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

case Var(_) => "a variable"

case _ => throw new RuntimeException // Should not happen

}

That works, but it is not ideal. You will probably not be very happy that you were forced to add code that will never be executed (or so you think), just to make the compiler shut up.

A more lightweight alternative is to add an @unchecked annotation to the selector expression of the match. This is done as follows:

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

case Var(_) => "a variable"

}

Annotations are described in Chapter 27. In general, you can add an annotation to an expression in the same way you add a type: follow the expression with a colon and the name of the annotation (preceded by an at sign). For example, in this case you add an @unchecked annotation to the variable e, with “e: @unchecked”. The @unchecked annotation has a special meaning for pattern matching. If a match’s selector expression carries this annotation, exhaustivity checking for the patterns that follow will be suppressed.

15.6 The Option type

Scala has a standard type named Option for optional values. Such a value can be of two forms. It can be of the form Some(x) where x is the actual value. Or it can be the None object, which represents a missing value.

Optional values are produced by some of the standard operations on Scala’s collections. For instance, the get method of Scala’s Map produces Some(value) if a value corresponding to a given key has been found, or None if the given key is not defined in the Map. Here’s an example:

scala> val capitals =

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

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scala> capitals get "France"

res23: Option[java.lang.String] = Some(Paris)

scala> capitals get "North Pole" res24: Option[java.lang.String] = None

The most common way to take optional values apart is through a pattern match. For instance:

scala> def show(x: Option[String]) = x match { case Some(s) => s

case None => "?"

}

show: (x: Option[String])String

scala> show(capitals get "Japan") res25: String = Tokyo

scala> show(capitals get "France") res26: String = Paris

scala> show(capitals get "North Pole") res27: String = ?

The Option type is used frequently in Scala programs. Compare this to the dominant idiom in Java of using null to indicate no value. For example, the get method of java.util.HashMap returns either a value stored in the HashMap, or null if no value was found. This approach works for Java, but is error prone, because it is difficult in practice to keep track of which variables in a program are allowed to be null. If a variable is allowed to be null, then you must remember to check it for null every time you use it. When you forget to check, you open the possibility that a NullPointerException may result at runtime. Because such exceptions may not happen very often, it can be difficult to discover the bug during testing. For Scala, the approach would not work at all, because it is possible to store value types in hash maps, and null is not a legal element for a value type. For instance, a HashMap[Int, Int] cannot return null to signify “no element.”

By contrast, Scala encourages the use of Option to indicate an optional value. This approach to optional values has several advantages over Java’s. First, it is far more obvious to readers of code that a variable whose type is Option[String] is an optional String than a variable of type String, which may sometimes be null. But most importantly, that programming

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error described earlier of using a variable that may be null without first checking it for null becomes in Scala a type error. If a variable is of type Option[String] and you try to use it as a String, your Scala program will not compile.

15.7 Patterns everywhere

Patterns are allowed in many parts of Scala, not just in standalone match expressions. Take a look at some other places you can use patterns.

Patterns in variable definitions

Any time you define a val or a var, you can use a pattern instead of a simple identifier. For example, you can use this to take apart a tuple and assign each of its parts to its own variable, as shown in Listing 15.17:

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

Listing 15.17 · Defining multiple variables with one assignment.

This construct is quite useful when working with case classes. If you know the precise case class you are working with, then you can deconstruct it with a pattern. Here’s an example:

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)

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Case sequences as partial functions

A sequence of cases (i.e., alternatives) in curly braces can be used anywhere a function literal can be used. Essentially, a case sequence is a function literal, only more general. Instead of having a single entry point and list of parameters, a case sequence has multiple entry points, each with their own list of parameters. Each case is an entry point to the function, and the parameters are specified with the pattern. The body of each entry point is the right-hand side of the case.

Here is a simple example:

val withDefault: Option[Int] => Int = { case Some(x) => x

case None => 0

}

The body of this function has two cases. The first case matches a Some, and returns the number inside the Some. The second case matches a None, and returns a default value of zero. Here is this function in use:

scala> withDefault(Some(10)) res28: Int = 10

scala> withDefault(None) res29: Int = 0

This facility is quite useful for the actors library, described in Chapter 32. Here is some typical actors code. It passes a pattern match directly to the react method:

react {

case (name: String, actor: Actor) => { actor ! getip(name)

act()

}

case msg => {

println("Unhandled message: "+ msg) act()

}

}

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One other generalization is worth noting: a sequence of cases gives you a partial function. If you apply such a function on a value it does not support, it will generate a run-time exception. For example, here is a partial function that returns the second element of a list of integers:

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

}

When you compile this, the compiler will correctly complain that the match is not exhaustive:

<console>:17: warning: match is not exhaustive!

This function will succeed if you pass it a three-element list, but not if you pass it an empty list:

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)

If you want to check whether a partial function is defined, you must first tell the compiler that you know you are working with partial functions. The type List[Int] => Int includes all functions from lists of integers to integers, whether or not the functions are partial. The type that only includes partial functions from lists of integers to integers is written

PartialFunction[List[Int],Int]. Here is the second function again, this time written with a partial function type:

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

}

Partial functions have a method isDefinedAt, which can be used to test whether the function is defined at a particular value. In this case, the function is defined for any list that has at least two elements:

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scala> second.isDefinedAt(List(5,6,7)) res30: Boolean = true

scala> second.isDefinedAt(List()) res31: Boolean = false

The typical example of a partial function is a pattern matching function literal like the one in the previous example. In fact, such an expression gets translated by the Scala compiler to a partial function by translating the patterns twice—once for the implementation of the real function, and once to test whether the function is defined or not. For instance, the function literal { case x :: y :: _ => y } above gets translated to the following partial function value:

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

}

}

This translation takes effect whenever the declared type of a function literal is PartialFunction. If the declared type is just Function1, or is missing, the function literal is instead translated to a complete function.

In general, you should try to work with complete functions whenever possible, because using partial functions allows for runtime errors that the compiler cannot help you with. Sometimes partial functions are really helpful, though. You might be sure that an unhandled value will never be supplied. Alternatively, you might be using a framework that expects partial functions and so will always check isDefinedAt before calling the function. An example of the latter is the react example given above, where the argument is a partially defined function, defined precisely for those messages that the caller wants to handle.

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Patterns in for expressions

You can also use a pattern in a for expression, as shown in Listing 15.18. This for expression retrieves all key/value pairs from the capitals map. Each pair is matched against the pattern (country, city), which defines the two variables country and city.

scala> for ((country, city) <- capitals)

println("The capital of "+ country +" is "+ city) The capital of France is Paris

The capital of Japan is Tokyo

Listing 15.18 · A for expression with a tuple pattern.

The pair pattern shown in Listing 15.18 was special because the match against it can never fail. Indeed, capitals yields a sequence of pairs, so you can be sure that every generated pair can be matched against a pair pattern. But it is equally possible that a pattern might not match a generated value. Listing 15.19 shows an example where that is the case:

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

Listing 15.19 · Picking elements of a list that match a pattern.

As you can see from this example, generated values that do not match the pattern are discarded. For instance, the second element None in the results list does not match the pattern Some(fruit); therefore it does not show up in the output.

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15.8 A larger example

After having learned the different forms of patterns, you might be interested in seeing them applied in a larger example. The proposed task is to write an expression formatter class that displays an arithmetic expression in a twodimensional layout. Divisions such as “x / (x + 1)” should be printed vertically, by placing the numerator on top of the denominator, like this:

x

-----

x + 1

As another example, here’s the expression ((a / (b * c) + 1 / n) / 3) in two dimensional layout:

---------

3

From these examples it looks like the class (we’ll call it ExprFormatter) will have to do a fair bit of layout juggling, so it makes sense to use the layout library developed in Chapter 10. We’ll also use the Expr family of case classes you saw previously in this chapter, and place both Chapter 10’s layout library and this chapter’s expression formatter into named packages. The full code for the example will be shown in Listings 15.20 and 15.21.

A useful first step is to concentrate on horizontal layout. A structured expression like:

BinOp("+",

BinOp("*",

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

Var("z")),

Number(1))

should print (x + y) * z + 1. Note that parentheses are mandatory around x + y, but would be optional around (x + y) * z. To keep the layout as legible as possible, your goal should be to omit parentheses wherever they are redundant, while ensuring that all necessary parentheses are present.

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To know where to put parentheses, the code needs to know about the relative precedence of each operator, so it’s a good idea to tackle this first. You could express the relative precedence directly as a map literal of the following form:

Map(

"|" -> 0, "||" -> 0, "&" -> 1, "&&" -> 1, ...

)

However, this would involve some amount of pre-computation of precedences on your part. A more convenient approach is to just define groups of operators of increasing precedence and then calculate the precedence of each operator from that. Listing 15.20 shows the code.

The precedence variable is a map from operators to their precedences, which are integers starting with 0. It is calculated using a for expression with two generators. The first generator produces every index i of the opGroups array. The second generator produces every operator op in opGroups(i). For each such operator the for expression yields an association from the operator op to its index i. Hence, the relative position of an operator in the array is taken to be its precedence. Associations are written with an infix arrow, e.g., op -> i. So far you have seen associations only as part of map constructions, but they are also values in their own right. In fact, the association op -> i is nothing else but the pair (op, i).

Now that you have fixed the precedence of all binary operators except /, it makes sense to generalize this concept to also cover unary operators. The precedence of a unary operator is higher than the precedence of every binary operator. Thus we can set unaryPrecedence (shown in Listing 15.20) to the length of the opGroups array, which is one more than the precedence of the * and % operators.

The precedence of a fraction is treated differently from the other operators because fractions use vertical layout. However, it will prove convenient to assign to the division operator the special precedence value -1, so we’ll initialize fractionPrecedence to -1 (shown in Listing 15.20).

After these preparations, you are ready to write the main format method. This method takes two arguments: an expression e, of type Expr, and the precedence enclPrec of the operator directly enclosing the expression e (if there’s no enclosing operator, enclPrec should be zero). The method yields a layout element that represents a two-dimensional array of characters.

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