There is a difference in the way the scala 2.13.3 compiler determines which overloaded function to call compared to which overloaded implicit to pick.
object Thing {
trait A;
trait B extends A;
trait C extends A;
def f(a: A): String = "A"
def f(b: B): String = "B"
def f(c: C): String = "C"
implicit val a: A = new A {};
implicit val b: B = new B {};
implicit val c: C = new C {};
}
import Thing._
scala> f(new B{})
val res1: String = B
scala> implicitly[B]
val res2: Thing.B = Thing$$anon$2#2f64f99f
scala> f(new A{})
val res3: String = A
scala> implicitly[A]
^
error: ambiguous implicit values:
both value b in object Thing of type Thing.B
and value c in object Thing of type Thing.C
match expected type Thing.A
As we can see, the overload resolution worked for the function call but not for the implicit pick. Why isn't the implicit offered by val a be chosen as occurs with function calls? If the callers ask for an instance of A why the compilers considers instances of B and C when an instance of A is in scope. There would be no ambiguity if the resolution logic were the same as for function calls.
Edit 2:
The Edit 1 was removed because the assertion I wrote there was wrong.
In response to the comments I added another test to see what happens when the implicit val c: C is removed. In that case the compiler don't complains and picks implicit val b: B despite the caller asked for an instance of A.
object Thing {
trait A { def name = 'A' };
trait B extends A { def name = 'B' };
trait C extends A { def name = 'C' };
def f(a: A): String = "A"
def f(b: B): String = "B"
implicit val a: A = new A {};
implicit val b: B = new B {};
}
import Thing._
scala> f(new A{})
val res0: String = A
scala> implicitly[A].name
val res3: Char = B
So, the overloading resolution of implicit differs from function calls more than I expected.
Anyway, I still don't find a reason why the designers of scala decided to apply a different resolution logic for function and implicit overloading. (Edit: Later noticed why).
Let's see what happens in a real world example.
Suppose we are doing a Json parser that converts a Json string directly to scala Abstract data types, and we want it to support many standard collections.
The snippet in charge of parsing the iterable collections would be something like this:
trait Parser[+A] {
def parse(input: Input): ParseResult;
///// many combinators here
}
implicit def summonParser[T](implicit parserT: Parser[T]) = parserT;
/** #tparam IC iterator type constructor
* #tparam E element's type */
implicit def iterableParser[IC[E] <: Iterable[E], E](
implicit
parserE: Parser[E],
factory: IterableFactory[IC]
): Parser[IC[E]] = '[' ~> skipSpaces ~> (parserE <~ skipSpaces).repSepGen(coma <~ skipSpaces, factory.newBuilder[E]) <~ skipSpaces <~ ']';
Which requires a Parser[E] for the elements and a IterableFactory[IC] to construct the collection specified by the type parameters.
So, we have to put in implicit scope an instance of IterableFactory for every collection type we want to support.
implicit val iterableFactory: IterableFactory[Iterable] = Iterable
implicit val setFactory: IterableFactory[Set] = Set
implicit val listFactory: IterableFactory[List] = List
With the current implicit resolution logic implemented by the scala compiler, this snippet works fine for Set and List, but not for Iterable.
scala> def parserInt: Parser[Int] = ???
def parserInt: read.Parser[Int]
scala> Parser[List[Int]]
val res0: read.Parser[List[Int]] = read.Parser$$anonfun$pursue$3#3958db82
scala> Parser[Vector[Int]]
val res1: read.Parser[Vector[Int]] = read.Parser$$anonfun$pursue$3#648f48d3
scala> Parser[Iterable[Int]]
^
error: could not find implicit value for parameter parserT: read.Parser[Iterable[Int]]
And the reason is:
scala> implicitly[IterableFactory[Iterable]]
^
error: ambiguous implicit values:
both value listFactory in object IterableParser of type scala.collection.IterableFactory[List]
and value vectorFactory in object IterableParser of type scala.collection.IterableFactory[Vector]
match expected type scala.collection.IterableFactory[Iterable]
On the contrary, if the overloading resolution logic of implicits was like the one for function calls, this would work fine.
Edit 3: After many many coffees I noticed that, contrary to what I said above, there is no difference between the way the compiler decides which overloaded functions to call and which overloaded implicit to pick.
In the case of function call: from all the functions overloads such that the type of the argument is asignable to the type of the parameter, the compiler chooses the one such that the function's parameter type is assignable to all the others. If no function satisfies that, a compilation error is thrown.
In the case of implicit pick up: from all the implicit in scope such that the type of the implicit is asignable to the asked type, the compiler chooses the one such that the declared type is asignable to all the others. If no implicit satisfies that, an compilation error is thrown.
My mistake was that I didn't notice the inversion of the assignability.
Anyway, the resolution logic I proposed above (give me what I asked for) is not entirely wrong. It's solves the particular case I mentioned. But for most uses cases the logic implemented by the scala compiler (and, I suppose, all the other languages that support type classes) is better.
As explained in the Edit 3 section of the question, there are similitudes between the way the compiler decides which overloaded functions to call and which overloaded implicit to pick. In both cases the compiler does two steps:
Filters out all the alternatives that are not asignable.
From the remaining alternatives choses the most specific or complains if there is more than one.
In the case of the function call, the most specific alternative is the function with the most specific parameter type; and in the case of implicit pick is the instance with the most specific declared type.
But, if the logic in both cases were exactly the same, then why did the example of the question give different results? Because there is a difference: the assignability requirement that determines which alternatives pass the first step are oposite.
In the case of the function call, after the first step remain the functions whose parameter type is more generic than the argument type; and in the case of implicit pick, remain the instances whose declared type is more specific than the asked type.
The above words are enough to answers the question itself but don't give a solution to the problem that motivated it, which is: How to force the compiler to pick the implicit instance whose declared type is exactly the same than the summoned type? And the answer is: wrapping the implicit instances inside a non variant wrapper.
Related
What is the difference between the implicit keyword in Scala 2 and given+using in Scala 3? Is it just that implicit has been split up into two keywords, or are the semantics also different, and if so, how?
For the most part, they are the same. However, implicit is no longer used for multiple different concepts. The docs go into more detail, but here's a summary of them:
Using
When declaring parameters, using is just the same as implicit. However, when explicitly passing an implicit argument, you must use using:
def foo(using bar: Bar) = ???
foo(using Bar()) //Cannot use just foo(Bar()) as you would in Scala 2
You can also have implicit by-name parameters in Scala 3.
Given
Givens are also pretty similar to implicit vals/objects/methods.
One nice thing about them is that they can be anonymous, and the compiler will generate a name for them, which looks something like given_F_X_Y if the type of the given were F[X, Y]. More details here.
Another change is that the type of a given must be written explicitly - it cannot be inferred like for an implicit in Scala 2.
A given without parameters maps to an implicit object. given foo: Foo with {...} becomes just implicit object foo extends Foo {...}.
A given with parameters is akin to an implicit def that takes in only more implicit parameters.
given listOrd[T](using ord: Ord[T]): Ord[List[T]] with { ... }
//^^ this maps to this vv
class listOrd[T](implicit ord: Ord[T]) extends Ord[List[T]] { ... }
final implicit def listOrd[T](implicit ord: Ord[T]): listOrd[T] = new listOrd[T]
A given that is merely an alias becomes an implicit def if it is just a reference, or an implicit lazy val otherwise.
val foo: Foo
given Foo = foo
would become final implicit def given_Foo = foo (note the compiler-generated name), but
given foo: Foo = new Foo()
would turn into final implicit lazy val foo: Foo = new Foo() because new Foo() shouldn't be computed unnecessarily.
Instead of using an implicit def for an implicit conversion from A to B, you can now define a given Conversion[A, B] instance.
You can also still use implicit classes in Dotty, but you can directly define extension methods. While methods inside extensions cannot take their own type parameters, they are easier to use than implicit classes.
An additional change in Scala 3 - summon is a method like implicitly, but it can return a type more specific than the one being requested.
Semantics is also different. In Scala 2 Not can be defined with ambiguity trick
trait Not[A]
object Not {
implicit def default[A]: Not[A] = null
implicit def ambig[A](implicit a: A): Not[A] = null
}
implicitly[Not[Int]] // compiles
implicit val s: String = null
// implicitly[Not[String]] // doesn't compile
But in Scala 3 this doesn't work because ambiguity error is not propagated
trait Not[A]
object Not {
given [A]: Not[A] = null
given [A](using a: A): Not[A] = null
// given ambig[A](using a: A): Not[A] = null
}
summon[Not[Int]] // compiles
given String = null
summon[Not[String]] // compiles
One should use scala.util.NotGiven instead
summon[NotGiven[Int]] // compiles
given String = null
// summon[NotGiven[String]] // doesn't compile
(Tested in 3.0.0-M3-bin-20201211-dbc1186-NIGHTLY)
http://dotty.epfl.ch/docs/reference/contextual/givens.html#negated-givens
http://dotty.epfl.ch/docs/reference/changed-features/implicit-resolution.html
I am working on a system of chained implicit functions, which is similar to the simplified example below. The test c1.payload == c2.payload represents a test I need to do that is not in "type-space"; I had expected that I would drop into a macro for the definition of witnessEvidence, however Scala apparently does not allow macro definitions with implicit arguments of arbitrary type (WeakTypeTag values only!), and so I am a bit stumped about how to proceed with this. The code below shows logically what I'd like to happen, however an implicit function can't conditionally produce or not produce evidence (unless it is inside a macro implementation).
case class Capsule[T](payload: Int)
trait A
trait B
trait C
implicit val capa = Capsule[A](3)
implicit val capb = Capsule[B](3)
implicit val capc = Capsule[C](7)
case class Evidence[T1, T2](e: Int)
implicit def witnessEvidence[T1, T2](implicit c1: Capsule[T1], c2: Capsule[T2]): Evidence[T1, T2] = {
if (c1.payload == c2.payload)
Evidence[T1, T2](c1.payload)
else
// Do not produce the evidence
}
def foo[T1, T2](implicit ev: Evidence[T1, T2]) = ev.e
val f1 = foo[A, B] // this should compile
val f2 = foo[A, C] // this should fail with missing implicit!
This would not be possible as-is, since the implicit resolution is done at compilation, while testing for value equivalence is done at runtime.
To make this work, you need to make the compiler understand values as types, so that you can ask for the type equality of the two 3s and use that to infer that capa =:= capb. To do that you can use singleton types: https://github.com/milessabin/shapeless/wiki/Feature-overview:-shapeless-2.0.0#singleton-typed-literals
If you need to do arithmetic beyond plain equality comparison, you will need to use Nat:https://github.com/milessabin/shapeless/blob/master/core/src/main/scala/shapeless/nat.scala
I'm trying to call this set method documented here, in the Java library jOOQ, with signature:
<T> ... set(Field<T> field, T value)
This Scala line is a problem:
.set(table.MODIFIED_BY, userId)
MODIFIED_BY is a Field<Integer> representing the table column. userId is Int. Predef has an implicit conversion from Int to Integer, so why doesn't it use it? I get this:
type mismatch; found: org.jooq.TableField[gen.tables.records.DocRecord,Integer]
required: org.jooq.Field[Any]
Note: Integer <: Any
(and org.jooq.TableField[gen.tables.records.DocRecord,Integer] <:
org.jooq.Field[Integer]), but Java-defined trait Field is invariant in type T.
You may wish to investigate a wildcard type such as `_ <: Any`. (SLS 3.2.10)
Update - About Vinicius's Example
Rather than try to explain this in comments, here is a demonstration that there is no implicit conversion being called when you use a type with covariant parameter, like List[+T]. Let's say I put this code in a file, compile, and run it...
case class Foo(str: String)
object StackOver1 extends App {
implicit def str2Foo(s: String): Foo = {
println("In str2Foo.")
new Foo(s)
}
def test[T](xs: List[T], x: T): List[T] = {
println("test " + x.getClass)
xs
}
val foo1 = new Foo("foo1")
test(List(foo1), "abc")
}
You'll see that it calls test, but never the implicit conversion from String "abc" to Foo. Instead it's picking a T for test[T] that is a common base class between String and Foo. When you use Int and Integer it picks Any, but it's confusing because the runtime representation of the Int in the list is Integer. So it looks like it used the implicit conversion, but it didn't. You can verify by opening a Scala prompt...
scala> :type StackOver1.test(List(new java.lang.Integer(1)), 2)
List[Any]
I don't know anything aboutjOOQ, but I think the issue is that Scala does not understand java generics very well. Try:
scala> def test[T](a : java.util.ArrayList[T], b: T) = { println(a,b) }
scala> val a = new java.util.ArrayList[Integer]()
scala> val b = 12
scala> test(a,b)
<console>:11: error: type mismatch;
found : java.util.ArrayList[Integer]
required: java.util.ArrayList[Any]
Note: Integer <: Any, but Java-defined class ArrayList is invariant in type E.
You may wish to investigate a wildcard type such as `_ <: Any`. (SLS 3.2.10)
test(a,b)
Sounds familiar??
And to fix, just inform the type T to call the method: test[Integer](a,b) works fine.
EDIT:
There a few things involved here:
Erasure -> When compiled the type of the generic will disappear by erasure. The compiler will use Object which Scala, will treat as Any. However a ArrayList[Integer] is not an ArrayList[Any], even though Integer is any. The same way that TableField[gen.tables.records.DocRecord,Integer] is not a Field[Any].
Type inference mechanism -> it will figure out what type T should be and to do that it will use the intersection dominator of the types passed (in our case the first common ancestor). Page 36 of Scala Language Spec, which in our examples above will lead use to Any.
Implicit conversion -> it is the last step and would be called if there was some type to be converted to another one, but since the type of the arguments were determined to be the first common ancestor, there is no need to convert and we will never have a implicit conversion if we don't force the type T.
A example to show how the common ancestor is used to determine T:
scala> def test[T](a: T, b: T): T = a
scala> class Foo
scala> class Boo extends Foo
scala> test(new Boo,new Foo)
res2: Foo = Boo#139c2a6
scala> test(new Boo,new Boo)
res3: Boo = Boo#141c803
scala> class Coo extends Foo
scala> test(new Boo,new Coo)
res4: Foo = Boo#aafc83
scala> test(new Boo,"qsasad")
res5: Object = Boo#16989d8
Summing up, the implicit method does not get called, because the type inference mechanism, determines the types before getting the argument and since it uses the common ancestor, there is no need for a implicit conversion.
Your code produces an error due to erasure mechanism which disappear with the type information that would be important to determine the correct type of the argument.
#RobN, thanks for questioning my answer, I learned a lot with the process.
Is it possible to write a method in Scala which returns an object of a type-parameterized class with different type paramter ? Something like this:
class A[T]
def f(switch: Boolean): A = if(switch) new A[Int] else new A[String]
Please note: The Code above is fictional to show the type of problem; The code above does not make semantically sense.
The code above will not compile because return type A is not parameterized.
You can, and you can even do it with type-safety with the aid of implicit arguments that encapsulate the pairings:
class TypeMapping[+A,B] {
def newListB = List.empty[B]
}
trait Logical
object True extends Logical
object False extends Logical
implicit val mapFalseToInt = new TypeMapping[False.type,Int]
implicit val mapTrueToString = new TypeMapping[True.type,String]
def f[A <: Logical,B](switch: A)(implicit tmap: TypeMapping[A,B]) = tmap.newListB
scala> f(True)
res2: List[String] = List()
scala> f(False)
res3: List[Int] = List()
You do have to explicitly map from boolean values to the custom True and False values.
(I have chosen List as the target class just as an example; you could pick anything or even make it generic with a little more work.)
(Edit: as oxbow_lakes points out, if you need all possible return values to be represented on the same code path, then this alone won't do it, because the superclass of List[Int] and List[String] is List[Any], which isn't much help. In that case, you should use an Either. My solution is for a single function that will be used only in the True or False contexts, and can maintain the type information there.)
One way of expressing this would be by using Either;
def f(switch: Boolean) = if (switch) Left(new A[Int]) else Right(newA[String])
This of course returns an Either[A[Int], A[String]]. You certainly cannot (at the moment) declare a method which returns some parameterized type P, with some subset of type parameters (i.e. only Int or String).
The language ceylon has union types and I understand the intention is to add these to scala in the near future, in which case, you could define a method:
def f(switch: Boolean): A[Int|String] = ...
Well, you could do something like that.
scala> class A {
| type T
| }
defined class A
scala> def f(b: Boolean): A = if(b) new A { type T = Int } else new A { type T = String }
f: (b: Boolean)A
But this is pointless. Types are a compile time information, and that information is getting lost here.
How about an absolutely minimal change to the "fictional code"? If we just add [_] after the "fictional" return type, the code will compile:
class A[T]
def f(switch: Boolean):A[_] = if(switch) new A[Int] else new A[String]
It is worth noting that A[_] is not the same as A[Any]. A[T] does not need to be defined covariant for the code to compile.
Unfortunately, information about the type gets lost.
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.