Method types have no value. How do we evaluate a method?
Using SML as an example, I have
fun myFunc(x) = x + 5
val b = myFunc(2)
In the second expression, myFun has a type and a value, we use its type to do type checking and use its value together with its argument to evaluate value for b
But in Scala methods without a value how do we evaluate? I am pretty new to Scala so it may not be very clear.
def myFunc(x) = x + 5
val b = myFunc(2)
From val b = myFunc(2) to val b = 2 + 5, what happened in between? From where or what object do we know that myFunc(x) is x + 5?
THanks!!
The simple answer is: just because a method is not a value in the sense of "a thing that can be manipulated by you" doesn't mean that it is not a value in the sense of "a thing that can be manipulated by the author of the compiler".
Of course, a method will have an object representing it inside of the compiler. In fact, that object will probably look very similar to the object representing a function inside, say, the MLTon SML compiler or SML/NJ.
In SML, syntax is not a value, but you are not questioning how it is possible to write a function call either, aren't you? After all, in order to call a function in SML, I need to write a function call using function call syntax, so how can I do that when syntax is not a value?
Well, the answer is the same: just because syntax is not a value that the programmer can manipulate, the compiler (or more precisely the parser) obviously does know about syntax.
I can't tell you why the decision was made to have functions be values in Scala but not methods, but I can make a guess. Scala is an object-oriented language. In an object-oriented language, every value is an object, and every object has methods that are bound to that object. So, if methods are objects, they need to have methods, which are objects, which have methods, which are objects, and so on.
There are ways to deal with this, of course, but it makes the language more complex. For a similar reason, classes aren't objects (unlike, say, in Smalltalk, Python, and Ruby). Note that even in highly reflective, introspective, dynamic languages like Ruby, methods are not objects. Classes are, but not methods.
It is possible using reflection to get a proxy object that represents a method, but that object is not the method itself. And you can actually do the same in Scala as well.
And of course it is possible to turn a method into a function value by η-expansion.
I'm assuming that you're compiling to Java Virtual Machine (JVM) bytecode, such as with scalac, which is probably the most common way to use Scala. Disclaimer: I'm not an expert on the JVM, so some parts of this answer might be a bit wrong, but the general idea is right.
Essentially, a method is a set of instructions for the runtime to execute. It exists as part of the compiled code on disk (e.g. a .class file). When the JVM loads the class, it pulls the entire class file into memory, including the methods. When the JVM encounters a method call, it looks up the method and starts executing the instructions in it. If the method returns a result, the JVM makes that result available in the calling code, then does whatever you wanted to do with it there, such as assigning to a variable.
With that knowledge, we can answer some of your questions:
From val b = myFunc(2) to val b = 2 + 5, what happened in between?
This isn't quite how it works, as the JVM doesn't "expand" myFunc in place, but instead looks up myFunc and executes the instructions in it.
From where or what object do we know that myFunc(x) is x + 5?
Not from any object. While myFunc is in memory, it's in an area of memory that you can't access directly (but the JVM can).
why can't it be a value since it is a chunk of memory?
Not all memory fits into the nice abstractions of types and values.
Related
I'm new in Scala and don't understand some base things.
Scala does not contains primitives. Hence int, short and other "simple" number types are objects. So, according to JMM, they are not located at stack and subject to cleaning by GB. Cleaning by GB may be too expensive for some cases.
So I don't clearly understand, why Scala is considered faster than Java (in which primitives located in stack).
Scala does not contains primitives. Hence int, short and other "simple" number types are objects.
That is correct.
So, according to JMM,
The Java Memory Model is for Java. It is completely irrelevant to Scala.
they are not located at stack and subject to cleaning by GB. Cleaning by GB may be too expensive for some cases.
There is no such thing as a "stack" in Scala. The Scala Language Specification only mentions the term "stack" in very few places, and none of them have anything to do with Ints:
In section 1 Lexical Syntax, subsection 1.6 XML mode, it is said that because XML literals and Scala code can be arbitrarily nested, the parser has to use a stack data structure to keep track of the context.
In section 7 Implicits, subsection 7.2 Implicit parameters, it is said that to prevent an infinite recursion when searching for implicit, the compiler keeps a stack of "open types", which are types that it is currently searching an implicit for.
In section 6 Expressions, subsection 6.6 Function Applications, there is the following statement, specifying Proper Direct Tail Recursion:
A function application usually allocates a new frame on the program's run-time stack. However, if a local method or a final method calls itself as its last action, the call is executed using the stack-frame of the caller.
In section 6 Expressions, subsection 6.20 Return Expressions, there is the following statement about one possible implementation strategy for non-local returns from nested functions:
Returning from the method from within a nested function may be implemented by throwing and catching a scala.runtime.NonLocalReturnControl. Any exception catches between the point of return and the enclosing methods might see and catch that exception. A key comparison makes sure that this exception is only caught by the method instance which is terminated by the return.
If the return expression is itself part of an anonymous function, it is possible that the enclosing method m has already returned before the return expression is executed. In that case, the thrown scala.runtime.NonLocalReturnControl will not be caught, and will propagate up the call stack.
Of these 4 instances, the first 2 clearly do not refer to the concept of a call stack but rather to the generic computer science data structure. The 4th one is only an example of a possible implementation strategy ("Returning from the method from within a nested function may be implemented by […]"). Only the 3rd one is actually relevant, as it indeed talks about a call stack. However, it does not say anything about allocating Ints, and it explicitly leaves the door open to alternative implementations as well, by stating that "usually" function application leads to allocation of a stack frame, but doesn't have to.
So I don't clearly understand, why Scala is considered faster than Java (in which primitives located in stack).
Actually, there is nothing in the Java Language Specification either that says that primitives are located on the stack. In fact, the Java Language Specification does not mandate the existence of a stack at all. It would be perfectly legal to implement Java without a stack.
There are exactly zero occurrences of the term "stack" in the JLS. There are a couple of mentions of the term "heap", but only in the compound term "heap pollution", which is simply a word describing a certain flaw in the type system, but does not necessarily require a heap, and does not mandate a heap.
And none of these mentions of "heap pollution" have anything to do with primitives.
Note that, when I say that the Scala Language Specification says nothing about stacks or heaps or how Ints are allocated, that is actually really important. Because the SLS doesn't say anything, implementors are allowed to do whatever they want, including making Ints primitive and allocating them on the stack.
And that is exactly what most Scala implementations do. The (now-defunct) Scala.NET implemented scala.Int as a .NET System.Int32. Scala-native implements scala.Int as a C int32_t. Scala.js implements scala.Int as an ECMAScript number. And Scala-JVM implements scala.Int as a JVM int.
If you check out the source code of scala.Int in the Scala-JVM repository (src/library/scala/Int.scala), you will find that it is actually empty! More precisely, it only contains documentation and declarations, but no definitions or implementations. Also, the class is marked final (meaning it can't be inherited from) and abstract (meaning it must be inherited from in order to provide overrides for the missing implementations), which is a contradiction.
How does this work? Well, the compiler knows what an Int is and how it works, and it simply generates the correct code for dealing with a JVM int. So, when it sees a call to scala.Int.+, it knows that instead it must generate an iadd bytecode instruction. Likewise, Scala-native will just generate the native integer addition instructions, and so on.
In other words, Ints are semantically defined as objects, but they are actually pragmatically implemented as primitives.
This is a general rule of how language specifications work: typically, they only describe what the result is that the programmer sees, but they leave it open to the implementor how to actually achieve that result. So, the SLS specifies that an Int must look as if it actually were an object, but there is nothing that says it actually has to be one.
They are handled the same way that Java handles those types, they're only boxed when strictly necessary. The details on how and when they are boxed may differ, but the compiler uses a primitive representation if it can do so. Here's what the docs say (this is just for Int, but it applies to other "primitive" types too):
Int, a 32-bit signed integer (equivalent to Java's int primitive type) is a subtype of scala.AnyVal. Instances of Int are not represented by an object in the underlying runtime system.
There is an implicit conversion from scala.Int => scala.runtime.RichInt which provides useful non-primitive operations.
https://www.scala-lang.org/api/2.13.6/scala/Int.html
The main difference, really, is that there aren't two separate types, like in Java, to represent the boxed and unboxed representations — both get the same Int type, whereas Java has int and Integer.
I am new to Scala and heard a lot that everything is an object in Scala. What I don't get is what's the advantage of "everything's an object"? What are things that I cannot do if everything is not an object? Examples are welcome. Thanks
The advantage of having "everything" be an object is that you have far fewer cases where abstraction breaks.
For example, methods are not objects in Java. So if I have two strings, I can
String s1 = "one";
String s2 = "two";
static String caps(String s) { return s.toUpperCase(); }
caps(s1); // Works
caps(s2); // Also works
So we have abstracted away string identity in our operation of making something upper case. But what if we want to abstract away the identity of the operation--that is, we do something to a String that gives back another String but we want to abstract away what the details are? Now we're stuck, because methods aren't objects in Java.
In Scala, methods can be converted to functions, which are objects. For instance:
def stringop(s: String, f: String => String) = if (s.length > 0) f(s) else s
stringop(s1, _.toUpperCase)
stringop(s2, _.toLowerCase)
Now we have abstracted the idea of performing some string transformation on nonempty strings.
And we can make lists of the operations and such and pass them around, if that's what we need to do.
There are other less essential cases (object vs. class, primitive vs. not, value classes, etc.), but the big one is collapsing the distinction between method and object so that passing around and abstracting over functionality is just as easy as passing around and abstracting over data.
The advantage is that you don't have different operators that follow different rules within your language. For example, in Java to perform operations involving objects, you use the dot name technique of calling the code (static objects still use the dot name technique, but sometimes the this object or the static object is inferred) while built-in items (not objects) use a different method, that of built-in operator manipulation.
Number one = Integer.valueOf(1);
Number two = Integer.valueOf(2);
Number three = one.plus(two); // if only such methods existed.
int one = 1;
int two = 2;
int three = one + two;
the main differences is that the dot name technique is subject to polymorphisim, operator overloading, method hiding, and all the good stuff that you can do with Java objects. The + technique is predefined and completely not flexible.
Scala circumvents the inflexibility of the + method by basically handling it as a dot name operator, and defining a strong one-to-one mapping of such operators to object methods. Hence, in Scala everything is an object means that everything is an object, so the operation
5 + 7
results in two objects being created (a 5 object and a 7 object) the plus method of the 5 object being called with the parameter 7 (if my scala memory serves me correctly) and a "12" object being returned as the value of the 5 + 7 operation.
This everything is an object has a lot of benefits in a functional programming environment, for example, blocks of code now are object too, making it possible to pass back and forth blocks of code (without names) as parameters, yet still be bound to strict type checking (the block of code only returns Long or a subclass of String or whatever).
When it boils down to it, it makes some kinds of solutions very easy to implement, and often the inefficiencies are mitigated by the lack of need to handle "move into primitives, manipulate, move out of primitives" marshalling code.
One specific advantage that comes to my mind (since you asked for examples) is what in Java are primitive types (int, boolean ...) , in Scala are objects that you can add functionality to with implicit conversions. For example, if you want to add a toRoman method to ints, you could write an implicit class like:
implicit class RomanInt(i:Int){
def toRoman = //some algorithm to convert i to a Roman representation
}
Then, you could call this method from any Int literal like :
val romanFive = 5.toRoman // V
This way you can 'pimp' basic types to adapt them to your needs
In addition to the points made by others, I always emphasize that the uniform treatment of all values in Scala is in part an illusion. For the most part it is a very welcome illusion. And Scala is very smart to use real JVM primitives as much as possible and to perform automatic transformations (usually referred to as boxing and unboxing) only as much as necessary.
However, if the dynamic pattern of application of automatic boxing and unboxing is very high, there can be undesirable costs (both memory and CPU) associated with it. This can be partially mitigated with the use of specialization, which creates special versions of generic classes when particular type parameters are of (programmer-specified) primitive types. This avoids boxing and unboxing but comes at the cost of more .class files in your running application.
Not everything is an object in Scala, though more things are objects in Scala than their analogues in Java.
The advantage of objects is that they're bags of state which also have some behavior coupled with them. With the addition of polymorphism, objects give you ways of changing the implicit behavior and state. Enough with the poetry, let's go into some examples.
The if statement is not an object, in either scala or java. If it were, you could be able to subclass it, inject another dependency in its place, and use it to do stuff like logging to a file any time your code makes use of the if statement. Wouldn't that be magical? It would in some cases help you debug stuff, and in other cases it would make your hairs grow white before you found a bug caused by someone overwriting the behavior of if.
Visiting an objectless, statementful world: Imaging your favorite OOP programming language. Think of the standard library it provides. There's plenty of classes there, right? They offer ways for customization, right? They take parameters that are other objects, they create other objects. You can customize all of these. You have polymorphism. Now imagine that all the standard library was simply keywords. You wouldn't be able to customize nearly as much, because you can't overwrite keywords. You'd be stuck with whatever cases the language designers decided to implement, and you'd be helpless in customizing anything there. Such languages exist, you know them well, they're the sequel-like languages. You can barely create functions there, but in order to customize the behavior of the SELECT statement, new versions of the language had to appear which included the features most desired. This would be an extreme world, where you'd only be able to program by asking the language designers for new features (which you might not get, because someone else more important would require some feature incompatible with what you want)
In conclusion, NOT everything is an object in scala: Classes, expressions, keywords and packages surely aren't. More things however are, like functions.
What's IMHO a nice rule of thumb is that more objects equals more flexibility
P.S. in Python for example, even more things are objects (like the classes themselves, the analogous concept for packages (that is python modules and packages). You'd see how there, black magic is easier to do, and that brings both good and bad consequences.
I have been reading about methods and functions in Scala. Jim's post and Daniel's complement to it do a good job of explaining what the differences between these are. Here is what I took with me:
functions are objects, methods are not;
as a consequence functions can be passed as argument, but methods can not;
methods can be type-parametrised, functions can not;
methods are faster.
I also understand the difference between def, val and var.
Now I have actually two questions:
Why can't we parametrise the apply method of a function to parametrise the function? And
Why can't the method be called by the function object to run faster? Or the caller of the function be made calling the original method directly?
Looking forward to your answers and many thanks in advance!
1 - Parameterizing functions.
It is theoretically possible for a compiler to parameterize the type of a function; one could add that as a feature. It isn't entirely trivial, though, because functions are contravariant in their argument and covariant in their return value:
trait Function1[+T,-R] { ... }
which means that another function that can take more arguments counts as a subclass (since it can process anything that the superclass can process), and if it produces a smaller set of results, that's okay (since it will also obey the superclass construct that way). But how do you encode
def fn[A](a: A) = a
in that framework? The whole point is that the return type is equal to the type passed in, whatever that type has to be. You'd need
Function1[ ThisCanBeAnything, ThisHasToMatch ]
as your function type. "This can be anything" is well-represented by Any if you want a single type, but then you could return anything as the original type is lost. This isn't to say that there is no way to implement it, but it doesn't fit nicely into the existing framework.
2 - Speed of functions.
This is really simple: a function is the apply method on another object. You have to have that object in order to call its method. This will always be slower (or at least no faster) than calling your own method, since you already have yourself.
As a practical matter, JVMs can do a very good job inlining functions these days; there is often no difference in performance as long as you're mostly using your method or function, not creating the function object over and over. If you're deeply nesting very short loops, you may find yourself creating way too many functions; moving them out into vals outside of the nested loops may save time. But don't bother until you've benchmarked and know that there's a bottleneck there; typically the JVM does the right thing.
Think about the type signature of a function. It explicitly says what types it takes. So then type-parameterizing apply() would be inconsistent.
A function is an object, which must be created, initialized, and then garbage-collected. When apply() is called, it has to grab the function object in addition to the parent.
I mean if there's some declarative way to prevent an object from changing any of it's members.
In the following example
class student(var name:String)
val s = new student("John")
"s" has been declared as a val, so it will always point to the same student.
But is there some way to prevent s.name from being changed by just declaring it like immutable???
Or the only solution is to declare everything as val, and manually force immutability?
No, it's not possible to declare something immutable. You have to enforce immutability yourself, by not allowing anyone to change it, that is remove all ways of modifying the class.
Someone can still modify it using reflection, but that's another story.
Scala doesn't enforce that, so there is no way to know. There is, however, an interesting compiler-plugin project named pusca (I guess it stands for Pure-Scala). Pure is defined there as not mutating a non-local variable and being side-effect free (e.g. not printing to the console)—so that calling a pure method repeatedly will always yield the same result (what is called referentially transparent).
I haven't tried out that plug-in myself, so I can't say if it's any stable or usable already.
There is no way that Scala could do this generally.
Consider the following hypothetical example:
class Student(var name : String, var course : Course)
def stuff(course : Course) {
magically_pure_val s = new Student("Fredzilla", course)
someFunctionOfStudent(s)
genericHigherOrderFunction(s, someFunctionOfStudent)
course.someMethod()
}
The pitfalls for any attempt to actually implement that magically_pure_val keyword are:
someFunctionOfStudent takes an arbitrary student, and isn't implemented in this compilation unit. It was written/compiled knowing that Student consists of two mutable fields. How do we know it doesn't actually mutate them?
genericHigherOrderFunction is even worse; it's going to take our Student and a function of Student, but it's written polymorphically. Whether or not it actually mutates s depends on what its other arguments are; determining that at compile time with full generality requires solving the Halting Problem.
Let's assume we could get around that (maybe we could set some secret flags that mean exceptions get raised if the s object is actually mutated, though personally I wouldn't find that good enough). What about that course field? Does course.someMethod() mutate it? That method call isn't invoked from s directly.
Worse than that, we only know that we'll have passed in an instance of Course or some subclass of Course. So even if we are able to analyze a particular implementation of Course and Course.someMethod and conclude that this is safe, someone can always add a new subclass of Course whose implementation of someMethod mutates the Course.
There's simply no way for the compiler to check that a given object cannot be mutated. The pusca plugin mentioned by 0__ appears to detect purity the same way Mercury does; by ensuring that every method is known from its signature to be either pure or impure, and by raising a compiler error if the implementation of anything declared to be pure does anything that could cause impurity (unless the programmer promises that the method is pure anyway).[1]
This is quite a different from simply declaring a value to be completely (and deeply) immutable and expecting the compiler to notice if any of the code that could touch it could mutate it. It's also not a perfect inference, just a conservative one
[1]The pusca README claims that it can infer impurity of methods whose last expression is a call to an impure method. I'm not quite sure how it can do this, as checking if that last expression is an impure call requires checking if it's calling a not-declared-impure method that should be declared impure by this rule, and the implementation might not be available to the compiler at that point (and indeed could be changed later even if it is). But all I've done is look at the README and think about it for a few minutes, so I might be missing something.
Some time ago Oracle decided that adding Closures to Java 8 would be an good idea. I wonder how design problems are solved there in comparison to Scala, which had closures since day one.
Citing the Open Issues from javac.info:
Can Method Handles be used for Function Types?
It isn't obvious how to make that work. One problem is that Method Handles reify type parameters, but in a way that interferes with function subtyping.
Can we get rid of the explicit declaration of "throws" type parameters?
The idea would be to use disjuntive type inference whenever the declared bound is a checked exception type. This is not strictly backward compatible, but it's unlikely to break real existing code. We probably can't get rid of "throws" in the type argument, however, due to syntactic ambiguity.
Disallow #Shared on old-style loop index variables
Handle interfaces like Comparator that define more than one method, all but one of which will be implemented by a method inherited from Object.
The definition of "interface with a single method" should count only methods that would not be implemented by a method in Object and should count multiple methods as one if implementing one of them would implement them all. Mainly, this requires a more precise specification of what it means for an interface to have only a single abstract method.
Specify mapping from function types to interfaces: names, parameters, etc.
We should fully specify the mapping from function types to system-generated interfaces precisely.
Type inference. The rules for type inference need to be augmented to accomodate the inference of exception type parameters. Similarly, the subtype relationships used by the closure conversion should be reflected as well.
Elided exception type parameters to help retrofit exception transparency.
Perhaps make elided exception type parameters mean the bound. This enables retrofitting existing generic interfaces that don't have a type parameter for the exception, such as java.util.concurrent.Callable, by adding a new generic exception parameter.
How are class literals for function types formed?
Is it #void().class ? If so, how does it work if object types are erased? Is it #?(?).class ?
The system class loader should dynamically generate function type interfaces.
The interfaces corresponding to function types should be generated on demand by the bootstrap class loader, so they can be shared among all user code. For the prototype, we may have javac generate these interfaces so prototype-generated code can run on stock (JDK5-6) VMs.
Must the evaluation of a lambda expression produce a fresh object each time?
Hopefully not. If a lambda captures no variables from an enclosing scope, for example, it can be allocated statically. Similarly, in other situations a lambda could be moved out of an inner loop if it doesn't capture any variables declared inside the loop. It would therefore be best if the specification promises nothing about the reference identity of the result of a lambda expression, so such optimizations can be done by the compiler.
As far as I understand 2., 6. and 7. aren't a problem in Scala, because Scala doesn't use Checked Exceptions as some sort of "Shadow type-system" like Java.
What about the rest?
1) Can Method Handles be used for Function Types?
Scala targets JDK 5 and 6 which don't have method handles, so it hasn't tried to deal with that issue yet.
2) Can we get rid of the explicit declaration of "throws" type parameters?
Scala doesn't have checked exceptions.
3) Disallow #Shared on old-style loop index variables.
Scala doesn't have loop index variables. Still, the same idea can be expressed with a certain kind of while loop . Scala's semantics are pretty standard here. Symbols bindings are captured and if the symbol happens to map to a mutable reference cell then on your own head be it.
4) Handle interfaces like Comparator that define more than one method all but one of which come from Object
Scala users tend to use functions (or implicit functions) to coerce functions of the right type to an interface. e.g.
[implicit] def toComparator[A](f : (A, A) => Int) = new Comparator[A] {
def compare(x : A, y : A) = f(x, y)
}
5) Specify mapping from function types to interfaces:
Scala's standard library includes FuncitonN traits for 0 <= N <= 22 and the spec says that function literals create instances of those traits
6) Type inference. The rules for type inference need to be augmented to accomodate the inference of exception type parameters.
Since Scala doesn't have checked exceptions it can punt on this whole issue
7) Elided exception type parameters to help retrofit exception transparency.
Same deal, no checked exceptions.
8) How are class literals for function types formed? Is it #void().class ? If so, how does it work if object types are erased? Is it #?(?).class ?
classOf[A => B] //or, equivalently,
classOf[Function1[A,B]]
Type erasure is type erasure. The above literals produce scala.lang.Function1 regardless of the choice for A and B. If you prefer, you can write
classOf[ _ => _ ] // or
classOf[Function1[ _,_ ]]
9) The system class loader should dynamically generate function type interfaces.
Scala arbitrarily limits the number of arguments to be at most 22 so that it doesn't have to generate the FunctionN classes dynamically.
10) Must the evaluation of a lambda expression produce a fresh object each time?
The Scala specification does not say that it must. But as of 2.8.1 the the compiler does not optimizes the case where a lambda does not capture anything from its environment. I haven't tested with 2.9.0 yet.
I'll address only number 4 here.
One of the things that distinguishes Java "closures" from closures found in other languages is that they can be used in place of interface that does not describe a function -- for example, Runnable. This is what is meant by SAM, Single Abstract Method.
Java does this because these interfaces abound in Java library, and they abound in Java library because Java was created without function types or closures. In their absence, every code that needed inversion of control had to resort to using a SAM interface.
For example, Arrays.sort takes a Comparator object that will perform comparison between members of the array to be sorted. By contrast, Scala can sort a List[A] by receiving a function (A, A) => Int, which is easily passed through a closure. See note 1 at the end, however.
So, because Scala's library was created for a language with function types and closures, there isn't need to support such a thing as SAM closures in Scala.
Of course, there's a question of Scala/Java interoperability -- while Scala's library might not need something like SAM, Java library does. There are two ways that can be solved. First, because Scala supports closures and function types, it is very easy to create helper methods. For example:
def runnable(f: () => Unit) = new Runnable {
def run() = f()
}
runnable { () => println("Hello") } // creates a Runnable
Actually, this particular example can be made even shorter by use of Scala's by-name parameters, but that's beside the point. Anyway, this is something that, arguably, Java could have done instead of what it is going to do. Given the prevalence of SAM interfaces, it is not all that surprising.
The other way Scala handles this is through implicit conversions. By just prepending implicit to the runnable method above, one creates a method that gets automatically (note 2) applied whenever a Runnable is required but a function () => Unit is provided.
Implicits are very unique, however, and still controversial to some extent.
Note 1: Actually, this particular example was choose with some malice... Comparator has two abstract methods instead of one, which is the whole problem with it. Since one of its methods can be implemented in terms of the other, I think they'll just "subtract" defender methods from the abstract list.
And, on the Scala side, even though there's a sort method that uses (A, A) => Boolean, not (A, A) => Int, the standard sorting method calls for a Ordering object, which is quite similar to Java's Comparator! In Scala's case, though, Ordering performs the role of a type class.
Note 2: Implicits are automatically applied, once they have been imported into scope.