L(@K;      !"#$%&'()*+,-./012345678 9 :  Safe-Inferedportable provisionalEdward Kmett <ekmett@gmail.com> Safe-InferedA ; sans <. Minimal definition: Either  or  OIf defining both, then the following laws (the default definitions) must hold:   join = (>>- id)  m >>- f = join (fmap f m) Laws:  4 induced definition of <.>: f <.> x = f >>- (<$> x) 1Finally, there are two associativity conditions:  G 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 ; associativity of (->-): (f ->- g) ->- h = f ->- (g ->- h) 8Transform a Apply into an Applicative by adding a unit. Wrap an = to be used as a member of   )A strong lax semi-monoidal endofunctor.  This is equivalent to an = without >. Laws: B associative composition: (.) <$> u <.> v <.> w = u <.> (v <.> w)   a .> b = const id <$> a <.> b   a <. b = const <$> a <.> b TODO: move into Data.Functor  A variant of  with the arguments reversed. 3Lift a binary function into a comonad with zipping 4Lift a ternary function into a comonad with zipping ?An @ is a =, but it is an instance of  AA B is not a ;, but it is an instance of  CAn IntMap is not =, but it is an instance of   D A Map is not =, but it is an instance of   [ EFG?AHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuCDvwxyz{|}~    R  EFG?AHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuCDvwxyz{|}~portable provisionalEdward Kmett <ekmett@gmail.com> Safe-Infered1A subset of monad transformers can transform any  as well.  portable provisionalEdward Kmett <ekmett@gmail.com> Safe-Infered" sans   !"# !"#"# !  !"#portable provisionalEdward Kmett <ekmett@gmail.com> Safe-Infered$%&$%&$%&$%& portable provisionalEdward Kmett <ekmett@gmail.com> Safe-Infered    portable provisionalEdward Kmett <ekmett@gmail.com> Safe-Infered-EUsable default for foldMap, but only if you define foldMap1 yourself '()*+,-'()*+,-'()*+,- '()*+,-portable provisionalEdward Kmett <ekmett@gmail.com> Safe-Infered ./01./01./01./01portable provisionalEdward Kmett <ekmett@gmail.com> Safe-Infered2Laws:  C <!> is associative: (a <!> b) <!> c = a <!> (b <!> c) K <$> left-distributes over <!>: f <$> (a <!> b) = (f <$> a) <!> (f <$> b) If extended to an  then 3 should equal . Ideally, an instance of 2 also satisfies the "left distributon" law of  MonadPlus with respect to  .:  K <.> right-distributes over <!>: (a <!> b) <.> c = (a <.> c) <!> (b <.> c) But , ,  a,  e m, and STM satisfy the alternative  " left catch" law instead:   pure a <!> b = pure a PHowever, this variation cannot be stated purely in terms of the dependencies of 2. IWhen 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: + (m <!> n) >>- f = (m >>- f) <!> (m >>- f) + (m <!> n) >>= f = (m >>= f) <!> (m >>= f) 3( |) without a required empty -This instance does not actually satisfy the ( .) right distributive law  It instead satisfies the  Left-Catch law 2345 234523452345portable provisionalEdward Kmett <ekmett@gmail.com> Safe-Infered6Laws:   zero <!> m = m  m <!> zero = m If extended to an  then 7 should equal . 67 2345676767  Safe-Infered89:89:89:89:     !"#$%&'()**+,-./01123456789:;<=>?@ABC D D E F G HI HJKLMNOLPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~   H H   H semigroupoids-1.3.4Data.Functor.BindData.Functor.Bind.TransData.SemigroupoidData.Semigroupoid.DualData.Semigroup.FoldableData.Semigroup.TraversableData.Functor.AltData.Functor.PlusData.Semigroupoid.StaticData.Traversable.InstancesData.Functor.ApplybaseGHC.BasefmapFunctor Data.Functor<$><$Bind>>-join MaybeApply runMaybeApplyWrappedApplicativeWrapApplicativeunwrapApplicativeApply<.>.><.$><..>liftF2liftF3 returning-<<->--<- apDefault BindTransliftBSemigetSemiWrappedCategory WrapCategoryunwrapCategory SemigroupoidoDualgetDual Foldable1fold1foldMap1 traverse1_for1_ sequenceA1_foldMapDefault1 Traversable1 traverse1 sequence1foldMap1DefaultAltsomemanyPluszeroStatic runStaticMonadreturnControl.Applicative Applicativepure $fBindIntMapcontainers-0.4.2.1 Data.IntMapIntMap $fBindMapData.MapMap $fApplyIntMap $fApplyMap$fArrowLoopCokleisli $fBindTree $fBindSeq $fBindContT $fBindRWST $fBindRWST0 $fBindStateT $fBindStateT0 $fBindWriterT$fBindWriterT0 $fBindReaderT $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 $fApplyContT $fApplyRWST $fApplyRWST0 $fApplyStateT$fApplyStateT0$fApplyWriterT$fApplyWriterT0 $fApplyListT$fApplyReaderT $fApplyErrorT $fApplyMaybeT $fApplyTree $fApplySeq$fApplyWrappedArrow$fApplyWrappedMonad$fApplyIdentityT$fApplyIdentity $fApplyOption $fApplyMaybe $fApplyIO $fApply[]$fApplyZipList $fApply(->) $fApplyConst $fApplyEither$fApplyNonEmpty $fApply(,)$fApplyProduct$fApplyCompose$fBindTransContT$fBindTransRWST$fBindTransRWST0$fBindTransStateT$fBindTransStateT0$fBindTransWriterT$fBindTransWriterT0$fBindTransReaderT$fBindTransIdentityTControl.CategoryCategoryid$fCategorySemi$fSemigroupoidSemi$fCategoryWrappedCategory$fSemigroupoidWrappedCategory$fSemigroupoidOp$fSemigroupoidCokleisli$fSemigroupoidKleisli$fSemigroupoid(->)$fCategoryDual$fSemigroupoidDual $fFunctorAct$fSemigroupAct$fFoldable1NonEmpty$fFoldable1Product$fFoldable1Compose$fFoldable1IdentityT$fFoldable1Identity$fFoldable1Tree$fTraversable1NonEmpty$fTraversable1Tree$fTraversable1Product$fTraversable1Compose$fTraversable1IdentityT$fTraversable1Identity Alternative<|> Data.MaybeMaybeghc-prim GHC.TypesIO Data.EitherEithertransformers-0.3.0.0Control.Monad.Trans.ErrorErrorT$fAltIO $fAltRWST $fAltRWST0 $fAltWriterT $fAltWriterT0 $fAltStateT $fAltStateT0 $fAltListT $fAltErrorT $fAltMaybeT $fAltReaderT$fAltIdentityT$fAltWrappedApplicative $fAltNonEmpty$fAltSeq $fAltIntMap$fAltMap$fAltWrappedArrow$fAltWrappedMonad $fAltOption $fAltMaybe$fAlt[] $fAltEitherempty $fPlusRWST $fPlusRWST0 $fPlusWriterT$fPlusWriterT0 $fPlusStateT $fPlusStateT0 $fPlusListT $fPlusErrorT $fPlusMaybeT $fPlusReaderT$fPlusIdentityT$fPlusWrappedApplicative $fPlusSeq $fPlusIntMap $fPlusMap$fPlusWrappedArrow$fPlusWrappedMonad $fPlusOption $fPlusMaybe$fPlus[]$fPlusIO$fArrowChoiceStatic$fArrowPlusStatic$fArrowZeroStatic $fArrowStatic$fCategoryStatic$fSemigroupoidStatic$fComonadStatic$fExtendStatic$fApplicativeStatic $fPlusStatic $fAltStatic $fApplyStatic$fFunctorStatic