Overview) Declara've)Languages) The)essence)of)IO) IO)in)Haskell)

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1 Overview Declara'veLanguages D7012E: GeneralmonadsinHaskell FredrikBengtsson/JohanNordlander TheIOGmonad Thesequencingoperator Thegeneralideaofeffectsandimplicitstate Themonadclass requirementsonamonad AnonGIOmonadiccomputa'on trivialexample usefulexample! IOinHaskell ExampleofsideGeffec'ngcomputa'ons: iosqr :: Int -> IO Int iosqr arg = let tmp = arg*arg in do putstrln (show tmp return tmp fun :: Int -> Int -> IO Int fun a b = do x <- iosqr a y <- iosqr b return (x+y TheessenceofIO Theideaofanimplicitmachine/worldstate Someopera'onsmutatethestate Someopera'onsjustreadit Someopera'onsdoneither(thepureones ProgrammersoSenwanttocontroloverthe orderofstateeffects butnotalways c.f.concurrency!

2 BuildingblocksofIOinHaskell: Atypesystemthatmakeseffectsexplicit(IO a Asetofprimi'veIOopera'ons: putstr, getline, writefile,... AmeanstobuildtrivialIOopera'ons: return e AmeanstoordertheeffectsofIOopera'ons: do result1 <- iocomp1 result2 <- iocomp2... iocompn Noimplicitstate! Analterna've The"prin'ngeffect" iosqr :: Int -> String -> (String,Int iosqr arg s = let t= arg*arg s' = s ++ show t in (s',t Thetrivial"effect" fun :: Int -> Int -> String -> (String,Int fun a b s0 = let (s1,x = iosqr a s0 (s2,y = iosqr b s1 in (s2,x+y Orderingof"effects" Analterna've Sequen'alorderingcanbeachievedbyexplicit datadependencies Thestateisthenjustapieceofdatapassed around Effectsbecomeopera'onsonthestatedata Butthere'sanota'onalburden Wri'ngoutallstateparametersandresultsisapain Themistakeofduplica'ngthestateiseaislydone UsinghigherGorderfunc'ons Makingstateimplicit! putstr x = \s -> (s++x,( return x = \s -> (s,x f >>= g = \s0 -> let (s1,x = f s0 in g x s1 iosqr arg = let t = arg*arg in putstr (show t >>= \_ -> return t fun a b = iosqr a >>= (\x -> iosqr b >>= (\y -> return (x+y

3 UsingHaskell'sdoGsyntax Letdo x <- e1; e2meane1 >>= \x -> e2 Letdo e1simplymeane1 Thenwecanwriteourexampleas iosqr arg = let t = arg*arg in do _ <- putstr (show t return t fun a b = do x <- iosqr a y <- iosqr b return (x+y Thatis,almostouroriginalformula'on! Generalmonads IO acomeswithseveralfunc'ons: return :: a -> IO a putstr :: String -> IO ( getline :: IO String sequencingusingdoconstructor>>= Butthiswholepa_ernisactuallyoverloaded inhaskell,usingaconceptcalledmonads! Let'slookatbitoftheory... Thesequencingoperator >>= pronounced"bind" usedtosequencetwoopera'ons >>= :: m a -> (a -> m b -> m b theresultofthelesac'onfeedsintotheright ac'on(whichisafunc'on,givinganewac'on theresultfromthissecondac'onistheresultof thewholesequence TheMonadClass Thedefini'onoftheMonadclass class Monad m where (>>= :: m a -> (a -> m b -> m b return :: a -> m a Informalrequirementsonamonad return x returnvaluewithouteffect(justaddmonadtype f >>= g performeffectoff,thenperformtheeffectachievedwhen applyingtheresultofftog m a m b

4 Requirementsonamonad returnislesandrightiden'ty: return x >>= f == f x f >>= return == f >>=isassocia've: (f >>= g >>= h == f >>= (\x -> g x >>= h Equivalentrequirements Since m >>= f isequivalentto do x <- m f x thefirsttworulesmean do y <- return x isequivalenttof x f y do x <- m return x equivalenttom Rule3(associa'vityisimplicitinthedoconstruct TheIOmonad JustaMonadinstancewithprimi'veopera'ons: instance Monad IO where return = primioreturn (>>= = primiobind TypeIO aisbuiltgin,butcanbethoughtofas type IO a = World -> (World,a NB:noworldstateisofcoursecarriedaround insidehaskellprogramsatrung'me thereal worldstateworksmuchbe_erforthatpurpose! ThisiswhyIO aisabuiltgintype. Theiden'tymonad Simplestexample:let return x = x andlet x >>= f = f x Representstrivialemptystate noac'onperformed valueimmediatelyreturned

5 TheMaybemonad Capturestheeffectoffailing: instance Monad Maybe where return x = Just x f >>= g = case f of Nothing -> Nothing Just x -> g x Nothingbecomesaneffectspecifictothis monad(c.f.putstrforio Monadiccomputa'onovertrees Atreedatatype data Tree a = Nil Node a (Tree a (Tree a Computesumofintegersintree Directrecursivesolu'on: stree :: Tree Int -> Int stree Nil = 0 stree (Node n t1 t2 = n + stree t1 + stree t2 Canalsobedonemonadicstyle... Monadiccomputa'onovertrees sumtree :: Monad m => Tree Int -> m Int misamonad(notdefinedyet sumtree Nil = return 0 sumtree (Node n t1 t2 = do num <- return n s1 <- sumtree t1 s2 <- sumtree t2 return (num + s1 + s2 Monadiccomputa'onovertrees NospecialsideGeffects useiden'tymonad: data Id a = Id a instance Monad Id where return x = Id x Id x >>= f = f x Thus,wewouldbefreetosay sumtree :: Tree Int -> Id Int

6 Monadiccomputa'onovertrees TheresulthastypeId Intbutwewouldlikeit tobejustint Define extract :: Id a -> a extract (Id x = x Now extract. sumtree :: Tree Int -> Int What sthepoint? Apurefunc'onalstylewouldhavebeeneasier There snopointusingthemonadicstyleifwe don tuseanysidegeffects Butisn tsidegeffectsabadideaingeneral? notnecessarily someproblemsarequitenaturally capturedusinganimplicitstate! themonadicstylegivestherightenvironmentfor customizingthisstatetotheproblemathand Anotherexample... Stateinmonadiccomputa'on Considerassigninganintegertoallvaluesinatree sameintegerforsamevalue Wewouldlookforsomethingoftype Eq a => Tree a -> Tree Int Howtoproceed? Let'sconstruct numbertree :: Eq a => Tree a -> State a (Tree Int wheremonadtypestate a bwillbedefinedsoon Stateinmonadiccomputa'on numbertreecoldlooklikethis numbertree Nil = return Nil numbertree (Node x t1 t2 = do num <- numbernode x nt1 <- numbertree t1 nt2 <- numbertree t2 return (Node num nt1 nt2

7 TheState Atypeforatableofaelements type Table a = [a] Atypeforcomputa'onsthatcanmanipulatea stateconsis'ngofsuchatable data State a b = State (Table a -> (Table a,b interpreta'on: takesatable returnsab andanewtableasa"sidegeffect" (constructorstateisjustalayerofwrappingpaper TheState TheStatemonad instance Monad (State a where return x = State (\tab -> (tab,x leavestateunchanged,justpairitwithvaluex (State st >>= f = State (\tab -> let (newtab,y = st tab (State trans = f y in trans newtab Apar'al typeapplica'on! Justareminder: data State a b = State (Table a -> (Table a, b Stateinmonadiccomputa'on numbernode :: Eq a => a -> State a Int numbernode x = State (nnode x nnode :: Eq a => a -> Table a -> (Table a, Int nnode x table elem x table = (table, findpos x table otherwise = (table++[x], length table ifxintable retriveposi'onofxfromtable otherwise addxtotable new int Stateinmonadiccomputa'on findpos :: Eq a => a -> Table a -> Int findpos x = fromjust. lookup. (`zip` [0..] extractst :: State a b -> b extractst (State st = snd (st [] func'onstappliedtoini'alstate[] returnsapair takesecondpart,theintwe'relookingfor numtree :: Eq a => Tree a -> Tree Int numtree = extractst. numbertree

8 Monadicstyleprogramming Incorporatesimpera've(monadicstyle intopurefunc'onallanguages withoutpoisoningothercode NotjustforIO,butforanyprogramming problemthatneedsanimplicitstateand sequencingofeffects Theorymightlookcomplex,fairlyeasytouse! Next:Implemen'ngfunc'onallanguages