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15 Case Classes and Pattern Matching

Sample run of chapter's interpreter examples

• 15.1 A simple example
• 15.2 Kinds of patterns
• 15.3 Pattern guards
• 15.4 Pattern overlaps
• 15.5 Sealed classes
• 15.6 The Option type
• 15.7 Patterns everywhere
• 15.8 A larger example
• 15.9 Conclusion

15.1 A simple example

  abstract class Expr
  case class Var(name: String) extends Expr
  case class Number(num: Double) extends Expr
  case class UnOp(operator: String, arg: Expr) extends Expr
  case class BinOp(operator: String, 
      left: Expr, right: Expr) extends Expr


  scala> val v = Var("x")
  v: Var = Var(x)


  scala> val op = BinOp("+", Number(1), v)
  op: BinOp = BinOp(+,Number(1.0),Var(x))


  scala> v.name
  res0: String = x

  scala> op.left
  res1: Expr = Number(1.0)


  scala> println(op)
  BinOp(+,Number(1.0),Var(x))

  scala> op.right == Var("x")
  res3: Boolean = true


  UnOp("-", UnOp("-", e))  => e   // Double negation
  BinOp("+", e, Number(0)) => e   // Adding zero
  BinOp("*", e, Number(1)) => e   // Multiplying by one


  scala> simplifyTop(UnOp("-", UnOp("-", Var("x"))))
  res4: Expr = Var(x)


  def simplifyTop(expr: Expr): Expr = expr match {
    case UnOp("-", UnOp("-", e))  => e   // Double negation
    case BinOp("+", e, Number(0)) => e   // Adding zero
    case BinOp("*", e, Number(1)) => e   // Multiplying by one
    case _ => expr
  }


  selector match { alternatives }


  switch (selector) { alternatives }


  UnOp("-", UnOp("-", e))


// In file pattern-matching/Misc.scala

  expr match {
    case BinOp(op, left, right) =>
      println(expr +" is a binary operation")
    case _ =>
  }


  

15.2 Kinds of patterns

// In file pattern-matching/Misc.scala

  expr match {
    case BinOp(op, left, right) =>
      println(expr +"is a binary operation")
    case _ =>
  }


// In file pattern-matching/Misc.scala

  expr match {
    case BinOp(_, _, _) => println(expr +"is a binary operation")
    case _ => println("It's something else")
  }


// In file pattern-matching/Misc.scala

  def describe(x: Any) = x match {
    case 5 => "five"
    case true => "truth"
    case "hello" => "hi!"
    case Nil => "the empty list"
    case _ => "something else"
  }


  scala> describe(5)
  res5: java.lang.String = five

  scala> describe(true)
  res6: java.lang.String = truth

  scala> describe("hello")
  res7: java.lang.String = hi!

  scala> describe(Nil)
  res8: java.lang.String = the empty list

  scala> describe(List(1,2,3))
  res9: java.lang.String = something else


// In file pattern-matching/Misc.scala

  expr match {
    case 0 => "zero"
    case somethingElse => "not zero: "+ somethingElse
  }


  scala> import Math.{E, Pi}
  import Math.{E, Pi}

  scala> E match {
       |   case Pi => "strange math? Pi = "+ Pi
       |   case _ => "OK"
       | }
  res10: java.lang.String = OK


  scala> val pi = Math.Pi
  pi: Double = 3.141592653589793

  scala> E match {
       |   case pi => "strange math? Pi = "+ pi
       | }
  res11: java.lang.String = strange math? Pi = 2.7182818...


  scala> E match {
       |   case pi => "strange math? Pi = "+ pi
       |   case _ => "OK"  
       | }
  <console>:9: error: unreachable code
           case _ => "OK"  
                     ^


  scala> E match {
       |   case `pi` => "strange math? Pi = "+ pi
       |   case _ => "OK"
       | }
  res13: java.lang.String = OK


// In file pattern-matching/Misc.scala

  expr match {
    case BinOp("+", e, Number(0)) => println("a deep match")
    case _ =>
  }


// In file pattern-matching/Misc.scala

  expr match {
    case List(0, _, _) => println("found it")
    case _ =>
  }


// In file pattern-matching/Misc.scala

  expr match {
    case List(0, _*) => println("found it")
    case _ =>
  }


  def tupleDemo(expr: Any) =
    expr match {
      case (a, b, c)  =>  println("matched "+ a + b + c)
      case _ =>
    }


  scala> tupleDemo(("a ", 3, "-tuple"))
  matched a 3-tuple


  def generalSize(x: Any) = x match {
    case s: String => s.length
    case m: Map[_, _] => m.size
    case _ => -1
  }


  scala> generalSize("abc")
  res14: Int = 3

  scala> generalSize(Map(1 -> 'a', 2 -> 'b'))
  res15: Int = 2

  scala> generalSize(Math.Pi)
  res16: Int = -1


// In file pattern-matching/Misc.scala

  expr.isInstanceOf[String]


// In file pattern-matching/Misc.scala

  expr.asInstanceOf[String]


  if (x.isInstanceOf[String]) {
    val s = x.asInstanceOf[String]
    s.length
  } else ...


  scala> def isIntIntMap(x: Any) = x match {
       |   case m: Map[Int, Int] => true
       |   case _ => false
       | }
  warning: there were unchecked warnings; re-run with 
     -unchecked for details
  isIntIntMap: (Any)Boolean


  scala> :quit
  $ scala -unchecked
  Welcome to Scala version 2.7.2
  (Java HotSpot(TM) Client VM, Java 1.5.0_13).
  Type in expressions to have them evaluated.
  Type :help for more information.

scala>  def isIntIntMap(x: Any) = x match {
     |   case m: Map[Int, Int] => true
     |   case _ => false
     | }
  <console>:5: warning: non variable type-argument Int in
  type pattern is unchecked since it is eliminated by erasure
           case m: Map[Int, Int] => true
                   ^


  scala> isIntIntMap(Map(1 -> 1))
  res17: Boolean = true

  scala> isIntIntMap(Map("abc" -> "abc"))
  res18: Boolean = true


  scala> def isStringArray(x: Any) = x match {
       |   case a: Array[String] => "yes"
       |   case _ => "no"
       | }
  isStringArray: (Any)java.lang.String

  scala> val as = Array("abc")
  as: Array[java.lang.String] = Array(abc)

  scala> isStringArray(as)
  res19: java.lang.String = yes

  scala> val ai = Array(1, 2, 3)
  ai: Array[Int] = Array(1, 2, 3)

  scala> isStringArray(ai)
  res20: java.lang.String = no


// In file pattern-matching/Misc.scala

  expr match {
    case UnOp("abs", e @ UnOp("abs", _)) => e
    case _ =>
  }


  

15.3 Pattern guards

  BinOp("+", Var("x"), Var("x"))


  BinOp("*", Var("x"), Number(2))


  scala> def simplifyAdd(e: Expr) = e match {
       |   case BinOp("+", x, x) => BinOp("*", x, Number(2))
       |   case _ => e
       | }
  <console>:10: error: x is already defined as value x
           case BinOp("+", x, x) => BinOp("*", x, Number(2))
                              ^


  scala> def simplifyAdd(e: Expr) = e match {
       |   case BinOp("+", x, y) if x == y =>
       |     BinOp("*", x, Number(2))
       |   case _ => e
       | }
  simplifyAdd: (Expr)Expr


  // match only positive integers
  case n: Int if 0 < n => ...  

  // match only strings starting with the letter `a'
  case s: String if s(0) == 'a' => ... 


  

15.4 Pattern overlaps

  def simplifyAll(expr: Expr): Expr = expr match {
    case UnOp("-", UnOp("-", e)) =>
      simplifyAll(e)   // `-' is its own inverse
    case BinOp("+", e, Number(0)) =>
      simplifyAll(e)   // `0' is a neutral element for `+'
    case BinOp("*", e, Number(1)) =>
      simplifyAll(e)   // `1' is a neutral element for `*'
    case UnOp(op, e) => 
      UnOp(op, simplifyAll(e))
    case BinOp(op, l, r) =>
      BinOp(op, simplifyAll(l), simplifyAll(r))
    case _ => expr
  }


  scala> def simplifyBad(expr: Expr): Expr = expr match {
       |   case UnOp(op, e) => UnOp(op, simplifyBad(e))
       |   case UnOp("-", UnOp("-", e)) => e
       | }
  <console>:17: error: unreachable code
           case UnOp("-", UnOp("-", e)) => e
                                           ^


  

15.5 Sealed classes

// In file pattern-matching/Misc.scala

  sealed abstract class Expr
  case class Var(name: String) extends Expr
  case class Number(num: Double) extends Expr
  case class UnOp(operator: String, arg: Expr) extends Expr
  case class BinOp(operator: String, 
      left: Expr, right: Expr) extends Expr


  def describe(e: Expr): String = e match {
    case Number(_) => "a number"
    case Var(_)    => "a variable"
  }


  warning: match is not exhaustive!
  missing combination           UnOp
  missing combination          BinOp


// In file pattern-matching/Misc.scala

  def describe(e: Expr): String = e match {
    case Number(_) => "a number"
    case Var(_) => "a variable"
    case _ => throw new RuntimeException // Should not happen
  }


// In file pattern-matching/Misc.scala

  def describe(e: Expr): String = (e: @unchecked) match {
    case Number(_) => "a number"
    case Var(_)    => "a variable"
  }


  

15.6 The Option type

  scala> val capitals = 
       |   Map("France" -> "Paris", "Japan" -> "Tokyo")
  capitals: 
    scala.collection.immutable.Map[java.lang.String,
    java.lang.String] = Map(France -> Paris, Japan -> Tokyo)

  scala> capitals get "France"
  res21: Option[java.lang.String] = Some(Paris)

  scala> capitals get "North Pole"
  res22: Option[java.lang.String] = None


  scala> def show(x: Option[String]) = x match {
       |   case Some(s) => s
       |   case None => "?"
       | }
  show: (Option[String])String

  scala> show(capitals get "Japan")
  res23: String = Tokyo

  scala> show(capitals get "France")
  res24: String = Paris

  scala> show(capitals get "North Pole")
  res25: String = ?


  

15.7 Patterns everywhere

  scala> val myTuple = (123, "abc")
  myTuple: (Int, java.lang.String) = (123,abc)

  scala> val (number, string) = myTuple
  number: Int = 123
  string: java.lang.String = abc


  scala> val exp = new BinOp("*", Number(5), Number(1))
  exp: BinOp = BinOp(*,Number(5.0),Number(1.0))

  scala> val BinOp(op, left, right) = exp
  op: String = *
  left: Expr = Number(5.0)
  right: Expr = Number(1.0)


  val withDefault: Option[Int] => Int = {
    case Some(x) => x
    case None => 0
  }


  scala> withDefault(Some(10))
  res25: Int = 10

  scala> withDefault(None)
  res26: Int = 0


  react {
    case (name: String, actor: Actor) => {
      actor ! getip(name)
      act()
    }
    case msg => {
      println("Unhandled message: "+ msg)
      act()
    }
  }


  val second: List[Int] => Int = {
    case x :: y :: _ => y
  }


  <console>:17: warning: match is not exhaustive!
  missing combination            Nil


  scala> second(List(5,6,7))
  res24: Int = 6

  scala> second(List())
  scala.MatchError: List()
  	at $anonfun$1.apply(<console>:17)
  	at $anonfun$1.apply(<console>:17)


  val second: PartialFunction[List[Int],Int] = {
    case x :: y :: _ => y
  }


  scala> second.isDefinedAt(List(5,6,7))
  res27: Boolean = true

  scala> second.isDefinedAt(List())
  res28: Boolean = false


  new PartialFunction[List[Int], Int] {
    def apply(xs: List[Int]) = xs match {
      case x :: y :: _ => y 
    }
    def isDefinedAt(xs: List[Int]) = xs match {
      case x :: y :: _ => true
      case _ => false
    }
  }


  scala> for ((country, city) <- capitals)
       |   println("The capital of "+ country +" is "+ city)
  The capital of France is Paris
  The capital of Japan is Tokyo


  scala> val results = List(Some("apple"), None,
       |     Some("orange"))
  results: List[Option[java.lang.String]] = List(Some(apple), 
      None, Some(orange))

  scala> for (Some(fruit) <- results) println(fruit)
  apple
  orange


  

15.8 A larger example

  BinOp("+", 
        BinOp("*", 
              BinOp("+", Var("x"), Var("y")), 
              Var("z")), 
        Number(1))


  Map(
    "|" -> 0, "||" -> 0,
    "&" -> 1, "&&" -> 1, ...
  )


// In file pattern-matching/ExprFormatter.scala

  package org.stairwaybook.expr
  import layout.Element.elem

  sealed abstract class Expr
  case class Var(name: String) extends Expr
  case class Number(num: Double) extends Expr
  case class UnOp(operator: String, arg: Expr) extends Expr
  case class BinOp(operator: String, 
      left: Expr, right: Expr) extends Expr

  class ExprFormatter {

    // Contains operators in groups of increasing precedence
    private val opGroups =
      Array(
        Set("|", "||"),
        Set("&", "&&"),
        Set("^"),
        Set("==", "!="),
        Set("<", "<=", ">", ">="),
        Set("+", "-"),
        Set("*", "%")
      )

    // A mapping from operators to their precedence
    private val precedence = {
      val assocs =
        for {
          i <- 0 until opGroups.length
          op <- opGroups(i)
        } yield op -> i
      Map() ++ assocs
    }

    private val unaryPrecedence = opGroups.length
    private val fractionPrecedence = -1

    // continued in Listing 15.21...


// In file pattern-matching/ExprFormatter.scala

  // ...continued from Listing 15.20

  private def format(e: Expr, enclPrec: Int): Element =

    e match {

      case Var(name) => 
        elem(name)

      case Number(num) => 
        def stripDot(s: String) = 
          if (s endsWith ".0") s.substring(0, s.length - 2)
          else s
        elem(stripDot(num.toString))

      case UnOp(op, arg) => 
        elem(op) beside format(arg, unaryPrecedence)

      case BinOp("/", left, right) => 
        val top = format(left, fractionPrecedence)
        val bot = format(right, fractionPrecedence)
        val line = elem('-', top.width max bot.width, 1)
        val frac = top above line above bot
        if (enclPrec != fractionPrecedence) frac
        else elem(" ") beside frac beside elem(" ")

      case BinOp(op, left, right) => 
        val opPrec = precedence(op)
        val l = format(left, opPrec) 
        val r = format(right, opPrec + 1)
        val oper = l beside elem(" "+ op +" ") beside r 
        if (enclPrec <= opPrec) oper
        else elem("(") beside oper beside elem(")")
    }

    def format(e: Expr): Element = format(e, 0)
  }


  case Var(name) => 
    elem(name)


      case Number(num) => 
        def stripDot(s: String) = 
          if (s endsWith ".0") s.substring(0, s.length - 2)
          else s
        elem(stripDot(num.toString))


      case UnOp(op, arg) => 
        elem(op) beside format(arg, unaryPrecedence)


      case BinOp("/", left, right) => 
        val top = format(left, fractionPrecedence)
        val bot = format(right, fractionPrecedence)
        val line = elem('-', top.width max bot.width, 1)
        val frac = top above line above bot
        if (enclPrec != fractionPrecedence) frac
        else elem(" ") beside frac beside elem(" ")


      case BinOp(op, left, right) => 
        val opPrec = precedence(op)
        val l = format(left, opPrec) 
        val r = format(right, opPrec + 1)
        val oper = l beside elem(" "+ op +" ") beside r 
        if (enclPrec <= opPrec) oper
        else elem("(") beside oper beside elem(")")


      case BinOp("/", left, right) => ...


  BinOp("-", Var("a"), BinOp("-", Var("b"), Var("c")))


// In file pattern-matching/Test.scala

  import org.stairwaybook.expr._

  object Express extends Application {

    val f = new ExprFormatter

    val e1 = BinOp("*", BinOp("/", Number(1), Number(2)), 
                        BinOp("+", Var("x"), Number(1)))
    val e2 = BinOp("+", BinOp("/", Var("x"), Number(2)), 
                        BinOp("/", Number(1.5), Var("x")))
    val e3 = BinOp("/", e1, e2)

    def show(e: Expr) = println(f.format(e)+ "\n\n")

    for (val e <- Array(e1, e2, e3)) show(e)
  }


  scala Express


  

15.9 Conclusion