,      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                                  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~(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> provisionalportableSafe2p 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)$7Transform a Apply into an Applicative by adding a unit.'Wrap an  to be used as a member of **BA strong lax semi-monoidal endofunctor. This is equivalent to an  without .Laws: ()  u + v + w = u + (v + w) x + (f  y) = ( f)  x + y f  (x + y) = (f )  x + y The laws imply that , and - really ignore their left and right results, respectively, and really return their right and left results, respectively. Specifically, (mf  m) , (nf  n) = nf  (m , n) (mf  m) - (nf  n) = mf  (m - n) ,  a , b =    a + b-  a - b =   a + b.2Lift a binary function into a comonad with zipping=A  is not , but it is an instance of *@An IntMap is not , but it is an instance of *A A Map is not , but it is an instance of *cA  is not a , but it is an instance of !fAn  is not a , but it is an instance of !gA  is not a , but it is an instance of ! !#"$%&'()*+-,./0*+,-.'()$%&!"#0/  !"#$%&'()*+,-.44 4"1+4,4-4(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafe7e A variant of + with the arguments reversed.3Lift a ternary function into a comonad with zipping$%&'()*+-,.*+,-.'()$%&4(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafe9!#"$%&'()*+-,./0*+,-.'()$%&!"#0/111(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafe=1A subset of monad transformers can transform any ! as well.(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportable Trustworthy>QSTVPLaws: <!> is associative: (a <!> b) <!> c = a <!> (b <!> c) <$> left-distributes over <!>: f <$> (a <!> b) = (f <$> a) <!> (f <$> b)If extended to an  then  should equal .Ideally, an instance of I 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 .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) without a required empty One or none.-This instance does not actually satisfy the (+3) right distributive law It instead satisfies the  Left-Catch law$%&'()*+-,.3(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafeTDLift binary functionsLift ternary functions     4(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafeSTX Laws: zero <!> m = m m <!> zero = mIf extended to an  then  should equal .$%&'()*+-,. (C) 2007-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableNone&',F[ sans  Ahttp://en.wikipedia.org/wiki/Band_(mathematics)#Rectangular_bands (C) 2007-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableNone,F^>         (C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisional polykindsNone&',;=Fbsemigroupoid with inverses. This technically should be a category with inverses, except we need to use Ob to define the valid objects for the category (C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisional polykindsNone,Fe (C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> experimentalnon-portable (flexible MPTCs)None,;<=>?Fg (C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisional polykindsNonei!"#!"#!"#(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisional polykindsSafel(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafeSTn123456745671231234567(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafeqp`FUsable default for foldMap, but only if you define bifoldMap1 yourself123]^_`123]^_`(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafec Insert an m- between each pair of 't m'. Equivalent to d with  as the second argument.4intercalate1 ", " $ "hello" :| ["how", "are", "you"]"hello, how, are, you"!intercalate1 ", " $ "hello" :| []"hello"3intercalate1 mempty $ "I" :| ["Am", "Fine", "You?"] "IAmFineYou?"dInsert m between each pair of m derived from a.0intercalateMap1 " " show $ True :| [False, True]"True False True"%intercalateMap1 " " show $ True :| []"True"hDUsable default for foldMap, but only if you define foldMap1 yourselfjlMonadic fold over the elements of a non-empty structure, associating to the right, i.e. from right to left. \let g = (=<<) . f in foldrM1 f (x1 :| [x2, ..., xn]) == x1 `g` (x2 `g` ... (xn-1 `f` xn)...)kkMonadic fold over the elements of a non-empty structure, associating to the left, i.e. from left to right. flet g = flip $ (=<<) . f in foldlM1 f (x1 :| [x2, ..., xn]) == (...((x1 `f` x2) `g` x2) `g`...) `g` xn 4567cdefghijk 4567cdefghijk(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafeSTpqrstustupqrpqrstu(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafepqrpqr(C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE)Edward Kmett <ekmett@gmail.com> provisionalportableSafestustu !"#$%&'()*+,-./0123456789:;<=>?@@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                         ! " # $ $ % & ' ( ) * + , - . . / 0 1 2 3 4 5 6 7 899:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~xy*semigroupoids-5.2.2-7pphhkgrwrsH9yUTWMSXXrData.Functor.ApplyData.Bifunctor.ApplyData.Functor.ExtendData.Functor.BindData.Functor.Bind.ClassData.Functor.Bind.TransData.Functor.AltData.Functor.PlusData.SemigroupoidData.Semigroupoid.Dual Data.GroupoidData.IsomorphismData.Semigroupoid.ObData.Semigroupoid.StaticData.Semigroup.Foldable.ClassData.Semigroup.BifoldableData.Semigroup.Foldable Data.Semigroup.Traversable.ClassData.Semigroup.TraversableData.Semigroup.BitraversableData.Traversable.InstancesbaseGHC.BasefmapFunctorData.Bifunctorsecondfirstbimap Bifunctor Data.Functor$><$><$%bifunctors-5.5-AZUUgF6dLEFFzYbnWHGLFxData.Biapplicative<<$>>Extend duplicatedextended $fExtendSum$fExtendNonEmpty$fExtendIdentityT$fExtendIdentity$fExtendTracedT$fExtendStoreT $fExtendEnvT $fExtendTree $fExtendSeq $fExtend(->) $fExtend(,)$fExtendEither $fExtendMaybe $fExtendProxy$fExtendTagged $fExtend[]Biapply<<.>>.>><<.Bind>>-join MaybeApply runMaybeApplyWrappedApplicativeWrapApplicativeunwrapApplicativeApply<.>.><.liftF2 returning apDefault$fApplyCokleisli$fApplyTracedT $fApplyStoreT $fApplyEnvT $fApplyContT$fApplyWriterT$fApplyWriterT0 $fApplyListT$fApplyReaderT$fApplyExceptT $fApplyErrorT $fApplyMaybeT$fApplyHashMap $fApplyTree $fApplySeq $fApplyIntMap $fApplyMap$fApplyQ$fApplyComplex$fApplyWrappedArrow$fApplyWrappedMonad$fApplyIdentityT$fApplyIdentity $fApplyOption $fApplyMaybe $fApplyIO $fApply[]$fApplyZipList $fApply(->) $fApplyConst $fApplyEither$fApplyNonEmpty $fApply(,)$fApplyReverse$fApplyProduct $fApplyLift$fApplyConstant$fApplyCompose$fApplyBackwards $fApplyProxy $fApplyTagged$fAlternativeWrappedApplicative$fApplicativeWrappedApplicative$fApplyWrappedApplicative$fFunctorWrappedApplicative$fComonadMaybeApply$fExtendMaybeApply$fApplicativeMaybeApply$fApplyMaybeApply$fFunctorMaybeApply $fBindHashMap $fBindTree $fBindSeq $fBindIntMap $fBindMap $fBindComplex $fBindContT $fBindRWST $fBindRWST0 $fBindStateT $fBindStateT0 $fBindWriterT$fBindWriterT0 $fBindReaderT $fBindExceptT $fBindErrorT $fBindListT $fBindMaybeT$fBindWrappedMonad$fBindIdentityT$fBindQ$fBindIdentity $fBindOption $fBindMaybe$fBindIO$fBindNonEmpty$fBind[] $fBind(->) $fBindProduct $fBindEither $fBindProxy $fBindTagged $fBind(,) $fApplyRWST $fApplyRWST0 $fApplyStateT$fApplyStateT0$fBiapplyWrappedBifunctor$fBiapplyTannen$fBiapplyProduct $fApplyJoin$fBiapplyJoker $fBiapplyFlip$fBiapplyClown $fBiapplyBiff$fBiapplyTagged$fBiapplyConst$fBiapply(,,,,)$fBiapply(,,,) $fBiapply(,,) $fBiapplyArg $fBiapply(,)<..>liftF3-<<->--<- BindTransliftB$fBindTransContT$fBindTransRWST$fBindTransRWST0$fBindTransStateT$fBindTransStateT0$fBindTransWriterT$fBindTransWriterT0$fBindTransReaderT$fBindTransIdentityTAltsomemanyoptional $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[]$fAltIO $fAltEither $fAltProxy$fAltV1$fAltU1$fAlt:*: $fAltRec1$fAltM1<<..>>bilift2bilift3Pluszero $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[]$fPlusIO $fPlusRec1$fPlusM1 $fPlus:*:$fPlusU1 $fPlusProxySemigetSemiWrappedCategory WrapCategoryunwrapCategory Semigroupoido$fSemigroupoidk:~~:$fSemigroupoidk:~:$fSemigroupoidkCoercion$fSemigroupoidTYPETagged$fSemigroupoidTYPEConst$fSemigroupoidTYPEOp$fSemigroupoidTYPECokleisli$fSemigroupoidTYPEKleisli$fSemigroupoidTYPE(,)$fSemigroupoidTYPE(->)$fCategorykWrappedCategory$fSemigroupoidkWrappedCategory$fCategorykSemi$fSemigroupoidkSemiDualgetDual$fCategorykDual$fSemigroupoidkDualGroupoidinv$fGroupoidk:~~:$fGroupoidk:~:$fGroupoidkCoercion$fGroupoidkDualIsoembedproject$fCategorykIso$fGroupoidkIso$fSemigroupoidkIsoObsemiid $fObTYPE(->)a$fObTYPECokleislia$fObTYPEKleisliaStatic runStatic$fArrowChoiceStatic$fArrowPlusStatic$fArrowZeroStatic $fArrowStatic$fCategoryTYPEStatic$fSemigroupoidTYPEStatic$fComonadStatic$fExtendStatic$fApplicativeStatic $fPlusStatic $fAltStatic $fApplyStatic$fFunctorStatic Bifoldable1bifold1 bifoldMap1 Foldable1fold1foldMap1 toNonEmpty$fFoldable1Joker$fFoldable1(,)$fFoldable1NonEmpty$fFoldable1Sum$fFoldable1Reverse$fFoldable1Product$fFoldable1Lift$fFoldable1Compose$fFoldable1Backwards$fFoldable1IdentityT$fFoldable1Tagged$fFoldable1Identity$fFoldable1Tree$fFoldable1Complex$fFoldable1:.: $fFoldable1V1$fFoldable1:+:$fFoldable1:*:$fFoldable1Par1 $fFoldable1M1$fFoldable1Rec1$fBifoldable1WrappedBifunctor$fBifoldable1Tannen$fBifoldable1Product$fBifoldable1Joker$fFoldable1Join$fBifoldable1Flip$fBifoldable1Clown$fBifoldable1Biff$fBifoldable1Tagged$fBifoldable1Const$fBifoldable1(,,,,)$fBifoldable1(,,,)$fBifoldable1(,,)$fBifoldable1(,)$fBifoldable1Either$fBifoldable1Arg bitraverse1_bifor1_ bisequenceA1_bifoldMapDefault1 $fFunctorAct$fSemigroupAct intercalate1intercalateMap1 traverse1_for1_ sequenceA1_foldMapDefault1asum1foldrM1foldlM1$fSemigroupJoinWith$fSemigroupAlt_ Traversable1 traverse1 sequence1Bitraversable1 bitraverse1 bisequence1 $fBitraversable1WrappedBifunctor$fBitraversable1Product$fBitraversable1Flip$fBitraversable1Tagged$fBitraversable1Const$fBitraversable1(,,,,)$fBitraversable1(,,,)$fBitraversable1(,,)$fBitraversable1(,)$fBitraversable1Either$fBitraversable1Arg$fTraversable1Joker$fTraversable1(,)$fTraversable1NonEmpty$fTraversable1Tree$fTraversable1Tagged$fTraversable1Complex$fTraversable1Sum$fTraversable1Reverse$fTraversable1Product$fTraversable1Lift$fTraversable1Compose$fTraversable1Backwards$fTraversable1IdentityT$fTraversable1Identity$fTraversable1:.:$fTraversable1:+:$fTraversable1:*:$fTraversable1V1$fTraversable1Par1$fTraversable1M1$fTraversable1Rec1$fBitraversable1Tannen$fBitraversable1Joker$fTraversable1Join$fBitraversable1Clown$fBitraversable1BifffoldMap1DefaultbifoldMap1DefaultconstControl.CategoryidMonadreturn Applicativepure.3unordered-containers-0.2.8.0-3iSQJVS3Sio885UUC852ojData.HashMap.BaseHashMapcontainers-0.5.10.2Data.IntMap.InternalIntMapData.Map.InternalMap Alternative<|>Maybeghc-prim GHC.TypesIO Data.EitherEithertransformers-0.5.2.0Control.Monad.Trans.ErrorErrorTMagicrunMagicemptyCategoryActgetActAlt_getAlt_JoinWithjoinee