Scalaz – Or: How I learned to stop worrying and love Monads

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Scalaz – Or: How I learned to stop worrying and love Monads

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Scalaz

Or: How I learned to stop worrying and love Monads

Noel Markham 

libraryDependencies += "org.scalaz" %% "scalaz-core" % "7.0.6"
                    
import scalaz._
import Scalaz._

That's it.

Useful methods

Using the "pimp my library" approach, many types have extra methods available:

.option on boolean types: 

scala> val boolT = 6 < 10
boolT: Boolean = true

scala> val boolF = 6 > 10
boolF: Boolean = false

scala> boolT.option("corrie")
res0: Option[String] = Some(corrie)

scala> boolF.option("emmerdale")
res1: Option[String] = None

Easier to read (in my opinion) than: 

scala> if(boolT) Some("corrie") else None
res2: Option[String] = Some(corrie)

Useful methods

.parseXXX on String types: 

scala> "6".parseInt
res3: scalaz.Validation[NumberFormatException,Int] = Success(6)

scala> "corrie".parseBoolean
res4: scalaz.Validation[IllegalArgumentException,Boolean] = 
      Failure(java.lang.IllegalArgumentException: For input string: "corrie")

(scalaz.Validation is a bit like Either)

Useful methods

The return of the ternary operator: 

scala> boolT ? "corrie" | "emmerdale"
res5: String = corrie

(Note the pipe separator rather than colon)

.allPairs on List types:

scala> List(1, 2, 3, 4).allPairs
res6: List[(Int, Int)] = List((1,2), (2,3), (3,4), (1,3), (2,4), (1,4))

.some on everything:

scala> val corrie = "corrie".some
corrie: Option[String] = Some(corrie)
                    
scala> case class Money(amount: Int, currency: String)
defined class Money

scala> Money(3, "GBP").some
res3: Option[Money] = Some(Money(3,GBP))

Useful methods

.fold on Option types: 

scala> corrie.fold(-1)(str => str.length)
res14: Int = 6

Also called a catamorphism.

The first parameter list is for the None case.

The second is a function for the type in the Some case.

Both parameter lists return the same type.

This is total.

No need for pattern matching. See this blog post for more.

Useful methods

There are plenty more.

Have a poke around in the source, or in IntelliJ:

Typeclasses

A typeclass allows ad-hoc polymorphism.

Think of it as adding your own interface to someone else's class.

Scalaz provides plenty of useful type classes...

... and instances for them.

Typeclasses: A Simple Example

First, a trait for defining order:

trait Ord[T] {
  def compare(a: T, b: T): Boolean
}

Next, an Ord instance for a specific type:

object intOrd extends Ord[Int] {
  def compare(a: Int, b: Int): Boolean = a <= b
}

Now this instance can be used when necessary:

def sort[T](xs: List[T])(ord: Ord[T]): List[T] = ...
                    
scala> sort(List(3, 2, 1))(intOrd)
res5: List[Int] = List(1, 2, 3)

Typeclasses: A Simple Example

By making the instance implicit, Ord can be passed automatically:

implicit object intOrd extends Ord[Int] ... // as before

def sort[T](xs: List[T])(implicit ord: Ord[T]): List[T] = ... // as before

As long as the implicit is in scope, the Ord instance is propagated automatically:

scala> sort[Int](List(4, 3, 6, 1, 7))
res4: List(1, 3, 4, 6, 7)

If there is no implicit in scope at compile time, then it won't even compile:

scala> sort[String](List("z", "y", "x", "w")
<console>:28: error: could not find implicit value for parameter ord: Ord[String]

(This example lifted from Martin Odersky's paper: Type Classes as Objects and Implicits)

Typeclasses

If this is new/daunting/confusing, take a look at Java's Comparator interface and its uses.

Typeclasses

Scalaz defines many type classes, including:

  • Equal
  • Order
  • Functor
  • Monoid
  • Monad
  • ...

Typeclasses

Equal
scala> "hello" === "world"
res3: Boolean = false
                    
scala> Some("corrie") === "corrie"
                    
<console>:14: error:
 could not find implicit value for parameter F0: scalaz.Equal[java.io.Serializable]

It doesn't even compile

Type safety FTW!

Why is the compiler searching for Equal[Serializable]?

Typeclasses

Functor

A Functor is something that can be mapped:

def addSix[F[_]](toAdd: F[Int])(implicit mapper: Functor[F]): F[Int] = {
  mapper.map(toAdd)(_ + 6)
}
                    
scala> addSix(10.some)
res0: Option[Int] = Some(16)

scala> addSix(List(10))
res1: List[Int] = List(16)
                    
scala> addSix(List(10, 11, 12, 13))
res2: List[Int] = List(16, 17, 18, 19)

Typeclasses

Monad

The Monad typeclass definition in Scalaz is effectively:

trait Monad[F] { self =>
  def point[A](a: => A): F[A]

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

  def map[A,B](fa: F[A])(f: A => B) = bind(fa)(a => point(f(a)))
}

If you have map and flatMap, you can use the for comprehension.

Typeclasses

Monad

My experience with monads:

  • There are plenty of silly analogies on the Internet.
  • The name of for comprehensions is confusing.
  • The List monad is quite a confusing place to start.
  • If you can define your API to be functions A => M[B], most other things slot into place easily.
  • Abstraction over monad types is the killer feature.

Typeclasses

Monoid

The Monoid typeclass definition in Scalaz is effectively:

trait Monoid[F] {
  def zero: F

  def append(f1: F, f2: => F): F
  def |+|(f1: F, f2: => F): F = append(f1, f2)
}

A Monoid is a structure with an identity element and an associative binary operation

Typeclasses

Monoid

Associative:

a + (b + c)

is the same as

(a + b) + c

Addition, multiplication and string concatenation, amongst others, are all associative binary operations

Typeclasses

Monoid

Identity element:

When an element is used with the identity element in an associative binary operation, the operation returns the original element unchanged.

For addition, this is zero:

6 + 0 === 6

For multiplication, this is one:

6 * 1 === 6

For string concatenation, this is an empty string:

"corrie".concat("") === "corrie"

Typeclasses

Monoid

What do you think the identity operation is for the binary associative operation Integer.min?

Integer.min(a, Integer.MAX_VALUE) === a

Typeclasses

Monoid

Types that have a Monoid typeclass can use the |+| operator:

scala> 1 |+| 2 |+| 3
res6: Int = 6

scala> "coronation" |+| "street"
res3: String = coronationstreet

Typeclasses

Monoid

What do you think this returns?

scala> val m1 = Map(1 -> List("A", "B", "C"), 2 -> List("AA", "BB"))
m1: scala.collection.immutable.Map[Int,List[String]] = Map(1 -> List(A, B...

scala> val m2 = Map(1 -> List("Z"), 3 -> List("YYY"))
m2: scala.collection.immutable.Map[Int,List[String]] = Map(1 -> List(Z)...

scala> m1 |+| m2
                    
res11: scala.collection.immutable.Map[Int,List[String]] =
           Map(1 -> List(A, B, C, Z), 3 -> List(YYY), 2 -> List(AA, BB))

Typeclasses

Monoid
Exercise!

Define a function, collapseList, which takes a list of elements whose type has a monoid, and returns the elements appended.

For example:

scala> collapseList(List(1, 2, 3, 4, 5))
res12: Int = 15

scala> collapseList(List("a", "bb", "ccc", "dddd"))
res13: String = abbcccdddd

Typeclasses

Monoid

If a class of type M has a monoid, then a class of type Option[M] also has a monoid

scala> 1 |+| 2 |+| 3
res4: Int = 6

scala> 1.some |+| 2.some |+| 3.some
res5: Option[Int] = Some(6)
Another Exercise!

Given a monoid M, define the monoid Future[M].

For example:

scala> val futureSum = Future(1) |+| Future(2) |+| Future(3)
futureSum: scala.concurrent.Future[Int] = scala.concurrent.impl.Promise...

scala> Await.result(futureSum, 100.milliseconds)
res6: Int = 6

Thanks!

That's all for now
More for next time?
  • More typeclasses
  • Monad transformers
  • Reader monad

Useful resources

GitHub

Learning Scalaz

YouTube: Scalaz for the Rest of Us

Learn You a Haskell for Great Good! Book