MONAD TRANSFORMERS

In The !ld

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SF SCALA

May 2012

* http://marakana.com/s/scala_typeclassopedia_with_john_kodumal_of_atlassian_video,1198/index.html

trait Monad[F[_]] extends Applicative[F] {

def flatMap[A, B](fa: F[A])(f :A=>F[B]):F[B]

}

* monad type class * flatMap also called bind, >>=

def point[A](a: => A): M[A]

def map[A,B](ma: M[A])(f: A => B): M[B]

def flatMap[A,B](ma: M[A])(f: A => M[B]): M[B]

* the functions we care about* lift pure value, lift pure function, chain “operations”

scala> import scalaz.Monad

scala> import scalaz.std.option._

scala> val a = Monad[Option].point(1)

a: Option[Int] = Some(1)scala> Monad[Option].map(a)(_.toString + "hi")

res2: Option[java.lang.String] = Some(1hi)

scala> Monad[Option].bind(a)(i => if (i < 0) None else Some(i + 1))res4: Option[Int] = Some(2)

* explicit type class usage in scalaz seven

scala> import scalaz.syntax.monad._import scalaz.syntax.monad._scala> Option(1).flatMap(i => if (i < 0) None else Some(i+1))res6: Option[Int] = Some(2)scala> 1.point[Option].flatMap(...)res7: Option[Int] = Some(2)

* implicit type class usage in scalaz7 using syntax extensions

“A MONADIC FOR

COMPREHENSION IS AN

EMBEDDED PROGRAMMING

LANGUAGE WITH SEMANTICS

DEFINED BY THE MONAD”

* “one intuition of monads” - john

MULTIPLE EFFECTS

C"position

Option[A]

* it may not exist

SEMANTICSSIDE NOTE:

* to an extent, you can “choose” the meaning of a monad* Option -- anon. exceptions -- more narrowly, the exception that something is not there. Validation - monad/not monad - can mean different things in different contexts

IO[Option[A]]

* but side-effects are needed to even look for that value

IO[Validation[Throwable,Option[A]]

* and looking for that value may throw exceptions (or fail in some way)

IO[(List[String], Validation[Throwable,Option[A])]

* and logging what is going on is necessary

MULTIPLE EFFECTS

A P#oblem

MONADS DO NOT

COMPOSE

* the problem in theory (core issue)

“COMPOSE”?

FUNCTORSDO

COMPOSE

* as well as applicatives

trait Functor[F[_]] {

def map[A, B](fa: F[A])(f :A=>B):F[B]

}

def composeFunctor[M[_],N[_]](implicit m: Functor[M], n: Functor[N]) = new Functor[({type MN[A]=[M[N[A]]]})#MN] { def map[A,B](mna: M[N[A]])(f: A => B): M[N[B]] = ... }

* generic function that composes any two functors M[_] and N[_]

def composeFunctor[M[_],N[_]](implicit m: Functor[M], n: Functor[N]) = new Functor[({type MN[A]=[M[N[A]]]})#MN] { def map[A,B](mna: M[N[A]])(f: A => B): M[N[B]] = { M.map(mna)(na => N.map(na)(f)) } }

scala> Option("abc").map(f)res1: Option[Int] = Some(3)

scala> List(Option("abc"), Option("d"), Option("ef")).map2(f)res2: List[Option[Int]] = List(Some(3), Some(1), Some(2))

* can compose functors infinitely deep but...* scalaz provides method to compose 2, with nice syntatic sugar, easily (map2)

def notPossible[M[_],N[_]](implicit m: Monad[M], n: Monad[N]) = new Monad[({type MN[A]=[M[N[A]]]})#MN] { def flatMap[A,B](mna: M[N[A]])(f: A => M[N[B]]): M[N[B]] = ... }

* cannot write the same function for any two monads M[_], N[_]

def notPossible[M[_],N[_]](implicit m: Monad[M], n: Monad[N]) = new Monad[({type MN[A]=[M[N[A]]]})#MN] { def flatMap[A,B](mna: M[N[A]])(f: A => M[N[B]]): M[N[B]] = ... } TRY IT

!

* best way to understand this is attempt to write it yourself* it won’t compile

http://blog.tmorris.net/monads-do-not-compose/

* good resource to dive into this in more detail* some of previous slides based on above* provides template, in the form of a gist, for trying this stuff out

STAIR

STEPPING

* the problem in practice*http://www.flickr.com/photos/caliperstudio/2667302181/

val a: IO[Option[MyData]] = ...

val b: IO[Option[MyData]] = ...

* have two values that require we communicate w/ outside world to fetch* those values may not exist (alternative meaning, fetching may result in exceptions that are anonymous)

for { data1 <- a data2 <- b} yield { data1 merge data2 // fail}

* want to merge the two pieces of data if they both exist

for { // we've escaped IO, fail d1 <- a.unsafePerformIO d2 <- b.unsafePerformIO} yield d1 merge d2

* don’t want to perform the actions until later (don’t escape the IO monad)

for { od1 <- a od2 <- b} yield (od1,od2) match { case (Some(d1),Some(d2) => Option(d1 merge d2) case (a@Some(d1),_)) => a case (_,a@Some(d2)) => a case _ => None}

for { od1 <- a od2 <- b} yield for { d1 <- od1 d2 <- od2} yield d1 merge d2

* may notice the semi-group here* can also write it w/ an applicative* this is a contrived example

def b(data: MyData): IO[Option[MyData]BUT WHAT IF...

* even w/ simple example, this minor change throws a monkey wrench in things

for {

  readRes <- readIO(domain)

  res <- readRes.fold(

   success = _.cata(

    some = meta =>

if (meta.enabledStatus /== status) {

writeIO(meta.copy(enabledStatus = status))

} else meta.successNel[BarneyException].pure[IO],

     none = new ReadFailure(domain).failNel[AppMetadata].pure[IO]

    ),    failure = errors => errors.fail[AppMetadata].pure[IO]

  ) } yield res

):* example of what not to do from something I wrote a while back

MULTIPLE EFFECTS

A Solution

case class IOOption[A](run: IO[Option[A]])

define type that boxes box the value, doesn’t need to be a case class, similar to haskell newtype.

new Monad[IOOption] {

def point[A](a: => A): IOOption[A] = IOOption(a.point[Option].point[IO])

def map[A,B](fa: IOOption[A])(f: A => B): IOOption[B] = IOOption(fa.run.map(opt => opt.map(f)))

def flatMap[A, B](fa: IOOption[A])(f :A=>IOOption[B]):IOOption[B] =

IOOption(fa.run.flatMap((o: Option[A]) => o match { case Some(a) => f(a).run case None => (None : Option[B]).point[IO] }))}

* can define a Monad instance for new type

val a: IOOption[MyData] = ...val b: IOOption[MyData] = ...

val c: IOOption[MyData] = for { data1 <- a data2 <- b} yield { data1 merge data2}

val d: IO[Option[MyData]] = c.run

can use new type to improve previous contrived example

type MyState[A] = State[StateData,A]case class MyStateOption[A](run: MyState[Option[A]])

* what if we don’t need effects, but state we can read and write to produce a final optional value and some new state* State[S,A] where S is fixed is a monad* can define a new type for that as well

new Monad[MyStateOption] {

def map[A,B](fa: MyStateOption[A])(f: A => B): MyStateOption[B] =

MyStateOption(Functor[MyState].map(fa)(opt => opt.map(f)))

def flatMap[A, B](fa: MyStateOption[A])(f :A=>IOOption[B]) =

MyStateOption(Monad[MyState]].bind(fa)((o: Option[A]) => o match { case Some(a) => f(a).run case None => (None : Option[B]).point[MyState] }))}

new Monad[IOOption] {

def map[A,B](fa: IOOption[A])(f: A => B): IOOption[B] = IOOption(Functor[IO].map(fa)(opt => opt.map(f)))

def flatMap[A, B](fa: IOOption[A])(f :A=>IOOption[B]) =

IOOption(Monad[IO]].bind(fa)((o: Option[A]) => o match { case Some(a) => f(a).run case None => (None : Option[B]).point[IO] }))}

* opportunity for more abstraction* if you were going to do this, not exactly the way you would define these in real code, cheated a bit using {Functor,Monad}.apply

case class OptionT[M[_], A](run: M[Option[A]])

define a new type parameterized * -> * and *.

case class OptionT[M[_], A](run: M[Option[A]]) { def map[B](f: A => B)(implicit F: Functor[M]): OptionT[M,B] def flatMap[B](f: A => OptionT[M,B])(implicit M: Monad[M]): OptionT[M,B]}

* define map/flatMap a little differently, can be done like previous as typeclass instance but convention is to define the interface on the transformer and later define typeclass instance using the interface

case class OptionT[M[_], A](run: M[Option[A]]) { def map[B](f: A => B)(implicit F: Functor[M]): OptionT[M,B] = OptionT[M,B](F.map(run)((o: Option[A]) => o map f)) def flatMap[B](f: A => OptionT[M,B])(implicit M: Monad[M]): OptionT[M,B] = OptionT[M,B](M.bind(run)((o: Option[A]) => o match { case Some(a) => f(a).run case None => M.point((None: Option[B])) }))}

* implementations resemble what has already been shown

new Monad[IOOption] {

def map[A,B](fa: IOOption[A])(f: A => B): IOOption[B] = IOOption(Functor[IO].map(fa)(opt => opt.map(f)))

def flatMap[A, B](fa: IOOption[A])(f :A=>IOOption[B]) =

IOOption(Monad[IO]].bind(fa)((o: Option[A]) => o match { case Some(a) => f(a).run case None => (None : Option[B]).point[IO] }))}

case class OptionT[M[_], A](run: M[Option[A]]) { def map[B](f: A => B)(implicit F: Functor[M]): OptionT[M,B] = OptionT[M,B](F.map(run)((o: Option[A]) => o map f)) def flatMap[B](f: A => OptionT[M,B])(implicit M: Monad[M]) = OptionT[M,B](M.bind(run)((o: Option[A]) => o match { case Some(a) => f(a).run case None => M.point((None: Option[B])) }))}

* it the generalization of what was written before

type FlowState[A] = State[ReqRespData, A]val f: Option[String] => FlowState[Boolean] = (etag: Option[String]) => { val a: OptionT[FlowState, Boolean] = for { // string <- OptionT[FlowState,String]     e <- optionT[FlowState](etag.point[FlowState]) // wrap FlowState[Option[String]] in OptionT     matches <- optionT[FlowState]((requestHeadersL member IfMatch))   } yield matches.split(",").map(_.trim).toList.contains(e) a getOrElse false // FlowState[Boolean]}

* check existence of etag in an http request, data lives in state* has minor bug, doesn’t deal w/ double quotes as written* https://github.com/stackmob/scalamachine/blob/master/core/src/main/scala/scalamachine/core/v3/WebmachineDecisions.scala#L282-285

val reqCType: OptionT[FlowState,ContentType] = for {      contentType <- optionT[FlowState]( (requestHeadersL member ContentTypeHeader) )      mediaInfo <- optionT[FlowState]( parseMediaTypes(contentType).headOption.point[FlowState] )} yield mediaInfo.mediaRange

* determine content type of the request, data lives in state, may not be specified* https://github.com/stackmob/scalamachine/blob/master/core/src/main/scala/scalamachine/core/v3/WebmachineDecisions.scala#L772-775

scala> type EitherTString[M[_],A] = EitherT[M,String,A]defined type alias EitherTString

scala> val items = eitherT[List,String,Int](List(1,2,3,4,5,6).map(Right(_)))items: scalaz.EitherT[List,String,Int] = ...

* adding features to a “embedded language”

for { i <- items } yield print(i)// 123456

for { i <- items _ <- if (i > 4) leftT[List,String,Unit]("fail") else rightT[List,String,Unit](()) } yield print(i)// 1234

* adding error handling, and early termination to non-deterministic computation

MONAD

TRANSFORMERS

In General

MyMonad[A]

NAMING CONVENTION

MyMonadT[M[_], A]

* transformer name ends in T

BOXES A VALUE

run: M[MyMonad[A]

* value is typically called “run” in scalaz7* often called “value” in scalaz6 (because of NewType)

A MONAD TRANSFORMER

IS A MONAD TOO

* i mean, its thats kinda the point of this whole exercise isn’t it :)

def optTMonad[M[_] : Monad] = new Monad[({type O[X]=OptionT[M,X]]})#O) { def point[A](a: => A): OptionT[M,A] = OptionT(a.point[Option].point[M]) def map[A,B](fa: OptionT[M,A])(f: A => B): OptionT[M,B] = fa map f def flatMap[A, B](fa: OptionT[M,A])(f :A=> OptionT[M,B]): OptionT[M, B] = fa flatMap f}

* monad instance definition for OptionT

HAS INTERFACE RESEMBLING UNDERLYING

MONAD’S INTERFACE

* can interact with the monad transformer in a manner similar to working with the actual monad* same methods, slightly different type signatures* different from haskell, “feature” of scala, since we can define methods on a type

case class OptionT[M[_], A](run: M[Option[A]]) { def getOrElse[AA >: A](d: => AA)(implicit F: Functor[M]): M[AA] = F.map(run)((_: Option[A]) getOrElse default) def orElse[AA >: A](o: OptionT[M,AA])(implicit M: Monad[M]): OptionT[M,AA] = OptionT[M,AA](M.bind(run) { case x@Some(_) => M.point(x) case None => o.run }}

MONAD

TRANSFORMERS

Stacked Effects

TRANSFORMER IS A MONAD

⇒TRANSFORMER CAN WRAP ANOTHER TRANSFORMER

* at the start, the goal was to stack effects (not just stack 2 effects)* this makes it possible

type VIO[A] = ValidationT[IO,Throwable,A]

def doWork(): VIO[Option[Int]] = ...

val r: OptionT[VIO,Int] = optionT[VIO](doWork())

* wrap the ValidationT with success type Option[A] in an OptionT* define type alias for connivence -- avoids nasty type lambda syntax inline

val action: OptionT[VIO, Boolean] = for { devDomain <- optionT[VIO] {    validationT(       bucket.fetch[CName]("%s.%s".format(devPrefix,hostname))       ).mapFailure(CNameServiceException(_))   } _ <- optionT[VIO] { validationT(deleteDomains(devDomain)).map(_.point[Option]) }} yield true

* code (slightly modified) from one of stackmob’s internal services* uses Scaliak to fetch hostname data from riak and then remove them* possible to clean this code up a bit, will discuss shortly (monadtrans)

KEEP ON STACKIN’

ON

* don’t have to stop at 2 levels deep, our new stack is monad too* each monad/transformer we add to the stack compose more types of effects

“ORDER” MATTERS

* how stack is built, which transformers wrap which monads, determines the overall semantics of the entire stack* changing that order can, and usually does, change semantics

OptionT[FlowState, A]vs.

StateT[Option,ReqRespData,A]

* what is the difference in semantics between the two? * type FlowState[A] = State[ReqRespData,A]

FlowState[Option[A]]vs.

Option[State[ReqRespData,A]

* unboxing makes things easier to see* a state action that returns an optional value vs a state action that may not exist* the latter probably doesn’t make as much sense in the majority of cases

MONADTRANS

The Type Class

* type classes beget more type classes

REMOVING REPETITION===

MORE ABSTRACTION

* previous examples have had a repetitive, annoying, & verbose task* can be abstracted away...by a type class of course

optionT[VIO](validationT(deleteDomains(devDomain)).map(_.point[Option]))eitherT[List,String,Int](List(1,2,3,4,5,6).map(Right(_))) resT[FlowState](encodeBodyIfSet(resource).map(_.point[Res]))

* some cases require lifting the value into the monad and then wrap it in the transformer* from previous examples

M[A] -> M[N[A]] -> NT[M[N[_]], A]

* this is basically what we are doing every time* taking some monad M[A], lifting A into N, a monad we have a transformer for, and then wrapping all of that in N’s monad transformer

trait MonadTrans[F[_[_], _]] {

  def liftM[G[_] : Monad, A](a: G[A]): F[G, A]

}

* liftM will do this for any transformer F[_[_],_] and any monad G[_] provided an instance of it is defined for F[_[_],_]

 def liftM[G[_], A](a: G[A])(implicit G: Monad[G]): OptionT[G, A] =

    OptionT[G, A](G.map[A, Option[A]](a)((a: A) => a.point[Option]))

* full definition requires some type ceremony* https://github.com/scalaz/scalaz/blob/scalaz-seven/core/src/main/scala/scalaz/OptionT.scala#L155-156

def liftM[G[_], A](ga: G[A])(implicit G: Monad[G]): ResT[G,A] =

      ResT[G,A](G.map(ga)(_.point[Res]))

* implementation for scalamachine’s Res monad* https://github.com/stackmob/scalamachine/blob/master/scalaz7/src/main/scala/scalamachine/scalaz/res/ResT.scala#L75-76

encodeBodyIfSet(resource).liftM[OptionT]List(1,2,3).liftM[EitherTString]validationT(deleteDomains(devDomain)).liftM[OptionT]

* cleanup of previous examples* method-like syntax requires a bit more work: https://github.com/scalaz/scalaz/blob/scalaz-seven/core/src/main/scala/scalaz/syntax/MonadSyntax.scala#L9

for { media <- (metadataL >=> contentTypeL).map(_ | ContentType("text/plain")).liftM[ResT]   charset <- (metadataL >=> chosenCharsetL).map2(";charset=" + _).getOrElse("")).liftM[ResT]   _ <- (responseHeadersL += (ContentTypeHeader, media.toHeader + charset)).liftM[ResT]   mbHeader <- (requestHeadersL member AcceptEncoding).liftM[ResT]   decision <- mbHeader >| f7.point[ResTFlow] | chooseEncoding(resource, "identity;q=1.0,*;q=0.5")} yield decision

* https://github.com/stackmob/scalamachine/blob/master/core/src/main/scala/scalamachine/core/v3/WebmachineDecisions.scala#L199-205

MONAD

TRANSFORMERS

In Review

STACKINGMONADS

COMPOSES EFFECTS

* when monads are stacked an embedded language is being built with multiple effects* this is not the only intuition of monads/transformers

CAN NOT COMPOSE MONADS

GENERICALLY

* cannot write generic function to compose any two monads M[_], N[_] like we can for any two functors

MONAD TRANSFORMERSCOMPOSE M[_] : MONAD WITH

ANY N[_] : MONAD

* can’t compose any two, but can compose a given one with any other

MONAD TRANSFORMERS WRAP OTHER

MONAD TRANSFORMERS

* monad transformers are monads* so they can be the N[_] : Monad that the transformer composes with its underlying monad

MONADTRANSREDUCES

REPETITION

* often need to take a value that is not entirely lifted into a monad transformer stack and do just that

STACK MONADSDON’T

STAIR-STEP

* monad transformers reduce ugly, stair-stepping or nested code and focuses on core task* focuses on intuition of mutiple effects instead of handling things haphazardly

THANK YOU

* stackmob, markana, john & atlassian, other sponsors, cosmin

QUESTIONS?