I'm reading through and working my way through using type classes and I came across this way of defining type classes from the Shapeless guide:
So here goes the example:
object CsvEncoder {
// "Summoner" method
def apply[A](implicit enc: CsvEncoder[A]): CsvEncoder[A] =
enc
// "Constructor" method
def instance[A](func: A => List[String]): CsvEncoder[A] =
new CsvEncoder[A] {
def encode(value: A): List[String] =
func(value)
}
// Globally visible type class instances
}
What I do not understand is the need for the apply method? What is it doing in this context above?
Later on, the guide describes how I could create a type class instance:
implicit val booleanEncoder: CsvEncoder[Boolean] =
new CsvEncoder[Boolean] {
def encode(b: Boolean): List[String] =
if(b) List("yes") else List("no")
}
is actually shortened to:
implicit val booleanEncoder: CsvEncoder[Boolean] =
instance(b => if(b) List("yes") else List("no"))
So my question now is, how does this work? What I do not get is the need for the apply method?
EDIT: I came across a blog post that describes the steps in creating type classes as below:
Define typeclass contract trait Foo.
Define a companion object Foo with a helper method apply that acts like implicitly, and a way of defining Foo instances typically from a function.
Define FooOps class that defines unary or binary operators.
Define FooSyntax trait that implicitly provides FooOps from a Foo instance.
So what is the deal with point number 2, 3 and 4?
Most of those practices came from Haskell (basically an intention to mimic Haskell's type-classes is a reason for so much boilerplate), some of it is just for convenience. So,
2) As #Alexey Romanov mentioned, companion object with apply is just for convenience, so instead of implicitly[CsvEncoder[IceCream]] you could write just CsvEncoder[IceCream] (aka CsvEncoder.apply[IceCream]()), which will return you a required type-class instance.
3) FooOps provides convenience methods for DSLs. For instance you could have something like:
trait Semigroup[A] {
...
def append(a: A, b: A)
}
import implicits._ //you should import actual instances for `Semigroup[Int]` etc.
implicitly[Semigroup[Int]].append(2,2)
But sometimes it's inconvenient to call append(2,2) method, so it's a good practice to provide a symbolic alias:
trait Ops[A] {
def typeClassInstance: Semigroup[A]
def self: A
def |+|(y: A): A = typeClassInstance.append(self, y)
}
trait ToSemigroupOps {
implicit def toSemigroupOps[A](target: A)(implicit tc: Semigroup[A]): Ops[A] = new Ops[A] {
val self = target
val typeClassInstance = tc
}
}
object SemiSyntax extends ToSemigroupOps
4) You can use it as follows:
import SemiSyntax._
import implicits._ //you should also import actual instances for `Semigroup[Int]` etc.
2 |+| 2
If you wonder why so much boilerplate, and why scala's implicit class syntax doesn't provide this functionality from scratch - the answer is that implicit class actually provides a way to create DSL's - it's just less powerful - it's (subjectively) harder to provide operation aliases, deal with more complex dispatching (when required) etc.
However, there is a macro solution that generates boilerplate automatically for you: https://github.com/mpilquist/simulacrum.
One another important point about your CsvEncoder example is that instance is convenience method for creating type-class instances, but apply is a shortcut for "summoning" (requiring) those instances. So, first one is for library extender (a way to implement interface), another one is for a user (a way to call a particular operation provided for that interface).
Another thing to note is that in shapeless the apply method is not only for cuter syntax.
Take for instance this simplified version of shapeless' Generic and some case class Foo.
trait Generic[T] {
type Repr
}
object Generic {
def apply[T](implicit gen: Generic[T]): Generic[T] { type Repr = gen.Repr } = gen
/* lots of macros to generate implicit instances omitted */
}
case class Foo(a: Int, b: String)
Now when I call Generic[Foo] I will get an instance that is typed as Generic[Foo] { type Repr = Int :: String :: HNil }. But if I call implicitly[Generic[Foo]] all the compiler knows about the result is that it's a Generic[Foo]. In other words: the concrete type of Repr is lost and I can't do anything useful with it. The reason is that implicitly is implemented as follows:
def implicitly[T](implicit e: T): T = e
That method declaration basically says: if you ask for a T I promise to give you a T, if I find one, and nothing more. So that means you'd have to ask implicitly[Generic[Foo] { type Repr = Int :: String :: HNil }] and that defeats the purpose of having automatic derivation.
Quoting the guide immediately after the object CsvEncoder definition:
The apply method ... allows us to summon a type class instance given a target type:
CsvEncoder[IceCream]
// res9: CsvEncoder[IceCream] = ...
Related
I was digging through the implementation of Monoids in Scalaz. I came across the |+| operator that is supposed to come out of the box if you define the append operation on Monoid. The definition of this operator is in SemigroupSyntax. That class gets to Monoid through Semigroup.
After examining these three classes I have one major question - How exactly is the comment from SemigroupSyntax achieved /** Wraps a value `self` and provides methods related to `Semigroup` */
There is some magic with implicits, calling .this on trait and more in the SemigroupSyntax that I honestly don't understand.
I would love if someone could take the time to enlighten me.
Thank you in advance!
EDIT:
I am keen to understand the workings of this class:
package scalaz
package syntax
/** Wraps a value `self` and provides methods related to `Semigroup` */
final class SemigroupOps[F] private[syntax](val self: F)(implicit val F: Semigroup[F]) extends Ops[F] {
////
final def |+|(other: => F): F = F.append(self, other)
final def mappend(other: => F): F = F.append(self, other)
final def ⊹(other: => F): F = F.append(self, other)
////
}
trait ToSemigroupOps {
implicit def ToSemigroupOps[F](v: F)(implicit F0: Semigroup[F]) =
new SemigroupOps[F](v)
////
////
}
trait SemigroupSyntax[F] {
implicit def ToSemigroupOps(v: F): SemigroupOps[F] = new SemigroupOps[F](v)(SemigroupSyntax.this.F)
def F: Semigroup[F]
////
def mappend(f1: F, f2: => F)(implicit F: Semigroup[F]): F = F.append(f1, f2)
////
}
And its call site in Semigroup:
val semigroupSyntax = new scalaz.syntax.SemigroupSyntax[F] { def F = Semigroup.this }
Most disorienting thing here is that there's actually two routes to getting operations on object.
First route, the default one, is by import scalaz.syntax.semigroup._. It adds operators for all implicitly available Semigroup instances.
Any Semigroup instance creates an implementation of SemigroupSyntax for itself, defining its F method in terms of this.
In scalaz/syntax/package.scala, there's a syntax singleton object that extends Syntaxes trait. It is the first part of import definition.
In scalaz/syntax/Syntax.scala, there's a semigroup singleton object within Syntaxes trait used in syntax, which extends ToSemigroupOps. We're importing contents of this object, containing only the implicit conversion. The purpose of conversion is to capture implicitly provided Semigroup instance and construct a wrapper, SemigroupOps, which contains all the operations.
Second route is a shortcut by import [your_semigroup_instance].semigroupSyntax._, a call site in Semigroup you're listed. It adds operators to a particular type, for which Semigroup instance is.
semigroupSyntax is an anonymous implementation of SemigroupSyntax trait, which F method is defined to be a particular instance of Semigroup.
SemigroupSyntax trait itself, like ToSemigroupOps, offers an implicit conversion to SemigroupOps, but instead of capturing implicitly provided instance, it uses its F method. So we get operators on type F, using particular Semigroup typeclass implementation.
I came from C++ world and new to Scala, and this behavior looks unusual.
class G1[A]( val a : A) {
//val c:A = new A //This gives compile error
def fcn1(b: A): Unit = {
//val aobj = new A // This gives compile error
println(a.getClass.getSimpleName)
println(b.getClass.getSimpleName)
}
}
def fcnWithTP[A](): Unit = {
//val a = new A // This gives compile error
//println(a.getClass.getSimpleName)
}
I am not able to crate a object using the type parameter in a class in a function body or a class body. I am only be able to use it in the function parameter.
What is the reason for this? Is this because of type erasure? At run time, the function does not know what the actual type A is, so it cannot create an object of that type?
What is the general rule for this? Does it that mean the type parameter cannot appear in function body or class definition at all? If they can actually appear, what are the examples?
Yes, you're right that this is because of erasure—you don't know anything about A at runtime that you haven't explicitly asserted about it as a constraint in the method signature.
Type erasure on the JVM is only partial, so you can do some horrible things in Scala like ask for the class of a value:
scala> List(1, 2, 3).getClass
res0: Class[_ <: List[Int]] = class scala.collection.immutable.$colon$colon
Once you get to generics, though, everything is erased, so for example you can't tell the following things apart:
scala> List(1, 2, 3).getClass == List("a", "b", "c").getClass
res1: Boolean = true
(In case it's not clear, I think type erasure is unambiguously a good thing, and that the only problem with type erasure on the JVM is that it's not more complete.)
You can write the following:
import scala.reflect.{ ClassTag, classTag }
class G1[A: ClassTag](val a: A) {
val c: A = classTag[A].runtimeClass.newInstance().asInstanceOf[A]
}
And use it like this:
scala> val stringG1: G1[String] = new G1("foo")
stringG1: G1[String] = G1#33d71170
scala> stringG1.c
res2: String = ""
This is a really bad idea, though, since it will crash at runtime for many, many type parameters:
scala> class Foo(i: Int)
defined class Foo
scala> val fooG1: G1[Foo] = new G1(new Foo(0))
java.lang.InstantiationException: Foo
at java.lang.Class.newInstance(Class.java:427)
... 43 elided
Caused by: java.lang.NoSuchMethodException: Foo.<init>()
at java.lang.Class.getConstructor0(Class.java:3082)
at java.lang.Class.newInstance(Class.java:412)
... 43 more
A better approach is to pass in the constructor:
class G1[A](val a: A)(empty: () => A) {
val c: A = empty()
}
And a much better approach is to use a type class:
trait Empty[A] {
def default: A
}
object Empty {
def instance[A](a: => A): Empty[A] = new Empty[A] {
def default: A = a
}
implicit val stringEmpty: Empty[String] = instance("")
implicit val fooEmpty: Empty[Foo] = instance(new Foo(0))
}
class G1[A: Empty](val a: A) {
val c: A = implicitly[Empty[A]].default
}
And then:
scala> val fooG1: G1[Foo] = new G1(new Foo(10101))
fooG1: G1[Foo] = G1#5a34b5bc
scala> fooG1.c
res0: Foo = Foo#571ccdd0
Here we're referring to A in the definition of G1, but we're only making reference to properties and operations that we've confirmed hold or are available at compile time.
Generics are not the same thing as templates. In C++ Foo<Bar> and Foo<Bat> are two different classes, generated at compile time.
In scala or java, Foo[T] is a single class that has with a type parameter. Consider this:
class Foo(val bar)
class Bar[T] {
val foo = new T // if this was possible ...
}
new Bar[Foo]
In C++, (an equivalent of) this would fail to compile, because there is no accessible constructor of Foo that takes no arguments. The compiler would know that when it tried to instantiate a template for Bar<Foo> class, and fail.
In scala, there is no separate class for Bar[Foo], so, at compilation time, the compiler doesn't know anything about T, other than that it is some type. It has no way of knowing whether calling a constructor (or any other method for that matter) is possible or sensible (you can't instantiate a trait for example, or an abstract class), so new T in that context has to fail: it simply does not make sense.
Roughly speaking, you can use type parameters in places where any type can be used (do declare a return type for example, or a variable), but when you are trying to do something that only works for some types, and not for others, you have to make your type param more specific. For example, this: def foo[T](t: T) = t.intValue does not work, but this: def foo[T <: Number](t: T) = t.intValue does.
Well the compiler does not know how to create an instance of type A. You need to either provide a factory function that returns instance of A, or use Manifest which creates instance of A from reflection.
With factory function:
class G1[A](val a:A)(f: () => A) {
val c:A = f()
}
With Manifest:
class G1[A](val a: A)(implicit m: scala.reflect.Manifest[A]) {
val c: A = m.erasure.newInstance.asInstanceOf[A]
}
When using type parameter, usually you will specify more details on the type A, unless you're implementing some sort of container for A that does not directly interact with A. If you need to interact with A, you need some specification on it. You can say A must be a subclass of B
class G1[A <: B](val a : A)
Now compiler would know A is a subclass of B so you can call all functions defined in B on a:A.
I have some code like this:
sealed trait Foo[A] {
def value: A
}
case class StringFoo(value: String) extends Foo[String]
case class IntFoo(value: Int) extends Foo[Int]
I'd like to have a function which can use the A type given a subtype's type parameter.
// Hypothetical invocation
val i: Int = dostuff[IntFoo](param)
val s: String = dostuff[StringFoo](param)
I can't figure out how to declare dostuff in a way that works. The closest thing I can figure out is
def dostuff[B <: Foo[A]](p: Param): A
But that doesn't work because A is undefined in that position. I can do something like
def dostuff[A, B <: Foo[A]](p: Param): A
But then I have to invoke it like dostuff[String, StringFoo](param) which is pretty ugly.
It seems like the compiler should have all the information it needs to move A across to the return type, how can I make this work, either in standard scala or with a library. I'm on scala 2.10 currently if that impacts the answer. I'm open to a 2.11-only solution if it's possible there but impossible in 2.10
Another option is to use type members:
sealed trait Foo {
type Value
def value: Value
}
case class StringFoo(value: String) extends Foo { type Value = String }
case class IntFoo(value: Int) extends Foo { type Value = Int }
def dostuff[B <: Foo](p: Any): B#Value = ???
// Hypothetical invocation
val i: Int = dostuff[IntFoo](param)
val s: String = dostuff[StringFoo](param)
Note that both solutions mainly work around the syntactic restriction in Scala, that you cannot fix one type parameter of a list and have the compiler infer the other.
As you might know, if you have a parameter of type Foo[A], then you can make the method generic in just A:
def dostuff[A](p: Foo[A]): A = ???
Since that might not always be the case, we can try to use an implicit parameter that can express the relationship between A and B. Since we can't only apply some of the generic parameters to a method call (generic parameter inference is all or nothing), we have to split this into 2 calls. This is an option:
case class Stuff[B <: Foo[_]]() {
def get[A](p: Param)(implicit ev: B => Foo[A]): A = ???
}
You can check the types in the REPL:
:t Stuff[IntFoo].get(new Param) //Int
:t Stuff[StringFoo].get(new Param) //String
Another option along the same lines, but using an anonymous class, is:
def stuff[B <: Foo[_]] = new {
def apply[A](p: Param)(implicit ev: B <:< Foo[A]): A = ???
}
:t stuff[IntFoo](new Param) //Int
Here, I've used apply in stead of get, so you can apply the method more naturally. Also, as suggested in your comment, here I've used <:< in the evidence type. For those looking to learn more about this type of generalized type constraint, you can read more here.
You might also consider using abstract type members instead of generic parameters here. When struggling with generic type inference, this often provides an elegant solution. You can read more about abstract type members and their relationship to generics here.
I have two case classes
case class StringCaseClass(argument: String)
case class IntCaseClass(argument: Int)
I want to define a structural type which will match the companion object of both of these
type HasApply1 {
def apply[A, R](argument: A): R
}
This will compile fine, but when I try to use it like this
def method(caseClass: HasApply1) {
// whatever
}
method(StringCaseClass)
I will get a compiler error
found : StringCaseClass.type
required: WithApply1
(which expands to) AnyRef{def apply[A, R](string: A): R}
Is there any way of accomplishing this? If I redefine the structural type to have concrete types for A and R it will compile correctly, but then I lose the flexiblity
#aloiscochard's comment is almost there. What he forgot to mention is that case class companion objects already implement the appropriate FunctionN trait, so you can simply do this,
scala> case class StringCaseClass(argument: String)
defined class StringCaseClass
scala> case class IntCaseClass(argument: Int)
defined class IntCaseClass
scala> def method[A, R](caseClass: A => R, a: A) = caseClass(a)
method: [A, R](caseClass: A => R, a: A)R
scala> method(StringCaseClass, "foo")
res0: StringCaseClass = StringCaseClass(foo)
scala> method(IntCaseClass, 23)
res1: IntCaseClass = IntCaseClass(23)
In general you should avoid structural typing as it's very expensive. The call will be converted into a reflection call because of limitations in the JVM. When you start using scala 2.10 structural types will result in a warning at compile time (though you could disable that using a flag).
If you're looking into a more general way to add functionality to classes that don't share an inheritance hierarchy you could use Type Classes.
Here's a quick example:
trait CanCreateRFromA[A,R]{
def createNew(a:A): R
}
implicit object CanCreateBlahFromInt extends CanCreateRFromA[Int,Blah2]{
def createNew(i:Int):Blah2 = new Blah2(i)
}
implicit object CanCreateBlah1FromString extends CanCreateRFromA[String,Blah1]{
def createNew(s:String):Blah1 = new Blah1(s)
}
case class Blah1(something:String)
case class Blah2(something:Int)
def createRFromA[A,R](a:A)(implicit tc:CanCreateRFromA[A,R])= tc.createNew(a)
Then you can call:
createRFromA(1) // This gives a Blah2
createRFromA("1") // This gives a Blah1
Again I'm not sure what you're trying to accomplish, but it probably is possible to do what you want with a type class and it will be much faster.
You didn't pass an instance of StringCaseClass to your method. What you passed there is companion object of StringCaseClass (which is automatically generated for case classes).
Try if this works: method(StringCaseClass("dummy")).
I have read the answer to my question about scala.math.Integral but I do not understand what happens when Integral[T] is passed as an implicit parameter. (I think I understand the implicit parameters concept in general).
Let's consider this function
import scala.math._
def foo[T](t: T)(implicit integral: Integral[T]) { println(integral) }
Now I call foo in REPL:
scala> foo(0)
scala.math.Numeric$IntIsIntegral$#581ea2
scala> foo(0L)
scala.math.Numeric$LongIsIntegral$#17fe89
How does the integral argument become scala.math.Numeric$IntIsIntegral and scala.math.Numeric$LongIsIntegral ?
The short answer is that Scala finds IntIsIntegral and LongIsIntegral inside the object Numeric, which is the companion object of the class Numeric, which is a super class of Integral.
Read on for the long answer.
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 compile changes seq.IndexOf(value) to conv(seq).indexOf(value).
This is so useful that there is a 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).
Please be aware that view bounds are deprecated from 2.11, you should avoid them.
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 a 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.reverse.sorted
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.
First look in current scope
Implicits defined in current scope
Explicit imports
wildcard imports
Same scope in other files
Now look at associated types in
Companion objects of a type
Companion objects of type parameters types
Outer objects for nested types
Other dimensions
Let's give 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
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 compile into
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.
Companion Objects of Type Parameters Types
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 parameter 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.
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. I hope. :-)
EDIT
Related questions of interest:
Context and view bounds
Chaining implicits
The parameter is implicit, which means that the Scala compiler will look if it can find an implicit object somewhere that it can automatically fill in for the parameter.
When you pass in an Int, it's going to look for an implicit object that is an Integral[Int] and it finds it in scala.math.Numeric. You can look at the source code of scala.math.Numeric, where you will find this:
object Numeric {
// ...
trait IntIsIntegral extends Integral[Int] {
// ...
}
// This is the implicit object that the compiler finds
implicit object IntIsIntegral extends IntIsIntegral with Ordering.IntOrdering
}
Likewise, there is a different implicit object for Long that works the same way.