Partial Functions

Composition

Partial functions are often used to define a total function in parts:

sealed trait SuperType
case object A extends SuperType
case object B extends SuperType
case object C extends SuperType

val pfA: PartialFunction[SuperType, Int] = {
  case A => 5
}

val pfB: PartialFunction[SuperType, Int] = {
  case B => 10
}

val input: Seq[SuperType] = Seq(A, B, C)

input.map(pfA orElse pfB orElse {
  case _ => 15
}) // Seq(5, 10, 15)

In this usage, the partial functions are attempted in order of concatenation with the orElse method. Typically, a final partial function is provided that matches all remaining cases. Collectively, the combination of these functions acts as a total function.

This pattern is typically used to separate concerns where a function may effectively act a dispatcher for disparate code paths. This is common, for example, in the receive method of an Akka Actor.

Usage with collect

While partial function are often used as convenient syntax for total functions, by including a final wildcard match (case _), in some methods, their partiality is key. One very common example in idiomatic Scala is the collect method, defined in the Scala collections library. Here, partial functions allow the common functions of examining the elements of a collection to map and/or filter them to occur in one compact syntax.

Example 1

Assuming that we have a square root function defined as partial function:

val sqRoot:PartialFunction[Double,Double] = { case n if n > 0 => math.sqrt(n) }

We can invoke it with the collect combinator:

List(-1.1,2.2,3.3,0).collect(sqRoot)

effectively performing the same operation as:

List(-1.1,2.2,3.3,0).filter(sqRoot.isDefinedAt).map(sqRoot)

Example 2

sealed trait SuperType // `sealed` modifier allows inheritance within current build-unit only
case class A(value: Int) extends SuperType
case class B(text: String) extends SuperType
case object C extends SuperType

val input: Seq[SuperType] = Seq(A(5), B("hello"), C, A(25), B(""))

input.collect {
  case A(value) if value < 10   => value.toString
  case B(text) if text.nonEmpty => text
} // Seq("5", "hello")

There are several things to note in the example above:

• The left-hand side of each pattern match effectively selects elements to process and include in the output. Any value that doesn’t have a matching case is simply omitted.
• The right-hand side defines the case-specific processing to apply.
• Pattern matching binds variable for use in guard statements (the if clauses) and the right-hand side.

Basic syntax

Scala has a special type of function called a partial function, which extends normal functions — meaning that a PartialFunction instance can be used wherever Function1 is expected. Partial functions can be defined anonymously using case syntax also used in pattern matching:

val pf: PartialFunction[Boolean, Int] = {
  case true => 7
}

pf.isDefinedAt(true) // returns true
pf(true) // returns 7

pf.isDefinedAt(false) // returns false
pf(false) // throws scala.MatchError: false (of class java.lang.Boolean)

As seen in the example, a partial function need not be defined over the whole domain of its first parameter. A standard Function1 instance is assumed to be total, meaning that it is defined for every possible argument.

Usage as a total function

Partial functions are very common in idiomatic Scala. They are often used for their convenient case-based syntax to define total functions over traits:

sealed trait SuperType // `sealed` modifier allows inheritance within current build-unit only
case object A extends SuperType
case object B extends SuperType
case object C extends SuperType

val input: Seq[SuperType] = Seq(A, B, C)

input.map {
  case A => 5
  case _ => 10
} // Seq(5, 10, 10)

This saves the additional syntax of a match statement in a regular anonymous function. Compare:

input.map { item => 
  item match {
    case A => 5
    case _ => 10
  }
} // Seq(5, 10, 10)

It is also frequently used to perform a parameter decomposition using pattern matching, when a tuple or a case class is passed to a function:

val input = Seq("A" -> 1, "B" -> 2, "C" -> 3)

input.map { case (a, i) =>
   a + i.toString
} // Seq("A1", "B2", "C3")

Usage to extract tuples in a map function

These three map functions are equivalent, so use the variation that your team finds most readable.

val numberNames = Map(1 -> "One", 2 -> "Two", 3 -> "Three")

// 1. No extraction
numberNames.map(it => s"${it._1} is written ${it._2}" )

// 2. Extraction within a normal function
numberNames.map(it => {
    val (number, name) = it
    s"$number is written $name"
})

// 3. Extraction via a partial function (note the brackets in the parentheses)
numberNames.map({ case (number, name) => s"$number is written $name" })

The partial function must match all input: any case which doesn’t match will throw an exception at runtime.