!2      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                 ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                               (C) 2011-2018 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportable TrustworthyX>w profunctorsFormally, the class  represents a profunctor from Hask -> Hask.nIntuitively it is a bifunctor where the first argument is contravariant and the second argument is covariant.You can define a  by either defining  or by defining both  and .If you supply , you should ensure that:    "a If you supply  and  , ensure:   "a    "a  +If you supply both, you should also ensure:  f g "a  f   gThese ensure by parametricity:  (f  g) (h  i) "a  g h   f i  (f  g) "a  g   f  (f  g) "a  f   g  profunctors)Map over both arguments at the same time.  f g "a  f   g profunctors'Map the first argument contravariantly.  f "a  f  profunctors$Map the second argument covariantly.  "a   profunctorsStrictly map the second argument argument covariantly with a function that is assumed operationally to be a cast, such as a newtype constructor.Note: This operation is explicitly unsafe- since an implementation may choose to use  unsafeCoerceh to implement this combinator and it has no way to validate that your function meets the requirements.'If you implement this combinator with  unsafeCoerceo, then you are taking upon yourself the obligation that you don't use GADT-like tricks to distinguish values.If you import Data.Profunctor.Unsafe you are taking upon yourself the obligation that you will only call this with a first argument that is operationally identity.\The semantics of this function with respect to bottoms should match the default definition: () "a \_ -> \p -> p `seq`   p profunctorsStrictly map the first argument argument contravariantly with a function that is assumed operationally to be a cast, such as a newtype constructor.Note: This operation is explicitly unsafe- since an implementation may choose to use  unsafeCoerceh to implement this combinator and it has no way to validate that your function meets the requirements.'If you implement this combinator with  unsafeCoerceo, then you are taking upon yourself the obligation that you don't use GADT-like tricks to distinguish values.If you import Data.Profunctor.Unsafe you are taking upon yourself the obligation that you will only call this with a second argument that is operationally identity. () "a \p -> p `seq` \f ->   p9 8(C) 2011-2015 Edward Kmett, BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportable TrustworthySUVXC# profunctorsWrap an arrow for use as a . profunctorsLift a  into a  (backwards). profunctorsLift a  into a  (forwards).0(C) 2014-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimentalportableSafeSUVXI7 profunctorsLaws: 8  > f "a f  8 8  9 "a  > 8  9 "a  9  9 "a > 9  9 : profunctorsLaws: > f  ; "a ;  f <  ; "a  <  > ; "a  <  < "a <  > < > profunctorsLaws: > f  > g "a > (f  g) >  "a  798:<;=>=>:<;798(C) 2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimentalnon-portable, MPTCs, fundepsSafe@ACSUVXM>F profunctorsLaws: G  H "a  H  G "a  FHGFHG(C) 2014-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisional Rank2TypesSafe &'@ASUVXiI profunctorsCopastro -| Cotambara%Copastro freely constructs costrengthL profunctors(Cotambara cofreely constructs costrengthN profunctors Analogous to ,  = OO profunctorsLaws: O "a P      (,()) "a O   (,()) O   ( f) "a O   ( f) O  O = O  S assoc unassoc where assoc ((a,b),c) = (a,(b,c)) unassoc (a,(b,c)) = ((a,b),c) P profunctorsLaws: P "a O      ((),) "a P   ((),) P   ( f) "a P   ( f) P  P = P  S unassoc assoc where assoc ((a,b),c) = (a,(b,c)) unassoc (a,(b,c)) = ((a,b),c) Q profunctorsPastro -| Tambara #Pastro p ~ exists z. Costar ((,)z)  Procompose p  Procompose Star ((,)z) Q freely makes any  V.S profunctorsS cofreely makes any  V.V profunctors Generalizing  of a strong Note: Every & in Haskell is strong with respect to (,).RThis describes profunctor strength with respect to the product structure of Hask. 8http://www.riec.tohoku.ac.jp/~asada/papers/arrStrMnd.pdfW profunctorsLaws: W "a     X   "a    W  (X f)  W "a  (X f)  W W  W "a  assoc unassoc  WE where assoc ((a,b),c) = (a,(b,c)) unassoc (a,(b,c)) = ((a,b),c) X profunctorsLaws: X "a     W   "a    X  (W f)  X "a  (W f)  X X  X "a  unassoc assoc  XE where assoc ((a,b),c) = (a,(b,c)) unassoc (a,(b,c)) = ((a,b),c) [ profunctors [ (\ f) "a f \ ([ f) "a f \ profunctors [ (\ f) "a f \ ([ f) "a f ] profunctors ] (^ f) "a f ^ (] f) "a f ^ profunctors ] (^ f) "a f ^ (] f) "a f _ profunctors _  ` "a  `  _ "a  ` profunctors _  ` "a  `  _ "a  e profunctors is V IJKLMNOPQRSTUVWXYZ[\]^_`VWXYZSTU[\QR]^NOPLM_`IJK(C) 2014-2018 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimentalportable Trustworthy &'/@ASUVXsa profunctors adjoins a  structure to any . Analogous to  for V. profunctorsBA strong profunctor allows the monoidal structure to pass through.@A closed profunctor allows the closed structure to pass through. profunctorsLaws:  ( f)   "a  ( f)      "a        (())   "a   profunctors    "a     "a   profunctors    "a     "a  (C) 2014-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisional Rank2TypesSafe &'@ASUVX profunctorsCopastroSum -| CotambaraSum. freely constructs costrength with respect to  (aka ) profunctors0 cofreely constructs costrength with respect to  (aka ) profunctorsLaws:  "a    swapE swapE where swapE ::  a b ->  b a swapE =     (  absurd) "a    (  absurd) O   ( f) "a O   ( f)    "a   # assocE unassocE where assocE ::  ( a b) c ->  a ( b c) assocE ( ( a)) =  a assocE ( ( b)) =  ( b) assocE ( c) =  ( c) unassocE ::  a ( b c) ->  ( a b) c unassocE ( a) =  ( a) unassocE ( ( b) =  ( b) unassocE ( ( c)) =  c)  profunctorsLaws:  "a    swapE swapE where swapE ::  a b ->  b a swapE =     ( absurd ) "a    ( absurd ) P   ( f) "a P   ( f)    "a   # unassocE assocE where assocE ::  ( a b) c ->  a ( b c) assocE ( ( a)) =  a assocE ( ( b)) =  ( b) assocE ( c) =  ( c) unassocE ::  a ( b c) ->  ( a b) c unassocE ( a) =  ( a) unassocE ( ( b) =  ( b) unassocE ( ( c)) =  c)  profunctorsPastroSum -| TambaraSum<PastroSum freely constructs strength with respect to Either. profunctors?TambaraSum is cofreely adjoins strength with respect to Either.Note: this is not dual to . It is $ with respect to a different tensor. profunctorsThe generalization of  of ! that is strong with respect to .Note: This is also a notion of strength, except with regards to another monoidal structure that we can choose to equip Hask with: the cocartesian coproduct. profunctorsLaws:  "a  swapE swapE   where swapE ::  a b ->  b a swapE =      "a      ( f)   "a  ( f)      "a  assocE unassocE   where assocE ::  ( a b) c ->  a ( b c) assocE ( ( a)) =  a assocE ( ( b)) =  ( b) assocE ( c) =  ( c) unassocE ::  a ( b c) ->  ( a b) c unassocE ( a) =  ( a) unassocE ( ( b) =  ( b) unassocE ( ( c)) =  c)  profunctorsLaws:  "a  swapE swapE   where swapE ::  a b ->  b a swapE =      "a      ( f)   "a  ( f)      "a  unassocE assocE   where assocE ::  ( a b) c ->  a ( b c) assocE ( ( a)) =  a assocE ( ( b)) =  ( b) assocE ( c) =  ( c) unassocE ::  a ( b c) ->  ( a b) c unassocE ( a) =  ( a) unassocE ( ( b) =  ( b) unassocE ( ( c)) =  c)  profunctors    "a     "a   profunctors    "a     "a   profunctors    "a     "a   profunctors    "a     "a   profunctors approximates  costrengthSafe&'4SX profunctors "FreeTraversing -| CofreeTraversing profunctorsNote: Definitions in terms of  are much more efficient! profunctorsLaws:  "a      f "a  ( f)      "a           "a   profunctors0This combinator is mutually defined in terms of  profunctorsA definition of  for $ instances that define an explicit . profunctors, may be a more efficient implementation of  than the default produced from . profunctors+ is the same as the default produced from . (C) 2015-2018 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimentalportableSafe&'4SX profunctors FreeMapping -| CofreeMapping profunctorsLaws:    f "a  ( f)      "a           "a   (C) 2011-2015 Edward Kmett, BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafeSUVX$NOPVWXY$VWXYNOP (C) 2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalMPTCs, fundeps Trustworthy=>?@AC@4 profunctorsA  p is a 4 on f if it is a subprofunctor of  f.!That is to say it is a subset of  Hom(f-,=) closed under  and .*Alternately, you can view it as a cosieve in the comma category f/Hask.6 profunctorsA  p is a 6 on f if it is a subprofunctor of  f.!That is to say it is a subset of  Hom(-,f=) closed under  and .(Alternately, you can view it as a sieve in the comma category Hask/f.45676745 (C) 2011-2015 Edward Kmett, BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisional Type-FamiliesSafe&'=>?HSUVX C profunctors C -|  :: [Hask, Hask] -> ProfThis gives rise to a monad in Prof, ( 'Star'.'Prep'), and a comonad in  [Hask,Hask] ( 'Prep'.'Star')E profunctorsA  p is E if there exists a  f such that p d c is isomorphic to f d -> c.G profunctorsLaws: G  5 "a  5  G "a  H profunctorsA  p is H if there exists a  f such that p d c is isomorphic to d -> f c.J profunctorsLaws: J  7 "a  7  J "a  K profunctorsDefault definition for W given that p is H.L profunctorsDefault definition for X given that p is H.M profunctorsJ and 7# form two halves of an isomorphism./This can be used with the combinators from the lens package. M :: H p => Iso' (d -> I p c) (p d c)N profunctorsDefault definition for O given that p is E.O profunctorsDefault definition for P given that p is E.P profunctorsDefault definition for  given that p is EQ profunctorsG and 5# form two halves of an isomorphism./This can be used with the combinators from the lens package. Q :: F f p => Iso' (f d -> c) (p d c)V profunctors @ -|  :: [Hask, Hask]^op -> Prof>Like all adjunctions this gives rise to a monad and a comonad.#This gives rise to a monad on Prof ('Costar'.'Coprep') and a comonad on [Hask, Hask]^op given by ('Coprep'.'Costar') which is a monad in  [Hask,Hask]@ABCDEFGHIJKLMNOPQRSTUVWXYHIJMKLEFGQNOPCDRSTU@ABVWXY (C) 2014-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimentalGADTs, TFs, MPTCs, RankNSafe &'@AHSUVXn f profunctors(This represents the right Kan lift of a  q along a  p in a limited version of the 2-category of Profunctors where the only object is the category Hask, 1-morphisms are profunctors composed and compose with Profunctor composition, and 2-morphisms are just natural transformations.i profunctorsi p q is the  composition of the s p and q.For a good explanation of 2 composition in Haskell see Dan Piponi's article: :http://blog.sigfpe.com/2011/07/profunctors-in-haskell.htmll profunctors(->)! functions as a lax identity for  composition.This provides an  for the lens1 package that witnesses the isomorphism between i (->) q d c and q d c", which is the left identity law. l ::  q => Iso' (i (->) q d c) (q d c) m profunctors(->)! functions as a lax identity for  composition.This provides an  for the lens1 package that witnesses the isomorphism between i q (->) d c and q d c#, which is the right identity law. m ::  q => Iso' (i q (->) d c) (q d c) n profunctorsThe associator for  composition.This provides an  for the lens1 package that witnesses the isomorphism between i p (i q r) a b and i (i p q) r a b, which arises because Prof7 is only a bicategory, rather than a strict 2-category.o profunctors composition generalizes  composition in two ways.$This is the first, which shows that exists b. (a -> f b, b -> g c) is isomorphic to  a -> f (g c). o ::  f => Iso' (i ( f) ( g) d c) ( ( f g) d c)p profunctors composition generalizes  composition in two ways.%This is the second, which shows that exists b. (f a -> b, g b -> c) is isomorphic to  g (f a) -> c. p ::  f => Iso' (i ( f) ( g) d c) ( ( g f) d c)q profunctorsThis is a variant on o that uses  instead of . q ::  f => Iso' (i ( f) ( g) d c) ( ( f g) d c)r profunctorsThis is a variant on p that uses  instead of . r ::  f => Iso' (i ( f) ( g) d c) ( ( g f) d c)s profunctors,The 2-morphism that defines a left Kan lift. Note: When p is right adjoint to f p (->) then s is the H of the adjunction.t profunctorsa  that is also a  is a  in Prof~ profunctorsThe composition of two H s is H. by the composition of their representations. profunctorsf p p forms a  in the . 2-category, which is isomorphic to a Haskell  instance.fghijklmnopqrstuijklmntuoqprfghs '(C) 2013-2015 Edward Kmett and Dan Doel BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalRank2Types, TFsSafeHSUVX  profunctors-This represents the right Kan extension of a  p\ along itself. This provides a generalization of the "difference list" trick to profunctors. profunctors-This represents the right Kan extension of a  q along a  p in a limited version of the 2-category of Profunctors where the only object is the category Hask, 1-morphisms are profunctors composed and compose with Profunctor composition, and 2-morphisms are just natural transformations. profunctors2The 2-morphism that defines a right Kan extension. Note: When q is left adjoint to  q (->) then  is the counit of the adjunction. profunctors p p forms a  in the . 2-category, which is isomorphic to a Haskell  instance.  (C) 2014-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimentalportable TrustworthySX+ profunctorsCayley transforms Comonads in Hask into comonads on Prof profunctorsCayley transforms Monads in Hask into monads on Prof(C) 2017 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalRank2Types, TFs Trustworthy &'HSUVX@ profunctors?This is the cofree profunctor given a data constructor of kind  * -> * -> * profunctors <   "a    < "a  < "a   profunctors <   "a    < "a   = ;  profunctors   8 "a  8   "a  9 "a   profunctors   9 "a  9   "a   "a 8   !"#$$%&'())*++,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZZ[\\]^_``abcdefghijklmnopqrstuvwxyz{|}~                ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B B C D D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f f g h h i j k l m n o p q r s t u v w x y z { | } ~                             &profunctors-5.4-2UhbPNu13Rk5t6Vj3UnZ95Data.Profunctor.UnsafeData.Profunctor.TypesData.Profunctor.MonadData.Profunctor.AdjunctionData.Profunctor.StrongData.Profunctor.ClosedData.Profunctor.ChoiceData.Profunctor.TraversingData.Profunctor.MappingData.Profunctor.SieveData.Profunctor.RepData.Profunctor.CompositionData.Profunctor.RanData.Profunctor.CayleyData.Profunctor.YonedaProfuctor.Unsafe#.Data.Profunctor.TambaraTambaraData.Profunctor Profunctordimaplmaprmap.#$fProfunctorTannen$fProfunctorSum$fProfunctorProduct$fProfunctorBiff$fProfunctorJoker$fProfunctorClown$fProfunctorCokleisli$fProfunctorKleisli$fProfunctorTagged$fProfunctor->Forget runForget WrappedArrow WrapArrow unwrapArrowCostar runCostarStarrunStar:->$fContravariantStar$fCategoryTYPEStar$fDistributiveStar$fMonadPlusStar $fMonadStar$fAlternativeStar$fApplicativeStar $fFunctorStar$fProfunctorStar $fMonadCostar$fApplicativeCostar$fFunctorCostar$fDistributiveCostar$fProfunctorCostar$fProfunctorWrappedArrow$fArrowLoopWrappedArrow$fArrowApplyWrappedArrow$fArrowChoiceWrappedArrow$fArrowZeroWrappedArrow$fArrowWrappedArrow$fCategoryTYPEWrappedArrow$fContravariantForget$fTraversableForget$fFoldableForget$fFunctorForget$fProfunctorForgetProfunctorComonad proextract produplicateProfunctorMonad proreturnprojoinProfunctorFunctorpromap$fProfunctorFunctorSum$fProfunctorFunctorProduct$fProfunctorFunctorTannen$fProfunctorMonadSum$fProfunctorMonadTannen$fProfunctorComonadProduct$fProfunctorComonadTannenProfunctorAdjunctionunitcounitCopastro runCopastro CotambaraCostrongunfirstunsecondPastro runTambaraStrongfirst'second'uncurry'strongtambara untambarapastrounpastro cotambara uncotambara$fStrongTannen$fStrongProduct $fStrongClown$fStrongForget$fStrongWrappedArrow $fStrongStar$fStrongKleisli $fStrong->$fMonoidTambara$fSemigroupTambara$fAlternativeTambara$fApplicativeTambara$fFunctorTambara$fArrowPlusTambara$fArrowZeroTambara$fArrowLoopTambara$fArrowApplyTambara$fArrowChoiceTambara$fArrowTambara$fCategoryTYPETambara$fStrongTambara$fProfunctorComonadTambara$fProfunctorFunctorTambara$fProfunctorTambara$fStrongPastro#$fProfunctorAdjunctionPastroTambara$fProfunctorMonadPastro$fProfunctorFunctorPastro$fProfunctorPastro$fCostrongProduct$fCostrongTannen$fCostrongCokleisli$fCostrongKleisli$fCostrongWrappedArrow$fCostrongTagged$fCostrongCostar $fCostrong->$fFunctorCotambara$fCostrongCotambara$fProfunctorComonadCotambara$fProfunctorFunctorCotambara$fProfunctorCotambara$fCostrongCopastro$fProfunctorMonadCopastro$fProfunctorFunctorCopastro'$fProfunctorAdjunctionCopastroCotambara$fProfunctorCopastro EnvironmentClosure runClosureClosedclosedcurry'closeunclose$fClosedTannen$fClosedProduct$fClosedKleisli $fClosedStar$fClosedCokleisli$fClosedCostar $fClosed->$fClosedTagged$fMonoidClosure$fSemigroupClosure$fAlternativeClosure$fApplicativeClosure$fFunctorClosure$fArrowPlusClosure$fArrowZeroClosure$fArrowLoopClosure$fArrowClosure$fCategoryTYPEClosure$fStrongClosure$fClosedClosure$fProfunctorComonadClosure$fProfunctorFunctorClosure$fProfunctorClosure$fClosedEnvironment($fProfunctorAdjunctionEnvironmentClosure$fProfunctorMonadEnvironment$fProfunctorFunctorEnvironment$fProfunctorEnvironment CopastroSumrunCopastroSum CotambaraSumCochoiceunleftunright PastroSum TambaraSum runTambaraSumChoiceleft'right' tambaraSum untambaraSum cotambaraSumuncotambaraSum$fChoiceTambara$fChoiceTannen$fChoiceProduct $fChoiceJoker$fChoiceForget$fChoiceWrappedArrow$fChoiceTagged$fChoiceCokleisli $fChoiceStar$fChoiceKleisli $fChoice->$fFunctorTambaraSum$fCategoryTYPETambaraSum$fChoiceTambaraSum$fProfunctorTambaraSum$fProfunctorComonadTambaraSum$fProfunctorFunctorTambaraSum$fChoicePastroSum$fProfunctorMonadPastroSum$fProfunctorFunctorPastroSum)$fProfunctorAdjunctionPastroSumTambaraSum$fProfunctorPastroSum$fCochoiceProduct$fCochoiceTannen$fCochoiceStar$fCochoiceCostar $fCochoice->$fFunctorCotambaraSum$fCochoiceCotambaraSum$fProfunctorComonadCotambaraSum$fProfunctorFunctorCotambaraSum$fProfunctorCotambaraSum$fCochoiceCopastroSum$fProfunctorMonadCopastroSum$fProfunctorFunctorCopastroSum-$fProfunctorAdjunctionCopastroSumCotambaraSum$fProfunctorCopastroSumFreeTraversingCofreeTraversingrunCofreeTraversing Traversing traverse'wanderfirstTraversingsecondTraversingdimapWandering lmapWandering rmapWanderingleftTraversingrightTraversing$fProfunctorBazaar$fApplicativeBazaar$fProfunctorBaz$fTraversableBaz $fFoldableBaz$fTraversingStar$fTraversingKleisli$fTraversingForget$fTraversing->#$fProfunctorComonadCofreeTraversing#$fProfunctorFunctorCofreeTraversing$fTraversingCofreeTraversing$fChoiceCofreeTraversing$fStrongCofreeTraversing$fProfunctorCofreeTraversing$fProfunctorMonadFreeTraversing!$fProfunctorFunctorFreeTraversing$fTraversingFreeTraversing$fChoiceFreeTraversing$fStrongFreeTraversing$fProfunctorFreeTraversing$fFunctorBazaar $fFunctorBaz FreeMapping CofreeMappingrunCofreeMappingMappingmap'roam wanderMappingtraverseMapping closedMapping $fMappingStar$fMappingKleisli $fMapping-> $fProfunctorComonadCofreeMapping $fProfunctorFunctorCofreeMapping$fMappingCofreeMapping$fTraversingCofreeMapping$fClosedCofreeMapping$fChoiceCofreeMapping$fStrongCofreeMapping$fProfunctorCofreeMapping$fProfunctorMonadFreeMapping$fProfunctorFunctorFreeMapping$fMappingFreeMapping$fTraversingFreeMapping$fClosedFreeMapping$fChoiceFreeMapping$fStrongFreeMapping$fProfunctorFreeMapping $fFunctorBarCosievecosieveSievesieve$fSieveForgetConst $fSieveStarf$fSieveKleislim$fSieve->Identity$fCosieveCostarf$fCosieveTaggedProxy$fCosieveCokleisliw$fCosieve->IdentityCoprep runCoprepPrepCorepresentableCorep cotabulate RepresentableReptabulatefirstRep secondRep tabulated unfirstCorep unsecondCorep closedCorep cotabulatedprepAdj unprepAdjprepUnit prepCounit coprepAdj uncoprepAdj coprepUnit coprepCounit$fRepresentableForget$fRepresentableStar$fRepresentableKleisli$fRepresentable->$fCorepresentableCostar$fCorepresentableTagged$fCorepresentableCokleisli$fCorepresentable-> $fMonadPrep$fApplicativePrep $fFunctorPrep$fFunctorCoprepRiftrunRift Procompose procomposedidlidrassocstarscostarskleislis cokleislis decomposeRiftetamu$fCostrongProcompose$fMappingProcompose$fTraversingProcompose$fClosedProcompose$fChoiceProcompose$fStrongProcompose$fCorepresentableProcompose$fCosieveProcomposeCompose$fRepresentableProcompose$fSieveProcomposeCompose$fFunctorProcompose$fProfunctorProcompose$fProfunctorMonadProcompose$fProfunctorFunctorProcompose$$fProfunctorAdjunctionProcomposeRift$fCategoryTYPERift $fFunctorRift$fProfunctorRift$fProfunctorComonadRift$fProfunctorFunctorRift Codensity runCodensityRanrunRan decomposeRan precomposeRancurryRan uncurryRandecomposeCodensity$fCategoryTYPERan $fFunctorRan$fProfunctorRan$fProfunctorComonadRan$fProfunctorFunctorRan$fCategoryTYPECodensity$fFunctorCodensity$fProfunctorCodensityCayley runCayley mapCayley$fArrowPlusCayley$fArrowZeroCayley$fArrowLoopCayley$fArrowChoiceCayley $fArrowCayley$fCategoryTYPECayley$fChoiceCayley$fStrongCayley$fProfunctorCayley$fProfunctorComonadCayley$fProfunctorMonadCayley$fProfunctorFunctorCayleyCoyonedaYoneda runYoneda extractYonedaduplicateYonedareturnCoyoneda joinCoyoneda$fTraversingYoneda$fMappingYoneda$fClosedYoneda$fCochoiceYoneda$fCostrongYoneda$fChoiceYoneda$fStrongYoneda$fCategoryTYPEYoneda$fProfunctorMonadYoneda$fProfunctorComonadYoneda$fProfunctorFunctorYoneda$fFunctorYoneda$fProfunctorYoneda$fTraversingCoyoneda$fMappingCoyoneda$fClosedCoyoneda$fCochoiceCoyoneda$fCostrongCoyoneda$fChoiceCoyoneda$fStrongCoyoneda$fCategoryTYPECoyoneda$fProfunctorMonadCoyoneda$fProfunctorComonadCoyoneda$fProfunctorFunctorCoyoneda$fProfunctorCoyonedabaseControl.Categoryid.ghc-primGHC.PrimcoerceGHC.BaseFunctor Control.Arrow ArrowLooploop Data.TupleswapsecondfirstfstsndArrowCategoryuncurrycurryconst$ Data.EitherEithereitherRightLeftrightleft$comonad-5.0.5-CprNqM1nSziKO1lkxx3cFpControl.ComonadextractData.TraversabletraversefmapData.Functor.ComposeCompose getComposeData.Functor.IdentityIdentity runIdentityIsoKleisliMonad CokleisliMonoid