úÎ'Ñ"µ`      !"#$%&'()*+,-./0123456789:;<=>?@ABC D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _  ,A representation of a contravariant functor #An adjunction from Hask^op to Hask   Op (f a) b ~ Hask a (g b)   rightAdjunct unit = id  leftAdjunct counit = id 5Any adjunction from Hask to Hask^op would indirectly 7 permit unsafePerformIO, and therefore does not exist.  :Represent a contravariant functor that has a left adjoint `'This gives rise to the Cont Bool monad a-This adjunction gives rise to the Cont monad    MPTCs, fundeps provisionalEdward Kmett <ekmett@gmail.com>     MPTCs, fundeps provisionalEdward Kmett <ekmett@gmail.com>    rank 2 types, MPTCs, fundeps experimentalEdward Kmett <ekmett@gmail.com> %An adjunction between Hask and Hask.  rightAdjunct unit = id  leftAdjunct counit = id !"#$  !"#$  !"#$  !"# !"#$non-portable (GADTs, MPTCs) experimentalEdward Kmett <ekmett@gmail.com>%&'WThe natural isomorphism between a comonad w and the comonad generated by w (forwards). ()%&'()%&'()%&&'()MPTCs, fundeps provisionalEdward Kmett <ekmett@gmail.com>*+,-./biExploiting this instance requires that we have the missing Traversables for Identity, (,)e and IdentityT *+,-./-/.*+,*+,+,-./"non-portable (rank-2 polymorphism) provisionalEdward Kmett <ekmett@gmail.com>01234501234501234501212345rank-2 types, MPTCs experimentalEdward Kmett <ekmett@gmail.com>6789:;<=c>?@AB 6789:;<=>?@AB 9:;<=>?678@AB 678789:;:;<=>?@AB MPTCs, fundeps provisionalEdward Kmett <ekmett@gmail.com>CDEFGHIJKLMNOPCDEFGHIJKLMNOPFGHIJCDEKLMNOPCDEDEFGHIJKLMNOP GADTs, MPTCs, fundeps provisionalEdward Kmett <ekmett@gmail.com> Q>The contravariant Yoneda lemma applied to a covariant functor RSTUVWXY QRSTUVWXY STUVWXYQR QRRSTUVWXY MPTCs, fundeps provisionalEdward Kmett <ekmett@gmail.com>Z[\]^_Z[\]^_]_^Z[\Z[\[\]^_d    !"#   $$%&'(()*+,--.//01234567 8 8 9 : ; < = > ? @ A B C D 8 8 : ; = > ? @ E      FGHIJadjunctions-0.5.0%Data.Functor.Contravariant.Adjunction)Control.Monad.Trans.Contravariant.AdjointControl.Monad.Trans.ContsData.Functor.AdjunctionControl.Comonad.Trans.DensityControl.Monad.Trans.AdjointControl.Monad.Trans.CodensityData.Functor.ZapData.Functor.Yoneda!Data.Functor.Yoneda.ContravariantControl.Comonad.Trans.AdjointRepresentationrepunrep Adjunctionunitcounit leftAdjunct rightAdjunct repAdjunctionrepFlippedAdjunctionAdjointT runAdjointTAdjointadjoint runAdjointContsT runContsTContsContcontrunContcontsrunContscallCCDensityT liftDensityTdensityTToAdjunctionadjunctionToDensityT CodensityT runCodensityTlowerCodensityTcodensityTToAdjunctionadjunctionToCodensityTBizap bizapWithZapzapWithzapflipZap zapAdjunction composeZapbizap flipBizapbizapProductSumYonedaT runYonedaTYonedayoneda runYoneda liftYoneda lowerYoneda liftYonedaT lowerYonedaTmaxFminFmaxMminMlowerM$fAdjunctionPredicatePredicate$fAdjunctionOpOp$fMonadTransAdjointTstrength