) instance LeftModule (->) Either ((,) x1)++deriving via (FromFunctor ((,,) x1 x2)) instance LeftModule (->) Either ((,,) x1 x2)+ deriving via (FromFunctor ((,,,) x1 x2 x3)) instance LeftModule (->) Either ((,,,) x1 x2 x3) -deriving via FromFunctor Identity           instance LeftModule (->) These Identity-deriving via FromFunctor (Compose f g)      instance (Functor f, Functor g) => LeftModule (->) These (Compose f g)-deriving via FromFunctor []                 instance LeftModule (->) These []-deriving via FromFunctor ZipList            instance LeftModule (->) These ZipList-deriving via FromFunctor NonEmpty           instance LeftModule (->) These NonEmpty-deriving via FromFunctor Maybe              instance LeftModule (->) These Maybe-deriving via FromFunctor (Either e)         instance LeftModule (->) These (Either e)-deriving via FromFunctor (These a)          instance LeftModule (->) These (These a)-deriving via FromFunctor IO                 instance LeftModule (->) These IO-deriving via FromFunctor (Sum f g)          instance (Functor f, Functor g) => LeftModule (->) These (Sum f g)-deriving via FromFunctor (Product f g)      instance (Functor f, Functor g) => LeftModule (->) These (Product f g)-deriving via (FromFunctor ((,) x1))         instance LeftModule (->) These ((,) x1)-deriving via (FromFunctor ((,,) x1 x2))     instance LeftModule (->) These ((,,) x1 x2)+deriving via FromFunctor Identity instance LeftModule (->) These Identity++deriving via FromFunctor (Compose f g) instance (Functor f, Functor g) => LeftModule (->) These (Compose f g)++deriving via FromFunctor [] instance LeftModule (->) These []++deriving via FromFunctor ZipList instance LeftModule (->) These ZipList++deriving via FromFunctor NonEmpty instance LeftModule (->) These NonEmpty++deriving via FromFunctor Maybe instance LeftModule (->) These Maybe++deriving via FromFunctor (Either e) instance LeftModule (->) These (Either e)++deriving via FromFunctor (These a) instance LeftModule (->) These (These a)++deriving via FromFunctor IO instance LeftModule (->) These IO++deriving via FromFunctor (Sum f g) instance (Functor f, Functor g) => LeftModule (->) These (Sum f g)++deriving via FromFunctor (Product f g) instance (Functor f, Functor g) => LeftModule (->) These (Product f g)++deriving via (FromFunctor ((,) x1)) instance LeftModule (->) These ((,) x1)++deriving via (FromFunctor ((,,) x1 x2)) instance LeftModule (->) These ((,,) x1 x2)+ deriving via (FromFunctor ((,,,) x1 x2 x3)) instance LeftModule (->) These ((,,,) x1 x2 x3) -deriving via FromFunctor Identity           instance LeftModule Op (,) Identity-deriving via FromFunctor (Compose f g)      instance (Functor f, Functor g) => LeftModule Op (,) (Compose f g)-deriving via FromFunctor []                 instance LeftModule Op (,) []-deriving via FromFunctor ZipList            instance LeftModule Op (,) ZipList-deriving via FromFunctor NonEmpty           instance LeftModule Op (,) NonEmpty-deriving via FromFunctor Maybe              instance LeftModule Op (,) Maybe-deriving via FromFunctor (Either e)         instance LeftModule Op (,) (Either e)-deriving via FromFunctor IO                 instance LeftModule Op (,) IO-deriving via FromFunctor (Sum f g)          instance (Functor f, Functor g) => LeftModule Op (,) (Sum f g)-deriving via FromFunctor (Product f g)      instance (Functor f, Functor g) => LeftModule Op (,) (Product f g)-deriving via (FromFunctor ((,) x1))         instance LeftModule Op (,) ((,) x1)-deriving via (FromFunctor ((,,) x1 x2))     instance LeftModule Op (,) ((,,) x1 x2)+deriving via FromFunctor Identity instance LeftModule Op (,) Identity++deriving via FromFunctor (Compose f g) instance (Functor f, Functor g) => LeftModule Op (,) (Compose f g)++deriving via FromFunctor [] instance LeftModule Op (,) []++deriving via FromFunctor ZipList instance LeftModule Op (,) ZipList++deriving via FromFunctor NonEmpty instance LeftModule Op (,) NonEmpty++deriving via FromFunctor Maybe instance LeftModule Op (,) Maybe++deriving via FromFunctor (Either e) instance LeftModule Op (,) (Either e)++deriving via FromFunctor IO instance LeftModule Op (,) IO++deriving via FromFunctor (Sum f g) instance (Functor f, Functor g) => LeftModule Op (,) (Sum f g)++deriving via FromFunctor (Product f g) instance (Functor f, Functor g) => LeftModule Op (,) (Product f g)++deriving via (FromFunctor ((,) x1)) instance LeftModule Op (,) ((,) x1)++deriving via (FromFunctor ((,,) x1 x2)) instance LeftModule Op (,) ((,,) x1 x2)+ deriving via (FromFunctor ((,,,) x1 x2 x3)) instance LeftModule Op (,) ((,,,) x1 x2 x3)  --------------------------------------------------------------------------------@@ -161,7 +233,7 @@   -- >>> :t rstrength @(->) @(,) @Predicate (Predicate @Int (> 10))   -- rstrength @(->) @(,) @Predicate (Predicate @Int (> 10)) :: Predicate (x, Int)   ---  -- >>> :t rstrength @(->) @Either @[] +  -- >>> :t rstrength @(->) @Either @[]   -- rstrength @(->) @Either @[] :: [a] -> [Either x a]   -- >>> rstrength @(->) @Either @[] [True, False]   -- [Right True,Right False]@@ -187,176 +259,324 @@   rstrength :: Op (FromFunctor f a) (FromFunctor f (x, a))   rstrength = Op (fmap snd) -deriving via (FromContra Comparison)    instance RightModule (->) (,) Comparison-deriving via (FromContra Equivalence)   instance RightModule (->) (,) Equivalence-deriving via (FromContra Predicate)     instance RightModule (->) (,) Predicate-deriving via (FromContra (Op a))        instance RightModule (->) (,) (Op a)-deriving via (FromContra Proxy)         instance RightModule (->) (,) Proxy-deriving via (FromContra U1)            instance RightModule (->) (,) U1-deriving via (FromContra V1)            instance RightModule (->) (,) V1-deriving via (FromContra (Const a))     instance RightModule (->) (,) (Const a)-deriving via (FromContra (Alt f))       instance Contravariant f => RightModule (->) (,) (Alt f)-deriving via (FromContra (Rec1 f))      instance Contravariant f => RightModule (->) (,) (Rec1 f)+deriving via (FromContra Comparison) instance RightModule (->) (,) Comparison++deriving via (FromContra Equivalence) instance RightModule (->) (,) Equivalence++deriving via (FromContra Predicate) instance RightModule (->) (,) Predicate++deriving via (FromContra (Op a)) instance RightModule (->) (,) (Op a)++deriving via (FromContra Proxy) instance RightModule (->) (,) Proxy++deriving via (FromContra U1) instance RightModule (->) (,) U1++deriving via (FromContra V1) instance RightModule (->) (,) V1++deriving via (FromContra (Const a)) instance RightModule (->) (,) (Const a)++deriving via (FromContra (Alt f)) instance Contravariant f => RightModule (->) (,) (Alt f)++deriving via (FromContra (Rec1 f)) instance Contravariant f => RightModule (->) (,) (Rec1 f)+ deriving via (FromContra (Product f g)) instance (Contravariant f, Contravariant g) => RightModule (->) (,) (Product f g)-deriving via (FromContra (Sum f g))     instance (Contravariant f, Contravariant g) => RightModule (->) (,) (Sum f g)-deriving via (FromContra (f :+: g))     instance (Contravariant f, Contravariant g) => RightModule (->) (,) (f :+: g)-deriving via (FromContra (f :*: g))     instance (Contravariant f, Contravariant g) => RightModule (->) (,) (f :*: g)-deriving via (FromContra (K1 i c))      instance RightModule (->) (,) (K1 i c)++deriving via (FromContra (Sum f g)) instance (Contravariant f, Contravariant g) => RightModule (->) (,) (Sum f g)++deriving via (FromContra (f :+: g)) instance (Contravariant f, Contravariant g) => RightModule (->) (,) (f :+: g)++deriving via (FromContra (f :*: g)) instance (Contravariant f, Contravariant g) => RightModule (->) (,) (f :*: g)++deriving via (FromContra (K1 i c)) instance RightModule (->) (,) (K1 i c)+ deriving via (FromContra (Compose f g)) instance (Functor f, Contravariant g) => RightModule (->) (,) (Compose f g)-deriving via (FromContra (f :.: g))     instance (Functor f, Contravariant g) => RightModule (->) (,) (f :.: g)-deriving via (FromContra (M1 i c f))    instance Contravariant f => RightModule (->) (,) (M1 i c f) -deriving via (FromContra Comparison)    instance RightModule Op Either Comparison-deriving via (FromContra Equivalence)   instance RightModule Op Either Equivalence-deriving via (FromContra Predicate)     instance RightModule Op Either Predicate-deriving via (FromContra (Op a))        instance RightModule Op Either (Op a)-deriving via (FromContra Proxy)         instance RightModule Op Either Proxy-deriving via (FromContra U1)            instance RightModule Op Either U1-deriving via (FromContra V1)            instance RightModule Op Either V1-deriving via (FromContra (Const a))     instance RightModule Op Either (Const a)-deriving via (FromContra (Alt f))       instance Contravariant f => RightModule Op Either (Alt f)-deriving via (FromContra (Rec1 f))      instance Contravariant f => RightModule Op Either (Rec1 f)+deriving via (FromContra (f :.: g)) instance (Functor f, Contravariant g) => RightModule (->) (,) (f :.: g)++deriving via (FromContra (M1 i c f)) instance Contravariant f => RightModule (->) (,) (M1 i c f)++deriving via (FromContra Comparison) instance RightModule Op Either Comparison++deriving via (FromContra Equivalence) instance RightModule Op Either Equivalence++deriving via (FromContra Predicate) instance RightModule Op Either Predicate++deriving via (FromContra (Op a)) instance RightModule Op Either (Op a)++deriving via (FromContra Proxy) instance RightModule Op Either Proxy++deriving via (FromContra U1) instance RightModule Op Either U1++deriving via (FromContra V1) instance RightModule Op Either V1++deriving via (FromContra (Const a)) instance RightModule Op Either (Const a)++deriving via (FromContra (Alt f)) instance Contravariant f => RightModule Op Either (Alt f)++deriving via (FromContra (Rec1 f)) instance Contravariant f => RightModule Op Either (Rec1 f)+ deriving via (FromContra (Product f g)) instance (Contravariant f, Contravariant g) => RightModule Op Either (Product f g)-deriving via (FromContra (Sum f g))     instance (Contravariant f, Contravariant g) => RightModule Op Either (Sum f g)-deriving via (FromContra (f :+: g))     instance (Contravariant f, Contravariant g) => RightModule Op Either (f :+: g)-deriving via (FromContra (f :*: g))     instance (Contravariant f, Contravariant g) => RightModule Op Either (f :*: g)-deriving via (FromContra (K1 i c))      instance RightModule Op Either (K1 i c)++deriving via (FromContra (Sum f g)) instance (Contravariant f, Contravariant g) => RightModule Op Either (Sum f g)++deriving via (FromContra (f :+: g)) instance (Contravariant f, Contravariant g) => RightModule Op Either (f :+: g)++deriving via (FromContra (f :*: g)) instance (Contravariant f, Contravariant g) => RightModule Op Either (f :*: g)++deriving via (FromContra (K1 i c)) instance RightModule Op Either (K1 i c)+ deriving via (FromContra (Compose f g)) instance (Functor f, Contravariant g) => RightModule Op Either (Compose f g)-deriving via (FromContra (f :.: g))     instance (Functor f, Contravariant g) => RightModule Op Either (f :.: g)-deriving via (FromContra (M1 i c f))    instance Contravariant f => RightModule Op Either (M1 i c f) -deriving via FromFunctor Identity           instance RightModule (->) Either Identity-deriving via FromFunctor (Compose f g)      instance (Functor f, Functor g) => RightModule (->) Either (Compose f g)-deriving via FromFunctor []                 instance RightModule (->) Either []-deriving via FromFunctor ZipList            instance RightModule (->) Either ZipList-deriving via FromFunctor NonEmpty           instance RightModule (->) Either NonEmpty-deriving via FromFunctor Maybe              instance RightModule (->) Either Maybe-deriving via FromFunctor (Either e)         instance RightModule (->) Either (Either e)-deriving via FromFunctor (These a)          instance RightModule (->) Either (These a)-deriving via FromFunctor IO                 instance RightModule (->) Either IO-deriving via FromFunctor (Sum f g)          instance (Functor f, Functor g) => RightModule (->) Either (Sum f g)-deriving via FromFunctor (Product f g)      instance (Functor f, Functor g) => RightModule (->) Either (Product f g)-deriving via (FromFunctor ((,) x1))         instance RightModule (->) Either ((,) x1)-deriving via (FromFunctor ((,,) x1 x2))     instance RightModule (->) Either ((,,) x1 x2)+deriving via (FromContra (f :.: g)) instance (Functor f, Contravariant g) => RightModule Op Either (f :.: g)++deriving via (FromContra (M1 i c f)) instance Contravariant f => RightModule Op Either (M1 i c f)++deriving via FromFunctor Identity instance RightModule (->) Either Identity++deriving via FromFunctor (Compose f g) instance (Functor f, Functor g) => RightModule (->) Either (Compose f g)++deriving via FromFunctor [] instance RightModule (->) Either []++deriving via FromFunctor ZipList instance RightModule (->) Either ZipList++deriving via FromFunctor NonEmpty instance RightModule (->) Either NonEmpty++deriving via FromFunctor Maybe instance RightModule (->) Either Maybe++deriving via FromFunctor (Either e) instance RightModule (->) Either (Either e)++deriving via FromFunctor (These a) instance RightModule (->) Either (These a)++deriving via FromFunctor IO instance RightModule (->) Either IO++deriving via FromFunctor (Sum f g) instance (Functor f, Functor g) => RightModule (->) Either (Sum f g)++deriving via FromFunctor (Product f g) instance (Functor f, Functor g) => RightModule (->) Either (Product f g)++deriving via (FromFunctor ((,) x1)) instance RightModule (->) Either ((,) x1)++deriving via (FromFunctor ((,,) x1 x2)) instance RightModule (->) Either ((,,) x1 x2)+ deriving via (FromFunctor ((,,,) x1 x2 x3)) instance RightModule (->) Either ((,,,) x1 x2 x3) -deriving via FromFunctor Identity           instance RightModule (->) These Identity-deriving via FromFunctor (Compose f g)      instance (Functor f, Functor g) => RightModule (->) These (Compose f g)-deriving via FromFunctor []                 instance RightModule (->) These []-deriving via FromFunctor ZipList            instance RightModule (->) These ZipList-deriving via FromFunctor NonEmpty           instance RightModule (->) These NonEmpty-deriving via FromFunctor Maybe              instance RightModule (->) These Maybe-deriving via FromFunctor (Either e)         instance RightModule (->) These (Either e)-deriving via FromFunctor (These a)          instance RightModule (->) These (These a)-deriving via FromFunctor IO                 instance RightModule (->) These IO-deriving via FromFunctor (Sum f g)          instance (Functor f, Functor g) => RightModule (->) These (Sum f g)-deriving via FromFunctor (Product f g)      instance (Functor f, Functor g) => RightModule (->) These (Product f g)-deriving via (FromFunctor ((,) x1))         instance RightModule (->) These ((,) x1)-deriving via (FromFunctor ((,,) x1 x2))     instance RightModule (->) These ((,,) x1 x2)+deriving via FromFunctor Identity instance RightModule (->) These Identity++deriving via FromFunctor (Compose f g) instance (Functor f, Functor g) => RightModule (->) These (Compose f g)++deriving via FromFunctor [] instance RightModule (->) These []++deriving via FromFunctor ZipList instance RightModule (->) These ZipList++deriving via FromFunctor NonEmpty instance RightModule (->) These NonEmpty++deriving via FromFunctor Maybe instance RightModule (->) These Maybe++deriving via FromFunctor (Either e) instance RightModule (->) These (Either e)++deriving via FromFunctor (These a) instance RightModule (->) These (These a)++deriving via FromFunctor IO instance RightModule (->) These IO++deriving via FromFunctor (Sum f g) instance (Functor f, Functor g) => RightModule (->) These (Sum f g)++deriving via FromFunctor (Product f g) instance (Functor f, Functor g) => RightModule (->) These (Product f g)++deriving via (FromFunctor ((,) x1)) instance RightModule (->) These ((,) x1)++deriving via (FromFunctor ((,,) x1 x2)) instance RightModule (->) These ((,,) x1 x2)+ deriving via (FromFunctor ((,,,) x1 x2 x3)) instance RightModule (->) These ((,,,) x1 x2 x3) -deriving via FromFunctor Identity           instance RightModule Op (,) Identity-deriving via FromFunctor (Compose f g)      instance (Functor f, Functor g) => RightModule Op (,) (Compose f g)-deriving via FromFunctor []                 instance RightModule Op (,) []-deriving via FromFunctor ZipList            instance RightModule Op (,) ZipList-deriving via FromFunctor NonEmpty           instance RightModule Op (,) NonEmpty-deriving via FromFunctor Maybe              instance RightModule Op (,) Maybe-deriving via FromFunctor (Either e)         instance RightModule Op (,) (Either e)-deriving via FromFunctor IO                 instance RightModule Op (,) IO-deriving via FromFunctor (Sum f g)          instance (Functor f, Functor g) => RightModule Op (,) (Sum f g)-deriving via FromFunctor (Product f g)      instance (Functor f, Functor g) => RightModule Op (,) (Product f g)-deriving via (FromFunctor ((,) x1))         instance RightModule Op (,) ((,) x1)-deriving via (FromFunctor ((,,) x1 x2))     instance RightModule Op (,) ((,,) x1 x2)+deriving via FromFunctor Identity instance RightModule Op (,) Identity++deriving via FromFunctor (Compose f g) instance (Functor f, Functor g) => RightModule Op (,) (Compose f g)++deriving via FromFunctor [] instance RightModule Op (,) []++deriving via FromFunctor ZipList instance RightModule Op (,) ZipList++deriving via FromFunctor NonEmpty instance RightModule Op (,) NonEmpty++deriving via FromFunctor Maybe instance RightModule Op (,) Maybe++deriving via FromFunctor (Either e) instance RightModule Op (,) (Either e)++deriving via FromFunctor IO instance RightModule Op (,) IO++deriving via FromFunctor (Sum f g) instance (Functor f, Functor g) => RightModule Op (,) (Sum f g)++deriving via FromFunctor (Product f g) instance (Functor f, Functor g) => RightModule Op (,) (Product f g)++deriving via (FromFunctor ((,) x1)) instance RightModule Op (,) ((,) x1)++deriving via (FromFunctor ((,,) x1 x2)) instance RightModule Op (,) ((,,) x1 x2)+ deriving via (FromFunctor ((,,,) x1 x2 x3)) instance RightModule Op (,) ((,,,) x1 x2 x3)  --------------------------------------------------------------------------------  class (LeftModule cat t1 f, RightModule cat t1 f) => Bimodule cat t1 f -instance Contravariant f => Bimodule (->) (,) (FromContra f) where-instance Contravariant f => Bimodule Op Either (FromContra f) where-instance Functor f => Bimodule (->) Either (FromFunctor f) where-instance Functor f => Bimodule (->) These (FromFunctor f) where-instance Functor f => Bimodule Op (,) (FromFunctor f) where+instance Contravariant f => Bimodule (->) (,) (FromContra f) -deriving via (FromContra Comparison)    instance Bimodule (->) (,) Comparison-deriving via (FromContra Equivalence)   instance Bimodule (->) (,) Equivalence-deriving via (FromContra Predicate)     instance Bimodule (->) (,) Predicate-deriving via (FromContra (Op a))        instance Bimodule (->) (,) (Op a)-deriving via (FromContra Proxy)         instance Bimodule (->) (,) Proxy-deriving via (FromContra U1)            instance Bimodule (->) (,) U1-deriving via (FromContra V1)            instance Bimodule (->) (,) V1-deriving via (FromContra (Const a))     instance Bimodule (->) (,) (Const a)-deriving via (FromContra (Alt f))       instance Contravariant f => Bimodule (->) (,) (Alt f)-deriving via (FromContra (Rec1 f))      instance Contravariant f => Bimodule (->) (,) (Rec1 f)+instance Contravariant f => Bimodule Op Either (FromContra f)++instance Functor f => Bimodule (->) Either (FromFunctor f)++instance Functor f => Bimodule (->) These (FromFunctor f)++instance Functor f => Bimodule Op (,) (FromFunctor f)++deriving via (FromContra Comparison) instance Bimodule (->) (,) Comparison++deriving via (FromContra Equivalence) instance Bimodule (->) (,) Equivalence++deriving via (FromContra Predicate) instance Bimodule (->) (,) Predicate++deriving via (FromContra (Op a)) instance Bimodule (->) (,) (Op a)++deriving via (FromContra Proxy) instance Bimodule (->) (,) Proxy++deriving via (FromContra U1) instance Bimodule (->) (,) U1++deriving via (FromContra V1) instance Bimodule (->) (,) V1++deriving via (FromContra (Const a)) instance Bimodule (->) (,) (Const a)++deriving via (FromContra (Alt f)) instance Contravariant f => Bimodule (->) (,) (Alt f)++deriving via (FromContra (Rec1 f)) instance Contravariant f => Bimodule (->) (,) (Rec1 f)+ deriving via (FromContra (Product f g)) instance (Contravariant f, Contravariant g) => Bimodule (->) (,) (Product f g)-deriving via (FromContra (Sum f g))     instance (Contravariant f, Contravariant g) => Bimodule (->) (,) (Sum f g)-deriving via (FromContra (f :+: g))     instance (Contravariant f, Contravariant g) => Bimodule (->) (,) (f :+: g)-deriving via (FromContra (f :*: g))     instance (Contravariant f, Contravariant g) => Bimodule (->) (,) (f :*: g)-deriving via (FromContra (K1 i c))      instance Bimodule (->) (,) (K1 i c)++deriving via (FromContra (Sum f g)) instance (Contravariant f, Contravariant g) => Bimodule (->) (,) (Sum f g)++deriving via (FromContra (f :+: g)) instance (Contravariant f, Contravariant g) => Bimodule (->) (,) (f :+: g)++deriving via (FromContra (f :*: g)) instance (Contravariant f, Contravariant g) => Bimodule (->) (,) (f :*: g)++deriving via (FromContra (K1 i c)) instance Bimodule (->) (,) (K1 i c)+ deriving via (FromContra (Compose f g)) instance (Functor f, Contravariant g) => Bimodule (->) (,) (Compose f g)-deriving via (FromContra (f :.: g))     instance (Functor f, Contravariant g) => Bimodule (->) (,) (f :.: g)-deriving via (FromContra (M1 i c f))    instance Contravariant f => Bimodule (->) (,) (M1 i c f) -deriving via (FromContra Comparison)    instance Bimodule Op Either Comparison-deriving via (FromContra Equivalence)   instance Bimodule Op Either Equivalence-deriving via (FromContra Predicate)     instance Bimodule Op Either Predicate-deriving via (FromContra (Op a))        instance Bimodule Op Either (Op a)-deriving via (FromContra Proxy)         instance Bimodule Op Either Proxy-deriving via (FromContra U1)            instance Bimodule Op Either U1-deriving via (FromContra V1)            instance Bimodule Op Either V1-deriving via (FromContra (Const a))     instance Bimodule Op Either (Const a)-deriving via (FromContra (Alt f))       instance Contravariant f => Bimodule Op Either (Alt f)-deriving via (FromContra (Rec1 f))      instance Contravariant f => Bimodule Op Either (Rec1 f)+deriving via (FromContra (f :.: g)) instance (Functor f, Contravariant g) => Bimodule (->) (,) (f :.: g)++deriving via (FromContra (M1 i c f)) instance Contravariant f => Bimodule (->) (,) (M1 i c f)++deriving via (FromContra Comparison) instance Bimodule Op Either Comparison++deriving via (FromContra Equivalence) instance Bimodule Op Either Equivalence++deriving via (FromContra Predicate) instance Bimodule Op Either Predicate++deriving via (FromContra (Op a)) instance Bimodule Op Either (Op a)++deriving via (FromContra Proxy) instance Bimodule Op Either Proxy++deriving via (FromContra U1) instance Bimodule Op Either U1++deriving via (FromContra V1) instance Bimodule Op Either V1++deriving via (FromContra (Const a)) instance Bimodule Op Either (Const a)++deriving via (FromContra (Alt f)) instance Contravariant f => Bimodule Op Either (Alt f)++deriving via (FromContra (Rec1 f)) instance Contravariant f => Bimodule Op Either (Rec1 f)+ deriving via (FromContra (Product f g)) instance (Contravariant f, Contravariant g) => Bimodule Op Either (Product f g)-deriving via (FromContra (Sum f g))     instance (Contravariant f, Contravariant g) => Bimodule Op Either (Sum f g)-deriving via (FromContra (f :+: g))     instance (Contravariant f, Contravariant g) => Bimodule Op Either (f :+: g)-deriving via (FromContra (f :*: g))     instance (Contravariant f, Contravariant g) => Bimodule Op Either (f :*: g)-deriving via (FromContra (K1 i c))      instance Bimodule Op Either (K1 i c)++deriving via (FromContra (Sum f g)) instance (Contravariant f, Contravariant g) => Bimodule Op Either (Sum f g)++deriving via (FromContra (f :+: g)) instance (Contravariant f, Contravariant g) => Bimodule Op Either (f :+: g)++deriving via (FromContra (f :*: g)) instance (Contravariant f, Contravariant g) => Bimodule Op Either (f :*: g)++deriving via (FromContra (K1 i c)) instance Bimodule Op Either (K1 i c)+ deriving via (FromContra (Compose f g)) instance (Functor f, Contravariant g) => Bimodule Op Either (Compose f g)-deriving via (FromContra (f :.: g))     instance (Functor f, Contravariant g) => Bimodule Op Either (f :.: g)-deriving via (FromContra (M1 i c f))    instance Contravariant f => Bimodule Op Either (M1 i c f) -deriving via FromFunctor Identity           instance Bimodule (->) Either Identity-deriving via FromFunctor (Compose f g)      instance (Functor f, Functor g) => Bimodule (->) Either (Compose f g)-deriving via FromFunctor []                 instance Bimodule (->) Either []-deriving via FromFunctor ZipList            instance Bimodule (->) Either ZipList-deriving via FromFunctor NonEmpty           instance Bimodule (->) Either NonEmpty-deriving via FromFunctor Maybe              instance Bimodule (->) Either Maybe-deriving via FromFunctor (Either e)         instance Bimodule (->) Either (Either e)-deriving via FromFunctor (These a)          instance Bimodule (->) Either (These a)-deriving via FromFunctor IO                 instance Bimodule (->) Either IO-deriving via FromFunctor (Sum f g)          instance (Functor f, Functor g) => Bimodule (->) Either (Sum f g)-deriving via FromFunctor (Product f g)      instance (Functor f, Functor g) => Bimodule (->) Either (Product f g)-deriving via (FromFunctor ((,) x1))         instance Bimodule (->) Either ((,) x1)-deriving via (FromFunctor ((,,) x1 x2))     instance Bimodule (->) Either ((,,) x1 x2)+deriving via (FromContra (f :.: g)) instance (Functor f, Contravariant g) => Bimodule Op Either (f :.: g)++deriving via (FromContra (M1 i c f)) instance Contravariant f => Bimodule Op Either (M1 i c f)++deriving via FromFunctor Identity instance Bimodule (->) Either Identity++deriving via FromFunctor (Compose f g) instance (Functor f, Functor g) => Bimodule (->) Either (Compose f g)++deriving via FromFunctor [] instance Bimodule (->) Either []++deriving via FromFunctor ZipList instance Bimodule (->) Either ZipList++deriving via FromFunctor NonEmpty instance Bimodule (->) Either NonEmpty++deriving via FromFunctor Maybe instance Bimodule (->) Either Maybe++deriving via FromFunctor (Either e) instance Bimodule (->) Either (Either e)++deriving via FromFunctor (These a) instance Bimodule (->) Either (These a)++deriving via FromFunctor IO instance Bimodule (->) Either IO++deriving via FromFunctor (Sum f g) instance (Functor f, Functor g) => Bimodule (->) Either (Sum f g)++deriving via FromFunctor (Product f g) instance (Functor f, Functor g) => Bimodule (->) Either (Product f g)++deriving via (FromFunctor ((,) x1)) instance Bimodule (->) Either ((,) x1)++deriving via (FromFunctor ((,,) x1 x2)) instance Bimodule (->) Either ((,,) x1 x2)+ deriving via (FromFunctor ((,,,) x1 x2 x3)) instance Bimodule (->) Either ((,,,) x1 x2 x3) -deriving via FromFunctor Identity           instance Bimodule (->) These Identity-deriving via FromFunctor (Compose f g)      instance (Functor f, Functor g) => Bimodule (->) These (Compose f g)-deriving via FromFunctor []                 instance Bimodule (->) These []-deriving via FromFunctor ZipList            instance Bimodule (->) These ZipList-deriving via FromFunctor NonEmpty           instance Bimodule (->) These NonEmpty-deriving via FromFunctor Maybe              instance Bimodule (->) These Maybe-deriving via FromFunctor (Either e)         instance Bimodule (->) These (Either e)-deriving via FromFunctor (These a)          instance Bimodule (->) These (These a)-deriving via FromFunctor IO                 instance Bimodule (->) These IO-deriving via FromFunctor (Sum f g)          instance (Functor f, Functor g) => Bimodule (->) These (Sum f g)-deriving via FromFunctor (Product f g)      instance (Functor f, Functor g) => Bimodule (->) These (Product f g)-deriving via (FromFunctor ((,) x1))         instance Bimodule (->) These ((,) x1)-deriving via (FromFunctor ((,,) x1 x2))     instance Bimodule (->) These ((,,) x1 x2)+deriving via FromFunctor Identity instance Bimodule (->) These Identity++deriving via FromFunctor (Compose f g) instance (Functor f, Functor g) => Bimodule (->) These (Compose f g)++deriving via FromFunctor [] instance Bimodule (->) These []++deriving via FromFunctor ZipList instance Bimodule (->) These ZipList++deriving via FromFunctor NonEmpty instance Bimodule (->) These NonEmpty++deriving via FromFunctor Maybe instance Bimodule (->) These Maybe++deriving via FromFunctor (Either e) instance Bimodule (->) These (Either e)++deriving via FromFunctor (These a) instance Bimodule (->) These (These a)++deriving via FromFunctor IO instance Bimodule (->) These IO++deriving via FromFunctor (Sum f g) instance (Functor f, Functor g) => Bimodule (->) These (Sum f g)++deriving via FromFunctor (Product f g) instance (Functor f, Functor g) => Bimodule (->) These (Product f g)++deriving via (FromFunctor ((,) x1)) instance Bimodule (->) These ((,) x1)++deriving via (FromFunctor ((,,) x1 x2)) instance Bimodule (->) These ((,,) x1 x2)+ deriving via (FromFunctor ((,,,) x1 x2 x3)) instance Bimodule (->) These ((,,,) x1 x2 x3) -deriving via FromFunctor Identity           instance Bimodule Op (,) Identity-deriving via FromFunctor (Compose f g)      instance (Functor f, Functor g) => Bimodule Op (,) (Compose f g)-deriving via FromFunctor []                 instance Bimodule Op (,) []-deriving via FromFunctor ZipList            instance Bimodule Op (,) ZipList-deriving via FromFunctor NonEmpty           instance Bimodule Op (,) NonEmpty-deriving via FromFunctor Maybe              instance Bimodule Op (,) Maybe-deriving via FromFunctor (Either e)         instance Bimodule Op (,) (Either e)-deriving via FromFunctor IO                 instance Bimodule Op (,) IO-deriving via FromFunctor (Sum f g)          instance (Functor f, Functor g) => Bimodule Op (,) (Sum f g)-deriving via FromFunctor (Product f g)      instance (Functor f, Functor g) => Bimodule Op (,) (Product f g)-deriving via (FromFunctor ((,) x1))         instance Bimodule Op (,) ((,) x1)-deriving via (FromFunctor ((,,) x1 x2))     instance Bimodule Op (,) ((,,) x1 x2)+deriving via FromFunctor Identity instance Bimodule Op (,) Identity++deriving via FromFunctor (Compose f g) instance (Functor f, Functor g) => Bimodule Op (,) (Compose f g)++deriving via FromFunctor [] instance Bimodule Op (,) []++deriving via FromFunctor ZipList instance Bimodule Op (,) ZipList++deriving via FromFunctor NonEmpty instance Bimodule Op (,) NonEmpty++deriving via FromFunctor Maybe instance Bimodule Op (,) Maybe++deriving via FromFunctor (Either e) instance Bimodule Op (,) (Either e)++deriving via FromFunctor IO instance Bimodule Op (,) IO++deriving via FromFunctor (Sum f g) instance (Functor f, Functor g) => Bimodule Op (,) (Sum f g)++deriving via FromFunctor (Product f g) instance (Functor f, Functor g) => Bimodule Op (,) (Product f g)++deriving via (FromFunctor ((,) x1)) instance Bimodule Op (,) ((,) x1)++deriving via (FromFunctor ((,,) x1 x2)) instance Bimodule Op (,) ((,,) x1 x2)+ deriving via (FromFunctor ((,,,) x1 x2 x3)) instance Bimodule Op (,) ((,,,) x1 x2 x3)

@@ -1,6 +1,13 @@ module Data.Functor.Monoidal   ( -- * Semigroupal     Semigroupal (..),+    (|?|),+    (|*|),+    type (|*|),+    (|+|),+    type (|+|),+    (|&|),+    type (|&|),      -- * Unital     Unital (..),@@ -13,13 +20,29 @@ --------------------------------------------------------------------------------  import Control.Applicative+import Control.Applicative.Backwards (Backwards) import Control.Arrow (ArrowMonad, ArrowPlus, ArrowZero, Kleisli) import Control.Category.Tensor+import Control.Comonad.Identity (IdentityT) import Control.Monad (MonadPlus)+import Control.Monad.Trans.Except (ExceptT)+import Control.Monad.Trans.Maybe+import Control.Monad.Trans.RWS.Lazy qualified as Lazy+import Control.Monad.Trans.RWS.Strict (RWST)+import Control.Monad.Trans.Reader (ReaderT)+import Control.Monad.Trans.State.Lazy qualified as Lazy+import Control.Monad.Trans.State.Strict (StateT)+import Control.Monad.Trans.Writer.Lazy qualified as Lazy+import Control.Monad.Trans.Writer.Strict (WriterT) import Data.Align import Data.Functor.Compose (Compose)+import Data.Functor.Constant (Constant)+import Data.Functor.Contravariant (Comparison, Contravariant, Equivalence, Op (..), Predicate)+import Data.Functor.Contravariant.Compose (ComposeCF, ComposeFC)+import Data.Functor.Contravariant.Divisible (Decidable, Divisible, chosen, conquered, divided, lost) import Data.Functor.Identity import Data.Functor.Product (Product)+import Data.Functor.Reverse (Reverse) import Data.Kind (Type) import Data.List.NonEmpty (NonEmpty) import Data.Monoid (Alt, Ap)@@ -43,7 +66,7 @@ -- -- __Associativity:__ ----- \[ +-- \[ -- \require{AMScd} -- \begin{CD} -- (F A \bullet F B) \bullet F C @>>{\alpha_{\mathcal{D}}}>     F A \bullet (F B \bullet F C) \\@@ -82,19 +105,38 @@   combine :: (FromApplicative f x, FromApplicative f x') -> FromApplicative f (x, x')   combine = uncurry (liftA2 (,)) -deriving via FromApplicative Identity           instance Semigroupal (->) (,) (,) Identity-deriving via FromApplicative (Compose f g)      instance (Applicative f, Applicative g) => Semigroupal (->) (,) (,) (Compose f g)-deriving via FromApplicative []                 instance Semigroupal (->) (,) (,) []-deriving via FromApplicative ZipList            instance Semigroupal (->) (,) (,) ZipList-deriving via FromApplicative NonEmpty           instance Semigroupal (->) (,) (,) NonEmpty-deriving via FromApplicative Maybe              instance Semigroupal (->) (,) (,) Maybe-deriving via FromApplicative (Either e)         instance Semigroupal (->) (,) (,) (Either e)-deriving via FromApplicative IO                 instance Semigroupal (->) (,) (,) IO-deriving via FromApplicative (Product f g)      instance (Applicative f, Applicative g) => Semigroupal (->) (,) (,) (Product f g)-deriving via (FromApplicative ((,) x1))         instance (Monoid x1) => Semigroupal (->) (,) (,) ((,) x1)-deriving via (FromApplicative ((,,) x1 x2))     instance (Monoid x1, Monoid x2) => Semigroupal (->) (,) (,) ((,,) x1 x2)+deriving via FromApplicative Identity instance Semigroupal (->) (,) (,) Identity++instance Semigroupal Op Either Either Identity where+  combine :: Op (Either (Identity x) (Identity x')) (Identity (Either x x'))+  combine = Op $ \case+    Identity (Left x) -> Left $ Identity x+    Identity (Right x') -> Right $ Identity x'++deriving via FromApplicative (Compose f g) instance (Applicative f, Applicative g) => Semigroupal (->) (,) (,) (Compose f g)++deriving via FromApplicative [] instance Semigroupal (->) (,) (,) []++deriving via FromApplicative ZipList instance Semigroupal (->) (,) (,) ZipList++deriving via FromApplicative NonEmpty instance Semigroupal (->) (,) (,) NonEmpty++deriving via FromApplicative Maybe instance Semigroupal (->) (,) (,) Maybe++deriving via FromApplicative (Either e) instance Semigroupal (->) (,) (,) (Either e)++deriving via FromApplicative IO instance Semigroupal (->) (,) (,) IO++deriving via FromApplicative (Product f g) instance (Applicative f, Applicative g) => Semigroupal (->) (,) (,) (Product f g)++deriving via (FromApplicative ((,) x1)) instance (Monoid x1) => Semigroupal (->) (,) (,) ((,) x1)++deriving via (FromApplicative ((,,) x1 x2)) instance (Monoid x1, Monoid x2) => Semigroupal (->) (,) (,) ((,,) x1 x2)+ deriving via (FromApplicative ((,,,) x1 x2 x3)) instance (Monoid x1, Monoid x2, Monoid x3) => Semigroupal (->) (,) (,) ((,,,) x1 x2 x3) +deriving via FromApplicative (Proxy :: Type -> Type) instance Semigroupal (->) (,) (,) (Proxy :: Type -> Type)+ newtype FromAlternative f a = FromAlternative (f a)   deriving newtype (Functor, Applicative, Alternative) @@ -102,45 +144,209 @@   combine :: (FromAlternative f x, FromAlternative f x') -> FromAlternative f (Either x x')   combine (fx, fx') = fmap Left fx <|> fmap Right fx' -deriving via FromAlternative ZipList                 instance Semigroupal (->) Either (,) ZipList-deriving via FromAlternative STM                     instance Semigroupal (->) Either (,) STM-deriving via FromAlternative ReadP                   instance Semigroupal (->) Either (,) ReadP-deriving via FromAlternative ReadPrec                instance Semigroupal (->) Either (,) ReadPrec-deriving via FromAlternative IO                      instance Semigroupal (->) Either (,) IO-deriving via FromAlternative Maybe                   instance Semigroupal (->) Either (,) Maybe-deriving via FromAlternative []                      instance Semigroupal (->) Either (,) []-deriving via FromAlternative (WrappedMonad m)        instance (MonadPlus m) => Semigroupal (->) Either (,) (WrappedMonad m)-deriving via FromAlternative (ArrowMonad a)          instance (ArrowPlus a) => Semigroupal (->) Either (,) (ArrowMonad a)+deriving via FromAlternative ZipList instance Semigroupal (->) Either (,) ZipList++deriving via FromAlternative STM instance Semigroupal (->) Either (,) STM++deriving via FromAlternative ReadP instance Semigroupal (->) Either (,) ReadP++deriving via FromAlternative ReadPrec instance Semigroupal (->) Either (,) ReadPrec++deriving via FromAlternative IO instance Semigroupal (->) Either (,) IO++deriving via FromAlternative Maybe instance Semigroupal (->) Either (,) Maybe++deriving via FromAlternative [] instance Semigroupal (->) Either (,) []++deriving via FromAlternative (WrappedMonad m) instance (MonadPlus m) => Semigroupal (->) Either (,) (WrappedMonad m)++deriving via FromAlternative (ArrowMonad a) instance (ArrowPlus a) => Semigroupal (->) Either (,) (ArrowMonad a)+ deriving via FromAlternative (Proxy :: Type -> Type) instance Semigroupal (->) Either (,) (Proxy :: Type -> Type)-deriving via FromAlternative (U1 :: Type -> Type)    instance Semigroupal (->) Either (,) (U1 :: Type -> Type)-deriving via FromAlternative (WrappedArrow a b)      instance (ArrowZero a, ArrowPlus a) => Semigroupal (->) Either (,) (WrappedArrow a b)-deriving via FromAlternative (Kleisli m a)           instance (Alternative m) => Semigroupal (->) Either (,) (Kleisli m a)-deriving via FromAlternative (Ap f)                  instance (Alternative f) => Semigroupal (->) Either (,) (Ap f)-deriving via FromAlternative (Alt f)                 instance (Alternative f) => Semigroupal (->) Either (,) (Alt f)-deriving via FromAlternative (Rec1 f)                instance (Alternative f) => Semigroupal (->) Either (,) (Rec1 f)-deriving via FromAlternative (Product f g)           instance (Alternative f, Alternative g) => Semigroupal (->) Either (,) (Product f g)-deriving via FromAlternative (f :*: g)               instance (Alternative f, Alternative g) => Semigroupal (->) Either (,) (f :*: g)-deriving via FromAlternative (f `Compose` g)         instance (Alternative f, Applicative g) => Semigroupal (->) Either (,) (f `Compose` g)-deriving via FromAlternative (f :.: g)               instance (Alternative f, Applicative g) => Semigroupal (->) Either (,) (f :.: g)-deriving via FromAlternative (M1 i c f)              instance (Alternative f) => Semigroupal (->) Either (,) (M1 i c f) +deriving via FromAlternative (U1 :: Type -> Type) instance Semigroupal (->) Either (,) (U1 :: Type -> Type)++deriving via FromAlternative (WrappedArrow a b) instance (ArrowZero a, ArrowPlus a) => Semigroupal (->) Either (,) (WrappedArrow a b)++deriving via FromAlternative (Kleisli m a) instance (Alternative m) => Semigroupal (->) Either (,) (Kleisli m a)++deriving via FromAlternative (Ap f) instance (Alternative f) => Semigroupal (->) Either (,) (Ap f)++deriving via FromAlternative (Alt f) instance (Alternative f) => Semigroupal (->) Either (,) (Alt f)++deriving via FromAlternative (Rec1 f) instance (Alternative f) => Semigroupal (->) Either (,) (Rec1 f)++deriving via FromAlternative (Product f g) instance (Alternative f, Alternative g) => Semigroupal (->) Either (,) (Product f g)++deriving via FromAlternative (f :*: g) instance (Alternative f, Alternative g) => Semigroupal (->) Either (,) (f :*: g)++deriving via FromAlternative (f `Compose` g) instance (Alternative f, Applicative g) => Semigroupal (->) Either (,) (f `Compose` g)++deriving via FromAlternative (f :.: g) instance (Alternative f, Applicative g) => Semigroupal (->) Either (,) (f :.: g)++deriving via FromAlternative (M1 i c f) instance (Alternative f) => Semigroupal (->) Either (,) (M1 i c f)+ newtype FromSemialign f a = FromSemialign (f a)-  deriving (Functor, Semialign)+  deriving newtype (Functor, Semialign)  instance Semialign f => Semigroupal (->) These (,) (FromSemialign f) where   combine :: (FromSemialign f x, FromSemialign f x') -> FromSemialign f (These x x')   combine = uncurry align -deriving via FromSemialign []                      instance Semigroupal (->) These (,) []-deriving via FromSemialign ZipList                 instance Semigroupal (->) These (,) ZipList-deriving via FromSemialign NonEmpty                instance Semigroupal (->) These (,) NonEmpty-deriving via FromSemialign Maybe                   instance Semigroupal (->) These (,) Maybe-deriving via FromSemialign Identity                instance Semigroupal (->) These (,) Identity+deriving via FromSemialign [] instance Semigroupal (->) These (,) []++deriving via FromSemialign ZipList instance Semigroupal (->) These (,) ZipList++deriving via FromSemialign NonEmpty instance Semigroupal (->) These (,) NonEmpty++deriving via FromSemialign Maybe instance Semigroupal (->) These (,) Maybe++deriving via FromSemialign Identity instance Semigroupal (->) These (,) Identity+ deriving via FromSemialign (Proxy :: Type -> Type) instance Semigroupal (->) These (,) (Proxy :: Type -> Type)-deriving via FromSemialign (Tagged b)              instance Semigroupal (->) These (,) (Tagged b)-deriving via FromSemialign (Product f g)           instance (Semialign f, Semialign g) => Semigroupal (->) These (,) (Product f g)-deriving via FromSemialign (f `Compose` g)         instance (Semialign f, Semialign g) => Semigroupal (->) These (,) (f `Compose` g) +deriving via FromSemialign (Tagged b) instance Semigroupal (->) These (,) (Tagged b)++deriving via FromSemialign (Product f g) instance (Semialign f, Semialign g) => Semigroupal (->) These (,) (Product f g)++deriving via FromSemialign (f `Compose` g) instance (Semialign f, Semialign g) => Semigroupal (->) These (,) (f `Compose` g)++newtype FromDivisible f a = FromDivisible (f a)+  deriving newtype (Contravariant, Divisible)++instance Divisible f => Semigroupal (->) (,) (,) (FromDivisible f) where+  combine :: (FromDivisible f x, FromDivisible f x') -> FromDivisible f (x, x')+  combine = uncurry divided++deriving via FromDivisible Predicate instance Semigroupal (->) (,) (,) Predicate++deriving via FromDivisible Comparison instance Semigroupal (->) (,) (,) Comparison++deriving via FromDivisible Equivalence instance Semigroupal (->) (,) (,) Equivalence++deriving via FromDivisible (U1 :: Type -> Type) instance Semigroupal (->) (,) (,) (U1 :: Type -> Type)++deriving via FromDivisible (Op r) instance Monoid r => Semigroupal (->) (,) (,) (Op r)++-- deriving via FromDivisible (Proxy :: Type -> Type) instance Semigroupal (->) (,) (,) (Proxy :: Type -> Type)+deriving via FromDivisible (MaybeT m) instance Divisible m => Semigroupal (->) (,) (,) (MaybeT m)++deriving via FromDivisible (Rec1 m) instance Divisible m => Semigroupal (->) (,) (,) (Rec1 m)++deriving via FromDivisible (Const m) instance Monoid m => Semigroupal (->) (,) (,) (Const m :: Type -> Type)++deriving via FromDivisible (Alt f) instance Divisible f => Semigroupal (->) (,) (,) (Alt f)++deriving via FromDivisible (Reverse f) instance Divisible f => Semigroupal (->) (,) (,) (Reverse f)++deriving via FromDivisible (Constant m) instance Monoid m => Semigroupal (->) (,) (,) (Constant m :: Type -> Type)++deriving via FromDivisible (WriterT w m) instance Divisible m => Semigroupal (->) (,) (,) (WriterT w m)++deriving via FromDivisible (Lazy.WriterT w m) instance Divisible m => Semigroupal (->) (,) (,) (Lazy.WriterT w m)++deriving via FromDivisible (StateT w m) instance Divisible m => Semigroupal (->) (,) (,) (StateT w m)++deriving via FromDivisible (Lazy.StateT w m) instance Divisible m => Semigroupal (->) (,) (,) (Lazy.StateT w m)++deriving via FromDivisible (ReaderT r m) instance Divisible m => Semigroupal (->) (,) (,) (ReaderT r m)++deriving via FromDivisible (IdentityT m) instance Divisible m => Semigroupal (->) (,) (,) (IdentityT m)++deriving via FromDivisible (ExceptT e m) instance Divisible m => Semigroupal (->) (,) (,) (ExceptT e m)++deriving via FromDivisible (Backwards f) instance Divisible f => Semigroupal (->) (,) (,) (Backwards f)++deriving via FromDivisible (ComposeCF f g) instance (Divisible f, Applicative g) => Semigroupal (->) (,) (,) (ComposeCF f g)++deriving via FromDivisible (ComposeFC f g) instance (Divisible g, Applicative f) => Semigroupal (->) (,) (,) (ComposeFC f g)++deriving via FromDivisible (f :*: g) instance (Divisible f, Divisible g) => Semigroupal (->) (,) (,) (f :*: g)++-- deriving via FromDivisible (Product f g)           instance (Divisible f, Divisible g) => Semigroupal (->) (,) (,) (Product f g)+deriving via FromDivisible (M1 i c f) instance Divisible f => Semigroupal (->) (,) (,) (M1 i c f)++deriving via FromDivisible (f :.: g) instance (Applicative f, Divisible g) => Semigroupal (->) (,) (,) (f :.: g)++-- deriving via FromDivisible (Compose f g)           instance (Applicative f, Divisible g) => Semigroupal (->) (,) (,) (Compose f g)+deriving via FromDivisible (RWST r w s m) instance (Divisible m) => Semigroupal (->) (,) (,) (RWST r w s m)++deriving via FromDivisible (Lazy.RWST r w s m) instance (Divisible m) => Semigroupal (->) (,) (,) (Lazy.RWST r w s m)++newtype FromDecidable f a = FromDecidable (f a)+  deriving newtype (Contravariant, Divisible, Decidable)++instance Decidable f => Semigroupal (->) Either (,) (FromDecidable f) where+  combine :: (FromDecidable f x, FromDecidable f x') -> FromDecidable f (Either x x')+  combine = uncurry chosen++deriving via FromDecidable Predicate instance Semigroupal (->) Either (,) Predicate++deriving via FromDecidable Comparison instance Semigroupal (->) Either (,) Comparison++deriving via FromDecidable Equivalence instance Semigroupal (->) Either (,) Equivalence++-- deriving via FromDecidable (U1 :: Type -> Type)    instance Semigroupal (->) Either (,) (U1 :: Type -> Type)+deriving via FromDecidable (Op r) instance Monoid r => Semigroupal (->) Either (,) (Op r)++-- deriving via FromDecidable (Proxy :: Type -> Type) instance Semigroupal (->) Either (,) (Proxy :: Type -> Type)+deriving via FromDecidable (MaybeT m) instance Decidable m => Semigroupal (->) Either (,) (MaybeT m)++-- deriving via FromDecidable (Rec1 m)                instance Decidable m => Semigroupal (->) Either (,) (Rec1 m)+-- deriving via FromDecidable (Alt f)                 instance Decidable f => Semigroupal (->) Either (,) (Alt f)+deriving via FromDecidable (Reverse f) instance Decidable f => Semigroupal (->) Either (,) (Reverse f)++deriving via FromDecidable (WriterT w m) instance Decidable m => Semigroupal (->) Either (,) (WriterT w m)++deriving via FromDecidable (Lazy.WriterT w m) instance Decidable m => Semigroupal (->) Either (,) (Lazy.WriterT w m)++deriving via FromDecidable (StateT w m) instance Decidable m => Semigroupal (->) Either (,) (StateT w m)++deriving via FromDecidable (Lazy.StateT w m) instance Decidable m => Semigroupal (->) Either (,) (Lazy.StateT w m)++deriving via FromDecidable (ReaderT r m) instance Decidable m => Semigroupal (->) Either (,) (ReaderT r m)++deriving via FromDecidable (IdentityT m) instance Decidable m => Semigroupal (->) Either (,) (IdentityT m)++deriving via FromDecidable (Backwards f) instance Decidable f => Semigroupal (->) Either (,) (Backwards f)++deriving via FromDecidable (ComposeFC f g) instance (Decidable g, Applicative f) => Semigroupal (->) Either (,) (ComposeFC f g)++-- deriving via FromDecidable (f :*: g)               instance (Decidable f, Decidable g) => Semigroupal (->) Either (,) (f :*: g)+-- deriving via FromDecidable (Product f g)           instance (Decidable f, Decidable g) => Semigroupal (->) Either (,) (Product f g)+-- deriving via FromDecidable (M1 i c f)              instance Decidable f => Semigroupal (->) Either (,) (M1 i c f)+-- deriving via FromDecidable (f :.: g)               instance (Applicative f, Decidable g) => Semigroupal (->) Either (,) (f :.: g)+-- deriving via FromDecidable (Compose f g)           instance (Applicative f, Decidable g) => Semigroupal (->) Either (,) (Compose f g)+deriving via FromDecidable (RWST r w s m) instance (Decidable m) => Semigroupal (->) Either (,) (RWST r w s m)++deriving via FromDecidable (Lazy.RWST r w s m) instance (Decidable m) => Semigroupal (->) Either (,) (Lazy.RWST r w s m)++infixr 9 |?|++(|?|) :: Semigroupal (->) t1 (,) f => f a -> f b -> f (a `t1` b)+(|?|) = curry combine++infixr 4 |*|++(|*|) :: Semigroupal (->) (,) (,) f => f a -> f b -> f (a, b)+(|*|) = curry combine++infixr 3 |+|++(|+|) :: Semigroupal (->) Either (,) f => f a -> f b -> f (Either a b)+(|+|) = curry combine++infixr 3 |&|++(|&|) :: Semigroupal (->) These (,) f => f a -> f b -> f (These a b)+(|&|) = curry combine++type (|*|) = (,)++type (|+|) = Either++type (|&|) = These+ --------------------------------------------------------------------------------  -- | Given monoidal categories \((\mathcal{C}, \otimes, I_{\mathcal{C}})\) and \((\mathcal{D}, \bullet, I_{\mathcal{D}})\).@@ -155,9 +361,9 @@   -- >>> introduce @(->) @() @() @Maybe ()   -- Just ()   ---  -- >>> :t introduce @(->) @Void @() @Maybe +  -- >>> :t introduce @(->) @Void @() @Maybe   -- introduce @(->) @Void @() @Maybe :: () -> Maybe Void-  -- +  --   -- >>> introduce @(->) @Void @() @Maybe ()   -- Nothing   introduce :: cat i0 (f i1)@@ -166,45 +372,180 @@   introduce :: () -> FromApplicative f ()   introduce = pure -deriving via FromApplicative Identity           instance Unital (->) () () Identity-deriving via FromApplicative (Compose f g)      instance (Applicative f, Applicative g) => Unital (->) () () (Compose f g)-deriving via FromApplicative []                 instance Unital (->) () () []-deriving via FromApplicative ZipList            instance Unital (->) () () ZipList-deriving via FromApplicative NonEmpty           instance Unital (->) () () NonEmpty-deriving via FromApplicative Maybe              instance Unital (->) () () Maybe-deriving via FromApplicative (Either e)         instance Unital (->) () () (Either e)-deriving via FromApplicative IO                 instance Unital (->) () () IO-deriving via FromApplicative (Product f g)      instance (Applicative f, Applicative g) => Unital (->) () () (Product f g)-deriving via (FromApplicative ((,) x1))         instance (Monoid x1) => Unital (->) () () ((,) x1)-deriving via (FromApplicative ((,,) x1 x2))     instance (Monoid x1, Monoid x2) => Unital (->) () () ((,,) x1 x2)+deriving via FromApplicative Identity instance Unital (->) () () Identity++deriving via FromApplicative (Compose f g) instance (Applicative f, Applicative g) => Unital (->) () () (Compose f g)++deriving via FromApplicative [] instance Unital (->) () () []++deriving via FromApplicative ZipList instance Unital (->) () () ZipList++deriving via FromApplicative NonEmpty instance Unital (->) () () NonEmpty++deriving via FromApplicative Maybe instance Unital (->) () () Maybe++deriving via FromApplicative (Either e) instance Unital (->) () () (Either e)++deriving via FromApplicative IO instance Unital (->) () () IO++deriving via FromApplicative (Product f g) instance (Applicative f, Applicative g) => Unital (->) () () (Product f g)++deriving via (FromApplicative ((,) x1)) instance (Monoid x1) => Unital (->) () () ((,) x1)++deriving via (FromApplicative ((,,) x1 x2)) instance (Monoid x1, Monoid x2) => Unital (->) () () ((,,) x1 x2)+ deriving via (FromApplicative ((,,,) x1 x2 x3)) instance (Monoid x1, Monoid x2, Monoid x3) => Unital (->) () () ((,,,) x1 x2 x3)  instance Alternative f => Unital (->) Void () (FromAlternative f) where   introduce :: () -> FromAlternative f Void   introduce () = empty -deriving via FromAlternative ZipList                 instance Unital (->) Void () ZipList-deriving via FromAlternative STM                     instance Unital (->) Void () STM-deriving via FromAlternative ReadP                   instance Unital (->) Void () ReadP-deriving via FromAlternative ReadPrec                instance Unital (->) Void () ReadPrec-deriving via FromAlternative IO                      instance Unital (->) Void () IO-deriving via FromAlternative Maybe                   instance Unital (->) Void () Maybe-deriving via FromAlternative []                      instance Unital (->) Void () []-deriving via FromAlternative (WrappedMonad m)        instance (MonadPlus m) => Unital (->) Void () (WrappedMonad m)-deriving via FromAlternative (ArrowMonad a)          instance (ArrowPlus a) => Unital (->) Void () (ArrowMonad a)+deriving via FromAlternative ZipList instance Unital (->) Void () ZipList++deriving via FromAlternative STM instance Unital (->) Void () STM++deriving via FromAlternative ReadP instance Unital (->) Void () ReadP++deriving via FromAlternative ReadPrec instance Unital (->) Void () ReadPrec++deriving via FromAlternative IO instance Unital (->) Void () IO++deriving via FromAlternative Maybe instance Unital (->) Void () Maybe++deriving via FromAlternative [] instance Unital (->) Void () []++deriving via FromAlternative (WrappedMonad m) instance (MonadPlus m) => Unital (->) Void () (WrappedMonad m)++deriving via FromAlternative (ArrowMonad a) instance (ArrowPlus a) => Unital (->) Void () (ArrowMonad a)+ deriving via FromAlternative (Proxy :: Type -> Type) instance Unital (->) Void () (Proxy :: Type -> Type)-deriving via FromAlternative (U1 :: Type -> Type)    instance Unital (->) Void () (U1 :: Type -> Type)-deriving via FromAlternative (WrappedArrow a b)      instance (ArrowZero a, ArrowPlus a) => Unital (->) Void () (WrappedArrow a b)-deriving via FromAlternative (Kleisli m a)           instance (Alternative m) => Unital (->) Void () (Kleisli m a)-deriving via FromAlternative (Ap f)                  instance (Alternative f) => Unital (->) Void () (Ap f)-deriving via FromAlternative (Alt f)                 instance (Alternative f) => Unital (->) Void () (Alt f)-deriving via FromAlternative (Rec1 f)                instance (Alternative f) => Unital (->) Void () (Rec1 f)-deriving via FromAlternative (Product f g)           instance (Alternative f, Alternative g) => Unital (->) Void () (Product f g)-deriving via FromAlternative (f :*: g)               instance (Alternative f, Alternative g) => Unital (->) Void () (f :*: g)-deriving via FromAlternative (f `Compose` g)         instance (Alternative f, Applicative g) => Unital (->) Void () (f `Compose` g)-deriving via FromAlternative (f :.: g)               instance (Alternative f, Applicative g) => Unital (->) Void () (f :.: g)-deriving via FromAlternative (M1 i c f)              instance (Alternative f) => Unital (->) Void () (M1 i c f) +deriving via FromAlternative (U1 :: Type -> Type) instance Unital (->) Void () (U1 :: Type -> Type)++deriving via FromAlternative (WrappedArrow a b) instance (ArrowZero a, ArrowPlus a) => Unital (->) Void () (WrappedArrow a b)++deriving via FromAlternative (Kleisli m a) instance (Alternative m) => Unital (->) Void () (Kleisli m a)++deriving via FromAlternative (Ap f) instance (Alternative f) => Unital (->) Void () (Ap f)++deriving via FromAlternative (Alt f) instance (Alternative f) => Unital (->) Void () (Alt f)++deriving via FromAlternative (Rec1 f) instance (Alternative f) => Unital (->) Void () (Rec1 f)++deriving via FromAlternative (Product f g) instance (Alternative f, Alternative g) => Unital (->) Void () (Product f g)++deriving via FromAlternative (f :*: g) instance (Alternative f, Alternative g) => Unital (->) Void () (f :*: g)++deriving via FromAlternative (f `Compose` g) instance (Alternative f, Applicative g) => Unital (->) Void () (f `Compose` g)++deriving via FromAlternative (f :.: g) instance (Alternative f, Applicative g) => Unital (->) Void () (f :.: g)++deriving via FromAlternative (M1 i c f) instance (Alternative f) => Unital (->) Void () (M1 i c f)++instance Divisible f => Unital (->) () () (FromDivisible f) where+  introduce :: () -> FromDivisible f ()+  introduce () = FromDivisible conquered++deriving via FromDivisible Predicate instance Unital (->) () () Predicate++deriving via FromDivisible Comparison instance Unital (->) () () Comparison++deriving via FromDivisible Equivalence instance Unital (->) () () Equivalence++deriving via FromDivisible (U1 :: Type -> Type) instance Unital (->) () () (U1 :: Type -> Type)++deriving via FromDivisible (Op r) instance Monoid r => Unital (->) () () (Op r)++-- deriving via FromDivisible (Proxy :: Type -> Type) instance Unital (->) () () (Proxy :: Type -> Type)+deriving via FromDivisible (MaybeT m) instance Divisible m => Unital (->) () () (MaybeT m)++deriving via FromDivisible (Rec1 m) instance Divisible m => Unital (->) () () (Rec1 m)++deriving via FromDivisible (Const m) instance Monoid m => Unital (->) () () (Const m :: Type -> Type)++deriving via FromDivisible (Alt f) instance Divisible f => Unital (->) () () (Alt f)++deriving via FromDivisible (Reverse f) instance Divisible f => Unital (->) () () (Reverse f)++deriving via FromDivisible (Constant m) instance Monoid m => Unital (->) () () (Constant m :: Type -> Type)++deriving via FromDivisible (WriterT w m) instance Divisible m => Unital (->) () () (WriterT w m)++deriving via FromDivisible (Lazy.WriterT w m) instance Divisible m => Unital (->) () () (Lazy.WriterT w m)++deriving via FromDivisible (StateT w m) instance Divisible m => Unital (->) () () (StateT w m)++deriving via FromDivisible (Lazy.StateT w m) instance Divisible m => Unital (->) () () (Lazy.StateT w m)++deriving via FromDivisible (ReaderT r m) instance Divisible m => Unital (->) () () (ReaderT r m)++deriving via FromDivisible (IdentityT m) instance Divisible m => Unital (->) () () (IdentityT m)++deriving via FromDivisible (ExceptT e m) instance Divisible m => Unital (->) () () (ExceptT e m)++deriving via FromDivisible (Backwards f) instance Divisible f => Unital (->) () () (Backwards f)++deriving via FromDivisible (ComposeCF f g) instance (Divisible f, Applicative g) => Unital (->) () () (ComposeCF f g)++deriving via FromDivisible (ComposeFC f g) instance (Divisible g, Applicative f) => Unital (->) () () (ComposeFC f g)++deriving via FromDivisible (f :*: g) instance (Divisible f, Divisible g) => Unital (->) () () (f :*: g)++-- deriving via FromDivisible (Product f g)           instance (Divisible f, Divisible g) => Unital (->) () () (Product f g)+deriving via FromDivisible (M1 i c f) instance Divisible f => Unital (->) () () (M1 i c f)++deriving via FromDivisible (f :.: g) instance (Applicative f, Divisible g) => Unital (->) () () (f :.: g)++-- deriving via FromDivisible (Compose f g)           instance (Applicative f, Divisible g) => Unital (->) () () (Compose f g)+deriving via FromDivisible (RWST r w s m) instance (Divisible m) => Unital (->) () () (RWST r w s m)++deriving via FromDivisible (Lazy.RWST r w s m) instance (Divisible m) => Unital (->) () () (Lazy.RWST r w s m)++instance Decidable f => Unital (->) Void () (FromDecidable f) where+  introduce :: () -> FromDecidable f Void+  introduce () = FromDecidable lost++deriving via FromDecidable Predicate instance Unital (->) Void () Predicate++deriving via FromDecidable Comparison instance Unital (->) Void () Comparison++deriving via FromDecidable Equivalence instance Unital (->) Void () Equivalence++-- deriving via FromDecidable (U1 :: Type -> Type)    instance Unital (->) Void () (U1 :: Type -> Type)+deriving via FromDecidable (Op r) instance Monoid r => Unital (->) Void () (Op r)++-- deriving via FromDecidable (Proxy :: Type -> Type) instance Unital (->) Void () (Proxy :: Type -> Type)+deriving via FromDecidable (MaybeT m) instance Decidable m => Unital (->) Void () (MaybeT m)++-- deriving via FromDecidable (Rec1 m)                instance Decidable m => Unital (->) Void () (Rec1 m)+-- deriving via FromDecidable (Alt f)                 instance Decidable f => Unital (->) Void () (Alt f)+deriving via FromDecidable (Reverse f) instance Decidable f => Unital (->) Void () (Reverse f)++deriving via FromDecidable (WriterT w m) instance Decidable m => Unital (->) Void () (WriterT w m)++deriving via FromDecidable (Lazy.WriterT w m) instance Decidable m => Unital (->) Void () (Lazy.WriterT w m)++deriving via FromDecidable (StateT w m) instance Decidable m => Unital (->) Void () (StateT w m)++deriving via FromDecidable (Lazy.StateT w m) instance Decidable m => Unital (->) Void () (Lazy.StateT w m)++deriving via FromDecidable (ReaderT r m) instance Decidable m => Unital (->) Void () (ReaderT r m)++deriving via FromDecidable (IdentityT m) instance Decidable m => Unital (->) Void () (IdentityT m)++deriving via FromDecidable (Backwards f) instance Decidable f => Unital (->) Void () (Backwards f)++deriving via FromDecidable (ComposeFC f g) instance (Decidable g, Applicative f) => Unital (->) Void () (ComposeFC f g)++-- deriving via FromDecidable (f :*: g)               instance (Decidable f, Decidable g) => Unital (->) Void () (f :*: g)+-- deriving via FromDecidable (Product f g)           instance (Decidable f, Decidable g) => Unital (->) Void () (Product f g)+-- deriving via FromDecidable (M1 i c f)              instance Decidable f => Unital (->) Void () (M1 i c f)+-- deriving via FromDecidable (f :.: g)               instance (Applicative f, Decidable g) => Unital (->) Void () (f :.: g)+-- deriving via FromDecidable (Compose f g)           instance (Applicative f, Decidable g) => Unital (->) Void () (Compose f g)+deriving via FromDecidable (RWST r w s m) instance (Decidable m) => Unital (->) Void () (RWST r w s m)++deriving via FromDecidable (Lazy.RWST r w s m) instance (Decidable m) => Unital (->) Void () (Lazy.RWST r w s m)+ --------------------------------------------------------------------------------  -- | Given monoidal categories \((\mathcal{C}, \otimes, I_{\mathcal{C}})\) and \((\mathcal{D}, \bullet, I_{\mathcal{D}})\).@@ -217,7 +558,7 @@ -- -- __Right Unitality__: ----- \[ +-- \[ -- \require{AMScd} -- \begin{CD} -- F A \bullet I_{\mathcal{D}}   @>{1 \bullet \phi}>>         F A \bullet F I_{\mathcal{C}};\\@@ -232,7 +573,7 @@ -- -- __ Left Unitality__: ----- \[ +-- \[ -- \begin{CD} -- I_{\mathcal{D}} \bullet F B   @>{\phi \bullet 1}>>            F I_{\mathcal{C}} \bullet F B;\\ -- @VV{\lambda_{\mathcal{D}}}V                                   @VV{\phi I_{\mathcal{C}},B}V \\@@ -244,47 +585,175 @@ --   'combine' 'Control.Category..' 'glmap' 'introduce' ≡ 'fmap' ('bwd' 'unitl') 'Control.Category..' 'fwd' 'unitl' -- @ class-  ( Tensor cat t1 i1-  , Tensor cat t0 i0-  , Semigroupal cat t1 t0 f-  , Unital cat i1 i0 f-  ) => Monoidal cat t1 i1 t0 i0 f+  ( Tensor cat t1 i1,+    Tensor cat t0 i0,+    Semigroupal cat t1 t0 f,+    Unital cat i1 i0 f+  ) =>+  Monoidal cat t1 i1 t0 i0 f  instance Applicative f => Monoidal (->) (,) () (,) () (FromApplicative f) -deriving via FromApplicative Identity           instance Monoidal (->) (,) () (,) () Identity-deriving via FromApplicative (Compose f g)      instance (Applicative f, Applicative g) => Monoidal (->) (,) () (,) () (Compose f g)-deriving via FromApplicative []                 instance Monoidal (->) (,) () (,) () []-deriving via FromApplicative ZipList            instance Monoidal (->) (,) () (,) () ZipList-deriving via FromApplicative NonEmpty           instance Monoidal (->) (,) () (,) () NonEmpty-deriving via FromApplicative Maybe              instance Monoidal (->) (,) () (,) () Maybe-deriving via FromApplicative (Either e)         instance Monoidal (->) (,) () (,) () (Either e)-deriving via FromApplicative IO                 instance Monoidal (->) (,) () (,) () IO-deriving via FromApplicative (Product f g)      instance (Applicative f, Applicative g) => Monoidal (->) (,) () (,) () (Product f g)-deriving via (FromApplicative ((,) x1))         instance (Monoid x1) => Monoidal (->) (,) () (,) () ((,) x1)-deriving via (FromApplicative ((,,) x1 x2))     instance (Monoid x1, Monoid x2) => Monoidal (->) (,) () (,) () ((,,) x1 x2)+deriving via FromApplicative Identity instance Monoidal (->) (,) () (,) () Identity++deriving via FromApplicative (Compose f g) instance (Applicative f, Applicative g) => Monoidal (->) (,) () (,) () (Compose f g)++deriving via FromApplicative [] instance Monoidal (->) (,) () (,) () []++deriving via FromApplicative ZipList instance Monoidal (->) (,) () (,) () ZipList++deriving via FromApplicative NonEmpty instance Monoidal (->) (,) () (,) () NonEmpty++deriving via FromApplicative Maybe instance Monoidal (->) (,) () (,) () Maybe++deriving via FromApplicative (Either e) instance Monoidal (->) (,) () (,) () (Either e)++deriving via FromApplicative IO instance Monoidal (->) (,) () (,) () IO++deriving via FromApplicative (Product f g) instance (Applicative f, Applicative g) => Monoidal (->) (,) () (,) () (Product f g)++deriving via (FromApplicative ((,) x1)) instance (Monoid x1) => Monoidal (->) (,) () (,) () ((,) x1)++deriving via (FromApplicative ((,,) x1 x2)) instance (Monoid x1, Monoid x2) => Monoidal (->) (,) () (,) () ((,,) x1 x2)+ deriving via (FromApplicative ((,,,) x1 x2 x3)) instance (Monoid x1, Monoid x2, Monoid x3) => Monoidal (->) (,) () (,) () ((,,,) x1 x2 x3)  instance Alternative f => Monoidal (->) Either Void (,) () (FromAlternative f) -deriving via FromAlternative ZipList                 instance Monoidal (->) Either Void (,) () ZipList-deriving via FromAlternative STM                     instance Monoidal (->) Either Void (,) () STM-deriving via FromAlternative ReadP                   instance Monoidal (->) Either Void (,) () ReadP-deriving via FromAlternative ReadPrec                instance Monoidal (->) Either Void (,) () ReadPrec-deriving via FromAlternative IO                      instance Monoidal (->) Either Void (,) () IO-deriving via FromAlternative Maybe                   instance Monoidal (->) Either Void (,) () Maybe-deriving via FromAlternative []                      instance Monoidal (->) Either Void (,) () []-deriving via FromAlternative (WrappedMonad m)        instance (MonadPlus m) => Monoidal (->) Either Void (,) () (WrappedMonad m)-deriving via FromAlternative (ArrowMonad a)          instance (ArrowPlus a) => Monoidal (->) Either Void (,) () (ArrowMonad a)+deriving via FromAlternative ZipList instance Monoidal (->) Either Void (,) () ZipList++deriving via FromAlternative STM instance Monoidal (->) Either Void (,) () STM++deriving via FromAlternative ReadP instance Monoidal (->) Either Void (,) () ReadP++deriving via FromAlternative ReadPrec instance Monoidal (->) Either Void (,) () ReadPrec++deriving via FromAlternative IO instance Monoidal (->) Either Void (,) () IO++deriving via FromAlternative Maybe instance Monoidal (->) Either Void (,) () Maybe++deriving via FromAlternative [] instance Monoidal (->) Either Void (,) () []++deriving via FromAlternative (WrappedMonad m) instance (MonadPlus m) => Monoidal (->) Either Void (,) () (WrappedMonad m)++deriving via FromAlternative (ArrowMonad a) instance (ArrowPlus a) => Monoidal (->) Either Void (,) () (ArrowMonad a)+ deriving via FromAlternative (Proxy :: Type -> Type) instance Monoidal (->) Either Void (,) () (Proxy :: Type -> Type)-deriving via FromAlternative (U1 :: Type -> Type)    instance Monoidal (->) Either Void (,) () (U1 :: Type -> Type)-deriving via FromAlternative (WrappedArrow a b)      instance (ArrowZero a, ArrowPlus a) => Monoidal (->) Either Void (,) () (WrappedArrow a b)-deriving via FromAlternative (Kleisli m a)           instance (Alternative m) => Monoidal (->) Either Void (,) () (Kleisli m a)-deriving via FromAlternative (Ap f)                  instance (Alternative f) => Monoidal (->) Either Void (,) () (Ap f)-deriving via FromAlternative (Alt f)                 instance (Alternative f) => Monoidal (->) Either Void (,) () (Alt f)-deriving via FromAlternative (Rec1 f)                instance (Alternative f) => Monoidal (->) Either Void (,) () (Rec1 f)-deriving via FromAlternative (Product f g)           instance (Alternative f, Alternative g) => Monoidal (->) Either Void (,) () (Product f g)-deriving via FromAlternative (f :*: g)               instance (Alternative f, Alternative g) => Monoidal (->) Either Void (,) () (f :*: g)-deriving via FromAlternative (f `Compose` g)         instance (Alternative f, Applicative g) => Monoidal (->) Either Void (,) () (f `Compose` g)-deriving via FromAlternative (f :.: g)               instance (Alternative f, Applicative g) => Monoidal (->) Either Void (,) () (f :.: g)-deriving via FromAlternative (M1 i c f)              instance (Alternative f) => Monoidal (->) Either Void (,) () (M1 i c f)++deriving via FromAlternative (U1 :: Type -> Type) instance Monoidal (->) Either Void (,) () (U1 :: Type -> Type)++deriving via FromAlternative (WrappedArrow a b) instance (ArrowZero a, ArrowPlus a) => Monoidal (->) Either Void (,) () (WrappedArrow a b)++deriving via FromAlternative (Kleisli m a) instance (Alternative m) => Monoidal (->) Either Void (,) () (Kleisli m a)++deriving via FromAlternative (Ap f) instance (Alternative f) => Monoidal (->) Either Void (,) () (Ap f)++deriving via FromAlternative (Alt f) instance (Alternative f) => Monoidal (->) Either Void (,) () (Alt f)++deriving via FromAlternative (Rec1 f) instance (Alternative f) => Monoidal (->) Either Void (,) () (Rec1 f)++deriving via FromAlternative (Product f g) instance (Alternative f, Alternative g) => Monoidal (->) Either Void (,) () (Product f g)++deriving via FromAlternative (f :*: g) instance (Alternative f, Alternative g) => Monoidal (->) Either Void (,) () (f :*: g)++deriving via FromAlternative (f `Compose` g) instance (Alternative f, Applicative g) => Monoidal (->) Either Void (,) () (f `Compose` g)++deriving via FromAlternative (f :.: g) instance (Alternative f, Applicative g) => Monoidal (->) Either Void (,) () (f :.: g)++deriving via FromAlternative (M1 i c f) instance (Alternative f) => Monoidal (->) Either Void (,) () (M1 i c f)++deriving via FromDivisible Predicate instance Monoidal (->) (,) () (,) () Predicate++deriving via FromDivisible Comparison instance Monoidal (->) (,) () (,) () Comparison++deriving via FromDivisible Equivalence instance Monoidal (->) (,) () (,) () Equivalence++deriving via FromDivisible (U1 :: Type -> Type) instance Monoidal (->) (,) () (,) () (U1 :: Type -> Type)++deriving via FromDivisible (Op r) instance Monoid r => Monoidal (->) (,) () (,) () (Op r)++-- deriving via FromDivisible (Proxy :: Type -> Type) instance Monoidal (->) (,) () (,) () (Proxy :: Type -> Type)+deriving via FromDivisible (MaybeT m) instance Divisible m => Monoidal (->) (,) () (,) () (MaybeT m)++deriving via FromDivisible (Rec1 m) instance Divisible m => Monoidal (->) (,) () (,) () (Rec1 m)++deriving via FromDivisible (Const m) instance Monoid m => Monoidal (->) (,) () (,) () (Const m :: Type -> Type)++deriving via FromDivisible (Alt f) instance Divisible f => Monoidal (->) (,) () (,) () (Alt f)++deriving via FromDivisible (Reverse f) instance Divisible f => Monoidal (->) (,) () (,) () (Reverse f)++deriving via FromDivisible (Constant m) instance Monoid m => Monoidal (->) (,) () (,) () (Constant m :: Type -> Type)++deriving via FromDivisible (WriterT w m) instance Divisible m => Monoidal (->) (,) () (,) () (WriterT w m)++deriving via FromDivisible (Lazy.WriterT w m) instance Divisible m => Monoidal (->) (,) () (,) () (Lazy.WriterT w m)++deriving via FromDivisible (StateT w m) instance Divisible m => Monoidal (->) (,) () (,) () (StateT w m)++deriving via FromDivisible (Lazy.StateT w m) instance Divisible m => Monoidal (->) (,) () (,) () (Lazy.StateT w m)++deriving via FromDivisible (ReaderT r m) instance Divisible m => Monoidal (->) (,) () (,) () (ReaderT r m)++deriving via FromDivisible (IdentityT m) instance Divisible m => Monoidal (->) (,) () (,) () (IdentityT m)++deriving via FromDivisible (ExceptT e m) instance Divisible m => Monoidal (->) (,) () (,) () (ExceptT e m)++deriving via FromDivisible (Backwards f) instance Divisible f => Monoidal (->) (,) () (,) () (Backwards f)++deriving via FromDivisible (ComposeCF f g) instance (Divisible f, Applicative g) => Monoidal (->) (,) () (,) () (ComposeCF f g)++deriving via FromDivisible (ComposeFC f g) instance (Divisible g, Applicative f) => Monoidal (->) (,) () (,) () (ComposeFC f g)++deriving via FromDivisible (f :*: g) instance (Divisible f, Divisible g) => Monoidal (->) (,) () (,) () (f :*: g)++-- deriving via FromDivisible (Product f g)           instance (Divisible f, Divisible g) => Monoidal (->) (,) () (,) () (Product f g)+deriving via FromDivisible (M1 i c f) instance Divisible f => Monoidal (->) (,) () (,) () (M1 i c f)++deriving via FromDivisible (f :.: g) instance (Applicative f, Divisible g) => Monoidal (->) (,) () (,) () (f :.: g)++-- deriving via FromDivisible (Compose f g)           instance (Applicative f, Divisible g) => Monoidal (->) (,) () (,) () (Compose f g)+deriving via FromDivisible (RWST r w s m) instance (Divisible m) => Monoidal (->) (,) () (,) () (RWST r w s m)++deriving via FromDivisible (Lazy.RWST r w s m) instance (Divisible m) => Monoidal (->) (,) () (,) () (Lazy.RWST r w s m)++deriving via FromDecidable Predicate instance Monoidal (->) Either Void (,) () Predicate++deriving via FromDecidable Comparison instance Monoidal (->) Either Void (,) () Comparison++deriving via FromDecidable Equivalence instance Monoidal (->) Either Void (,) () Equivalence++-- deriving via FromDecidable (U1 :: Type -> Type)    instance Monoidal (->) Either Void (,) () (U1 :: Type -> Type)+deriving via FromDecidable (Op r) instance Monoid r => Monoidal (->) Either Void (,) () (Op r)++-- deriving via FromDecidable (Proxy :: Type -> Type) instance Monoidal (->) Either Void (,) () (Proxy :: Type -> Type)+deriving via FromDecidable (MaybeT m) instance Decidable m => Monoidal (->) Either Void (,) () (MaybeT m)++-- deriving via FromDecidable (Rec1 m)                instance Decidable m => Monoidal (->) Either Void (,) () (Rec1 m)+-- deriving via FromDecidable (Alt f)                 instance Decidable f => Monoidal (->) Either Void (,) () (Alt f)+deriving via FromDecidable (Reverse f) instance Decidable f => Monoidal (->) Either Void (,) () (Reverse f)++deriving via FromDecidable (WriterT w m) instance Decidable m => Monoidal (->) Either Void (,) () (WriterT w m)++deriving via FromDecidable (Lazy.WriterT w m) instance Decidable m => Monoidal (->) Either Void (,) () (Lazy.WriterT w m)++deriving via FromDecidable (StateT w m) instance Decidable m => Monoidal (->) Either Void (,) () (StateT w m)++deriving via FromDecidable (Lazy.StateT w m) instance Decidable m => Monoidal (->) Either Void (,) () (Lazy.StateT w m)++deriving via FromDecidable (ReaderT r m) instance Decidable m => Monoidal (->) Either Void (,) () (ReaderT r m)++deriving via FromDecidable (IdentityT m) instance Decidable m => Monoidal (->) Either Void (,) () (IdentityT m)++deriving via FromDecidable (Backwards f) instance Decidable f => Monoidal (->) Either Void (,) () (Backwards f)++deriving via FromDecidable (ComposeFC f g) instance (Decidable g, Applicative f) => Monoidal (->) Either Void (,) () (ComposeFC f g)++-- deriving via FromDecidable (f :*: g)               instance (Decidable f, Decidable g) => Monoidal (->) Either Void (,) () (f :*: g)+-- deriving via FromDecidable (Product f g)           instance (Decidable f, Decidable g) => Monoidal (->) Either Void (,) () (Product f g)+-- deriving via FromDecidable (M1 i c f)              instance Decidable f => Monoidal (->) Either Void (,) () (M1 i c f)+-- deriving via FromDecidable (f :.: g)               instance (Applicative f, Decidable g) => Monoidal (->) Either Void (,) () (f :.: g)+-- deriving via FromDecidable (Compose f g)           instance (Applicative f, Decidable g) => Monoidal (->) Either Void (,) () (Compose f g)+deriving via FromDecidable (RWST r w s m) instance (Decidable m) => Monoidal (->) Either Void (,) () (RWST r w s m)++deriving via FromDecidable (Lazy.RWST r w s m) instance (Decidable m) => Monoidal (->) Either Void (,) () (Lazy.RWST r w s m)

@@ -24,7 +24,7 @@ -- -- __Associativity:__ ----- \[ +-- \[ -- \require{AMScd} -- \begin{CD} -- (F A B C \bullet F X Y Z) \bullet F P Q R                                              @>>{\alpha_{\mathcal{D}}}>     F A B C \bullet (F X Y Z \bullet F P Q R) \\@@ -39,12 +39,14 @@ -- 'combine' 'Control.Category..' 'Control.Category.Tensor.grmap' 'Control.Category.Tensor.combine' 'Control.Category..' 'Control.Category.Tensor.bwd' 'Control.Category.Tensor.assoc' ≡ 'Data.Functor.fmap' ('Control.Category.Tensor.bwd' 'Control.Category.Tensor.assoc') 'Control.Category..' 'combine' 'Control.Category..' 'Control.Category.Tensor.glmap' 'combine' -- @ class-  ( Associative cat t1-  , Associative cat t2-  , Associative cat t3-  , Associative cat to-  ) => Semigroupal cat t1 t2 t3 to f where-  -- | A natural transformation \(\phi_{ABC,XYZ} : F\ A\ B\ C \bullet F\ X\ Y\ Z \to F\ (A \otimes X)\ (B \otimes Y) (C \otimes Z)\). +  ( Associative cat t1,+    Associative cat t2,+    Associative cat t3,+    Associative cat to+  ) =>+  Semigroupal cat t1 t2 t3 to f+  where+  -- | A natural transformation \(\phi_{ABC,XYZ} : F\ A\ B\ C \bullet F\ X\ Y\ Z \to F\ (A \otimes X)\ (B \otimes Y) (C \otimes Z)\).   combine :: to (f x y z) (f x' y' z') `cat` f (t1 x x') (t2 y y') (t3 z z')  --------------------------------------------------------------------------------@@ -70,7 +72,7 @@ -- -- __Right Unitality:__ ----- \[ +-- \[ -- \require{AMScd} -- \begin{CD} -- F A B C \bullet I_{\mathcal{D}}   @>{1 \bullet \phi}>>                                                            F A B \bullet F I_{\mathcal{C_{1}}} I_{\mathcal{C_{2}}} I_{\mathcal{C_{3}}}\\@@ -85,7 +87,7 @@ -- -- __ Left Unitality__: ----- \[ +-- \[ -- \begin{CD} -- I_{\mathcal{D}} \bullet F A B C   @>{\phi \bullet 1}>>                                                                    F I_{\mathcal{C_{1}}} I_{\mathcal{C_{2}}} \bullet F A B C\\ -- @VV{\lambda_{\mathcal{D}}}V                                                                                               @VV{I_{\mathcal{C_{1}}}I_{\mathcal{C_{2}}}I_{\mathcal{C_{3}}},\phi ABC}V \\@@ -97,10 +99,11 @@ -- 'combine' 'Control.Category..' 'Control.Category.Tensor.glmap' 'introduce' ≡ 'Data.Functor.fmap' ('Control.Category.Tensor.bwd' 'Control.Category.Tensor.unitl') 'Control.Category..' 'Control.Category.Tensor.fwd' 'Control.Category.Tensor.unitl' -- @ class-  ( Tensor cat t1 i1-  , Tensor cat t2 i2-  , Tensor cat t3 i3-  , Tensor cat to io-  , Semigroupal cat t1 t2 t3 to f-  , Unital cat i1 i2 i3 io f-  ) => Monoidal cat t1 i1 t2 i2 t3 i3 to io f+  ( Tensor cat t1 i1,+    Tensor cat t2 i2,+    Tensor cat t3 i3,+    Tensor cat to io,+    Semigroupal cat t1 t2 t3 to f,+    Unital cat i1 i2 i3 io f+  ) =>+  Monoidal cat t1 i1 t2 i2 t3 i3 to io f