Case classes can be seen as plain and immutable data-holding objects that should exclusively depend on their constructor arguments.

This functional concept allows us to

• use a compact initialization syntax (Node(1, Leaf(2), None)))
• decompose them using pattern matching
• have equality comparisons implicitly defined

In combination with inheritance, case classes are used to mimic algebraic datatypes.

If an object performs stateful computations on the inside or exhibits other kinds of complex behaviour, it should be an ordinary class.

Types of Implicits

Implicits in Scala refers to either a value that can be passed "automatically", so to speak, or a conversion from one type to another that is made automatically.

Implicit Conversion

Speaking very briefly about the latter type, if one calls a method m on an object o of a class C, and that class does not support method m, then Scala will look for an implicit conversion from C to something that does support m. A simple example would be the method map on String:

"abc".map(_.toInt)

String does not support the method map, but StringOps does, and there's an implicit conversion from String to StringOps available (see implicit def augmentString on Predef).

Implicit Parameters

The other kind of implicit is the implicit parameter. These are passed to method calls like any other parameter, but the compiler tries to fill them in automatically. If it can't, it will complain. One can pass these parameters explicitly, which is how one uses breakOut, for example (see question about breakOut, on a day you are feeling up for a challenge).

In this case, one has to declare the need for an implicit, such as the foo method declaration:

def foo[T](t: T)(implicit integral: Integral[T]) {println(integral)}

View Bounds

There's one situation where an implicit is both an implicit conversion and an implicit parameter. For example:

def getIndex[T, CC](seq: CC, value: T)(implicit conv: CC => Seq[T]) = seq.indexOf(value)

getIndex("abc", 'a')

The method getIndex can receive any object, as long as there is an implicit conversion available from its class to Seq[T]. Because of that, I can pass a String to getIndex, and it will work.

Behind the scenes, the compiler changes seq.IndexOf(value) to conv(seq).indexOf(value).

This is so useful that there is syntactic sugar to write them. Using this syntactic sugar, getIndex can be defined like this:

def getIndex[T, CC <% Seq[T]](seq: CC, value: T) = seq.indexOf(value)

This syntactic sugar is described as a view bound, akin to an upper bound (CC <: Seq[Int]) or a lower bound (T >: Null).

Context Bounds

Another common pattern in implicit parameters is the type class pattern. This pattern enables the provision of common interfaces to classes which did not declare them. It can both serve as a bridge pattern -- gaining separation of concerns -- and as an adapter pattern.

The Integral class you mentioned is a classic example of type class pattern. Another example on Scala's standard library is Ordering. There's a library that makes heavy use of this pattern, called Scalaz.

This is an example of its use:

def sum[T](list: List[T])(implicit integral: Integral[T]): T = {
    import integral._   // get the implicits in question into scope
    list.foldLeft(integral.zero)(_ + _)
}

There is also syntactic sugar for it, called a context bound, which is made less useful by the need to refer to the implicit. A straight conversion of that method looks like this:

def sum[T : Integral](list: List[T]): T = {
    val integral = implicitly[Integral[T]]
    import integral._   // get the implicits in question into scope
    list.foldLeft(integral.zero)(_ + _)
}

Context bounds are more useful when you just need to pass them to other methods that use them. For example, the method sorted on Seq needs an implicit Ordering. To create a method reverseSort, one could write:

def reverseSort[T : Ordering](seq: Seq[T]) = seq.sorted.reverse

Because Ordering[T] was implicitly passed to reverseSort, it can then pass it implicitly to sorted.

Where do Implicits come from?

When the compiler sees the need for an implicit, either because you are calling a method which does not exist on the object's class, or because you are calling a method that requires an implicit parameter, it will search for an implicit that will fit the need.

This search obey certain rules that define which implicits are visible and which are not. The following table showing where the compiler will search for implicits was taken from an excellent presentation about implicits by Josh Suereth, which I heartily recommend to anyone wanting to improve their Scala knowledge. It has been complemented since then with feedback and updates.

The implicits available under number 1 below has precedence over the ones under number 2. Other than that, if there are several eligible arguments which match the implicit parameter’s type, a most specific one will be chosen using the rules of static overloading resolution (see Scala Specification §6.26.3). More detailed information can be found in a question I link to at the end of this answer.

1. First look in current scope
   • Implicits defined in current scope
   • Explicit imports
   • wildcard imports
   • Same scope in other files
2. Now look at associated types in
   • Companion objects of a type
   • Implicit scope of an argument's type (2.9.1)
   • Implicit scope of type arguments (2.8.0)
   • Outer objects for nested types
   • Other dimensions

Let's give some examples for them:

Implicits Defined in Current Scope

implicit val n: Int = 5
def add(x: Int)(implicit y: Int) = x + y
add(5) // takes n from the current scope

Explicit Imports

import scala.collection.JavaConversions.mapAsScalaMap
def env = System.getenv() // Java map
val term = env("TERM")    // implicit conversion from Java Map to Scala Map

Wildcard Imports

def sum[T : Integral](list: List[T]): T = {
    val integral = implicitly[Integral[T]]
    import integral._   // get the implicits in question into scope
    list.foldLeft(integral.zero)(_ + _)
}

Same Scope in Other Files

Edit: It seems this does not have a different precedence. If you have some example that demonstrates a precedence distinction, please make a comment. Otherwise, don't rely on this one.

This is like the first example, but assuming the implicit definition is in a different file than its usage. See also how package objects might be used in to bring in implicits.

Companion Objects of a Type

There are two object companions of note here. First, the object companion of the "source" type is looked into. For instance, inside the object Option there is an implicit conversion to Iterable, so one can call Iterable methods on Option, or pass Option to something expecting an Iterable. For example:

for {
    x <- List(1, 2, 3)
    y <- Some('x')
} yield (x, y)

That expression is translated by the compiler to

List(1, 2, 3).flatMap(x => Some('x').map(y => (x, y)))

However, List.flatMap expects a TraversableOnce, which Option is not. The compiler then looks inside Option's object companion and finds the conversion to Iterable, which is a TraversableOnce, making this expression correct.

Second, the companion object of the expected type:

List(1, 2, 3).sorted

The method sorted takes an implicit Ordering. In this case, it looks inside the object Ordering, companion to the class Ordering, and finds an implicit Ordering[Int] there.

Note that companion objects of super classes are also looked into. For example:

class A(val n: Int)
object A { 
    implicit def str(a: A) = "A: %d" format a.n
}
class B(val x: Int, y: Int) extends A(y)
val b = new B(5, 2)
val s: String = b  // s == "A: 2"

This is how Scala found the implicit Numeric[Int] and Numeric[Long] in your question, by the way, as they are found inside Numeric, not Integral.

Implicit Scope of an Argument's Type

If you have a method with an argument type A, then the implicit scope of type A will also be considered. By "implicit scope" I mean that all these rules will be applied recursively -- for example, the companion object of A will be searched for implicits, as per the rule above.

Note that this does not mean the implicit scope of A will be searched for conversions of that parameter, but of the whole expression. For example:

class A(val n: Int) {
  def +(other: A) = new A(n + other.n)
}
object A {
  implicit def fromInt(n: Int) = new A(n)
}

// This becomes possible:
1 + new A(1)
// because it is converted into this:
A.fromInt(1) + new A(1)

This is available since Scala 2.9.1.

Implicit Scope of Type Arguments

This is required to make the type class pattern really work. Consider Ordering, for instance: It comes with some implicits in its companion object, but you can't add stuff to it. So how can you make an Ordering for your own class that is automatically found?

Let's start with the implementation:

class A(val n: Int)
object A {
    implicit val ord = new Ordering[A] {
        def compare(x: A, y: A) = implicitly[Ordering[Int]].compare(x.n, y.n)
    }
}

So, consider what happens when you call

List(new A(5), new A(2)).sorted

As we saw, the method sorted expects an Ordering[A] (actually, it expects an Ordering[B], where B >: A). There isn't any such thing inside Ordering, and there is no "source" type on which to look. Obviously, it is finding it inside A, which is a type argument of Ordering.

This is also how various collection methods expecting CanBuildFrom work: the implicits are found inside companion objects to the type parameters of CanBuildFrom.

Note: Ordering is defined as trait Ordering[T], where T is a type parameter. Previously, I said that Scala looked inside type parameters, which doesn't make much sense. The implicit looked for above is Ordering[A], where A is an actual type, not type parameter: it is a type argument to Ordering. See section 7.2 of the Scala specification.

This is available since Scala 2.8.0.

Outer Objects for Nested Types

I haven't actually seen examples of this. I'd be grateful if someone could share one. The principle is simple:

class A(val n: Int) {
  class B(val m: Int) { require(m < n) }
}
object A {
  implicit def bToString(b: A#B) = "B: %d" format b.m
}
val a = new A(5)
val b = new a.B(3)
val s: String = b  // s == "B: 3"

Other Dimensions

I'm pretty sure this was a joke, but this answer might not be up-to-date. So don't take this question as being the final arbiter of what is happening, and if you do noticed it has gotten out-of-date, please inform me so that I can fix it.

EDIT

Related questions of interest:

• Context and view bounds
• Chaining implicits
• Scala: Implicit parameter resolution precedence