xc      !"#$%&'()*+,-./0123456789:; < = > ? @ A B C D E F GHIJKLMNOPQRSTUVWXYZ[\]^_`ab(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisional polykinds Safe-Inferred(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportable Safe-Inferred# cdefghijklmnopqrstuvwxyz{|}~     cdefghijklmnopqrstuvwxyz{|}~(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafe Iduplicated = extended id fmap (fmap f) . duplicated = duplicated . fmap f !extended f = fmap f . duplicated(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafe  a " b "a    a ! b  a # b "a   a ! b A  sans .Minimal definition: Either  or NIf defining both, then the following laws (the default definitions) must hold: )join = (>>- id) m >>- f = join (fmap f m)Laws: 2induced definition of <.>: f <.> x = f >>- (<$> x)0Finally, there are two associativity conditions: associativity of (>>-): (m >>- f) >>- g == m >>- (\x -> f x >>- g) associativity of join: join . join = join . fmap join>These can both be seen as special cases of the constraint that 9associativity of (->-): (f ->- g) ->- h = f ->- (g ->- h)7Transform a Apply into an Applicative by adding a unit.Wrap an  to be used as a member of  BA strong lax semi-monoidal endofunctor. This is equivalent to an  without .Laws: @associative composition: (.) <$> u <.> v <.> w = u <.> (v <.> w)" a .> b = const id <$> a <.> b# a <. b = const <$> a <.> bAn  is not a , but it is an instance of A  is not a , but it is an instance of An IntMap is not , but it is an instance of   A Map is not , but it is an instance of  o !"#$% !"#$% !"#%$c !"#$%!"#(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafe& A variant of ! with the arguments reversed.'2Lift a binary function into a comonad with zipping(3Lift a ternary function into a comonad with zipping&'( !"#&'( !"#&'(&'(&(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportable Safe-Inferred,FUsable default for foldMap, but only if you define bifoldMap1 yourself )*+, )*+, )*+,)*+,(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafe-./ !"#$%&'(-./ !"#&'(-/.%$-./-./(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafe0Laws: <!> is associative: (a <!> b) <!> c = a <!> (b <!> c) <$> left-distributes over <!>: f <$> (a <!> b) = (f <$> a) <!> (f <$> b)If extended to an  then 1 should equal .Ideally, an instance of 0I also satisfies the "left distributon" law of MonadPlus with respect to !: I<.> right-distributes over <!>: (a <!> b) <.> c = (a <.> c) <!> (b <.> c)But , ,  a,  e m, and STM3 satisfy the alternative "left catch" law instead: pure a <!> b = pure aPHowever, this variation cannot be stated purely in terms of the dependencies of 0.rWhen and if MonadPlus is successfully refactored, this class should also be refactored to remove these instances.BThe right distributive law should extend in the cases where the a  or @ is provided to yield variations of the right distributive law: S(m <!> n) >>- f = (m >>- f) <!> (m >>- f) (m <!> n) >>= f = (m >>= f) <!> (m >>= f)1 without a required empty-This instance does not actually satisfy the (!3) right distributive law It instead satisfies the  Left-Catch law!0123      !"#&'(012301230123     1(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportable Safe-Inferred4 Insert an m- between each pair of 't m'. Equivalent to 5 with  as the second argument.4intercalate1 ", " $ "hello" :| ["how", "are", "you"]"hello, how, are, you"!intercalate1 ", " $ "hello" :| []"hello"3intercalate1 mempty $ "I" :| ["Am", "Fine", "You?"] "IAmFineYou?"5Insert m between each pair of m derived from a.0intercalateMap1 " " show $ True :| [False, True]"True False True"%intercalateMap1 " " show $ True :| []"True"9DUsable default for foldMap, but only if you define foldMap1 yourself !"#$456789:%&'( 456789: 456789: !"#$456789:%&'( (C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportable Safe-Inferred#;<=>?@)*+,-./0123456789:;<=>?@ABCDE;<=>?@>?@;<=;<=>?@)*+,-./0123456789:;<=>?@ABCDE (C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportable Safe-InferredA>?@A>?@AA (C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportable Safe-InferredB;<=B;<=BB (C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportable Safe-InferredC1A subset of monad transformers can transform any  as well. CDFGHIJKLMNCDCD CDFGHIJKLMN (C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafeELaws: zero <!> m = m m <!> zero = mIf extended to an  then F should equal O.EFPQRSTUVWXYZ[\]^_`abcdefghij !"#&'(0123EFEFEFPQRSTUVWXYZ[\]^_`abcdefghij(C) 2007-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafe'=Mk sans l Ahttp://en.wikipedia.org/wiki/Band_(mathematics)#Rectangular_bandsGHIJKLMNmnopqrsltGHIJKLMNMNJKLGHI GHIJKLMNmnopqrslt(C) 2007-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportable Safe-Inferred'=OPQuvOPQOPQOPQuv(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisional polykinds Safe-Inferred'24=Rsemigroupoid with inverses. This technically should be a category with inverses, except we need to use Ob to define the valid objects for the categoryRSwRSRSRSw(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisional polykinds Safe-Inferred'=TUVWxyzTUVWTUVWTUVWxyz(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisional polykindsSafeXYZ{|}~XYZXYZXYZ{|}~(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimentalnon-portable (flexible MPTCs) Safe-Inferred'2346=[\]^_[\[\_^][\]^_(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportable Safe-InferredaLift binary functionsbLift ternary functions`ab  `ab `ab`ab` !"!#!$!%&'()*+,-./01234566789:;<=>?@ABCDEFGHIJKLMNOPQRSTU V W X Y Z [ \ ] ^ _ ` abbcdefghiijklmmnoppqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<<=>>?@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 gh i j k l m n o p q r s t u v w x y z { | } ~     semigroupoids-5Data.Functor.ApplyData.Bifunctor.ApplyData.Semigroup.Foldable.ClassData.Functor.ExtendData.Functor.BindData.Semigroup.BifoldableData.Functor.AltData.Semigroup.Foldable Data.Semigroup.Traversable.ClassData.Semigroup.BitraversableData.Semigroup.TraversableData.Functor.Bind.TransData.Functor.PlusData.SemigroupoidData.Semigroupoid.Dual Data.GroupoidData.IsomorphismData.Semigroupoid.StaticData.Semigroupoid.ObData.Traversable.InstancesData.Functor.Bind.ClassbaseGHC.BasefmapFunctor Data.Functor$><$><$ bifunctors-5Data.Biapplicative<<$>>Data.Bifunctorsecondfirstbimap Bifunctor Bifoldable1bifold1 bifoldMap1 Foldable1fold1foldMap1Extend duplicatedextendedBiapply<<.>>.>><<.Bind>>-join MaybeApply runMaybeApplyWrappedApplicativeWrapApplicativeunwrapApplicativeApply<.>.><. returning apDefault<..>liftF2liftF3 bitraverse1_bifor1_ bisequenceA1_bifoldMapDefault1-<<->--<-Altsomemany intercalate1intercalateMap1 traverse1_for1_ sequenceA1_foldMapDefault1asum1 Traversable1 traverse1 sequence1Bitraversable1 bitraverse1 bisequence1bifoldMap1DefaultfoldMap1Default BindTransliftBPluszeroSemigetSemiWrappedCategory WrapCategoryunwrapCategory SemigroupoidoDualgetDualGroupoidinvIsoembedprojectStatic runStaticObsemiid $fOb*(->)a$fOb*Cokleislia $fOb*Kleislia<<..>>bilift2bilift3$fFoldable1Joker$fFoldable1(,)$fFoldable1NonEmpty$fFoldable1Coproduct$fFoldable1Sum$fFoldable1Reverse$fFoldable1Product$fFoldable1Lift$fFoldable1Compose$fFoldable1Backwards$fFoldable1IdentityT$fFoldable1Identity$fFoldable1Tree$fBifoldable1WrappedBifunctor$fBifoldable1Tannen$fBifoldable1Product$fBifoldable1Joker$fFoldable1Join$fBifoldable1Flip$fBifoldable1Clown$fBifoldable1Biff$fBifoldable1Tagged$fBifoldable1Const$fBifoldable1(,,,,)$fBifoldable1(,,,)$fBifoldable1(,,)$fBifoldable1(,)$fBifoldable1Either$fBifoldable1Arg$fExtendNonEmpty$fExtendIdentityT$fExtendIdentity$fExtendTracedT$fExtendStoreT $fExtendEnvT$fExtendCoproduct $fExtendTree $fExtendSeq $fExtend(->) $fExtend(,)$fExtendEither $fExtendMaybe $fExtend[]constControl.CategoryidMonadreturnControl.Applicative Applicativepure $fBindIntMapcontainers-0.5.5.1Data.IntMap.BaseIntMap $fBindMap Data.Map.BaseMap $fApplyIntMap $fApplyMap$fBiapplyWrappedBifunctor$fBiapplyTannen$fBiapplyProduct $fApplyJoin$fBiapplyJoker $fBiapplyFlip$fBiapplyClown $fBiapplyBiff$fBiapplyTagged$fBiapplyConst$fBiapply(,,,,)$fBiapply(,,,) $fBiapply(,,) $fBiapplyArg $fBiapply(,) $fBindTree $fBindSeq $fBindContT $fBindRWST $fBindRWST0 $fBindStateT $fBindStateT0 $fBindWriterT$fBindWriterT0 $fBindReaderT $fBindExceptT $fBindErrorT $fBindListT $fBindMaybeT$fBindWrappedMonad$fBindIdentityT$fBindIdentity $fBindOption $fBindMaybe$fBindIO$fBindNonEmpty$fBind[] $fBind(->) $fBindProduct $fBindEither $fBind(,)$fApplyCokleisli$fComonadMaybeApply$fExtendMaybeApply$fApplicativeMaybeApply$fApplyMaybeApply$fFunctorMaybeApply$fAlternativeWrappedApplicative$fApplicativeWrappedApplicative$fApplyWrappedApplicative$fFunctorWrappedApplicative$fApplyTracedT $fApplyStoreT $fApplyEnvT $fApplyContT $fApplyRWST $fApplyRWST0 $fApplyStateT$fApplyStateT0$fApplyWriterT$fApplyWriterT0 $fApplyListT$fApplyReaderT$fApplyExceptT $fApplyErrorT $fApplyMaybeT $fApplyTree $fApplySeq$fApplyWrappedArrow$fApplyWrappedMonad$fApplyIdentityT$fApplyIdentity $fApplyOption $fApplyMaybe $fApplyIO $fApply[]$fApplyZipList $fApply(->) $fApplyConst $fApplyEither$fApplyNonEmpty $fApply(,)$fApplyReverse$fApplyProduct $fApplyLift$fApplyConstant$fApplyCompose$fApplyBackwardsActgetActignore $fFunctorAct$fSemigroupAct Alternative<|> Data.MaybeMaybeghc-prim GHC.TypesIO Data.EitherEithertransformers-0.4.3.0Control.Monad.Trans.ErrorErrorT$fAltIO $fAltReverse $fAltProduct $fAltLift $fAltCompose$fAltBackwards $fAltRWST $fAltRWST0 $fAltWriterT $fAltWriterT0 $fAltStateT $fAltStateT0 $fAltListT $fAltExceptT $fAltErrorT $fAltMaybeT $fAltReaderT$fAltIdentityT$fAltWrappedApplicative $fAltNonEmpty$fAltSeq $fAltIntMap$fAltMap$fAltWrappedArrow$fAltWrappedMonad $fAltOption $fAltMaybe$fAlt[] $fAltEitherAlt_getAlt_JoinWithjoinee$fSemigroupAlt_$fSemigroupJoinWith$fTraversable1Joker$fTraversable1(,)$fTraversable1NonEmpty$fTraversable1Tree$fTraversable1Coproduct$fTraversable1Sum$fTraversable1Reverse$fTraversable1Product$fTraversable1Lift$fTraversable1Compose$fTraversable1Backwards$fTraversable1IdentityT$fTraversable1Identity $fBitraversable1WrappedBifunctor$fBitraversable1Tannen$fBitraversable1Product$fBitraversable1Joker$fTraversable1Join$fBitraversable1Flip$fBitraversable1Clown$fBitraversable1Biff$fBitraversable1Tagged$fBitraversable1Const$fBitraversable1(,,,,)$fBitraversable1(,,,)$fBitraversable1(,,)$fBitraversable1(,)$fBitraversable1Either$fBitraversable1Arg$fBindTransContT$fBindTransRWST$fBindTransRWST0$fBindTransStateT$fBindTransStateT0$fBindTransWriterT$fBindTransWriterT0$fBindTransReaderT$fBindTransIdentityTempty $fPlusReverse $fPlusProduct $fPlusLift $fPlusCompose$fPlusBackwards $fPlusRWST $fPlusRWST0 $fPlusWriterT$fPlusWriterT0 $fPlusStateT $fPlusStateT0 $fPlusListT $fPlusExceptT $fPlusErrorT $fPlusMaybeT $fPlusReaderT$fPlusIdentityT$fPlusWrappedApplicative $fPlusSeq $fPlusIntMap $fPlusMap$fPlusWrappedArrow$fPlusWrappedMonad $fPlusOption $fPlusMaybe$fPlus[]$fPlusIOCategory$fSemigroupoid*(,)$fCategorykSemi$fSemigroupoidkSemi$fCategorykWrappedCategory$fSemigroupoidkWrappedCategory$fSemigroupoid*Op$fSemigroupoid*Cokleisli$fSemigroupoid*Kleisli$fSemigroupoid*(->)$fCategorykDual$fSemigroupoidkDual$fGroupoidkDual$fCategorykIso$fGroupoidkIso$fSemigroupoidkIso$fArrowChoiceStatic$fArrowPlusStatic$fArrowZeroStatic $fArrowStatic$fCategory*Static$fSemigroupoid*Static$fComonadStatic$fExtendStatic$fApplicativeStatic $fPlusStatic $fAltStatic $fApplyStatic$fFunctorStatic