I have a monad that is very similar to a collection monad. I'm currently trying to implement a monad transformer for it, but I'm failing.
I've looked at the ListT implementation in Scalaz 6 and 7, but I cannot understand how it works. It uses some additional type Step, whose purpose is unclear to me.
So can someone please explain to me how to implement a list monad transformer, either by explaining the Scalaz approach or using a different implementation?
I am not quite sure, what the Step means in scalaz, but implementing a ListT is pretty straight forward. Depending on how many operations you want to put on it, it can be a little work, but the basic monad operations can be implemented as follows.
First we need typeclasses for monad and functor (we could also add applicative, but that is not necessary for this example):
trait Functor[F[_]] {
def map[A,B](fa: F[A])(f: A => B): F[B]
}
trait Monad[F[_]] extends Functor[F] {
def flatMap[A,B](fa: F[A])(f: A => F[B]): F[B]
def pure[A](x: A): F[A]
}
object Monad {
implicit object ListMonad extends Monad[List] {
def map[A,B](fa: List[A])(f: A => B) = fa map f
def flatMap[A,B](fa: List[A])(f: A => List[B]) = fa flatMap f
def pure[A](x: A) = x :: Nil
}
implicit object OptionMonad extends Monad[Option] {
def map[A,B](fa: Option[A])(f: A => B) = fa map f
def flatMap[A,B](fa: Option[A])(f: A => Option[B]) = fa flatMap f
def pure[A](x: A) = Some(x)
}
def apply[F[_] : Monad]: Monad[F] = implicitly[Monad[F]]
}
Once we have those, we can create the transformer, which basically just wraps the F[List[A]] and forwards the call to its map and flatMap function to the list by calling map on the containing functor and then calling map or flatMap resp. on the contained List/s.
final case class ListT[F[_] : Monad, A](fa: F[List[A]]) {
def map[B](f: A => B) = ListT(Monad[F].map(fa)(_ map f))
def flatMap[B](f: A => ListT[F, B]) = ListT(Monad[F].flatMap(fa) { _ match {
case Nil => Monad[F].pure(List[B]())
case list => list.map(f).reduce(_ ++ _).run
}})
def ++(that: ListT[F,A]) = ListT(Monad[F].flatMap(fa) { list1 =>
Monad[F].map(that.run)(list1 ++ _)
})
def run = fa
}
Once we are done with modifying, we can get the resulting object by calling the run method on the ListT object. If you want, you can also add other list specific operations like in scalaz. This should be pretty straight forward. For example a :: could look as follows:
def ::(x: A) = ListT(Monad[F].map(fa)(x :: _))
Usage:
scala> ListT(Option(List(1,2,3)))
res6: ListT[Option,Int] = ListT(Some(List(1, 2, 3)))
scala> res6.map(_+45)
res7: ListT[Option,Int] = ListT(Some(List(46, 47, 48)))
scala> 13 :: res7
res8: ListT[Option,Int] = ListT(Some(List(13, 46, 47, 48)))
scala> res8.run
res10: Option[List[Int]] = Some(List(13, 46, 47, 48))
I think scalaz.ListT is incorrect in scalaz 7.0.x and 7.1.x.
https://github.com/scalaz/scalaz/issues/921
6.x version is correct. but it is same as StreamT.
Related
I've tried
exstension[A] (f: Iterator[Iterator[A]){
def mapInner[B](f: A => B): Iterator[Iterator[B]
but this loses type information since if I give it a list[list[Int]] I get back Iterator[Iterator[Int]
Try functors and friends:
trait Functor[F[_]]:
extension [A](fa: F[A]) def fmap[B](fmap: A => B): F[B]
object Functor:
given Functor[List] with
extension [A](fa: List[A]) def fmap[B](fmap: A => B): List[B] =
fa.map(fmap)
given [F[_], G[_]](using F: Functor[F], G: Functor[G]): Functor[[x] =>> F[G[x]]] with
extension [A](fa: F[G[A]]) def fmap[B](fmap: A => B): F[G[B]] =
F.fmap(fa)(ga => G.fmap(ga)(fmap))
import Functor.given
val xs = List(1, 2, 3, 4)
val xss = xs.map(x => List(x, x))
val fxss = summon[Functor[[x] =>> List[List[x]]]]
println(fxss.fmap(xss)((a: Int) => a * 2))
It's a lot of setup but likely you don't have to do it yourself and use a library like scalaz or cats where all these things are already defined.
I know I can traverse Lists
import cats.instances.list._
import cats.syntax.traverse._
def doMagic(item: A): M[B] = ???
val list: List[A] = ???
val result: M[List[B]] = list.traverse(doMagic)
And I can convert a Seq back and forth to List
val seq: Seq[A] = ???
val result: M[Seq[B]] = seq.toList.traverse(doMagic).map(_.toSeq)
But can I also traverse Seq without the boilerplate?
val seq: Seq[A] = ???
val result: M[Seq[B]] = seq.traverse(doMagic)
Or what's an easy way to get an instance of Traverse[Seq]?
Cats does not provide typeclass instances for Seq, so besides implementing it yourself you're stuck with the conversion.
As to why, there's an ongoing discussion in an (somewhat old) Cats issue. To sum it up, you won't know enough about Seq underlying characteristics to make sure some of the typeclasses instances laws hold.
EDIT : Nevermind, it exists now, see linked thread
As of cats 2.3, support for immutable.Seq is now built in. See "Where are implicit instances for Seq?" on the FAQ or this PR where the functionality was added.
If you are absolutely sure that the conversion from all Seq to List will always succeed in your code, you can simply transfer the Traverse structure from List to Seq over an (pseudo-)isomorphism:
def traverseFromIso[F[_], Z[_]]
(forward: F ~> Z, inverse: Z ~> F)
(implicit zt: Traverse[Z])
: Traverse[F] = new Traverse[F] {
def foldLeft[A, B](fa: F[A], b: B)(f: (B, A) ⇒ B): B = zt.foldLeft(forward(fa), b)(f)
def foldRight[A, B](fa: F[A], lb: Eval[B])(f: (A, Eval[B]) => Eval[B]): Eval[B] =
zt.foldRight(forward(fa), lb)(f)
def traverse[G[_], A, B]
(fa: F[A])
(f: (A) ⇒ G[B])
(implicit appG: Applicative[G])
: G[F[B]] = {
(zt.traverse(forward(fa))(f)(appG)).map(zb => inverse(zb))
}
}
This isn't really an isomorphism, because the conversion from Seq to List can fail badly (e.g. if the sequence is infinite). What it does is simply converting Seq to List back and forth, and forwarding all method calls to those of Traverse[List].
Now you can use this method to build an instance of Traverse[Seq]:
implicit val seqTraverse: Traverse[Seq] = traverseFromIso(
new FunctionK[Seq, List] { def apply[X](sx: Seq[X]): List[X] = sx.toList },
new FunctionK[List, Seq] { def apply[X](lx: List[X]): Seq[X] = lx }
)
Full code snippet (compiles with scala 2.12.4 and cats 1.0.1):
import cats._
import cats.implicits._
import cats.arrow.FunctionK
import scala.language.higherKinds
object TraverseFromIso {
// This method can build you a `Traversable[Seq]` from
// an `Traversable[List]` and a pair of polymorphic conversion
// functions:
def traverseFromIso[F[_], Z[_]]
(forward: F ~> Z, inverse: Z ~> F)
(implicit zt: Traverse[Z])
: Traverse[F] = new Traverse[F] {
def foldLeft[A, B](fa: F[A], b: B)(f: (B, A) ⇒ B): B = zt.foldLeft(forward(fa), b)(f)
def foldRight[A, B](fa: F[A], lb: Eval[B])(f: (A, Eval[B]) => Eval[B]): Eval[B] =
zt.foldRight(forward(fa), lb)(f)
def traverse[G[_], A, B]
(fa: F[A])
(f: (A) ⇒ G[B])
(implicit appG: Applicative[G])
: G[F[B]] = {
(zt.traverse(forward(fa))(f)(appG)).map(zb => inverse(zb))
}
}
// A little demo
def main(args: Array[String]): Unit = {
// To instantiate a `Traverse[Seq]`, we have to provide
// two natural transformations (from List to Seq and back):
implicit val seqTraverse: Traverse[Seq] = traverseFromIso(
new FunctionK[Seq, List] { def apply[X](sx: Seq[X]): List[X] = sx.toList },
new FunctionK[List, Seq] { def apply[X](lx: List[X]): Seq[X] = lx }
)
// do stuff with `Traversable[Seq]` here
}
}
we are creating our own OptionT of cats for understanding, how monads are work and monads transformation flow. While creating our own custom monad getting some of the errors. First thing below is our code:
case class WhateverOpt[W[_], A] (value: W[Option[A]]) {
def map[B] (f: A => B) (implicit M: Monad[W]): WhateverOpt[W, B] =
WhateverOpt(M.map(value)(_.map(f)))
def flatMap[B] (f: A => WhateverOpt[W, B]) (implicit M: Monad[W]): WhateverOpt[W, B] =
WhateverOpt(M.flatMap(value)(optA => optA match {
case Some(v) => f(v).value
}))
}
implicit val optionTMonad = new Monad[Option] {
override def map[A, B](fa: Option[A])(f: A => B): Option[B] = fa.map(f)
override def flatMap[A, B](fa: Option[A])(f: A => Option[B]): Option[B] = fa.flatMap(f)
}
val optionResult = for {
user <- WhateverOpt(repository.getUserOption(1))
addres <- WhateverOpt(repository.getAddressOption(user))
} yield addres.city
Below are the points, where we stuck:
How to handle None case in WhateverOpt flatMap method?
When executing the code, getting runtime error:
Error:(26, 12) could not find implicit value for parameter M: usercases.mtransfomer.Monad[scala.concurrent.Future]
addres <- WhateverOpt(repository.getAddressOption(user))
We are not sure about the error because we are creating optionTMonad implicit and by default, all are in the same scope. How can we resolve these two issues?
Update
Full code is available on Github branch https://github.com/harmeetsingh0013/fp_scala/blob/master/src/main/scala/usercases/mtransfomer/Example5.scala
About how to deal with None:
case class WhateverOpt[W[_], A] (value: W[Option[A]]) {
def map[B] (f: A => B) (implicit M: Monad[W]): WhateverOpt[W, B] =
WhateverOpt(M.map(value)(_.map(f)))
def flatMap[B]
(f: A => WhateverOpt[W, B])
(implicit wMonad: Monad[W])
: WhateverOpt[W, B] = {
WhateverOpt(wMonad.flatMap(value) { (oa: Option[A]) =>
oa match {
case None => wMonad.pure(None)
case Some(a) => f(a).value
}
})
}
}
Imagine for a second that W is Future. Then the above code says:
wait until the wrapped value yields a result oa of type Option[A]
If oa turns out to be None, then there is nothing we can do, because we cannot obtain any instances of type A in order to call f. Therefore, immediately return None. The immediately return is the pure-method of the Future-monad, so for the general case we have to invoke wMonad.pure(None).
If oa yields Some(a), we can give this a to f, and then immediately unpack it to get to the value of type W[Option[B]].
Once we have the W[Option[B]] (whether empty or not), we can wrap it into WhateverOpt and return from the flatMap method.
I assume that you wanted to reimplement Monad[Option] just for fun (it's already in the library (the catsStdInstancesForOption thing is a CommutativeMonad), but here is how you could re-build it:
implicit val optionTMonad = new Monad[Option] {
override def map[A, B](fa: Option[A])(f: A => B): Option[B] = fa.map(f)
def flatMap[A, B](fa: Option[A])(f: A => Option[B]): Option[B] = fa.flatMap(f)
def pure[A](a: A): Option[A] = Some(a)
def tailRecM[A, B](a: A)(f: (A) => Option[Either[A, B]]): Option[B] = {
f(a) match {
case Some(Left(nextA)) => tailRecM(nextA)(f)
case Some(Right(res)) => Some(res)
case None => None
}
}
}
Notice that 1.0.1 requires to implement pure and tailRecM, and does not provide default implementations for that.
I don't want to say much about the necessary imports for future, but the latest version has cats.instances.future which provides a Monad instance. Check this again, because it seems as if you are using a different version of cats (your version didn't complain because of the missing tailRecM in your Option-monad).
How to handle None case in WhateverOpt flatMap method?
This answer is already explained by #Gabriele Petronella and #Andrey Tyukin with details.
When executing the code, getting runtime error: Error:(26, 12) could
not find implicit value for parameter M:
usercases.mtransfomer.Monad[scala.concurrent.Future] addres <-
WhateverOpt(repository.getAddressOption(user))
This error occurs, because In WhateverOpt constructor we know that our value is W[Option[A]], where Option is already defined and handle by the code, but repository.getUserOption(1) return Future[Option[User]] where Future is handled by generic parameter W and in that, case, we need to define, how to handle monads for Future. For resolving that issue, we need to implement new Monad[Future] rather than, new Monad[Option] as below:
case class WhateverOpt[W[_], A] (value: W[Option[A]]) {
def map[B] (f: A => B) (implicit M: Monad[W]): WhateverOpt[W, B] =
WhateverOpt(M.map(value)(_.map(f)))
def flatMap[B] (f: A => WhateverOpt[W, B]) (implicit M: Monad[W]): WhateverOpt[W, B] =
WhateverOpt(M.flatMap(value)(optA => optA match {
case Some(v) => f(v).value
case None => M.pure(None)
}))
}
implicit val futureMonad = new Monad[Future] {
override def pure[A](a: A): Future[A] = Future.successful(a)
override def map[A, B](fa: Future[A])(f: A => B): Future[B] = fa.map(f)
override def flatMap[A, B](fa: Future[A])(f: A => Future[B]): Future[B] = fa.flatMap(f)
}
val optionResult: WhateverOpt[Future, String] = for {
user <- WhateverOpt(repository.getUserOption(1))
addres <- WhateverOpt(repository.getAddressOption(user))
} yield addres.city
I am not sure about my disription, which I mention in answere, but current my assumptions are this and for me above code is working fine. For a complete example, please click on the GitHub repo, which is mention in the question.
How to handle None case in WhateverOpt flatMap method?
When you flatMap over None you return None. When you flatMap over WhateverOpt[W[_], B] you want to return the pure of it, which in your code would be M.pure(None).
When executing the code, getting runtime error: Error:(26, 12) could not find implicit value for parameter M: usercases.mtransfomer.Monad[scala.concurrent.Future]
addres <- WhateverOpt(repository.getAddressOption(user))
That's a compile-time error (not a runtime one) and it's due to the missing instance of Monad[Future]. In order to get an instance of Monad[Future] in scope with cats, you can do:
import cats.instances.future._
import scala.concurrent.ExecutionContext.Implicits.global
Also, you can avoid declaring your own Monad[Option] by importing it from cats with
import cats.instances.option._
Maybe I don't understand some fundamentals, but what is the signature of flatMap in general? Let's imagine I'd like to implement type T supporting for expression, then I required map, flatmap and withFilter implemented by T. Is there any interface of something like that?
More precisely what is the source of the signature:
class T[+A] {
def flatMap[B](f: (A) => T[B]): T[B]
}
Or is it a definition? May I implement flatmap with different signature?
In general flatMap has signature:
class T[+A] {
def flatMap[B](f: (A) ⇒ T[B]): T[B]
def map[B](f: (A) ⇒ B): T[B]
}
For example for Option:
def flatMap[B](f: (A) ⇒ Option[B]): Option[B]
For Seq:
def flatMap[B](f: (A) ⇒ Seq[B]): Seq[B]
Of course in scala API you will see other signatures for Seq, List - because there is generic signature in trait TraversableLike for all collections.
For monad function map should:
m map f == m flatMap (x => unit(f(x)))
Where unit unit(x) = single(x), for example:
List is a monad with unit(x) = List(x)
Set is monad with unit(x) = Set(x)
Option is a monad with unit(x) = Some(x)
Update
There is no interface for flatMap/map. See example (copy to your REPL):
class C[+A](val a:A) {
def flatMap[B](f:(A) => C[B]):C[B] = f(a)
def map[B](f:(A)=>B):B = f(a)
}
Then call in REPL for method:
scala> for { k<- new C(3)} yield {k}
res2: Int = 3
No special interface needed.
But if so you can implement FilterMonadic[+A, +Repr] generic interface.
Update
SLS - 6.19 For Comprehensions and For Loops.
Methods: map, withFilter, flatMap, and foreach - can be implemented in different
ways for different carrier types. Code:
class A {
def map(f: Int => Boolean): Boolean = f(10)
def flatMap(f: Int => Boolean): Boolean = f(20)
}
for(x <- new A; y <- new A) yield x == y
And
class T[+A] {
def flatMap[B](f: (A) ⇒ T[B]): T[B]
}
is not single way to define flatMap method.
In Haskell, liftM2 can be defined as:
liftM2 :: (Monad m) => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
liftM2 f m1 m2 = do
x1 <- m1
x2 <- m2
return $ f x1 x2
I'd like to translate this to Scala. My first attempt was the following:
def liftM2[T1, T2, R, M[_]](f: (T1, T2) => R)(ma: M[T1], mb: M[T2]) : M[R] = for {
a <- ma
b <- mb
} yield f(a, b)
This fails in what I guess is the most obvious way possible: "value flatMap is not a member of type parameter M[T1]". Right, I haven't indicated that M[_] is some kind of monad. So the next thing I tried was to define some structural type like:
type Monad[A] = {
def flatMap[B](f: (A) => Monad[B]): Monad[B]
}
... and to have M[A] <: Monad[A]. But that doesn't work, because Scala doesn't have recursive structural types.
So the next few things I tried involved gyrations similar to M[A] <: FilterMonadic[A, _]. Those all failed, probably because I wasn't able to figure out the right implicit-fu for CanBuildFrom.
The most closely-related question I could find here on StackOverflow was this one, touching both on recursive structural types and how to mimic Haskell's typeclasses in Scala. But that approach requires defining an implicit conversion from each type you care about to the trait defining the typeclass, which seems terribly circular in this case...
Is there any good way to do what I'm trying to do?
The usual way to encode type classes in Scala turns out to follow Haskell pretty closely: List doesn't implement a Monad interface (as you might expect in an object-oriented language), but rather we define the type class instance in a separate object.
trait Monad[M[_]] {
def point[A](a: => A): M[A]
def bind[A, B](ma: M[A])(f: A => M[B]): M[B]
def map[A, B](ma: M[A])(f: A => B): M[B] = bind(ma)(a => point(f(a)))
}
implicit object listMonad extends Monad[List] {
def point[A](a: => A) = List(a)
def bind[A, B](ma: List[A])(f: A => List[B]) = ma flatMap f
}
This idea is introduced in Poor Man's Type Classes and explored more deeply in Type Classes as Objects and Implicits. Notice that the point method could not have been defined in an object-oriented interface, as it doesn't have M[A] as one of it's arguments to be converted to the this reference in an OO encoding. (Or put another way: it can't be part of an interface for the same reason a constructor signature can't be represented in an interface.)
You can then write liftM2 as:
def liftM2[M[_], A, B, C](f: (A, B) => C)
(implicit M: Monad[M]): (M[A], M[B]) => M[C] =
(ma, mb) => M.bind(ma)(a => M.map(mb)(b => f(a, b)))
val f = liftM2[List, Int, Int, Int](_ + _)
f(List(1, 2, 3), List(4, 5)) // List(5, 6, 6, 7, 7, 8)
This pattern has been applied extensively in Scalaz. Version 7, currently in development, includes an index of the type classes.
In addition to providing type classes and instances for standard library types, it provides a 'syntactic' layer that allows the more familiar receiver.method(args) style of method invocation. This often affords better type inference (accounting for Scala's left-to-right inference algorithm), and allows use of the for-comprehension syntactic sugar. Below, we use that to rewrite liftM2, based on the map and flatMap methods in MonadV.
// Before Scala 2.10
trait MonadV[M[_], A] {
def self: M[A]
implicit def M: Monad[M]
def flatMap[B](f: A => M[B]): M[B] = M.bind(self)(f)
def map[B](f: A => B): M[B] = M.map(self)(f)
}
implicit def ToMonadV[M[_], A](ma: M[A])
(implicit M0: Monad[M]) =
new MonadV[M, A] {
val M = M0
val self = ma
}
// Or, as of Scala 2.10
implicit class MonadOps[M[_], A](self: M[A])(implicit M: Monad[M]) {
def flatMap[B](f: A => M[B]): M[B] = M.flatMap(self)(f)
def map[B](f: A => B): M[B] = M.map(self)(f)
}
def liftM2[M[_]: Monad, A, B, C](f: (A, B) => C): (M[A], M[B]) => M[C] =
(ma, mb) => for {a <- ma; b <- mb} yield f(a, b)
Update
Yep, its possible to write less generic version of liftM2 for the Scala collections. You just have to feed in all the required CanBuildFrom instances.
scala> def liftM2[CC[X] <: TraversableLike[X, CC[X]], A, B, C]
| (f: (A, B) => C)
| (implicit ba: CanBuildFrom[CC[A], C, CC[C]], bb: CanBuildFrom[CC[B], C, CC[C]])
| : (CC[A], CC[B]) => CC[C] =
| (ca, cb) => ca.flatMap(a => cb.map(b => f(a, b)))
liftM2: [CC[X] <: scala.collection.TraversableLike[X,CC[X]], A, B, C](f: (A, B) => C)(implicit ba: scala.collection.generic.CanBuildFrom[CC[A],C,CC[C]], implicit bb: scala.collection.generic.CanBuildFrom[CC[B],C,CC[C]])(CC[A], CC[B]) => CC[C]
scala> liftM2[List, Int, Int, Int](_ + _)
res0: (List[Int], List[Int]) => List[Int] = <function2>
scala> res0(List(1, 2, 3), List(4, 5))
res1: List[Int] = List(5, 6, 6, 7, 7, 8)