Go to comments.
Functional abstractions like Monads are often presented in the contexts of typeclasses, with attendent libraries and syntax to learn.
I think typeclasses are fantastic. But I also think that this creates an additional hurdle. So I’d like to focus on abstractions as design patterns. We want to solve an issue; we have some goal in mind which we don’t know how to reach yet, but the pattern gives us some relatively easy-to-assemble but not immediately straightforward methods to reach that goal.
With that in mind, today I’d like to cover Monads, with a glance at Applicatives as well (later, I’ll cover the similarities and differences between them). In the next post, I’ll present Comonads as a similar design pattern.
So to be clear:
Goal: To be able to compose multiple items with the same added functionality Pattern: Implement flatMap, map, and unit methods.
(You may notice that I’m taking a Scala approach here instead of the previous Haskell-based posts. First, if you’re learning Haskell, you have probably already been convinced of the use of abstractions such as Monads. Second, I’m working as a Scala dev now, so this is my life at the moment, for good or for ill.)
The Reader Monad
To start, let’s take the Reader monad. Reader[R,A] is dependency injection - give a value of type R, and use it to calculate some A. The following example doesn’t use any typeclass magic or anything, or actually any libraries at all; just the basic few functions required by a Monad so that we can compose steps.
class Reader[R,A](runReader: R => A) {
// To create some syntactic sugar for using Reader instances && properly encapsulate
// `runReader` above
def apply(r: R): A = runReader(r)
// To change the value of a Reader without changing how it uses its dependency R
def map[B](f: A => B): Reader[R,B] = Reader((r: R) => f(runReader(r)))
// To change the value of a Reader in a way that uses its dependency R
def flatMap[B](f: A => Reader[R,B]): Reader[R,B] = Reader((r: R) => f(runReader(r))(r))
}
object Reader {
// More syntactic sugar to not have to type `new` all the time
def apply[R,A](f: R => A): Reader[R,A] = new Reader(f)
// Take a value which doesn't use a dependency R and let it be treated as a Reader
// which ignores the input
def unit[R,A](a: A): Reader[R,A] = Reader((_r: R) => a)
// Technically part of a `Traversable` pattern, but I leave it here to illustrate
// something `Monad`s can do that `Applicative`s could not
def sequence[R,A](values: Seq[Reader[R,A]]): Reader[R, Seq[A]] =
values.foldLeft(Reader.unit[R, Seq[A]](Seq.empty[A])) { case (acc, next) =>
acc.flatMap( currentList => next.map(currentList :+ _))
}
}And with that, let’s create some sort of config which can be passed in as a dependency:
case class Config(name: Option[String], exclamations: Int)Now that we have the setup, let’s create some config-dependent values:
val greet: Reader[Config, String] = Reader(cfg => "hello " + cfg.name.getOrElse("world"))
val exclaim: Reader[Config, String] = Reader(cfg => "!" * cfg.exclamations)We have two different ways to combine these before having to pass in any configuration - we can stack our Reader legos together to get more Readers. The first way uses the fact that we implemented flatMap and map to use Scala’s for syntax:
val fored: Reader[Config, String] = for {
greeting <- greet
exclamation <- exclaim
} yield (greeting + exclamation)And the second way uses the sequence function we implemented to be able to take an entire sequence of config-dependent values (perhaps determined dynamically at runtime) and wrap them into a single config-dependent value:
val sequenced: Reader[Config, String] =
Reader.sequence(List(greet, exclaim)).map(_.mkString)Now let’s run all three versions with configuration added:
@ sequenced(Config(Some("Scala"), 3))
res36: String = "hello Scala!!!"
@ fored(Config(Some("FP"), 5))
res37: String = "hello FP!!!!!"
@ lifted(Config(None, 10))
res47: String = "hello world!!!!!!!!!!"The State Monad
The Reader monad allows us to read in dependencies, but not to alter them. It is essentially a wrapper around a function R => A. If we want to update the value passed in, we’ll have to make sure that we output the updated version. This would give us a function such as: S => (A, S). We can reuse most of the above code:
class State[S,A](runState: S => (A, S)) {
def apply(s: S): (A, S) = runState(s)
def map[B](f: A => B): State[S,B] =
State((s1: S) => {
val (a, s2) = runState(s1)
(f(a), s2)
})
def flatMap[B](f: A => State[S,B]): State[S,B] =
State((s1: S) => {
val (a, s2) = runState(s1)
f(a)(s2)
})
// Helper function for dealing with States
def modify(f: S => S): State[S, A] =
State( s1 => {
val (a, s2) = runState(s1)
(a, f(s2))
})
}
object State {
def apply[S,A](f: S => (A, S)): State[S,A] = new State(f)
def unit[S,A](a: A): State[S,A] = State((s: S) => (a, s))
def sequence[S,A](values: Seq[State[S,A]]): State[S, Seq[A]] =
values.foldLeft(State.unit[S, Seq[A]](Seq.empty[A])) { case (acc, next) =>
acc.flatMap( currentList => next.map(currentList :+ _))
}
// Readers are just States which pass their arguments through unchanged
def fromReader[R,A](reader: Reader[R,A]): State[R, A] =
State(r => (reader(r), r))
// Helper functions for dealing with States
def get[S]: State[S, S] = State( s => (s, s))
def put[S](newS: S): State[S, Unit] = State( _s => ((), newS))
}It’s no fun having State to modify if we don’t modify it, so let’s add some functions to do so:
val langs: List[String] = List("Scala", "Haskell", "Purescript")
def rotateLangs(cfg: Config): Config =
cfg.copy(name = cfg.name.flatMap(currLang => langs lift (langs.indexOf(currLang) + 1) % langs.length))
def toneItUp(cfg: Config): Config = cfg.copy(exclamations = cfg.exclamations + 1)We’ll reuse our Readers and have them modify the state while they read it:
val sGreet = State.fromReader(greet).modify(rotateLangs)
val sExclaim = State.fromReader(exclaim).modify(toneItUp)Running it once gives us the same results as before, except it also returns an updated version of our Config:
val once = for {
greeting <- sGreet
exclamation <- sExclaim
} yield (greeting + exclamation)
@ once(Config(None, 5))
res33: (String, Config) = ("hello world!!!!!", Config(None, 6))But we can also try running it multiple times in succession:
val thrice = State.sequence(List(sGreet, sExclaim, sGreet, sExclaim, sGreet, sExclaim))
.map(_.mkString)
@ thrice(Config(Some("Scala"), 1))
res47: (String, Config) = ("hello Scala!hello Haskell!!hello Purescript!!!", Config(Some("Scala"), 4))Return to post.
