I have just started to learn Scala cats framework. I am reading Functor. I understood its features but I don't understand it's usage. Why should I use it if there is a map method already available in Functors like List, Option etc.
As an example,
val list = List(1, 2, 3)
Functor[List].map(list)(x => x * 2)
But the same can be achieved with
list.map(x => x * 2)
What do we get when we abstract the method map inside Functor trait.
Can someone please throw some light on it so that I understand its usage.
You can call .map on object, when you know that this object has this method, and that this method is called this way. If you know exact type of the object, then compiler can check that, indeed, this is the case. But what if you don't know the type of the object? And what if you don't want to use runtime reflection?
Imagine situation like this:
def doubleIntInF[F[_]: Functor](fInt: F[Int]): F[Int] =
fInt.map(_ * 2)
Here, we don't know the type of F - it might be List, Option, Future, IO, Either[String, *]. And yet we are able to .map over it without using reflection - we use Functor[F] to power extension methods. We could do it also without extension method like this:
def doubleIntInF[F[_]: Functor](fInt: F[Int]): F[Int] =
Functor[F].map(fInt)(_ * 2)
and it would work (as long as we have the right implicits in scope):
doubleIntInF(List(1,2,3,4,5,6)) // List(2, 4, 6, 8, 10, 12
doubleIntInF(Option(4)) // Some(2)
In cases, where we know, that F=List, Option, etc - we have no reason to use it. But we have all the reasons to use if this F is dynamic.
And why would we like to make this F dynamic? To use it in libraries which e.g. could combine several functionalities provided through type classes together.
E.g. if you have F[_] and G[_] and you have Traverse[F] and Applicative[G] (more powerful Functor) you are able to turn F[G[A]] into G[F[A]]:
val listOption: List[Option] = List(Some(1), Some(2))
listOption.sequence // Some(List(1, 2))
val listFuture: List[Option] = List(Future(1), Future(2))
listFuture.sequence // Future(List(1, 2))
Virtually all libraries in Cats ecosystem use this concept (called typeclasses) to implement functionality without assuming that you pick the same data structures and IO components as they would. As long as you can provide typeclass instances that proves that they can safely use some methods on your type, they can implement the functionality (e.g. Cats Effect are extending Cats with some typeclasses and Doobie, FS2, Http4s, and so on build on top of these without making assumption about what you use to run your computations).
So long story short - in cases like your it doesn't make sense to use Functor, but in general they enable you to still use .map in situations which are NOT as simple and you don't have a hardcoded type.
The question is similar to why in OOP someone needs an interface (trait) while its implementations have the same methods.
Interface is an abstraction. Abstractions are useful. While programming we prefer to focus on significant things and ignore details that are currently not significant. Also programming with interfaces helps to decouple entities creating better architecture.
Interfaces (like Comparable, Iterable, Serializable etc.) is the way to describe behavior in OOP. Type classes (like Functor, Monad, Show, Read etc.) is the way to describe behavior in FP.
If you just want to map (or flatMap) over a list (or an Option) you don't need Functor. If you want to work with all mappable things you need Functor, if you want to work with all flatMappable things you need Monad etc.
Related
I'm quite new to functional programming. However, I read about the Free Monad, and I'm trying to use it in a toy project. In this project, I model the stock's portfolio domain. As suggested in many books, I defined an algebra for the PortfolioService and an algebra for the PortfolioRepository.
I want to use the Free monad in the definition of the PortfolioRepository algebra and interpreter. For now, I did not define the PortfolioService algebra in terms of the Free monad.
However, if I do so, in the PortfolioService interpreter, I cannot use the algebra of the PortfolioRepository because of different used monads. For example, I cannot use the monads Either[List[String], Portfolio], and Free[PortfolioRepoF, Portfolio] inside the same for-comprehension :(
I doubt that if I start to use the Free monad to model an algebra, all the other algebra that need to compose with it must be defined in terms of the Free monad.
Is it true?
I am using Scala and Cats 2.2.0.
99% of the time Free monad is interchangeable with Tagless final:
you can pass Free[S, *] as your Monad instance
you can .foldMap Free[S, A] using S ~> F mapping with Monad[F] into F[A]
The only difference is when do you interpret:
tagless interprets immediately, so it require you to pass around type class instances for your F, but since F is a type parameter it gives the impression that it is deferred - because it defers the moment when the type is chosen
free monad lets you create the value immediately with no dependencies on type classes, you can store them as vals in objects, there are no dependencies on type classes. The price you pay is intermediate representation that you ultimately want to discard as soon as you will be able to interpret into useful result. On the other hand it is missing tagless' ability to constrain your operation only to certain algebras (e.g. only Functor, only Applicative, etc to better control effects in dependencies).
Nowadays things moved in favor of tagless final. Free monad is used internally in IO monad implementation (Cats Effect IO, Monix Task, ZIO) and in e.g. Doobie (though from what I heard Doobie's author was thinking about rewriting it into tagless, or at least regretting not using tagless?).
If you want to learn how to use that in modelling there is a book by Gabriel Volpe - Practical FP in Scala that uses tagless final as well as my own small project that uses Cats, FS2, Tapir, tagless etc which can demonstrate some ideas.
If you intend to use Free, then well, there are some challenges:
sealed trait DomainA[A] extends Product with Serializable
object DomainA {
case class Service1(input1: X, input2: Y) extends DomainA[Z]
// ...
def service1(input1: X, input2: Y): Free[DomainA, Z] =
Free.liftF(Service1(input1, input2))
}
val interpreterA: DomainA ~> IO = ...
You use Free[DomainA, *], combine it using .map, .flatMap, etc, interpret it with interpretA.
Then you add another domain, DomainB. And the fun begins:
you cannot just combine Free[DomainA, *] with Free[DomainB, *] because they are different types, you need to align them to make that possible!
so, you have to combine all algebras into one:
type BusinessLogic[A] = EitherK[DomainA, DomainB, A]
implicit val injA: InjectK[DomainA, BusinessLogic] = ...
implicit val injB: InjectK[DomainB, BusinessLogic] = ...
your services cannot hardcode one algebra, you have to inject current algebra into a "bigger" one:
def service1[Total[_]](input1: X, input2: Y)(
implicit inject: InjectK[DomainA, Total]
): Free[Total, Z] =
Free.liftF(inject.inj(Service1(input1, input2)))
your interpreter is also more complex now:
val interpreterTotal: EitherK[DomainA, DomainB, *] ~> IO =
new (EitherK[DomainA, DomainB, *] ~> IO) {
def apply[A](fa: EitherK[DomainA, DomainB, A]) =
fa.run.fold(interpreterA, interpreterB)
}
and it gets more complex with each new added algebra (EitherK[DomainA, EitherK[DomainB, ..., *], *]).
In tagless final there is always a dependency but almost always on one type - F - and empirical evidences of many people shows that is easier to use despite being theoretically equal in power to a free monad. But it is not a scientific argument, so feel free to experiment with free monad on your own. See e.g. this Underscore article about using multiple DSLs at once.
Whether you pick one or the other you are NOT forced to use it everywhere - everything that is Free can be (should be) interpreted into a specific implementation, tagless makes you pass the specific implementation as argument so you can use either for a single component, that is interpreted on its edge.
I'm using the Reader monad in Scala as provided by the scalaz library. I'm familiar with this monad as defined in Haskell. The problem is that I cannot find the functions equivalent to return, local, and sequence (among others).
Currently I use constructs that I do not like since I'm repeating myself or making my code a bit obscure.
Regarding return, I'm currently using:
Reader{_ => someValue}
I'd rather just use a construct like unit(someValue), but I could not find anything on the internet. There are tutorials like this one that use the approach above, and which I consider not optimal.
Regarding local I also have to do something similar: instead of typing something like: local f myReader I have to unfold its definition:
Reader{env => myReader.run(f(env))
Finally, sequence is a bit closer to what I would expect (being a Haskell refugee doing Scala):
readers: List[Reader[Env, T]]
readerTs: Reader[Env, List[T]] = readers.sequenceU
My problem with this implementation is that, being relatively new to Scala, the type of sequenceU
final class TraverseOps[F[_],A] private[syntax](val self: F[A])(implicit val F: Traverse[F]) extends Ops[F[A]] {
//...
def sequenceU(implicit G: Unapply[Applicative, A]): G.M[F[G.A]]
appears like rather obscure, and seems like black magic. Ideally I would like to use a sequence operations on Monads.
Is there a better translation of these constructs to Scala available on scalaz or similar library? I'm not married to any Functional library for Scala, so any solution using other libraries will do, although I'd rather have an answer using scalaz, since I already implemented my code using it.
To make the things simpler, I fill in some types. Changing them to defs with generic types should still work.
Also I extracted the ReaderInt type, to avoid confusion with type lambdas.
return / pure / point
Scala does not have automatic typeclass resolution, so you need to provide them implicitly. For Kleisli (being a monad transformer for reader),
Kleisli[Id, ?, ?] is enough
implicit val KA = scalaz.Kleisli.kleisliIdApplicative[Int]
type ReaderInt[A] = Kleisli[Id.Id, Int, A]
val alwaysHello = KA.point("hello")
or with imported syntax:
import scalaz.syntax.applicative._
val alwaysHello = "hello".point[ReaderInt]
So as a general rule, you
1) import the applicative intance, which usually located in scalaz.std.something.somethingInstance
2) import scalaz.syntax.something._
3) then you can write x.point[F], where F is your applicative.
local
Not sure, that it answers your question, but Kleisli has a local method.
val f: String ⇒ Int = _.length
val alwaysEleven = alwaysHello local f
sequencing
The same way, you are free to choose to use syntax for or to specify type classes explicitly.
import scalaz.std.list.listInstance
val initial: List[ReaderInt[String]] = ???
val sequenced: ReaderInt[List[String]] = Traverse[List].sequence[ReaderInt, String](initial)
import scalaz.syntax.traverse._
val z = x.sequence[ReaderInt, String]
I prefer not to use sequenceU, which uses Unapply typelcass to infer the G type, because sometimes scala has troubles of figuring out the right one.
And I personally do not find it messy to put in some types myself.
It may worth to look into cats, though it does not have much yet.
I'd like to create a simple wrapper for computations. The built-in scala monads (TraversableLike) seems sufficient for me. And they have already syntax sugar. From some point of view scala collection traits are accidental monads. And there intended monads provided by the scalaz library.
What uses cases benefit from complex type classed monads of scalaz? What functionality is unfeasible for built-in monads and indicate need for scalaz?
Some clarification.
This question is not a holy war inheritance vs type classes. My question is about infrastructure that provides scalaz. Not any library with type classes approach, but this mentioned library. It slightly complicates things. But also it have bunch of utility classes that have no matches in scala collection library. Because it is a collection library, not a monadic. So the question is about the additional functionality provided by scalaz. In which cases does it matter?
First for a point about terminology: it's sometimes useful shorthand to say things like "Option is a monad", but "Option has a monad instance" or "Option is monadic" is clearer. It's potentially a little confusing to say that Scalaz provides a bunch of monads—what it provides is a Monad type class and instances of that type class for a number of types, including some of its own (e.g. \/, Task, etc.) and some from the standard library (List, Option, etc.).
So I'm going to answer a question which is similar to your question: what's the value of an explicit Monad type class over the monadic syntactic sugar provided by the standard library?
One place where having an explicit Monad representation is useful is when you want to define your own generic combinators or operations. Suppose I want to write a method addM that takes two monadic M[Int] values and adds them in the monad. It's easy to write for Option:
def addM(oa: Option[Int], ob: Option[Int]): Option[Int] = for {
a <- oa
b <- ob
} yield a + b
Or for lists:
def addM(oa: List[Int], ob: List[Int]): List[Int] = for {
a <- oa
b <- ob
} yield a + b
These two implementations obviously have a lot in common, and it'd be nice to be able to write a single generic implementation that would work in both cases—and for any other monadic type as well. This is really hard if we only have the standard library's hand-wavy monadic syntax, and really easy if we have a Monad type class.
I know what the monads are and how to use them. What I don't understand is what makes, let's say, Option a monad?
In Haskell a monad Maybe is a monad because it's instantiated from Monad class (which has at least 2 necessary functions return and bind that makes class Monad, indeed, a monad).
But in Scala we've got this:
sealed abstract class Option[+A] extends Product with Serializable { ... }
trait Product extends Any with Equals { ... }
Nothing related to a monad.
If I create my own class in Scala, will it be a monad by default? Why not?
Monad is a concept, an abstract interface if you will, that simply defines a way of composing data.
Option supports composition via flatMap, and that's pretty much everything that is needed to wear the "monad badge".
From a theoretical point of view, it should also:
support a unit operation (return, in Haskell terms) to create a monad out of a bare value, which in case of Option is the Some constructor
respect the monadic laws
but this is not strictly enforced by Scala.
Monads in scala are a much looser concept that in Haskell, and the approach is more practical.
The only thing monads are relevant for, from a language perspective, is the ability of being used in a for-comprehension.
flatMap is a basic requirement, and you can optionally provide map, withFilter and foreach.
However, there's no such thing as strict conformance to a Monad typeclass, like in Haskell.
Here's an example: let's define our own monad.
class MyMonad[A](value: A) {
def map[B](f: A => B) = new MyMonad(f(value))
def flatMap[B](f: A => MyMonad[B]) = f(value)
override def toString = value.toString
}
As you see, we're only implementing map and flatMap (well, and toString as a commodity).
Congratulations, we have a monad! Let's try it out:
scala> for {
a <- new MyMonad(2)
b <- new MyMonad(3)
} yield a + b
// res1: MyMonad[Int] = 5
Nice! We are not doing any filtering, so we don't need to implement withFilter. Also since we're yielding a value, we don't need foreach either. Basically you implement whatever you wish to support, without strict requirements. If you try to filter in a for-comprehension and you haven't implemented withFilter, you'll simply get a compile-time error.
Anything that (partially) implements, through duck-typing, the FilterMonadic trait is considered to be a monad in Scala. This is different than how monads are represented in Haskell, or the Monad typeclass in scalaz. However, in order to benefit of the for comprehension syntactic sugar in Scala, an object has to expose some of the methods defined in the FilterMonadic trait.
Also, in Scala, the equivalent of the Haskell return function is the yield keyword used for producing values out of a for comprehension. The desugaring of yield is a call to the map method of the "monad".
The way I'd put it is that there's an emerging distinction between monads as a design pattern vs. a first-class abstraction. Haskell has the latter, in the form of the Monad type class. But if you have a type that has (or can implement) the monadic operations and obeys the laws, that's a monad as well.
These days you can see monads as a design pattern in Java 8's libraries. The Optional and Stream types in Java 8 come with a static of method that corresponds to Haskell return, and a flatMap method. There is however no Monad type.
Somewhere in between you also have the "duck-typed" approach, as Ionuț G. Stan's answer calls out. C# has this as well—LINQ syntax isn't tied to a specific type, but rather it can be used with any class that implements certain methods.
Scala, per se, does not provide the notion of a monad. You can express a monad as a typeclass but Scala also doesn't provide the notion of a typeclass. But Cats does. So you can create a Monad in Scala with the necessary boiler plate, e.g. traits and implicits cleverly used, or you can use cats which provides a monad trait out of the box. As a comparison, Haskel provides monads as part of the language. Regarding your specific question, an Option can be represented as a monad because it has a flatMap method and a unit method (wrapping a value in a Some or a Future, for example).
I was exchanging emails with an acquaintance that is a big Kotlin, Clojure and Java8 fan and asked him why not Scala. He provided many reasons (Scala is too academic, too many features, not the first time I hear this and I think this is very subjective)
but his biggest pain point was as an example, that he doesn't like a language where he can't understand the implementation of basic data structures, and he gave LinkedList as an example.
I took a look at scala.collection.LinkedList and counted the things I either understand or somewhat understand.
CanBuildFrom - after some effort, I get it, type classes, not the longest suicide note
in history [1]
LinkedListLike - I can't remember where I read it, but I got convinced this is there for a good reason
But then I started to stare at these
GenericTraversableTemplate - now I'm scratching my head as well...
SeqFactory, GenericCompanion - OK, now you lost me, I start to understand his point
Can someone who understand this well please explain GenericTraversableTemplate SeqFactory and GenericCompanion in the context of LinkedList? What they are for, what impact on the end user they have (e.g. I'm sure they are there for a good reason, what is that reason?)
Are they there for a practical reason? or is it a level of abstraction that could have been simplified?
I like Scala collections because I don't have to understand the internals to be able to effectively use them. I don't mind a complex implementation if it helps me to keep my usage simpler. e.g. I don't mind paying the price of a complex library if I get the ability to write cleaner more elegant code using it in return. but it will sure be nice to better understand it.
[1] - Is the Scala 2.8 collections library a case of "the longest suicide note in history"?
I will try to describe the concepts from the point of view of a random pedestrian (I've never contributed a single line to the Scala collection library, so don't hit me too hard if I'm wrong).
Since LinkedList is now deprecated, and because Maps provide a better example, I will use TreeMap as example.
CanBuildFrom
The motivation is this: If we take a TreeMap[Int, Int] and map it with
case (x, y) => (2 * x, y * y * 0.3d)
we get TreeMap[Int, Double]. This type safety alone would already explain the necessity for
simple genericBuilder[X] constructs.
However, if we map it with
case (x, y) => x
we obtain an Iterable[Int] (more precisely: a List[Int]), this is no longer a Map, the type of the container has changed. This is where CBF's come into play:
CanBuildFrom[This, X, That]
can be seen as a kind of "type-level function" that tells us: if we map a collection of type
This with a function that returns values of type X, we can build a That. The most specific
CBF is provided at compile time, in the first case it will be something like
CanBuildFrom[TreeMap[_,_], (X,Y), TreeMap[X,Y]]
in the second case it will be something like
CanBuildFrom[TreeMap[_,_], X, Iterable[X]]
and so we always get the right type of the container. The pattern is pretty general.
Every time you have a generic function
foo[X1, ..., Xn](x1: X1, ..., xn: Xn): Y
where the result type Y depends on X1, ..., Xn, you can introduce an implicit parameter as
follows:
foo[X1, ...., Xn, Y](x1: X1, ..., xn: Xn)(implicit CanFooFrom[X1, ..., Xn, Y]): Y
and then define the type-level function X1, ..., Xn -> Y piecewise by providing multiple
implicit CanFooFrom's.
LinkedListLike
In the class definition, we see something like this:
TreeMap[A, B] extends SortedMap[A, B] with SortedMapLike[A, B, TreeMap[A, B]]
This is Scala's way to express the so-called F-bounded polymorphism.
The motivation is as follows: Suppose we have a dozen (or at least two...) implementations of the trait SortedMap[A, B]. Now we want to implement a method withoutHead, it could look
somewhat like this:
def withoutHead = this.remove(this.head)
If we move the implementation into SortedMap[A, B] itself, the best we can do is this:
def withoutHead: SortedMap[A, B] = this.remove(this.head)
But is this the most specific result type we can get? No, that's too vague.
We would like to return TreeMap[A, B] if the original map is a TreeMap, and
CrazySortedLinkedHashMap (or whatever...) if the original was a CrazySortedLinkedHashMap.
This is why we move the implementation into SortedMapLike, and give the following signature to the withoutHead method:
trait SortedMapLike[A, B, Repr <: SortedMap[A, B]] {
...
def withoutHead: Repr = this.remove(this.head)
}
now because TreeMap[A, B] extends SortedMapLike[A, B, TreeMap[A, B]], the result type of
withoutHead is TreeMap[A,B]. The same holds for CrazySortedLinkedHashMap: we get the exact type back. In Java, you would either have to return SortedMap[A, B] or override the method in each subclass (which turned out to be a maintenance nightmare for the feature-rich traits in Scala)
GenericTraversableTemplate
The type is: GenericTraversableTemplate[+A, +CC[X] <: GenTraversable[X]]
As far as i can tell, this is just a trait that provides implementations of
methods that somehow return regular collections with same container type but
possibly different content type (stuff like flatten, transpose, unzip).
Stuff like foldLeft, reduce, exists are not here because these methods care only about content type, not container type.
Stuff like flatMap is not here, because the container type can change (again, CBF's).
Why is it a separate trait, is there a fundamental reason why it exists?
I don't think so... It probably would be possible to group the godzillion of methods somewhat differently. But this is just what happens naturally: you start to implement a trait, and it turns out that it has very many methods. So instead you group loosely related methods, and put them into 10 different traits with awkward names like "GenTraversableTemplate", and them mix them all into traits/classes where you need them...
GenericCompanion
This is just an abstract class that implements some basic functionality which is common
for companion objects of most collection classes (essentially, it just implements very
simple factory methods apply(varargs) and empty).
For example there is method apply that takes varargs of some type A and returns a collection of type CC[A]:
Array(1, 2, 3, 4) // calls Array.apply[A](elems: A*) on the companion object
List(1, 2, 3, 4) // same for List
The implementation is very simple, it's something like this:
def apply[A](varargs: A*): CC[A] = {
val builder = newBuilder[A]
for (arg <- varargs) builder += arg
builder.result()
}
This is obviously the same for Arrays and Lists and TreeMaps and almost everything else, except 'constrained irregular Collections' like Bitset. So this is just common functionality in a common ancestor class of most companion objects. Nothing special about that.
SeqFactory
Similar to GenericCompanion, but this time more specifically for Sequences.
Adds some common factory methods like fill() and iterate() and tabulate() etc.
Again, nothing particularly rocket-scientific here...
Few general remarks
In general: I don't think that one should attempt to understand every single trait in this library. Rather, one should try to look at the library as a whole. As a whole, it has a very interesting architecture. And in my personal opinion, it's actually a very aesthetic piece of software, but one has to stare at it for quite a while (and try to re-implement the whole architectural pattern several times) to grasp it. On the other hand: for example CBF's are kind of "design pattern" that clearly should be eliminated in successors of this language. The whole story with the scope of implicit CBF's still seems like a total nightmare to me. But many things seemed completely inscrutable at first, and almost always, it ended with an epiphany (which is very specific for Scala: for the majority of other languages, such struggles usually end with the thought "Author of this is a complete idiot").