Multi-Dispatch in the Java Virtual Machine: Design and Implementation

Mainstream object-oriented languages, such as C++ and Java ¹, provide only a restricted form of polymorphic methods, namely uni-receiver dispatch. In common programming situations, developers must work around this limitation. We describe how to extend the Java Virtual Machine to support multi-dispatch and examine the complications that Java imposes on multi-dispatch in practice. Our technique avoids changes to the Java programming language itself, maintains source code and library compatibility, and isolates the performance penalty and semantic changes of multi-method dispatch to the program sections which use it. We have micro-benchmark and application-level performance results for a dynamic Most Specific Applicable (MSA) dispatcher, a framework-based Single Receiver Projections (SRP) dispatcher, and a tuned SRP dispatcher. Our general-purpose technique provides smaller dispatch latency than programmer-written double-dispatch code with equivalent functionality.

Introduction

Object-oriented (OO) languages provide powerful tools for expressing computations. One key abstraction is the concept of a type hierarchy which describes the relationships among types. Objects represent instances of these different types. Most existing object-oriented languages require each object variable to have a programmer-assigned static type. The compiler uses this information to recognize some coding errors. The principle of substitutability mandates that in any location where type T is expected, any sub-type of T is acceptable. But, substitutability allows that object variable to have a different (but related) dynamic type at runtime.

Another key facility found in OO languages is method selection based upon the types of the arguments. This method selection process is known as dispatch. It can occur at compile-time or at execution-time. In the former case, where only the static type information is available, we have static dispatch (method overloading). The latter case is known as dynamic dispatch (dynamic method overriding or virtual functions) and object-oriented languages leverage it to provide polymorphism -- the execution of type-specific program code.

We can divide OO languages into two broad categories based upon how many arguments are considered during dispatch. Uni-dispatch languages select a method based upon the type of one distinguished argument; multi-dispatch languages consider more than one, and potentially all, of the arguments at dispatch time. For example, Smalltalk [14] is a uni-dispatch language. CLOS [23] and Cecil [6] are multi-dispatch languages. Other terms, like multiple dispatch, are used in the literature. However, the term multiple dispatch is confusing since it can mean either successive uni-dispatches or a single multi-dispatch. In fact, in this paper, we compare multi-dispatch to double dispatch, which uses two uni-dispatches.

C++ [24] and Java [15] are dynamic uni-dispatch languages. However, for both languages, the compiler considers the static types of all arguments when compiling method invocations. Therefore, we can regard these languages as supporting static multi-dispatch. Figure 1 depicts both dynamic uni-dispatch and static multi-dispatch in Java.

Uni-dispatch limits the method selection process to consider only a single argument, usually the receiver. This is a substantial limitation and standard programming idioms exist to overcome this restriction. As a motivation for multi-dispatch, we describe one programming idiom that demonstrates the need for multi-dispatch, describe how it can be replaced by multi-dispatch, list the advantages of using multi-dispatch to replace the idiomatic code, and measure the cost of using multi-dispatch with one of our current multi-dispatch algorithms.

**Figure 1:** Dispatch Techniques in Java
$\fbox {\begin{minipage}[t]{18pc}\vspace{-9pt}\texttt{\footnotesize{\begin{tabbin... ...Pc.draw(aCanvas); \textit{// ColorPoint::draw()} \end{tabbing}}}\end{minipage}}$

Double Dispatch

Double dispatch occurs when a method explicitly checks an argument type and executes different code as a result of this check. Double dispatch is illustrated in Figure 2(a) (from Sun's AWT classes) where the processEvent(AWTEvent) method must process events in different ways, since event objects are instances of different classes. Since all of the events are placed in a queue whose static element type is AWTEvent, the compiler loses the more specific dynamic type information. When an element is removed from the queue for processing, its dynamic type must be explicitly checked to pick the appropriate action. This is an example of the well-known container problem [5].

**Figure 2:** Double vs. Multi-Dispatch in Java
$\fbox {\begin{minipage}[t]{18pc}\vspace{-9pt} \texttt{\scriptsize{\begin{tabbing... ...] \textrm{\textbf{(a) Double Dispatch in Java}} \end{tabbing}}} \end{minipage}}$ $\fbox {\begin{minipage}[t]{18pc}\vspace{-9pt}\texttt{\scriptsize{\begin{tabbing}... ...bf{(b) Equivalent Code in Multi-Dispatch Java}} \end{tabbing}}} \end{minipage}}$

Double dispatch suffers from a number of disadvantages. First, double dispatch has the overhead of invoking a second method. Second, the double-dispatch program is longer and more complex; this provides more opportunity for coding errors. Third, the double-dispatch program is more difficult to maintain since adding a new event type requires not only the code to handle the new event, but another cascaded else if statement.

The need for double dispatch develops naturally in several common situations. Consider binary operations [4], such as the compareTo(Object) method defined in interface Comparable. The programmer must ascertain the type of the Object argument before continuing to perform a type-specific comparison. Another common use for double dispatch is in drag-and-drop applications, where the result of a user action depends on both the data object dragged and on the target object. A generic drag-and-drop schema forces the programmer to test data types and re-dispatch to a more specific method. A third example is in event-driven programming. As we saw in Figure 2, applications are written using base classes such as Component and Event, but we need to take action based upon the specific types of both Component and Event. Indeed, the need for multi-dispatch is ubiquitous enough that two of the original design patterns, Visitor and Strategy, are work-arounds to supply multi-dispatch functionality within uni-dispatch languages.

Consider how the AWT example could be re-written if dynamic multi-dispatch was available in Java. An equivalent program, partially using multi-dispatch, would resemble Figure 2(b). For clarity, we have not completely converted the code to use multi-dispatch; we maintain the case statement and double dispatch to select among MouseEvent categories. A more complete factoring of MouseEvent into MouseButtonEvent and MouseMotionEvent would eliminate the remaining double dispatch, resulting in a Full Multi-Dispatch version of the code. The dynamic multi-dispatcher will select the correct method at runtime based upon the dispatchable arguments in addition to the receiver argument (the instance of Component). Individual component types can still override the methods that accept specific event types (e.g. KeyEvent, FocusEvent) and will do so without invoking the double-dispatch code.

The multi-dispatch version is shorter and clearer. However, it requires the Java Virtual Machine (JVM) [20] to directly dispatch an Event to the correct processEvent(AWTEvent) method. Our modified JVM provides this facility and correctly executes the multi-dispatch code discussed above. Furthermore, Table 1, a subset of Table 4, shows that multi-dispatch is substantially faster than interpreted double dispatch and even faster than JIT-ed double dispatch. Note that the numbers in Table 1 are based on single-threaded code.

Our experience with the Swing GUI classes [26] reinforces our belief that double dispatch in AWT is a significant factor in Swing applications. First, Swing does not operate without AWT; instead each AWTEvent is accepted by a Swing JComponent. Therefore, every mouse-click and key-press is double dispatched through AWT into Swing. Next, Swing type-checks the event and double dispatches again. Internally, Swing avoids further double dispatch by coding the AWTEvent type into the selector (e.g. fireInternalEvent()). Despite the limitations this imposes on the programmer, it is clear that double dispatch is still the standard technique in Swing as well.

Also, a multi-dispatch JVM could benefit other languages. For example, Standard ML, Scheme, and Eiffel have implementations which generate JVM-compatible binary files. Extending these languages to include multi-dispatch semantics becomes straightforward. Unlike techniques based on source code translation, our multi-dispatch JVM can be directly used by other languages.

We begin by reviewing some important details about the uni-dispatch JVM. Next, we sketch our JVM modifications to enable multi-dispatch. Then, we present experimental results for implementations of our multi-dispatch techniques. This is followed by a discussion of several complex issues that a practical multi-dispatch Java must address and a description of some of the details of our implementation. Finally, we close with a description of future work and a review of related approaches to multi-dispatch.

Background

The Java Programming Language [15] is a static multi-dispatch, dynamic uni-dispatch, dynamic loading object-oriented language. Our primary design goal is to extend the dynamic method selection to optionally and efficiently consider all arguments, without affecting the syntax of the language or any other semantics. Our secondary goals are to retain the dynamic and reflective properties of Java.

In order to meet these goals, we chose to modify the JVM [20] implementation, rather than modifying the programming language itself. Java programs are compiled by javac (or other compiler) into sequences of bytecodes -- primitive operations of a simple stack-based computer. These bytecodes are interpreted by a JVM written for each hardware platform. We began with the classic VM (now known as the Research Virtual Machine²) written in C and distributed by Sun Microsystems, Inc. Other JVM implementations exist and many include just-in-time (JIT) compiler technology to enhance the interpretation speed at runtime by replacing the bytecodes with equivalent native machine instructions. At present, our modified JVM is compatible with the OpenJIT 1.1.15 [21] compiler.

Before we look at how to implement multi-dispatch in the virtual machine, we first need to understand the binary representation that the virtual machine executes, how method invocations are translated into the virtual machine code, and how the JVM actually dispatches the call-sites.

Java Classfile format

The JVM reads the bytecodes, along with some necessary symbolic information from a binary representation, known as a .class file. Each .class file contains a symbol table for one class, a description of its superclasses, and a series of method descriptions containing the actual bytecodes to interpret. We leverage the symbolic information, called the constant pool, to implement multi-dispatch.

Figure 3 shows the layout of the constant pool for the ColorPoint class shown in Figure 1.

Conceptually, the constant pool consists of an array containing text strings and tagged references to text strings. In Figure 3, class Point is represented by a tag entry at location 1 that indicates that it is a CLASS tag and that we should look at constant pool location 2 for the name text. Then, the constant pool contains the text string `` Point'' at location 2. Therefore, a class symbol requires two constant pool entries. Method references are similar, except they require five constant pool entries.

**Figure 3:** A Simple Constant Pool
$\begin{figure} \centering \fbox {\epsfig{file=constantpool.eps}} \vspace*{-4pt}\end{figure}$

In our example, constant pool location 9 contains the tag declaring that it contains a METHOD. It references the CLASS tag at location 1, to define the static type of the class containing the method to be invoked. In this case, the class happens to be Point itself, but, more often, this is not the case. The METHOD entry also references the NAME-AND-TYPE entry at location 10. This NAME-AND-TYPE entry contains pointers to text entries at locations 11 and 12. The first location, 11, contains the method name, `` draw''. The second location, 12, contains an encoded signature `` (LCanvas;)V'' describing the number of arguments to the method, their types, and the return type from the method. In our example, we see one class argument with name `` Canvas'' and that the return type is void.

Static Multi-Dispatch in Javac

The Java compiler converts source code into a binary representation. When it encounters a method invocation, javac must emit a constant pool entry that describes the method to be invoked. It must provide an exact description, so that, for instance, the two translate(...) methods in Point can be distinguished at runtime. Therefore, it must examine the types of the arguments at a call-site and select between them. This selection process, which considers the static types of all arguments, can be viewed as a static multi-dispatch.

The Java Language Specification, 2nd Edition (JLS) [15] provides an explicit algorithm for static multi-dispatch called Most Specific Applicable (MSA). At a call-site, the compiler begins with a list of all methods implemented and inherited by the (static) receiver type. Through a series of culling operations, the compiler reduces the set of methods down to a single most specific method. The first operation removes methods with the wrong name, methods that accept an incorrect number of arguments, and methods that are not accessible from the call-site. This latter group includes private methods called from another class and protected methods called from outside of the package.

Next, any methods which are not compatible with the static type of the arguments are also removed. This test relies upon testing widening conversions, where one type $T_{sub}$ can be widened to another $T_{super}$ if and only if $T_{sub}$ is the same type as $T_{super}$ or a subtype of $T_{super}$ . For example, a FocusEvent can be widened to an AWTEvent because the latter is a super-type of the former ³. The opposite is not valid: an AWTEvent cannot be widened to a FocusEvent; indeed a type-cast from AWTEvent to FocusEvent would need to be a type-checked narrowing conversion.

Finally, javac attempts to locate the single most specific method among the remaining subset of statically applicable methods. One method M is considered more specific than M if and only if each argument type $T_{1,i}$ can be widened to $T_{2,i}$ for each $(i=1, \ldots, n)$ , and for some

, $T_{2,j}$ cannot be widened to $T_{1,j}$ . In effect, this means that any set of arguments acceptable to M is also acceptable to M , but not vice versa.

Given the subset of applicable methods, javac selects one $M_{t}$ as its tentatively most specific. It then checks each other candidate method $M_{c}$ by testing whether its arguments can be widened to the corresponding argument in $M_{t}$ . If this is successful, then $M_{c}$ is at least as specific as $M_{t}$ ; the compiler adopts $M_{c}$ as the new tentatively most specific method -- the method $M_{t}$ is culled from the candidate list. If the first test, whether $M_{c}$ be widened to $M_{t}$ , is unsuccessful, then the compiler checks the other direction: can $M_{t}$ be widened to $M_{c}$ . If so, then the compiler drops $M_{c}$ from the candidate list.

Unfortunately, both tests can fail. To illustrate this, consider the first two methods in Figure 4. The first argument of the first method ( ColorPoint) can be widened to the type of the first argument of the second method ( Point). But the opposite is true for the second argument of each method. If we invoke colorBox with two ColorPoint arguments, both methods apply. If the third method was not present, we would have an ambiguous method error. The third method, taking two ColorPoints, removes the ambiguity because it is more specific than both of the other methods. It allows both of the others to be culled, giving a single most specific method.

**Figure 4:** Ambiguous and Conflict Methods
$\fbox {\begin{minipage}[t]{16pc}\vspace{-9pt} \texttt{\footnotesize{\begin{tabbi... ...olorBox(ColorPoint p1, ColorPoint p2) \{\ldots\} \end{tabbing}}}\end{minipage}}$

Primitive types⁴, when used as arguments, are tested at compilation time in the same way as other types. Primitive widening conversions are defined which effectively impose a standard type hierarchy on the primitive types. The compiler inserts widening casts as needed.

Dynamic Uni-Dispatch in the JVM

Now we turn our attention to dispatching polymorphic call-sites at runtime. Methods are stored in the .class file as sequences of virtual machine instructions. Within a stream of bytecodes, method invocations are represented by invoke bytecodes that occupy three bytes ⁵. The first byte contains the opcode ( 0xb6 for invokevirtual). The remaining two bytes form an index into the constant pool. The constant pool must contain a METHOD entry at the given index. This entry contains the static type of the receiver argument (as the CLASS linked entry), and the method name and signature (through the NAME&TYPE entry). Figure 5 shows the pseudo-bytecode ⁶for invoking the method Component.processEvent(AWTEvent) twice.

**Figure 5:** Polymorphic Call-sites -- two views
$\begin{figure} \centering\fbox {\epsfig{file=callsite.eps}} \vspace*{-4pt}\end{figure}$

From the opcode, invokevirtual, the JVM knows that the next two bytes contain the constant pool index of a METHOD descriptor. From that descriptor, the JVM can locate the method name and signature. The JVM parses the signature to discover that the method to be invoked requires a receiver argument and one other argument. Therefore, the JVM peeks into the operand stack and locates the receiver argument. At this point, the JVM has the information it needs to begin searching for the method to invoke. The JVM has the name, the signature, and the receiver of the message.

The JVM Specification (section 5.4.3.3) provides a recursive algorithm for resolving a method reference and locating the correct method: Beginning with the methods defined for the precise receiver argument type, scan for an exact match for the name and signature. If one is not found, search the superclass ⁷of the receiver argument, continuing up the superclass chain until Object, the root of the type hierarchy, is searched. If an exact match is not found, throw an AbstractMethodError. This look-up process applies to each of the invoke bytecodes.

This look-up process is a time-intensive operation. To reduce the overhead of method look-up, the resolved method is cached in the constant pool alongside the original method reference. The next time this method reference is applied by another invoke bytecode, the cached method is used directly.

Once a method is resolved, a method-specific invoker is executed to begin the interpretation of the new method. This invoker performs method-specific operations, such as acquiring a lock in the case of synchronized methods, constructing a JVM activation record in the case of bytecode methods, or preparing a machine-level activation record for native methods.

The Research JVM recognizes a special case in invoking methods: any private methods, final methods, or constructors can be handled in a non-virtual mode. Each of these situations do not require dynamic dispatch. But, multi-dispatch will need to handle these special cases.

Design

We now have sufficient information to describe the general design for extending the JVM to support multi-dispatch. In short, we mark classes which are to use multi-dispatch and replace their method invokers with one that selects a more specific method based on the actual arguments. Hence, existing uni-dispatch method invocations are unchanged in any way.

Marking the .class files without changing the language syntax is straightforward. We created an empty interface MultiDispatchable and any class which will provide multi-dispatch methods must implement that interface. The .class file retains that interface name and the virtual machine can easily check for this at class loading time. Our implementation does not change the syntax of the Java programming language or the binary .class file format in any way.

Our interface-based technique allows us to retain compatibility with existing programs, compilers, and libraries. Any class that implements our marker interface has different semantics for dispatch. But, the semantics of existing uni-dispatch programs and libraries are not changed since they do not implement the interface. The programmer retains complete control and responsibility for designating multi-dispatchable classes. This allows the developer to consciously target the multi-dispatch technique to known programming situations, such as double dispatch.

At dispatch time, our multi-invoker executes instead of the original JVM invoker. Our invoker locates a more-precise method based on the dynamic types of the invocation arguments and executes it in place of the original method.

The non-virtual mode invocations need to be handled specially. Constructors are never multi-dispatched. We found that constructor chaining within a class could cause infinite loops. Private and final multi-methods are still multi-dispatched.

We implemented two different dispatch algorithms. First, MSA implements a dynamic version of the Java Most Specific Applicable algorithm used by the javac compiler. Second, Single Receiver Projections (SRP) [17] is a high performance table-based technique developed at the University of Alberta. We examine both a framework-based SRP and a tuned SRP implementation. Section 6 provides implementation details, but we first present the results of our experiments.

Experimental Results

So far, we have used four different micro-benchmarks and a new implementation of Swing/AWT to test our multi-dispatcher.

The first micro-benchmark uses the javac compiler to recompile itself while running on the multi-dispatch VM. The javac compiler has not been modified, therefore the experiment demonstrates the backward compatibility of the modified VM for uni-dispatch applications. The measured overheads of uni-dispatch javac running on the multi-dispatch VM are minimal. The other three micro-benchmarks demonstrate multi-dispatch correctness, multi-dispatch performance as compared to double dispatch, and multi-dispatch performance as arity increases. All of the micro-benchmarks are single-threaded.

For our application-level tests, we modified Swing, the second-generation GUI library bundled with Java 2, to use multi-dispatch. As expected, Swing is a double-dispatch-intensive library. We also converted AWT because Swing depends heavily on AWT to dispatch the events into top-level Swing components.

All experiments were executed on a dedicated Intel-architecture PC equipped with two 550MHz Celeron processors, a 100MHz front-side bus, and 256 MB of memory. The operating system is Linux 2.2.16 with glibc version 2.1. The Sun Linux JDK 1.2.2 code was compiled using GNU C version 2.95.2, with optimization flags as supplied by Sun's makefiles ⁸. The table-based multi-dispatch code [22] was compiled using GNU G++ version 2.95.2 ⁹. The Sun JDK only supports the green threading model, which is implemented using pthreads under Linux. We report average and standard deviations for 10 runs of each benchmark.

We tested three different virtual machines. First, we have jdk, the standard JDK 1.2.2 Linux runtime, running in interpreter mode. This JVM serves as a baseline for comparing the remaining four multi-dispatch systems. Second, we have a non-JIT multi-dispatch JVM with three different multi-dispatch techniques, jdk-MSA, and two implementations (jdk-fSRP, and jdk-tSRP) of the same algorithm. Third, we have customized OpenJIT 1.1.15 to be compatible with our multi-dispatch JVM.

For the first and second micro-benchmarks, (Tables 2 and 3) we report user+system time in seconds, along with normalized values against the jdk runtime. For the third and fourth experiments (Table 4 and Figure 7), we describe individual dispatch times in microseconds, ignoring other costs. In the final benchmark, Swing, we report execution times for a synthetic application that creates a number of components and inserts 200,000 events into the event queue.

Javac -- Compatibility Test

The first experiment requires the runtime to load and execute the javac compiler to translate the entire sun.tools hierarchy of Java source files into .class files. This hierarchy includes 234 source files encompassing 49,798 lines of code (excluding comments). Each compilation was verified by comparing the error messages ¹⁰ and by checksumming the generated binaries. Each virtual machine passed the test; the timing results are shown in Table 2. These times come from the Unix time user command and are averages, with standard deviation, of 10 runs.

The negligible differences between the uni-dispatch and multi-dispatch execution times demonstrate that the overhead of running uni-dispatch code on a multi-dispatch VM is essentially zero. Note that in our implementation, table-based JVMs do not construct a dispatch table until the first multi-dispatchable method is inserted.

Simple Multi-Dispatch

In this micro-benchmark, we show that multi-dispatch is correct and measure its overhead. The testing code is short and is shown in Figure 6. Note that class MDJDriver implements the marker interface MultiDispatchable. The compiler uses static multi-dispatch to code all four calls to MDJDriver.m(X,X) to execute the method for two arguments of type A, because that is the static type of both anA and aB. Multi-dispatch actually selects among the four methods based upon the dynamic types of the arguments. Therefore, correct output consists of 100,000 repetitions of four consecutive lines: AA, AB, BA, and BB. For timing purposes, all output was redirected to /dev/null to reduce the impact of input/output. Our results are summarized in Table 3.

**Figure 6:** Simple Multi-Dispatch Testing Code
$\fbox {\begin{minipage}[t]{18pc}\vspace{-9pt} \texttt{\footnotesize{\begin{tabbi... ...ln(d.m(aB, aB)); \\ \>\> \} \\ \> \} \\ \} \end{tabbing}}}\end{minipage}}$

The table-based techniques, jdk-fSRP and jdk-tSRP, suffer from a substantial startup time, whereas jdk-MSA primarily uses existing data structures found in the JVM interpreter and lazily computes any additional values. This reduces the cost of program startup.

Double Dispatch of Events

Our third experiment involves computing the performance differences between double dispatch and the two multi-dispatch implementations of the example given in Figure 2. We constructed a synthetic type hierarchy of AWTEvent classes, to match those in Figure 2. The discussion of Swing follows in Section 4.5. We also constructed three different component types:

To avoid inlining effects, we added code for updating an instance variable to the body of each processEvent(AWTEvent). This experiment consists of dispatching a total of one million events through processEvent(AWTEvent). Each event type appears equally often, as we iterate over an array containing equal numbers of each event. We compute the loop overhead, subtract the overhead amount, and then divide the remaining time by the number of events dispatched. The timing results are shown in Table 4.

Also, we give an additional timing value for our custom SRP implementation, where we disabled mutual exclusion in the dispatcher. Currently our implementation uses a costly monitor to ensure that no other thread is updating the dispatch tables during a multi-dispatch. High-performance concurrent-read exclusive-write protocols can eliminate this overhead; the nolock value represents this highest-performance case.

As DD does not declare itself multi-dispatchable, the similarity of the results in column 2 of Table 4 again shows that our multi-dispatchable virtual machines do not significantly penalize uni-dispatch code. Further, we see that the cost of interpreting numerous expensive JVM bytecodes, such as instanceof, followed by another invokevirtual (which is DD's strategy), is more costly than our multi-dispatch techniques. The full multi-dispatch implementation (FMD) is faster than the partial multi-dispatch (MD). This is reasonable because MD ends up double-dispatching two of every six events.

Again, we see that the framework-based SRP technique suffers from considerable initial overhead. We hypothesize that it is a result of the object-oriented nature of our implementation of the table-based techniques. In each dispatch, several C++ objects are created and destroyed on the heap. Our tuned SRP implementation, jdk-tSRP, removes this overhead and provides faster dispatch performance than programmer-coded double dispatch.

OpenJIT compilation gains only minor improvements for the multi-dispatch system. This matches our expectations since OpenJIT calls the same selectMultiMethod() routine that the interpreter uses, there is only a slight benefit from avoiding some interpreter frame manipulations.

Arity Effects

Our final micro-benchmark explores the time penalties as the number of dispatchable arguments and applicable methods grow. To do this, we built a simple hierarchy of five classes (one root class A, with three subclasses B, C, and D, and finally class E as a subclass of C) and constructed methods of different arities against that hierarchy. We defined the following methods:

MSA looks at one fewer dispatchable arguments than the table-based techniques because the receiver argument has already been dispatched by the JVM. For instance, given a unary method, MSA makes no widening conversions for dispatchable arguments. A binary method requires MSA to check only one widening conversion. The table-based techniques dispatch on all arguments and gain no benefit from the dispatch done by the JVM.

We invoke one million methods for each arity. This means that each of the unary methods is executed 200,000 times. However each of the quaternary methods is executed only 1,600 times. After computing the loop overhead via an empty loop, we determine the elapsed time to millisecond accuracy and determine the time taken for each dispatch. Our results are shown in Figure 7.

We can evaluate the arity effects in the uni-dispatch case by coding a third level of double dispatch. Already the overhead of constructing a third activation record exceeds the dispatch time of our tuned SRP implementation. Also, our SRP implementations suffer only linear growth in time-penalties as arity increases, whereas MSA suffers quadratic effects.

**Figure 7:** Impact of Arity on Dispatch Latency
$\begin{figure} \centering \fbox {\epsfig{file=arity.eps, width=3in}}\vspace*{-12pt}\end{figure}$

Swing and AWT

Our final test is to apply multi-dispatch to AWT and Swing applications. To do this, we needed to rewrite AWT and Swing to take advantage of multi-dispatch.

We modified 11% (92 out of 846) of the classes in the AWT and Swing hierarchies. We eliminated 171 decision points, but needed to insert 123 new methods to replace existing double-dispatch code sections. Within the modified classes, we removed 5% of the conditionals and reduced the average number of choice points per method from 3.8 to 2.0 per method. This reduction illustrates the value of multi-dispatch in reducing code complexity.

In all, 57 classes were added, all of them new event types to replace those previously recognized only by a special type id (as in the AWT examples described previously). Our multi-dispatch libraries are a drop-in replacement that executes a total of 7.7% fewer method invocations and gives virtually identical performance with applications such as SwingSet. In our sample application, we found that the number of multi-dispatches executed almost exactly equaled the total reduction in method invocations. This suggests that every multi-dispatch replaced a double dispatch in the original Swing and AWT libraries.

We verified the operation of the entire unmodified SwingSet application with our replacement libraries. Finally to measure performance, we timed a simple Swing application that handles 200,000 AWTEvents of different types. The timing results are given in Table 6.

The Swing and AWT conversion also demonstrates the robustness of our approach. We needed to support multi-dispatch on instance and static methods. Nolock values are not given because Swing breaks our simplification that dispatch tables are not updated concurrently, and jdk-fSRP values are not given because the framework-based system does not support static methods. Swing and AWT expect to dispatch differently on Object and array types. In modifying the libraries, we found numerous opportunities to apply multi-dispatch to private, protected, and super method invocations. In addition, several multi-methods required the JVM to accept covariant return types from multi-methods. All of these features are required for a mainstream programming language.

Multi-Dispatch Issues

Besides performance and correctness, multi-dispatch must contend with a number of serious difficulties which the javac compiler cannot recognize. They are: ambiguous method invocations caused by inheritance conflicts, incompatible return type changes, masking of methods by primitive widening operations, and null arguments. Each of these is illustrated in Figure 8. We have developed a tool called MDLint that can identify these problems and warn the programmer.

The first difficulty is that multi-dispatch, even in a single-inheritance language, can suffer from ambiguous methods. The two examples using the m1 methods illustrate this. For the first method invocation, the compiler knows that A.m1(B) and B.m1(A) are candidates. Neither one is more specific than the other, so the compiler aborts with an error. We can fix that by statically typing the receiver argument to A, but multi-dispatch sees exactly the same conflict at runtime. Our MDLint program warns about the problem. If the programmer disregards the warning, our JVM detects the error and throws an AmbiguousMethodException.

Throwing a runtime exception may seem neither elegant nor acceptable, but one of the key attributes of the JVM is to maintain security. A malicious programmer can separately compile each class so that errors are not evident until execution. The JVM must protect itself from these possibilities, and throwing an exception is the only option. As we noted, our MDLint tool can recognize and report potential ambiguities, exception inconsistencies and return-type conflicts at compile time.

The second difficulty centers around the fact that javac considers methods with different argument types as distinct. This means that they can have different return types. Multi-dispatch forges additional connections between classes based on the additional dispatchable arguments. This means that methods which javac considered distinct are now overriding each other. In the example, we see that the two m2(...) methods override each other for multi-dispatch. Our multi-dispatch implementations throw an IllegalReturnTypeChange exception, unless the more specific method returns a subtype of the original returned value.

Another ramification of the fact that uni-dispatch Java considers different argument combinations as distinct methods is that javac does not ensure that the throws clauses are compatible. As with any overriding method, we would want a more specific multi-method to covariantly-specialize the set of exceptions. Our type-checker validates this, but, in compliance with the VM specification, our virtual machine neither checks nor reports this inconsistency.

The third difficulty involves the use of literal null as an argument. If null is typed, as in the first invocation of m3(), then javac performs static multi-dispatch with that type. This restricts the set of applicable methods javac will consider. In our example, an ordinary JVM can avoid loading class C. The multi-dispatch JVM recognizes that m3(C) might apply (since a is dynamically of null type and null is subtype of class C). Therefore, multi-dispatch Java loads class C in order to determine its place in the type hierarchy, and decides that m3(C) is the most-specific method. Literal nulls, as shown in the second invocation of m3(), illustrate the inconsistency of standard Java; it now agrees with the multi-dispatch JVM that m3(C) should be invoked. The ordinary JVM can still avoid loading class C, because javac has already static multi-dispatched to m3(C)¹². Presumably, the argument is used in m3(C), so the ordinary JVM will end up loading class C, just like the multi-dispatch JVM.

The null argument problem is an example of a more general referential transparency problem in Java. Inconsistent invocations can occur when expressions are substituted in place of variables. This is because javac might apply more precise type information from the substituted expression. As an example, compare the execution of the third and fourth invocations of m3(...). By replacing Ab with its value, we have altered the execution of a program.

The last difficulty is more complex and, at this time, unsolved. The compiler selects a method based upon widening operations and may change the type of primitive arguments. In the example, the compiler inserts instructions to convert b from a byte to an int. At runtime, we have lost all traces that b was originally specified as a byte. Indeed, the programmer might have wanted to force that exact conversion; the bytecodes would be identical to compiler-generated conversions.

Implementation

In this section, we describe how the JVM is extended to support dynamic multi-dispatch. We begin by examining how to indicate to the JVM which classes are multi-dispatchable. We then examine where multi-dispatch must occur and, finally, we review three different multi-dispatch implementations.

Marking Multi-Dispatch Classes

We tell the JVM that multi-dispatch is required on a class-by-class basis by implementing the empty interface MultiDispatchable in each class that is multi-dispatchable. The Java programming language has already leveraged this idea for marking class capabilities with the Cloneable interface. We use the MultiDispatchable interface to denote that any method sent to a multi-dispatch receiver should be handled by the multi-dispatcher. For efficiency, we add a flag to the internal class representation to indicate that a class is multi-dispatchable, rather than searching its list of interfaces at each method invocation. The value of this flag is set once, at class load time.

Our selection of MultiDispatchable as the marker requires us to recognize multi-dispatch on a class-by-class basis, not on a method-by-method or argument-by-argument basis. That is, every method invocation where the uni-dispatch receiver is a member of a multi-dispatchable class goes through our multi-dispatcher. Furthermore, because interfaces are inherited, this approach requires any subclass of a multi-dispatchable class to also be multi-dispatchable. Most importantly, any method invocation where the receiver argument is not marked for multi-dispatch continues unchanged through the uni-dispatcher. The benefit of this is that the syntax of Java programs is unchanged, and the performance and semantics of uni-dispatch remains intact.

The techniques used to mark code as multi-dispatchable and to implement multi-dispatch method invocations are independent. MultiDispatchable marks entire classes without language extensions, but our JVM actually supports multi-dispatch on a method-by-method basis. An alternate tagging mechanism, that marked individual methods as multi-dispatchable, may be possible if we permitted language extensions.

Adding Multi-Dispatch

As part of the uni-dispatch of an invoke bytecode, the JVM finds a method pointer from the array of methods in the receiver argument class. At this point, the interpreter loop is about to build a new frame to execute the found method. The interpreter loop (and classic VM JIT compilers) proceed to call a special function, called the invoker that handles the details of building the new frame and starting the new method. The Research JVM uses different invokers for native, bytecode, synchronized, JIT-compiled, and other method types. Similar to the OpenJIT system [21], we replace this invoker function with a custom multi-invoker that computes the correct multi-dispatch method. Once the more precise method is known, we simply invoke it directly.

The multi-invoker is installed at class-load time. The interpreter loop and invoker for uni-dispatch are unchanged. This supports our claim that uni-dispatch programs and libraries suffer no execution time penalties.

OpenJIT is supported in exactly the same way. Every method contains a compiledCode function pointer onto which OpenJIT installs its compiled method body. Once the compilation is complete, OpenJIT saves the compiled method body of any multi-method to a new field oldCompiledCode and installs a pointer to a routine DispatchMulti(). This replacement invoker simply calls the same method specializer selectMultiMethod() that the interpreter uses. If the more precise method-body is already compiled, then OpenJIT jumps into the oldCompiledCode, executing the more specific compiled method. Alternately, if the more precise method is not already JIT-ed, then DispatchMulti() sets it to be compiled and invokes the interpreter on the bytecode version.

Unfortunately, we must disable much of the inlining facility of OpenJIT when using multi-dispatch. The uni-dispatch OpenJIT compiler can inline private, static, and final methods because they can never change. With multi-dispatch, this is no longer true -- at a given call-site, the selected multi-method may change depending on the arguments to the current invocation. The JIT compiler and VM must work together to ensure that every method invocation is checked for multi-dispatch and correctly specialized.

The core component of our system is the selectMultiMethod() routine, which locates a more-specific method applicable to a set of arguments. We have experimented with three different multi-dispatch techniques; they are examined in the following sections. For each technique, we also describe our solution for the implementation issues described in section 5.

Reference Implementation: MSA

Our reference implementation is an extension of the Most Specific Applicable algorithm described in section 15.11 of The Java Language Specification and in section 2.2 of this paper. In particular, we re-examine the steps described in section 2.2 in light of the dynamic argument types being used.

When the multi-invoker is called, it has access to the methodblock that has already been found by the uni-dispatch resolution mechanism. We also have the top of the operand stack, so we can peek at each of the arguments. Last, we have the actual receiver, which can provide the list of methods (including inherited ones) that it implements.

Every method is represented by a methodblock containing many useful pieces of information. First, it holds the name of the method. Second, it contains a handle to the class that contains this method ¹³. Third, it contains the signature which we can parse to get the arity and types of the dispatchable arguments. For performance, we parse the signature only once. We add two fields to the methodblock: int arity to cache the arity and ClassClass **argClass to hold the class handles for the dispatchable arguments.

With these three pieces of information, we implement a dynamic version of the MSA algorithm directly. Wherever the original algorithm would use the static type of an argument, we apply the known dynamic type instead. In step 2(b) from section 2.2, the compiler would compare the static type of each argument with the corresponding declared type for the candidate method. In the dynamic case, we have the arguments on the stack, so we can find their dynamic types. We compare each argument's dynamic type against the declared type of the corresponding argument of the method. We discard any method that is not applicable due to access rights ( private methods) or whose declared types do not match the arguments on the stack. The remaining methods are dynamically applicable.

The issue of null-valued arguments becomes significant at this point. JLS chapter 4 recognizes the need for a null type to represent (untyped) null values. It further declares in section 4.1 that the null type can be coerced to any non-primitive type. Also, section 5.1.4 allows null types to be widened to any object, array or interface type. Statically, this means that an (untyped) null argument can be widened to any class. In the dynamic case, we want to do the same. Therefore, whenever we encounter a null argument we accept the conversion of that null to a method argument of type class, array, or interface.

Unfortunately, if we have a null argument, we may retain a method which accepts arguments of classes that are not yet loaded. We need to force these classes to be loaded to ensure that the next step operates correctly.

Given the list of applicable methods, step 2(d) finds the unique most specific method. Again the operation is identical to the process that the javac compiler follows. One applicable method is tentatively selected as the most specific. Each other applicable method is tested by comparing argument by argument (including the receiver argument) against the tentatively most specific. At each step, we discard any methods that are less specific. We continue this process until only one candidate method remains, or two or more equally specific methods remain. In the latter case, we have an ambiguous method invocation and we throw an AmbiguousMethodException to advertise this fact.

Next, we verify that the return type for our more specific method is compatible with the compiler-selected method. This check relaxes JLS 8.4.6.3, where we must reject any invocation that has a different return type, yet ensures type-safety. If the return type is different, we throw an IllegalReturnTypeChange exception at runtime.

Table-based Dispatch

Our SRP framework-based techniques is taken from the Dispatch Table Framework (DTF) [22]. This is a toolkit of many different uni-dispatch and multi-dispatch techniques. In order to call the DTF to dispatch a call-site, we need to inform the DTF of the various classes and methods present in our Java program. Our interface consists of a number of straight-forward routines to perform this registration.

The JVM maintains in-memory structures for each loaded .class file. We have extended that ClassClass structure to contain a DTF_Type field. It contains a pointer to the C++ object generated by the DTF. Once a class is dynamically loaded by the JVM, we check to see if we must register it with the dispatcher. If the dispatcher has already been instantiated, we register the class via javaAddClass(...) and store away the returned DTF_Type pointer.

If a dispatcher has not been instantiated, and the just-loaded class is uni-dispatch only, we defer the registration in order to reduce the overhead to uni-dispatch programs. If the just-loaded class is marked for multi-dispatch and the dispatcher has not been instantiated, the process is more complex. First, we instantiate a new dispatcher. Then, we register each class that has already been loaded, ensuring that its superclasses and superinterfaces are registered first.

Finally, as the last part of registering a class with the dispatcher, we need to see whether any methods from other classes were held in abeyance until this class was loaded. This can occur if the methods from other classes expect dispatchable arguments of the class we are just now loading. As we shall see below, we deferred registering these methods until the class was loaded.

Java's facility for dynamically reloading classes forces us to ensure that two classes with the same name are assigned different DTF_Types. Java ensures that two classes with the same name are treated as distinct by insisting that each one is loaded by a different classloader [19]. We apply the same technique by supplying the DTF framework with a name consisting of the classloader name, followed by `` ::'' and followed by the class name. They system classloader is given the empty name `` ''.

For a class marked for multi-dispatch, we need to register its methods along with their types, via javaAddMethod(...). If this class implements MultiDispatchable directly, then we register all of its methods, including inherited ones. Alternately, if MultiDispatchable is an inherited interface for this class, then we know that its superclass has already registered its methods. Therefore, we do not need to register them; we only need to register the methods that we directly implement.

This method registration process is complicated by our desire to load classes lazily. If a method accepts an argument with a class not yet seen by the JVM, we know that we could never dispatch to it until that class is loaded ¹⁴. We set that method aside for future registration.

If all of the argument types for the method are already registered with the DTF, then we proceed to register the method. We provide a methodblock pointer that we want the framework to return if this method is the dispatched target. We bundle up the DTF_Type values found in the ClassClass structures for each argument class (including the receiver argument) and pass them to the framework. The framework returns a DTF_Behavior pointer that we store in the methodblock.

Dispatch becomes a very simple operation. We build an array of the DTF_Type pointers from the arguments on the Java stack. If we encounter a null argument, we throw a NullPointerException. The DTF_Type array, along with the DTF_Behavior pointer from the compiler-selected method allow the framework to locate the methodblock pointer that we had previously registered.

We expect that the returned methodblock pointer is the method for multi-dispatch. We validate it against the compiler-selected method. If the return type has changed, we abort the dispatch and throw an IllegalReturnTypeChange exception. Otherwise, we call the found method's original invoker and return its value as the result of the interpreter's call to a method invoker.

Single Receiver Projections Single Receiver Projections (SRP) [16] is a technique that considers a multi-dispatch as a request for the joint most specific method available on each argument. For a given argument position and type, an ordered (most-specific to least-specific) vector of potential methods is maintained. The vectors for all the argument positions are intersected to provide an ordered vector of all applicable methods. Because of the ordering, this vector can be quickly searched for the most applicable method.

SRP uses a uni-dispatch technique to maintain the vector of potential methods for each individual argument. These vectors are typically compressed to conserve space. Many different compression techniques are known: row displacement, selector coloring [2], and compressed selector table indexing [25]. Our implementation uses selector coloring, because timing experiments [17] indicates that technique provides the fastest dispatch times.

Future Work

Our MSA and tuned SRP dispatchers are the most complete. They support null as a dispatchable argument, multi-dispatch on other invoke bytecodes ¹⁵, widening of primitive dispatchable arguments, and multi-threaded dispatch. Our table-framework-based dispatchers do not currently support all of these facilities. Adding them would provide additional flexibility and allow them to fully support the Java programming language semantics. In particular, we have a two-table design that will allow one thread to dispatch through an existing table, while we register additional methods and/or classes to a new one.

Our custom SRP code implements multi-dispatch as a critical section, protected by a mutual-exclusion lock. We have devised, but not as yet implemented, a technique which would eliminate the lock overhead (approximately 0.38 $\mu$ s for every multi-dispatch) and allow concurrent multi-dispatch. The trade-off is that every thread would need to halt while the multi-dispatch tables are being updated.

The OpenJIT support for multi-dispatch is still primitive; in particular, we eliminate all inlining actions. This is a conservative approach and one can identify situations where inlining in multi-dispatch Java would provide correct results. Identifying these opportunities will yield higher overall performance.

Other multi-dispatch techniques exist, including compressed n-dimensional tables [1,12], look-up automata [9,10], and efficient multiple and predicate dispatch [7]. A comprehensive exploration of these techniques using Java is incomplete at this time.

Another significant improvement for multi-dispatch is to incorporate our code testing tool into the javac compiler. At this time, MDLint exists as a separate executable which will recognize and warn the programmer about common ambiguities and difficulties. It analyzes a complete application and identifies the code sections where the programmer could invoke an ambiguous method, or have a conflicting return type.

Our reference implementation, MSA, supports multi-dispatch on all method types (instance, static, interface, private, etc.), except constructors. Because the same bytecode is used to invoke a constructor in the superclass and a constructor with different arguments, we cannot distinguish the two possibilities. This issue is a specific instance of the need to apply a super to an argument other than the receiver. Fortunately, in our experience, this requirement does not arise in common programming practice (except for constructors).

Our tuned SRP implementation allows our dispatch tables to identify only those types that are multi-dispatched. This lazy type numbering is reversible, allowing the tables to shrink as classes are unloaded. In turn, multi-methods can revert to lower arity multi-dispatch (or even uni-dispatch). We see great promise in this technique for long-lived Java server applications.

The DTF framework contains another dispatcher, Multiple Row Displacement [22] (MRD) that operates 15% faster than SRP. Therefore, we expect that dispatch could be enhanced to provide even lower latency by applying this technique. Unfortunately, MRD currently does not support incremental dispatch table updates in the same way that SRP does. In a dynamic environment such as Java, incremental updating of dispatch tables is desirable. Enhancing MRD to support incremental updates is another research priority.

Last, our marker interface MultiDispatchable denotes that each method in a given class is to be multi-dispatched. Our JVM relies on this tag only to inform it about which methods are eligible for multi-dispatch. Therefore, without changing our multi-dispatch implementation, alternate Java syntax would allow us to selectively mark individual methods (and their overriding multi-methods) as multi-dispatchable, rather than entire classes. We would like to explore the space of conservative language extensions to expose this feature.

Related Work

Others have attempted to add multi-dispatch to Java through language preprocessors. Boyland and Castagna [3] provide an additional keyword parasite to mark methods which should have multi-dispatch properties. They effectively translate these methods into equivalent double-dispatch Java code. By translating directly into compiled code, they apply a textual priority to avoid the thorny issue of ambiguous methods. Unfortunately, the parasitic method selection process is a sequence of several dispatches to search over a potentially exponential tree of overriding methods.

The language extension and preprocessor approach has other limitations. First, existing tools do not support the extensions; for example, debuggers do not elide the automatically generated double-dispatch routines. Second, instance methods appear to only take arguments that are objects, which is too limiting. Our experience with Swing shows that existing programs often double dispatch on literal null and array arguments and pass primitive types as arguments; multi-methods need to support these non-object types. Third, preprocessors limit code reuse and extensibility; adding multi-methods to an existing behaviour requires either access to the original source code or additional double-dispatch layers.

Chatterton [8] examines two different multi-dispatch techniques in mainstream languages: C++ and Java. First, he considers providing a specialized dispatcher class. Each class that participates as a method receiver must register itself with the dispatcher. To relieve the programmer of this repetitive coding process, he provides a preprocessor that rewrites the Java source to include the appropriate calls. Each method, marked with the keyword multi, is also expanded by the preprocessor into many individual methods, one for each combination of classes (and superclasses). A method invocation is replaced by a call to the dispatcher which searches via reflection for an exact match. That method is then invoked. This system suffers from exponential blowup of methods.

Chatterton's second approach examines the performance of various double dispatch enhancements. He provides a modified C++ preprocessor which analyses the entire Java program. It can build a number of different double-dispatch structures, including cascaded and nested if ...else-if ...else statements, inline switch statements, and simple two-dimensional tables. Again, he expands every possible argument-type combination in order to apply fast equality tests rather than slow subtype checks. A significant restriction is that full-program analysis is required. This defeats the ability to use existing libraries and diminishes Java's dynamic class loading benefits.

One interesting language for multi-dispatch is Leavens and Millstein's Tuple [18]. They describe a language ``similar in spirit to C++ and Java'' that permits the programmer to specify at each call-site the individual arguments that will be considered for multi-dispatch. This paper does not describe an implementation; it appears to be a model of potential syntax and semantics only. A future project might be to implement his syntax specifically into the Java environment. In particular, a simple syntax extension would allow super method invocations on arbitrary multi-dispatch arguments.

Another recent development is MultiJava [11]. There, the authors extend the Java language with additional syntax to support open classes and multi-dispatch. The MultiJava compiler emits double-dispatch type-case bytecodes for invocations of the open-class methods and multi-methods. The emitted bytecode is accepted by standard JVMs, but suffers a substantial overhead from interpreting slow subtype-testing bytecodes. Unfortunately, multi-dispatch can only apply to methods defined using the open-class syntax and only within the program text that imports the open-class definitions. If subclasses wish to further specialize the multi-methods, additional open-class definitions are required. Compilation of these further open-subclasses may result in multiple layers of type-case double-dispatch. Internally, MultiJava inlines the multi-method bodies into a static method in a separate anchor class - this means that the multi-methods disappear from the binary code and become invisible to the reflective subsystem in Java. Finally, MultiJava is a paper design at this time ¹⁶, so performance comparisons are not possible.

Concluding Remarks

We have presented the design and implementation of an extended Java Virtual Machine that supports multi-dispatch. This is the first published description of how to implement arbitrary-arity multi-dispatch in Java. In contrast to the more verbose and error-prone double-dispatch technique, currently found in the AWT (Figure 2), multi-dispatch typically reduces the amount of programmer-written code and generally improves the readability and level of abstraction of the code.

Our approach preserves both the performance and semantics of the existing dynamic uni-dispatch in Java while allowing the programmer to select dynamic multi-dispatch on a class-by-class basis without any language or compiler extensions. The changes to the JVM itself are small and highly-localized. Existing Java compilers, libraries, and programs are not affected by our JVM modifications and the programs can achieve performance comparable to the original JVM (Table 2).

In a series of micro-benchmarks, we showed that our prototype implementation adds no performance overhead to dispatch if only uni-dispatch is used (Table 2) and the overhead of multi-dispatch can be competitive with explicit double dispatch (Table 4).

We have also introduced and implemented an extension of the Java Most Specific Applicable (MSA) static multi-dispatch algorithm for dynamic multi-dispatch. In addition, we have performed the first head-to-head comparison of table-based multi-dispatch techniques implemented in a mainstream language. In particular, we implemented Single Receiver Projections (SRP). Overall, our tuned SRP implementation performs as well (or better) than programmer-targeted multi-dispatch. With performance improvements in concurrency, we expect our tuned system to out-perform type-case double dispatch.

Bibliography

About this document ...

This document was generated using the LaTeX2HTML translator Version 99.1 release (March 30, 1999)

Multi-Dispatch in the Java Virtual Machine: Design and Implementation

Abstract:

Introduction

Double Dispatch

Background

Java Classfile format

Static Multi-Dispatch in `Javac`

Dynamic Uni-Dispatch in the JVM

Design

Experimental Results

`Javac` -- Compatibility Test

Simple Multi-Dispatch

Double Dispatch of Events

Arity Effects

Swing and AWT

Multi-Dispatch Issues

Implementation

Marking Multi-Dispatch Classes

Adding Multi-Dispatch

Reference Implementation: MSA

Table-based Dispatch

Future Work

Related Work

Concluding Remarks

Bibliography

About this document ...

Footnotes

Multi-Dispatch in the Java Virtual Machine: Design and Implementation

Abstract:

Introduction

Double Dispatch

Background

Java Classfile format

Static Multi-Dispatch in Javac

Dynamic Uni-Dispatch in the JVM

Design

Experimental Results

Javac -- Compatibility Test

Simple Multi-Dispatch

Double Dispatch of Events

Arity Effects

Swing and AWT

Multi-Dispatch Issues

Implementation

Marking Multi-Dispatch Classes

Adding Multi-Dispatch

Reference Implementation: MSA

Table-based Dispatch

Future Work

Related Work

Concluding Remarks

Bibliography

About this document ...

Footnotes

Static Multi-Dispatch in `Javac`

`Javac` -- Compatibility Test