Structuring Information

Introduction

Programs are systems that process information. Therefore, programming languages provide ways to model the domain of a program.

This section introduces the ways you can structure information in Scala. We will base our examples on the following domain, a music sheet:

Aggregating Information With Case Classes

First, let’s focus on notes. Suppose that, in our program, we are interested in the following properties of notes: their name (A, B, C, etc.), their duration (whole, half, quarter, etc.) and their octave number.

In summary, our note model aggregates several data (name, duration and octave). We express this in Scala by using a case class definition:

case class Note(
  name: String,
  duration: String,
  octave: Int
)

This definition introduces a new type, Note. You can create values of this type by calling its constructor:

val c3 = Note("C", "Quarter", 3)

c3 is a value that aggregates the arguments passed to the Note constructor.

Then, you can retrieve the information carried by each member (name, duration and octave) by using the dot notation:

case class Note(name: String, duration: String, octave: Int)
val c3 = Note("C", "Quarter", 3)
c3.name shouldBe "C"
c3.duration shouldBe res0
c3.octave shouldBe res1

Defining Alternatives With Sealed Traits

If we look at the introductory picture, we see that musical symbols can be either notes or rests (but nothing else).

So, we want to introduce the concept of symbol, as something that can be embodied by a fixed set of alternatives: a note or rest. We can express this in Scala using a sealed trait definition:

sealed trait Symbol
case class Note(name: String, duration: String, octave: Int) extends Symbol
case class Rest(duration: String) extends Symbol

A sealed trait definition introduces a new type (here, Symbol), but no constructor for it. Constructors are defined by alternatives that extend the sealed trait:

val symbol1: Symbol = Note("C", "Quarter", 3)
val symbol2: Symbol = Rest("Whole")

Pattern Matching

Since the Symbol type has no members, we can not do anything useful when we manipulate one. We need a way to distinguish between the different cases of symbols. Pattern matching allows us to do so:

def symbolDuration(symbol: Symbol): String =
  symbol match {
    case Note(name, duration, octave) => duration
    case Rest(duration) => duration
  }

The above match expression first checks if the given Symbol is a Note, and if it is the case it extracts its fields (name, duration and octave) and evaluates the expression at the right of the arrow. Otherwise, it checks if the given Symbol is a Rest, and if it is the case it extracts its duration field, and evaluates the expression at the right of the arrow.

When we write case Rest(duration) => …, we say that Rest(…) is a constructor pattern: it matches all the values of type Rest that have been constructed with arguments matching the pattern duration.

The pattern duration is called a variable pattern. It matches any value and binds its name (here, duration) to this value.

More generally, an expression of the form

e match {
  case p1 => e1
  case p2 => e2
  …
  case pn => en
}

matches the value of the selector e with the patterns p1, …, pn in the order in which they are written.

The whole match expression is rewritten to the right-hand side of the first case where the pattern matches the selector e.

References to pattern variables are replaced by the corresponding parts in the selector.

Exhaustivity

Having defined Symbol as a sealed trait gives us the guarantee that the possible case of symbols is fixed. The compiler can leverage this knowledge to warn us if we write code that does not handle all the cases:

def unexhaustive(): Unit = {
  sealed trait Symbol
  case class Note(name: String, duration: String, octave: Int) extends Symbol
  case class Rest(duration: String) extends Symbol

  def nonExhaustiveDuration(symbol: Symbol): String =
    symbol match {
      case Rest(duration) => duration
    }
}

If we try to run the above code to see how the compiler informs us that we don’t handle all the cases in nonExhaustiveDuration.

Equals

It is worth noting that, since the purpose of case classes is to aggregate values, comparing case class instances compare their values:

case class Note(name: String, duration: String, octave: Int)
val c3 = Note("C", "Quarter", 3)
val otherC3 = Note("C", "Quarter", 3)
val f3 = Note("F", "Quarter", 3)
(c3 == otherC3) shouldBe res0
(c3 == f3) shouldBe res1

Enumerations

Our above definition of the Note type allows users to create instances with invalid names and durations:

val invalidNote = Note("not a name", "not a duration", 3)

It is generally a bad idea to work with a model that makes it possible to reach invalid states. In our case, we want to restrict the space of the possible note names and durations to a set of fixed alternatives.

In the case of note names, the alternatives are either A, B, C, D, E, F or G. We can express the fact that note names are a fixed set of alternatives by using a sealed trait, but in contrast to the previous example alternatives are not case classes because they aggregate no information:

sealed trait NoteName
case object A extends NoteName
case object B extends NoteName
case object C extends NoteName
…
case object G extends NoteName

Algebraic Data Types

Data types defined with sealed trait and case classes are called algebraic data types. An algebraic data type definition can be thought of as a set of possible values.

Algebraic data types are a powerful way to structure information.

If a concept of your program’s domain can be formulated in terms of an is relationship, you will express it with a sealed trait:

“A symbol is either a note or a rest.”

sealed trait Symbol
case class Note(…) extends Symbol
case class Rest(…) extends Symbol

On the other hand, if a concept of your program’s domain can be formulated in terms of an has relationship, you will express it with a case class:

“A note has a name, a duration and an octave number.”

case class Note(name: String, duration: String, octave: Int) extends Symbol

Exercise

Consider the following algebraic data type that models note durations. Complete the implementation of the function fractionOfWhole, which takes as parameter a duration and returns the corresponding fraction of the Whole duration.

sealed trait Duration
case object Whole extends Duration
case object Half extends Duration
case object Quarter extends Duration

def fractionOfWhole(duration: Duration): Double =
  duration match {
    case Whole => 1.0
    case Half => res0
    case Quarter => res1
  }

fractionOfWhole(Half) shouldBe 0.5
fractionOfWhole(Quarter) shouldBe 0.25