Case Classes

Scala supports the notion of case classes. Case classes are regular classes which export their constructor parameters and which provide a recursive decomposition mechanism via pattern matching.

Here is an example for a class hierarchy which consists of an abstract super class Term and three concrete case classes Var, Fun, and App.

abstract class Term
case class Var(name: String) extends Term
case class Fun(arg: String, body: Term) extends Term
case class App(f: Term, v: Term) extends Term

This class hierarchy can be used to represent terms of the untyped lambda calculus. To facilitate the construction of case class instances, Scala does not require that the new primitive is used. One can simply use the class name as a function.

Here is an example:

Fun("x", Fun("y", App(Var("x"), Var("y"))))

The constructor parameters of case classes are treated as public values and can be accessed directly.

val x = Var("x")
println(x.name)

For every case class the Scala compiler generates an equals method which implements structural equality and a toString method. For instance:

val x1 = Var("x")
val x2 = Var("x")
val y1 = Var("y")
println("" + x1 + " == " + x2 + " => " + (x1 == x2))
println("" + x1 + " == " + y1 + " => " + (x1 == y1))

will print

Var(x) == Var(x) => true
Var(x) == Var(y) => false

It makes only sense to define case classes if pattern matching is used to decompose data structures. The following object defines a pretty printer function for our lambda calculus representation:

object TermTest extends scala.App {
  def printTerm(term: Term) {
    term match {
      case Var(n) =>
        print(n)
      case Fun(x, b) =>
        print("^" + x + ".")
        printTerm(b)
      case App(f, v) =>
        print("(")
        printTerm(f)
        print(" ")
        printTerm(v)
        print(")")
    }
  }
  def isIdentityFun(term: Term): Boolean = term match {
    case Fun(x, Var(y)) if x == y => true
    case _ => false
  }
  val id = Fun("x", Var("x"))
  val t = Fun("x", Fun("y", App(Var("x"), Var("y"))))
  printTerm(t)
  println
  println(isIdentityFun(id))
  println(isIdentityFun(t))
}

In our example, the function printTerm is expressed as a pattern matching statement starting with the match keyword and consisting of sequences of case Pattern => Body clauses. The program above also defines a function isIdentityFun which checks if a given term corresponds to a simple identity function. This example uses deep patterns and guards. After matching a pattern with a given value, the guard (defined after the keyword if) is evaluated. If it returns true, the match succeeds; otherwise, it fails and the next pattern will be tried.

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