Accurate Garbage Collection with LLVM

  1. Introduction
  2. Getting started
  3. Core support
  4. Compiler plugin interface
  5. Implementing a collector runtime
  6. References

Written by Chris Lattner and Gordon Henriksen

Introduction

Garbage collection is a widely used technique that frees the programmer from having to know the lifetimes of heap objects, making software easier to produce and maintain. Many programming languages rely on garbage collection for automatic memory management. There are two primary forms of garbage collection: conservative and accurate.

Conservative garbage collection often does not require any special support from either the language or the compiler: it can handle non-type-safe programming languages (such as C/C++) and does not require any special information from the compiler. The Boehm collector is an example of a state-of-the-art conservative collector.

Accurate garbage collection requires the ability to identify all pointers in the program at run-time (which requires that the source-language be type-safe in most cases). Identifying pointers at run-time requires compiler support to locate all places that hold live pointer variables at run-time, including the processor stack and registers.

Conservative garbage collection is attractive because it does not require any special compiler support, but it does have problems. In particular, because the conservative garbage collector cannot know that a particular word in the machine is a pointer, it cannot move live objects in the heap (preventing the use of compacting and generational GC algorithms) and it can occasionally suffer from memory leaks due to integer values that happen to point to objects in the program. In addition, some aggressive compiler transformations can break conservative garbage collectors (though these seem rare in practice).

Accurate garbage collectors do not suffer from any of these problems, but they can suffer from degraded scalar optimization of the program. In particular, because the runtime must be able to identify and update all pointers active in the program, some optimizations are less effective. In practice, however, the locality and performance benefits of using aggressive garbage collection techniques dominates any low-level losses.

This document describes the mechanisms and interfaces provided by LLVM to support accurate garbage collection.

Goals and non-goals

LLVM's intermediate representation provides garbage collection intrinsics that offer support for a broad class of collector models. For instance, the intrinsics permit:

We hope that the primitive support built into the LLVM IR is sufficient to support a broad class of garbage collected languages including Scheme, ML, Java, C#, Perl, Python, Lua, Ruby, other scripting languages, and more.

However, LLVM does not itself provide a garbage collector—this should be part of your language's runtime library. LLVM provides a framework for compile time code generation plugins. The role of these plugins is to generate code and data structures which conforms to the binary interface specified by the runtime library. This is similar to the relationship between LLVM and DWARF debugging info, for example. The difference primarily lies in the lack of an established standard in the domain of garbage collection—thus the plugins.

The aspects of the binary interface with which LLVM's GC support is concerned are:

There are additional areas that LLVM does not directly address:

In general, LLVM's support for GC does not include features which can be adequately addressed with other features of the IR and does not specify a particular binary interface. On the plus side, this means that you should be able to integrate LLVM with an existing runtime. On the other hand, it leaves a lot of work for the developer of a novel language. However, it's easy to get started quickly and scale up to a more sophisticated implementation as your compiler matures.

Getting started

Using a GC with LLVM implies many things, for example:

To help with several of these tasks (those indicated with a *), LLVM includes a highly portable, built-in ShadowStack code generator. It is compiled into llc and works even with the interpreter and C backends.

In your compiler

To turn the shadow stack on for your functions, first call:

F.setGC("shadow-stack");

for each function your compiler emits. Since the shadow stack is built into LLVM, you do not need to load a plugin.

Your compiler must also use @llvm.gcroot as documented. Don't forget to create a root for each intermediate value that is generated when evaluating an expression. In h(f(), g()), the result of f() could easily be collected if evaluating g() triggers a collection.

There's no need to use @llvm.gcread and @llvm.gcwrite over plain load and store for now. You will need them when switching to a more advanced GC.

In your runtime

The shadow stack doesn't imply a memory allocation algorithm. A semispace collector or building atop malloc are great places to start, and can be implemented with very little code.

When it comes time to collect, however, your runtime needs to traverse the stack roots, and for this it needs to integrate with the shadow stack. Luckily, doing so is very simple. (This code is heavily commented to help you understand the data structure, but there are only 20 lines of meaningful code.)

/// @brief The map for a single function's stack frame. One of these is
///        compiled as constant data into the executable for each function.
/// 
/// Storage of metadata values is elided if the %metadata parameter to
/// @llvm.gcroot is null.
struct FrameMap {
  int32_t NumRoots;    //< Number of roots in stack frame.
  int32_t NumMeta;     //< Number of metadata entries. May be < NumRoots.
  const void *Meta[0]; //< Metadata for each root.
};

/// @brief A link in the dynamic shadow stack. One of these is embedded in the
///        stack frame of each function on the call stack.
struct StackEntry {
  StackEntry *Next;    //< Link to next stack entry (the caller's).
  const FrameMap *Map; //< Pointer to constant FrameMap.
  void *Roots[0];      //< Stack roots (in-place array).
};

/// @brief The head of the singly-linked list of StackEntries. Functions push
///        and pop onto this in their prologue and epilogue.
/// 
/// Since there is only a global list, this technique is not threadsafe.
StackEntry *llvm_gc_root_chain;

/// @brief Calls Visitor(root, meta) for each GC root on the stack.
///        root and meta are exactly the values passed to
///        @llvm.gcroot.
/// 
/// Visitor could be a function to recursively mark live objects. Or it
/// might copy them to another heap or generation.
/// 
/// @param Visitor A function to invoke for every GC root on the stack.
void visitGCRoots(void (*Visitor)(void **Root, const void *Meta)) {
  for (StackEntry *R = llvm_gc_root_chain; R; R = R->Next) {
    unsigned i = 0;
    
    // For roots [0, NumMeta), the metadata pointer is in the FrameMap.
    for (unsigned e = R->Map->NumMeta; i != e; ++i)
      Visitor(&R->Roots[i], R->Map->Meta[i]);
    
    // For roots [NumMeta, NumRoots), the metadata pointer is null.
    for (unsigned e = R->Map->NumRoots; i != e; ++i)
      Visitor(&R->Roots[i], NULL);
  }
}

About the shadow stack

Unlike many GC algorithms which rely on a cooperative code generator to compile stack maps, this algorithm carefully maintains a linked list of stack roots [Henderson2002]. This so-called "shadow stack" mirrors the machine stack. Maintaining this data structure is slower than using a stack map compiled into the executable as constant data, but has a significant portability advantage because it requires no special support from the target code generator, and does not require tricky platform-specific code to crawl the machine stack.

The tradeoff for this simplicity and portability is:

Still, it's an easy way to get started. After your compiler and runtime are up and running, writing a plugin will allow you to take advantage of more advanced GC features of LLVM in order to improve performance.

IR features

This section describes the garbage collection facilities provided by the LLVM intermediate representation. The exact behavior of these IR features is specified by the binary interface implemented by a code generation plugin, not by this document.

These facilities are limited to those strictly necessary; they are not intended to be a complete interface to any garbage collector. A program will need to interface with the GC library using the facilities provided by that program.

Specifying GC code generation: gc "..."

define ty @name(...) gc "name" { ...

The gc function attribute is used to specify the desired GC style to the compiler. Its programmatic equivalent is the setGC method of Function.

Setting gc "name" on a function triggers a search for a matching code generation plugin "name"; it is that plugin which defines the exact nature of the code generated to support GC. If none is found, the compiler will raise an error.

Specifying the GC style on a per-function basis allows LLVM to link together programs that use different garbage collection algorithms (or none at all).

Identifying GC roots on the stack: llvm.gcroot

void @llvm.gcroot(i8** %ptrloc, i8* %metadata)

The llvm.gcroot intrinsic is used to inform LLVM that a stack variable references an object on the heap and is to be tracked for garbage collection. The exact impact on generated code is specified by a compiler plugin.

A compiler which uses mem2reg to raise imperative code using alloca into SSA form need only add a call to @llvm.gcroot for those variables which a pointers into the GC heap.

It is also important to mark intermediate values with llvm.gcroot. For example, consider h(f(), g()). Beware leaking the result of f() in the case that g() triggers a collection.

The first argument must be a value referring to an alloca instruction or a bitcast of an alloca. The second contains a pointer to metadata that should be associated with the pointer, and must be a constant or global value address. If your target collector uses tags, use a null pointer for metadata.

The %metadata argument can be used to avoid requiring heap objects to have 'isa' pointers or tag bits. [Appel89, Goldberg91, Tolmach94] If specified, its value will be tracked along with the location of the pointer in the stack frame.

Consider the following fragment of Java code:

       {
         Object X;   // A null-initialized reference to an object
         ...
       }

This block (which may be located in the middle of a function or in a loop nest), could be compiled to this LLVM code:

Entry:
   ;; In the entry block for the function, allocate the
   ;; stack space for X, which is an LLVM pointer.
   %X = alloca %Object*
   
   ;; Tell LLVM that the stack space is a stack root.
   ;; Java has type-tags on objects, so we pass null as metadata.
   %tmp = bitcast %Object** %X to i8**
   call void @llvm.gcroot(i8** %X, i8* null)
   ...

   ;; "CodeBlock" is the block corresponding to the start
   ;;  of the scope above.
CodeBlock:
   ;; Java null-initializes pointers.
   store %Object* null, %Object** %X

   ...

   ;; As the pointer goes out of scope, store a null value into
   ;; it, to indicate that the value is no longer live.
   store %Object* null, %Object** %X
   ...

Reading and writing references in the heap

Some collectors need to be informed when the mutator (the program that needs garbage collection) either reads a pointer from or writes a pointer to a field of a heap object. The code fragments inserted at these points are called read barriers and write barriers, respectively. The amount of code that needs to be executed is usually quite small and not on the critical path of any computation, so the overall performance impact of the barrier is tolerable.

Barriers often require access to the object pointer rather than the derived pointer (which is a pointer to the field within the object). Accordingly, these intrinsics take both pointers as separate arguments for completeness. In this snippet, %object is the object pointer, and %derived is the derived pointer:

    ;; An array type.
    %class.Array = type { %class.Object, i32, [0 x %class.Object*] }
    ...

    ;; Load the object pointer from a gcroot.
    %object = load %class.Array** %object_addr

    ;; Compute the derived pointer.
    %derived = getelementptr %object, i32 0, i32 2, i32 %n

LLVM does not enforce this relationship between the object and derived pointer (although a plugin might). However, it would be an unusual collector that violated it.

The use of these intrinsics is naturally optional if the target GC does require the corresponding barrier. Such a GC plugin will replace the intrinsic calls with the corresponding load or store instruction if they are used.

Write barrier: llvm.gcwrite

void @llvm.gcwrite(i8* %value, i8* %object, i8** %derived)

For write barriers, LLVM provides the llvm.gcwrite intrinsic function. It has exactly the same semantics as a non-volatile store to the derived pointer (the third argument). The exact code generated is specified by a compiler plugin.

Many important algorithms require write barriers, including generational and concurrent collectors. Additionally, write barriers could be used to implement reference counting.

Read barrier: llvm.gcread

i8* @llvm.gcread(i8* %object, i8** %derived)

For read barriers, LLVM provides the llvm.gcread intrinsic function. It has exactly the same semantics as a non-volatile load from the derived pointer (the second argument). The exact code generated is specified by a compiler plugin.

Read barriers are needed by fewer algorithms than write barriers, and may have a greater performance impact since pointer reads are more frequent than writes.

Implementing a collector plugin

User code specifies which GC code generation to use with the gc function attribute or, equivalently, with the setGC method of Function.

To implement a GC plugin, it is necessary to subclass llvm::GCStrategy, which can be accomplished in a few lines of boilerplate code. LLVM's infrastructure provides access to several important algorithms. For an uncontroversial collector, all that remains may be to compile LLVM's computed stack map to assembly code (using the binary representation expected by the runtime library). This can be accomplished in about 100 lines of code.

This is not the appropriate place to implement a garbage collected heap or a garbage collector itself. That code should exist in the language's runtime library. The compiler plugin is responsible for generating code which conforms to the binary interface defined by library, most essentially the stack map.

To subclass llvm::GCStrategy and register it with the compiler:

// lib/MyGC/MyGC.cpp - Example LLVM GC plugin

#include "llvm/CodeGen/GCStrategy.h"
#include "llvm/CodeGen/GCMetadata.h"
#include "llvm/Support/Compiler.h"

using namespace llvm;

namespace {
  class LLVM_LIBRARY_VISIBILITY MyGC : public GCStrategy {
  public:
    MyGC() {}
  };
  
  GCRegistry::Add<MyGC>
  X("mygc", "My bespoke garbage collector.");
}

This boilerplate collector does nothing. More specifically:

Using the LLVM makefiles (like the sample project), this code can be compiled as a plugin using a simple makefile:

# lib/MyGC/Makefile

LEVEL := ../..
LIBRARYNAME = MyGC
LOADABLE_MODULE = 1

include $(LEVEL)/Makefile.common

Once the plugin is compiled, code using it may be compiled using llc -load=MyGC.so (though MyGC.so may have some other platform-specific extension):

$ cat sample.ll
define void @f() gc "mygc" {
entry:
        ret void
}
$ llvm-as < sample.ll | llc -load=MyGC.so

It is also possible to statically link the collector plugin into tools, such as a language-specific compiler front-end.

Overview of available features

GCStrategy provides a range of features through which a plugin may do useful work. Some of these are callbacks, some are algorithms that can be enabled, disabled, or customized. This matrix summarizes the supported (and planned) features and correlates them with the collection techniques which typically require them.

Algorithm Done shadow stack refcount mark-sweep copying incremental threaded concurrent
stack map
initialize roots
derived pointers NO ✘* ✘*
custom lowering
gcroot
gcwrite
gcread
safe points
in calls
before calls
for loops NO
before escape
emit code at safe points NO
output
assembly
JIT NO
obj NO
live analysis NO
register map NO
* Derived pointers only pose a hazard to copying collectors.
in gray denotes a feature which could be utilized if available.

To be clear, the collection techniques above are defined as:

Shadow Stack
The mutator carefully maintains a linked list of stack roots.
Reference Counting
The mutator maintains a reference count for each object and frees an object when its count falls to zero.
Mark-Sweep
When the heap is exhausted, the collector marks reachable objects starting from the roots, then deallocates unreachable objects in a sweep phase.
Copying
As reachability analysis proceeds, the collector copies objects from one heap area to another, compacting them in the process. Copying collectors enable highly efficient "bump pointer" allocation and can improve locality of reference.
Incremental
(Including generational collectors.) Incremental collectors generally have all the properties of a copying collector (regardless of whether the mature heap is compacting), but bring the added complexity of requiring write barriers.
Threaded
Denotes a multithreaded mutator; the collector must still stop the mutator ("stop the world") before beginning reachability analysis. Stopping a multithreaded mutator is a complicated problem. It generally requires highly platform specific code in the runtime, and the production of carefully designed machine code at safe points.
Concurrent
In this technique, the mutator and the collector run concurrently, with the goal of eliminating pause times. In a cooperative collector, the mutator further aids with collection should a pause occur, allowing collection to take advantage of multiprocessor hosts. The "stop the world" problem of threaded collectors is generally still present to a limited extent. Sophisticated marking algorithms are necessary. Read barriers may be necessary.

As the matrix indicates, LLVM's garbage collection infrastructure is already suitable for a wide variety of collectors, but does not currently extend to multithreaded programs. This will be added in the future as there is interest.

Computing stack maps

LLVM automatically computes a stack map. One of the most important features of a GCStrategy is to compile this information into the executable in the binary representation expected by the runtime library.

The stack map consists of the location and identity of each GC root in the each function in the module. For each root:

Also, for the function as a whole:

To access the stack map, use GCFunctionMetadata::roots_begin() and -end() from the GCMetadataPrinter:

for (iterator I = begin(), E = end(); I != E; ++I) {
  GCFunctionInfo *FI = *I;
  unsigned FrameSize = FI->getFrameSize();
  size_t RootCount = FI->roots_size();

  for (GCFunctionInfo::roots_iterator RI = FI->roots_begin(),
                                      RE = FI->roots_end();
                                      RI != RE; ++RI) {
    int RootNum = RI->Num;
    int RootStackOffset = RI->StackOffset;
    Constant *RootMetadata = RI->Metadata;
  }
}

If the llvm.gcroot intrinsic is eliminated before code generation by a custom lowering pass, LLVM will compute an empty stack map. This may be useful for collector plugins which implement reference counting or a shadow stack.

Initializing roots to null: InitRoots

MyGC::MyGC() {
  InitRoots = true;
}

When set, LLVM will automatically initialize each root to null upon entry to the function. This prevents the GC's sweep phase from visiting uninitialized pointers, which will almost certainly cause it to crash. This initialization occurs before custom lowering, so the two may be used together.

Since LLVM does not yet compute liveness information, there is no means of distinguishing an uninitialized stack root from an initialized one. Therefore, this feature should be used by all GC plugins. It is enabled by default.

Custom lowering of intrinsics: CustomRoots, CustomReadBarriers, and CustomWriteBarriers

For GCs which use barriers or unusual treatment of stack roots, these flags allow the collector to perform arbitrary transformations of the LLVM IR:

class MyGC : public GCStrategy {
public:
  MyGC() {
    CustomRoots = true;
    CustomReadBarriers = true;
    CustomWriteBarriers = true;
  }
  
  virtual bool initializeCustomLowering(Module &M);
  virtual bool performCustomLowering(Function &F);
};

If any of these flags are set, then LLVM suppresses its default lowering for the corresponding intrinsics and instead calls performCustomLowering.

LLVM's default action for each intrinsic is as follows:

If CustomReadBarriers or CustomWriteBarriers are specified, then performCustomLowering must eliminate the corresponding barriers.

performCustomLowering must comply with the same restrictions as FunctionPass::runOnFunction. Likewise, initializeCustomLowering has the same semantics as Pass::doInitialization(Module&).

The following can be used as a template:

#include "llvm/Module.h"
#include "llvm/IntrinsicInst.h"

bool MyGC::initializeCustomLowering(Module &M) {
  return false;
}

bool MyGC::performCustomLowering(Function &F) {
  bool MadeChange = false;
  
  for (Function::iterator BB = F.begin(), E = F.end(); BB != E; ++BB)
    for (BasicBlock::iterator II = BB->begin(), E = BB->end(); II != E; )
      if (IntrinsicInst *CI = dyn_cast<IntrinsicInst>(II++))
        if (Function *F = CI->getCalledFunction())
          switch (F->getIntrinsicID()) {
          case Intrinsic::gcwrite:
            // Handle llvm.gcwrite.
            CI->eraseFromParent();
            MadeChange = true;
            break;
          case Intrinsic::gcread:
            // Handle llvm.gcread.
            CI->eraseFromParent();
            MadeChange = true;
            break;
          case Intrinsic::gcroot:
            // Handle llvm.gcroot.
            CI->eraseFromParent();
            MadeChange = true;
            break;
          }
  
  return MadeChange;
}

Generating safe points: NeededSafePoints

LLVM can compute four kinds of safe points:

namespace GC {
  /// PointKind - The type of a collector-safe point.
  /// 
  enum PointKind {
    Loop,    //< Instr is a loop (backwards branch).
    Return,  //< Instr is a return instruction.
    PreCall, //< Instr is a call instruction.
    PostCall //< Instr is the return address of a call.
  };
}

A collector can request any combination of the four by setting the NeededSafePoints mask:

MyGC::MyGC() {
  NeededSafePoints = 1 << GC::Loop
                   | 1 << GC::Return
                   | 1 << GC::PreCall
                   | 1 << GC::PostCall;
}

It can then use the following routines to access safe points.

for (iterator I = begin(), E = end(); I != E; ++I) {
  GCFunctionInfo *MD = *I;
  size_t PointCount = MD->size();

  for (GCFunctionInfo::iterator PI = MD->begin(),
                                PE = MD->end(); PI != PE; ++PI) {
    GC::PointKind PointKind = PI->Kind;
    unsigned PointNum = PI->Num;
  }
}

Almost every collector requires PostCall safe points, since these correspond to the moments when the function is suspended during a call to a subroutine.

Threaded programs generally require Loop safe points to guarantee that the application will reach a safe point within a bounded amount of time, even if it is executing a long-running loop which contains no function calls.

Threaded collectors may also require Return and PreCall safe points to implement "stop the world" techniques using self-modifying code, where it is important that the program not exit the function without reaching a safe point (because only the topmost function has been patched).

Emitting assembly code: GCMetadataPrinter

LLVM allows a plugin to print arbitrary assembly code before and after the rest of a module's assembly code. At the end of the module, the GC can compile the LLVM stack map into assembly code. (At the beginning, this information is not yet computed.)

Since AsmWriter and CodeGen are separate components of LLVM, a separate abstract base class and registry is provided for printing assembly code, the GCMetadaPrinter and GCMetadataPrinterRegistry. The AsmWriter will look for such a subclass if the GCStrategy sets UsesMetadata:

MyGC::MyGC() {
  UsesMetadata = true;
}

This separation allows JIT-only clients to be smaller.

Note that LLVM does not currently have analogous APIs to support code generation in the JIT, nor using the object writers.

// lib/MyGC/MyGCPrinter.cpp - Example LLVM GC printer

#include "llvm/CodeGen/GCMetadataPrinter.h"
#include "llvm/Support/Compiler.h"

using namespace llvm;

namespace {
  class LLVM_LIBRARY_VISIBILITY MyGCPrinter : public GCMetadataPrinter {
  public:
    virtual void beginAssembly(std::ostream &OS, AsmPrinter &AP,
                               const TargetAsmInfo &TAI);
  
    virtual void finishAssembly(std::ostream &OS, AsmPrinter &AP,
                                const TargetAsmInfo &TAI);
  };
  
  GCMetadataPrinterRegistry::Add<MyGCPrinter>
  X("mygc", "My bespoke garbage collector.");
}

The collector should use AsmPrinter and TargetAsmInfo to print portable assembly code to the std::ostream. The collector itself contains the stack map for the entire module, and may access the GCFunctionInfo using its own begin() and end() methods. Here's a realistic example:

#include "llvm/CodeGen/AsmPrinter.h"
#include "llvm/Function.h"
#include "llvm/Target/TargetMachine.h"
#include "llvm/Target/TargetData.h"
#include "llvm/Target/TargetAsmInfo.h"

void MyGCPrinter::beginAssembly(std::ostream &OS, AsmPrinter &AP,
                                const TargetAsmInfo &TAI) {
  // Nothing to do.
}

void MyGCPrinter::finishAssembly(std::ostream &OS, AsmPrinter &AP,
                                 const TargetAsmInfo &TAI) {
  // Set up for emitting addresses.
  const char *AddressDirective;
  int AddressAlignLog;
  if (AP.TM.getTargetData()->getPointerSize() == sizeof(int32_t)) {
    AddressDirective = TAI.getData32bitsDirective();
    AddressAlignLog = 2;
  } else {
    AddressDirective = TAI.getData64bitsDirective();
    AddressAlignLog = 3;
  }
  
  // Put this in the data section.
  AP.SwitchToDataSection(TAI.getDataSection());
  
  // For each function...
  for (iterator FI = begin(), FE = end(); FI != FE; ++FI) {
    GCFunctionInfo &MD = **FI;
    
    // Emit this data structure:
    // 
    // struct {
    //   int32_t PointCount;
    //   struct {
    //     void *SafePointAddress;
    //     int32_t LiveCount;
    //     int32_t LiveOffsets[LiveCount];
    //   } Points[PointCount];
    // } __gcmap_<FUNCTIONNAME>;
    
    // Align to address width.
    AP.EmitAlignment(AddressAlignLog);
    
    // Emit the symbol by which the stack map entry can be found.
    std::string Symbol;
    Symbol += TAI.getGlobalPrefix();
    Symbol += "__gcmap_";
    Symbol += MD.getFunction().getName();
    if (const char *GlobalDirective = TAI.getGlobalDirective())
      OS << GlobalDirective << Symbol << "\n";
    OS << TAI.getGlobalPrefix() << Symbol << ":\n";
    
    // Emit PointCount.
    AP.EmitInt32(MD.size());
    AP.EOL("safe point count");
    
    // And each safe point...
    for (GCFunctionInfo::iterator PI = MD.begin(),
                                     PE = MD.end(); PI != PE; ++PI) {
      // Align to address width.
      AP.EmitAlignment(AddressAlignLog);
      
      // Emit the address of the safe point.
      OS << AddressDirective
         << TAI.getPrivateGlobalPrefix() << "label" << PI->Num;
      AP.EOL("safe point address");
      
      // Emit the stack frame size.
      AP.EmitInt32(MD.getFrameSize());
      AP.EOL("stack frame size");
      
      // Emit the number of live roots in the function.
      AP.EmitInt32(MD.live_size(PI));
      AP.EOL("live root count");
      
      // And for each live root...
      for (GCFunctionInfo::live_iterator LI = MD.live_begin(PI),
                                            LE = MD.live_end(PI);
                                            LI != LE; ++LI) {
        // Print its offset within the stack frame.
        AP.EmitInt32(LI->StackOffset);
        AP.EOL("stack offset");
      }
    }
  }
}

References

[Appel89] Runtime Tags Aren't Necessary. Andrew W. Appel. Lisp and Symbolic Computation 19(7):703-705, July 1989.

[Goldberg91] Tag-free garbage collection for strongly typed programming languages. Benjamin Goldberg. ACM SIGPLAN PLDI'91.

[Tolmach94] Tag-free garbage collection using explicit type parameters. Andrew Tolmach. Proceedings of the 1994 ACM conference on LISP and functional programming.

[Henderson2002] Accurate Garbage Collection in an Uncooperative Environment. Fergus Henderson. International Symposium on Memory Management 2002.


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