Chapter 5, 6, and 7 of the ocaml/kaleidoscope tutorial
and fix some tabs in chapter 3 and 4.


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+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
+                      "http://www.w3.org/TR/html4/strict.dtd">
+
+<html>
+<head>
+  <title>Kaleidoscope: Extending the Language: Mutable Variables / SSA
+         construction</title>
+  <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
+  <meta name="author" content="Chris Lattner">
+  <meta name="author" content="Erick Tryzelaar">
+  <link rel="stylesheet" href="../llvm.css" type="text/css">
+</head>
+
+<body>
+
+<div class="doc_title">Kaleidoscope: Extending the Language: Mutable Variables</div>
+
+<ul>
+<li><a href="index.html">Up to Tutorial Index</a></li>
+<li>Chapter 7
+  <ol>
+    <li><a href="#intro">Chapter 7 Introduction</a></li>
+    <li><a href="#why">Why is this a hard problem?</a></li>
+    <li><a href="#memory">Memory in LLVM</a></li>
+    <li><a href="#kalvars">Mutable Variables in Kaleidoscope</a></li>
+    <li><a href="#adjustments">Adjusting Existing Variables for
+     Mutation</a></li>
+    <li><a href="#assignment">New Assignment Operator</a></li>
+    <li><a href="#localvars">User-defined Local Variables</a></li>
+    <li><a href="#code">Full Code Listing</a></li>
+  </ol>
+</li>
+<li><a href="LangImpl8.html">Chapter 8</a>: Conclusion and other useful LLVM
+ tidbits</li>
+</ul>
+
+<div class="doc_author">
+	<p>
+		Written by <a href="mailto:sabre@nondot.org">Chris Lattner</a>
+		and <a href="mailto:idadesub@users.sourceforge.net">Erick Tryzelaar</a>
+	</p>
+</div>
+
+<!-- *********************************************************************** -->
+<div class="doc_section"><a name="intro">Chapter 7 Introduction</a></div>
+<!-- *********************************************************************** -->
+
+<div class="doc_text">
+
+<p>Welcome to Chapter 7 of the "<a href="index.html">Implementing a language
+with LLVM</a>" tutorial.  In chapters 1 through 6, we've built a very
+respectable, albeit simple, <a
+href="http://en.wikipedia.org/wiki/Functional_programming">functional
+programming language</a>.  In our journey, we learned some parsing techniques,
+how to build and represent an AST, how to build LLVM IR, and how to optimize
+the resultant code as well as JIT compile it.</p>
+
+<p>While Kaleidoscope is interesting as a functional language, the fact that it
+is functional makes it "too easy" to generate LLVM IR for it.  In particular, a
+functional language makes it very easy to build LLVM IR directly in <a
+href="http://en.wikipedia.org/wiki/Static_single_assignment_form">SSA form</a>.
+Since LLVM requires that the input code be in SSA form, this is a very nice
+property and it is often unclear to newcomers how to generate code for an
+imperative language with mutable variables.</p>
+
+<p>The short (and happy) summary of this chapter is that there is no need for
+your front-end to build SSA form: LLVM provides highly tuned and well tested
+support for this, though the way it works is a bit unexpected for some.</p>
+
+</div>
+
+<!-- *********************************************************************** -->
+<div class="doc_section"><a name="why">Why is this a hard problem?</a></div>
+<!-- *********************************************************************** -->
+
+<div class="doc_text">
+
+<p>
+To understand why mutable variables cause complexities in SSA construction,
+consider this extremely simple C example:
+</p>
+
+<div class="doc_code">
+<pre>
+int G, H;
+int test(_Bool Condition) {
+  int X;
+  if (Condition)
+    X = G;
+  else
+    X = H;
+  return X;
+}
+</pre>
+</div>
+
+<p>In this case, we have the variable "X", whose value depends on the path
+executed in the program.  Because there are two different possible values for X
+before the return instruction, a PHI node is inserted to merge the two values.
+The LLVM IR that we want for this example looks like this:</p>
+
+<div class="doc_code">
+<pre>
+@G = weak global i32 0   ; type of @G is i32*
+@H = weak global i32 0   ; type of @H is i32*
+
+define i32 @test(i1 %Condition) {
+entry:
+  br i1 %Condition, label %cond_true, label %cond_false
+
+cond_true:
+  %X.0 = load i32* @G
+  br label %cond_next
+
+cond_false:
+  %X.1 = load i32* @H
+  br label %cond_next
+
+cond_next:
+  %X.2 = phi i32 [ %X.1, %cond_false ], [ %X.0, %cond_true ]
+  ret i32 %X.2
+}
+</pre>
+</div>
+
+<p>In this example, the loads from the G and H global variables are explicit in
+the LLVM IR, and they live in the then/else branches of the if statement
+(cond_true/cond_false).  In order to merge the incoming values, the X.2 phi node
+in the cond_next block selects the right value to use based on where control
+flow is coming from: if control flow comes from the cond_false block, X.2 gets
+the value of X.1.  Alternatively, if control flow comes from cond_true, it gets
+the value of X.0.  The intent of this chapter is not to explain the details of
+SSA form.  For more information, see one of the many <a
+href="http://en.wikipedia.org/wiki/Static_single_assignment_form">online
+references</a>.</p>
+
+<p>The question for this article is "who places the phi nodes when lowering
+assignments to mutable variables?".  The issue here is that LLVM
+<em>requires</em> that its IR be in SSA form: there is no "non-ssa" mode for it.
+However, SSA construction requires non-trivial algorithms and data structures,
+so it is inconvenient and wasteful for every front-end to have to reproduce this
+logic.</p>
+
+</div>
+
+<!-- *********************************************************************** -->
+<div class="doc_section"><a name="memory">Memory in LLVM</a></div>
+<!-- *********************************************************************** -->
+
+<div class="doc_text">
+
+<p>The 'trick' here is that while LLVM does require all register values to be
+in SSA form, it does not require (or permit) memory objects to be in SSA form.
+In the example above, note that the loads from G and H are direct accesses to
+G and H: they are not renamed or versioned.  This differs from some other
+compiler systems, which do try to version memory objects.  In LLVM, instead of
+encoding dataflow analysis of memory into the LLVM IR, it is handled with <a
+href="../WritingAnLLVMPass.html">Analysis Passes</a> which are computed on
+demand.</p>
+
+<p>
+With this in mind, the high-level idea is that we want to make a stack variable
+(which lives in memory, because it is on the stack) for each mutable object in
+a function.  To take advantage of this trick, we need to talk about how LLVM
+represents stack variables.
+</p>
+
+<p>In LLVM, all memory accesses are explicit with load/store instructions, and
+it is carefully designed not to have (or need) an "address-of" operator.  Notice
+how the type of the @G/@H global variables is actually "i32*" even though the
+variable is defined as "i32".  What this means is that @G defines <em>space</em>
+for an i32 in the global data area, but its <em>name</em> actually refers to the
+address for that space.  Stack variables work the same way, except that instead of
+being declared with global variable definitions, they are declared with the
+<a href="../LangRef.html#i_alloca">LLVM alloca instruction</a>:</p>
+
+<div class="doc_code">
+<pre>
+define i32 @example() {
+entry:
+  %X = alloca i32           ; type of %X is i32*.
+  ...
+  %tmp = load i32* %X       ; load the stack value %X from the stack.
+  %tmp2 = add i32 %tmp, 1   ; increment it
+  store i32 %tmp2, i32* %X  ; store it back
+  ...
+</pre>
+</div>
+
+<p>This code shows an example of how you can declare and manipulate a stack
+variable in the LLVM IR.  Stack memory allocated with the alloca instruction is
+fully general: you can pass the address of the stack slot to functions, you can
+store it in other variables, etc.  In our example above, we could rewrite the
+example to use the alloca technique to avoid using a PHI node:</p>
+
+<div class="doc_code">
+<pre>
+@G = weak global i32 0   ; type of @G is i32*
+@H = weak global i32 0   ; type of @H is i32*
+
+define i32 @test(i1 %Condition) {
+entry:
+  %X = alloca i32           ; type of %X is i32*.
+  br i1 %Condition, label %cond_true, label %cond_false
+
+cond_true:
+  %X.0 = load i32* @G
+        store i32 %X.0, i32* %X   ; Update X
+  br label %cond_next
+
+cond_false:
+  %X.1 = load i32* @H
+        store i32 %X.1, i32* %X   ; Update X
+  br label %cond_next
+
+cond_next:
+  %X.2 = load i32* %X       ; Read X
+  ret i32 %X.2
+}
+</pre>
+</div>
+
+<p>With this, we have discovered a way to handle arbitrary mutable variables
+without the need to create Phi nodes at all:</p>
+
+<ol>
+<li>Each mutable variable becomes a stack allocation.</li>
+<li>Each read of the variable becomes a load from the stack.</li>
+<li>Each update of the variable becomes a store to the stack.</li>
+<li>Taking the address of a variable just uses the stack address directly.</li>
+</ol>
+
+<p>While this solution has solved our immediate problem, it introduced another
+one: we have now apparently introduced a lot of stack traffic for very simple
+and common operations, a major performance problem.  Fortunately for us, the
+LLVM optimizer has a highly-tuned optimization pass named "mem2reg" that handles
+this case, promoting allocas like this into SSA registers, inserting Phi nodes
+as appropriate.  If you run this example through the pass, for example, you'll
+get:</p>
+
+<div class="doc_code">
+<pre>
+$ <b>llvm-as &lt; example.ll | opt -mem2reg | llvm-dis</b>
+@G = weak global i32 0
+@H = weak global i32 0
+
+define i32 @test(i1 %Condition) {
+entry:
+  br i1 %Condition, label %cond_true, label %cond_false
+
+cond_true:
+  %X.0 = load i32* @G
+  br label %cond_next
+
+cond_false:
+  %X.1 = load i32* @H
+  br label %cond_next
+
+cond_next:
+  %X.01 = phi i32 [ %X.1, %cond_false ], [ %X.0, %cond_true ]
+  ret i32 %X.01
+}
+</pre>
+</div>
+
+<p>The mem2reg pass implements the standard "iterated dominance frontier"
+algorithm for constructing SSA form and has a number of optimizations that speed
+up (very common) degenerate cases. The mem2reg optimization pass is the answer
+to dealing with mutable variables, and we highly recommend that you depend on
+it.  Note that mem2reg only works on variables in certain circumstances:</p>
+
+<ol>
+<li>mem2reg is alloca-driven: it looks for allocas and if it can handle them, it
+promotes them.  It does not apply to global variables or heap allocations.</li>
+
+<li>mem2reg only looks for alloca instructions in the entry block of the
+function.  Being in the entry block guarantees that the alloca is only executed
+once, which makes analysis simpler.</li>
+
+<li>mem2reg only promotes allocas whose uses are direct loads and stores.  If
+the address of the stack object is passed to a function, or if any funny pointer
+arithmetic is involved, the alloca will not be promoted.</li>
+
+<li>mem2reg only works on allocas of <a
+href="../LangRef.html#t_classifications">first class</a>
+values (such as pointers, scalars and vectors), and only if the array size
+of the allocation is 1 (or missing in the .ll file).  mem2reg is not capable of
+promoting structs or arrays to registers.  Note that the "scalarrepl" pass is
+more powerful and can promote structs, "unions", and arrays in many cases.</li>
+
+</ol>
+
+<p>
+All of these properties are easy to satisfy for most imperative languages, and
+we'll illustrate it below with Kaleidoscope.  The final question you may be
+asking is: should I bother with this nonsense for my front-end?  Wouldn't it be
+better if I just did SSA construction directly, avoiding use of the mem2reg
+optimization pass?  In short, we strongly recommend that you use this technique
+for building SSA form, unless there is an extremely good reason not to.  Using
+this technique is:</p>
+
+<ul>
+<li>Proven and well tested: llvm-gcc and clang both use this technique for local
+mutable variables.  As such, the most common clients of LLVM are using this to
+handle a bulk of their variables.  You can be sure that bugs are found fast and
+fixed early.</li>
+
+<li>Extremely Fast: mem2reg has a number of special cases that make it fast in
+common cases as well as fully general.  For example, it has fast-paths for
+variables that are only used in a single block, variables that only have one
+assignment point, good heuristics to avoid insertion of unneeded phi nodes, etc.
+</li>
+
+<li>Needed for debug info generation: <a href="../SourceLevelDebugging.html">
+Debug information in LLVM</a> relies on having the address of the variable
+exposed so that debug info can be attached to it.  This technique dovetails
+very naturally with this style of debug info.</li>
+</ul>
+
+<p>If nothing else, this makes it much easier to get your front-end up and
+running, and is very simple to implement.  Lets extend Kaleidoscope with mutable
+variables now!
+</p>
+
+</div>
+
+<!-- *********************************************************************** -->
+<div class="doc_section"><a name="kalvars">Mutable Variables in
+Kaleidoscope</a></div>
+<!-- *********************************************************************** -->
+
+<div class="doc_text">
+
+<p>Now that we know the sort of problem we want to tackle, lets see what this
+looks like in the context of our little Kaleidoscope language.  We're going to
+add two features:</p>
+
+<ol>
+<li>The ability to mutate variables with the '=' operator.</li>
+<li>The ability to define new variables.</li>
+</ol>
+
+<p>While the first item is really what this is about, we only have variables
+for incoming arguments as well as for induction variables, and redefining those only
+goes so far :).  Also, the ability to define new variables is a
+useful thing regardless of whether you will be mutating them.  Here's a
+motivating example that shows how we could use these:</p>
+
+<div class="doc_code">
+<pre>
+# Define ':' for sequencing: as a low-precedence operator that ignores operands
+# and just returns the RHS.
+def binary : 1 (x y) y;
+
+# Recursive fib, we could do this before.
+def fib(x)
+  if (x &lt; 3) then
+    1
+  else
+    fib(x-1)+fib(x-2);
+
+# Iterative fib.
+def fibi(x)
+  <b>var a = 1, b = 1, c in</b>
+  (for i = 3, i &lt; x in
+     <b>c = a + b</b> :
+     <b>a = b</b> :
+     <b>b = c</b>) :
+  b;
+
+# Call it.
+fibi(10);
+</pre>
+</div>
+
+<p>
+In order to mutate variables, we have to change our existing variables to use
+the "alloca trick".  Once we have that, we'll add our new operator, then extend
+Kaleidoscope to support new variable definitions.
+</p>
+
+</div>
+
+<!-- *********************************************************************** -->
+<div class="doc_section"><a name="adjustments">Adjusting Existing Variables for
+Mutation</a></div>
+<!-- *********************************************************************** -->
+
+<div class="doc_text">
+
+<p>
+The symbol table in Kaleidoscope is managed at code generation time by the
+'<tt>named_values</tt>' map.  This map currently keeps track of the LLVM
+"Value*" that holds the double value for the named variable.  In order to
+support mutation, we need to change this slightly, so that it
+<tt>named_values</tt> holds the <em>memory location</em> of the variable in
+question.  Note that this change is a refactoring: it changes the structure of
+the code, but does not (by itself) change the behavior of the compiler.  All of
+these changes are isolated in the Kaleidoscope code generator.</p>
+
+<p>
+At this point in Kaleidoscope's development, it only supports variables for two
+things: incoming arguments to functions and the induction variable of 'for'
+loops.  For consistency, we'll allow mutation of these variables in addition to
+other user-defined variables.  This means that these will both need memory
+locations.
+</p>
+
+<p>To start our transformation of Kaleidoscope, we'll change the
+<tt>named_values</tt> map so that it maps to AllocaInst* instead of Value*.
+Once we do this, the C++ compiler will tell us what parts of the code we need to
+update:</p>
+
+<p><b>Note:</b> the ocaml bindings currently model both <tt>Value*</tt>s and
+<tt>AllocInst*</tt>s as <tt>Llvm.llvalue</tt>s, but this may change in the
+future to be more type safe.</p>
+
+<div class="doc_code">
+<pre>
+let named_values:(string, llvalue) Hashtbl.t = Hashtbl.create 10
+</pre>
+</div>
+
+<p>Also, since we will need to create these alloca's, we'll use a helper
+function that ensures that the allocas are created in the entry block of the
+function:</p>
+
+<div class="doc_code">
+<pre>
+(* Create an alloca instruction in the entry block of the function. This
+ * is used for mutable variables etc. *)
+let create_entry_block_alloca the_function var_name =
+  let builder = builder_at (instr_begin (entry_block the_function)) in
+  build_alloca double_type var_name builder
+</pre>
+</div>
+
+<p>This funny looking code creates an <tt>Llvm.llbuilder</tt> object that is
+pointing at the first instruction of the entry block.  It then creates an alloca
+with the expected name and returns it.  Because all values in Kaleidoscope are
+doubles, there is no need to pass in a type to use.</p>
+
+<p>With this in place, the first functionality change we want to make is to
+variable references.  In our new scheme, variables live on the stack, so code
+generating a reference to them actually needs to produce a load from the stack
+slot:</p>
+
+<div class="doc_code">
+<pre>
+let rec codegen_expr = function
+  ...
+  | Ast.Variable name -&gt;
+      let v = try Hashtbl.find named_values name with
+        | Not_found -&gt; raise (Error "unknown variable name")
+      in
+      <b>(* Load the value. *)
+      build_load v name builder</b>
+</pre>
+</div>
+
+<p>As you can see, this is pretty straightforward.  Now we need to update the
+things that define the variables to set up the alloca.  We'll start with
+<tt>codegen_expr Ast.For ...</tt> (see the <a href="#code">full code listing</a>
+for the unabridged code):</p>
+
+<div class="doc_code">
+<pre>
+  | Ast.For (var_name, start, end_, step, body) -&gt;
+      let the_function = block_parent (insertion_block builder) in
+
+      (* Create an alloca for the variable in the entry block. *)
+      <b>let alloca = create_entry_block_alloca the_function var_name in</b>
+
+      (* Emit the start code first, without 'variable' in scope. *)
+      let start_val = codegen_expr start in
+
+      <b>(* Store the value into the alloca. *)
+      ignore(build_store start_val alloca builder);</b>
+
+      ...
+
+      (* Within the loop, the variable is defined equal to the PHI node. If it
+       * shadows an existing variable, we have to restore it, so save it
+       * now. *)
+      let old_val =
+        try Some (Hashtbl.find named_values var_name) with Not_found -&gt; None
+      in
+      <b>Hashtbl.add named_values var_name alloca;</b>
+
+      ...
+
+      (* Compute the end condition. *)
+      let end_cond = codegen_expr end_ in
+
+      <b>(* Reload, increment, and restore the alloca. This handles the case where
+       * the body of the loop mutates the variable. *)
+      let cur_var = build_load alloca var_name builder in
+      let next_var = build_add cur_var step_val "nextvar" builder in
+      ignore(build_store next_var alloca builder);</b>
+      ...
+</pre>
+</div>
+
+<p>This code is virtually identical to the code <a
+href="OCamlLangImpl5.html#forcodegen">before we allowed mutable variables</a>.
+The big difference is that we no longer have to construct a PHI node, and we use
+load/store to access the variable as needed.</p>
+
+<p>To support mutable argument variables, we need to also make allocas for them.
+The code for this is also pretty simple:</p>
+
+<div class="doc_code">
+<pre>
+(* Create an alloca for each argument and register the argument in the symbol
+ * table so that references to it will succeed. *)
+let create_argument_allocas the_function proto =
+  let args = match proto with
+    | Ast.Prototype (_, args) | Ast.BinOpPrototype (_, args, _) -&gt; args
+  in
+  Array.iteri (fun i ai -&gt;
+    let var_name = args.(i) in
+    (* Create an alloca for this variable. *)
+    let alloca = create_entry_block_alloca the_function var_name in
+
+    (* Store the initial value into the alloca. *)
+    ignore(build_store ai alloca builder);
+
+    (* Add arguments to variable symbol table. *)
+    Hashtbl.add named_values var_name alloca;
+  ) (params the_function)
+</pre>
+</div>
+
+<p>For each argument, we make an alloca, store the input value to the function
+into the alloca, and register the alloca as the memory location for the
+argument.  This method gets invoked by <tt>Codegen.codegen_func</tt> right after
+it sets up the entry block for the function.</p>
+
+<p>The final missing piece is adding the mem2reg pass, which allows us to get
+good codegen once again:</p>
+
+<div class="doc_code">
+<pre>
+let main () =
+  ...
+  let the_fpm = PassManager.create_function the_module_provider in
+
+  (* Set up the optimizer pipeline.  Start with registering info about how the
+   * target lays out data structures. *)
+  TargetData.add (ExecutionEngine.target_data the_execution_engine) the_fpm;
+
+  <b>(* Promote allocas to registers. *)
+  add_memory_to_register_promotion the_fpm;</b>
+
+  (* Do simple "peephole" optimizations and bit-twiddling optzn. *)
+  add_instruction_combining the_fpm;
+
+  (* reassociate expressions. *)
+  add_reassociation the_fpm;
+</pre>
+</div>
+
+<p>It is interesting to see what the code looks like before and after the
+mem2reg optimization runs.  For example, this is the before/after code for our
+recursive fib function.  Before the optimization:</p>
+
+<div class="doc_code">
+<pre>
+define double @fib(double %x) {
+entry:
+  <b>%x1 = alloca double
+  store double %x, double* %x1
+  %x2 = load double* %x1</b>
+  %cmptmp = fcmp ult double %x2, 3.000000e+00
+  %booltmp = uitofp i1 %cmptmp to double
+  %ifcond = fcmp one double %booltmp, 0.000000e+00
+  br i1 %ifcond, label %then, label %else
+
+then:    ; preds = %entry
+  br label %ifcont
+
+else:    ; preds = %entry
+  <b>%x3 = load double* %x1</b>
+  %subtmp = sub double %x3, 1.000000e+00
+  %calltmp = call double @fib( double %subtmp )
+  <b>%x4 = load double* %x1</b>
+  %subtmp5 = sub double %x4, 2.000000e+00
+  %calltmp6 = call double @fib( double %subtmp5 )
+  %addtmp = add double %calltmp, %calltmp6
+  br label %ifcont
+
+ifcont:    ; preds = %else, %then
+  %iftmp = phi double [ 1.000000e+00, %then ], [ %addtmp, %else ]
+  ret double %iftmp
+}
+</pre>
+</div>
+
+<p>Here there is only one variable (x, the input argument) but you can still
+see the extremely simple-minded code generation strategy we are using.  In the
+entry block, an alloca is created, and the initial input value is stored into
+it.  Each reference to the variable does a reload from the stack.  Also, note
+that we didn't modify the if/then/else expression, so it still inserts a PHI
+node.  While we could make an alloca for it, it is actually easier to create a
+PHI node for it, so we still just make the PHI.</p>
+
+<p>Here is the code after the mem2reg pass runs:</p>
+
+<div class="doc_code">
+<pre>
+define double @fib(double %x) {
+entry:
+  %cmptmp = fcmp ult double <b>%x</b>, 3.000000e+00
+  %booltmp = uitofp i1 %cmptmp to double
+  %ifcond = fcmp one double %booltmp, 0.000000e+00
+  br i1 %ifcond, label %then, label %else
+
+then:
+  br label %ifcont
+
+else:
+  %subtmp = sub double <b>%x</b>, 1.000000e+00
+  %calltmp = call double @fib( double %subtmp )
+  %subtmp5 = sub double <b>%x</b>, 2.000000e+00
+  %calltmp6 = call double @fib( double %subtmp5 )
+  %addtmp = add double %calltmp, %calltmp6
+  br label %ifcont
+
+ifcont:    ; preds = %else, %then
+  %iftmp = phi double [ 1.000000e+00, %then ], [ %addtmp, %else ]
+  ret double %iftmp
+}
+</pre>
+</div>
+
+<p>This is a trivial case for mem2reg, since there are no redefinitions of the
+variable.  The point of showing this is to calm your tension about inserting
+such blatent inefficiencies :).</p>
+
+<p>After the rest of the optimizers run, we get:</p>
+
+<div class="doc_code">
+<pre>
+define double @fib(double %x) {
+entry:
+  %cmptmp = fcmp ult double %x, 3.000000e+00
+  %booltmp = uitofp i1 %cmptmp to double
+  %ifcond = fcmp ueq double %booltmp, 0.000000e+00
+  br i1 %ifcond, label %else, label %ifcont
+
+else:
+  %subtmp = sub double %x, 1.000000e+00
+  %calltmp = call double @fib( double %subtmp )
+  %subtmp5 = sub double %x, 2.000000e+00
+  %calltmp6 = call double @fib( double %subtmp5 )
+  %addtmp = add double %calltmp, %calltmp6
+  ret double %addtmp
+
+ifcont:
+  ret double 1.000000e+00
+}
+</pre>
+</div>
+
+<p>Here we see that the simplifycfg pass decided to clone the return instruction
+into the end of the 'else' block.  This allowed it to eliminate some branches
+and the PHI node.</p>
+
+<p>Now that all symbol table references are updated to use stack variables,
+we'll add the assignment operator.</p>
+
+</div>
+
+<!-- *********************************************************************** -->
+<div class="doc_section"><a name="assignment">New Assignment Operator</a></div>
+<!-- *********************************************************************** -->
+
+<div class="doc_text">
+
+<p>With our current framework, adding a new assignment operator is really
+simple.  We will parse it just like any other binary operator, but handle it
+internally (instead of allowing the user to define it).  The first step is to
+set a precedence:</p>
+
+<div class="doc_code">
+<pre>
+let main () =
+  (* Install standard binary operators.
+   * 1 is the lowest precedence. *)
+  <b>Hashtbl.add Parser.binop_precedence '=' 2;</b>
+  Hashtbl.add Parser.binop_precedence '&lt;' 10;
+  Hashtbl.add Parser.binop_precedence '+' 20;
+  Hashtbl.add Parser.binop_precedence '-' 20;
+  ...
+</pre>
+</div>
+
+<p>Now that the parser knows the precedence of the binary operator, it takes
+care of all the parsing and AST generation.  We just need to implement codegen
+for the assignment operator.  This looks like:</p>
+
+<div class="doc_code">
+<pre>
+let rec codegen_expr = function
+      begin match op with
+      | '=' -&gt;
+          (* Special case '=' because we don't want to emit the LHS as an
+           * expression. *)
+          let name =
+            match lhs with
+            | Ast.Variable name -&gt; name
+            | _ -&gt; raise (Error "destination of '=' must be a variable")
+          in
+</pre>
+</div>
+
+<p>Unlike the rest of the binary operators, our assignment operator doesn't
+follow the "emit LHS, emit RHS, do computation" model.  As such, it is handled
+as a special case before the other binary operators are handled.  The other
+strange thing is that it requires the LHS to be a variable.  It is invalid to
+have "(x+1) = expr" - only things like "x = expr" are allowed.
+</p>
+
+
+<div class="doc_code">
+<pre>
+          (* Codegen the rhs. *)
+          let val_ = codegen_expr rhs in
+
+          (* Lookup the name. *)
+          let variable = try Hashtbl.find named_values name with
+          | Not_found -&gt; raise (Error "unknown variable name")
+          in
+          ignore(build_store val_ variable builder);
+          val_
+      | _ -&gt;
+			...
+</pre>
+</div>
+
+<p>Once we have the variable, codegen'ing the assignment is straightforward:
+we emit the RHS of the assignment, create a store, and return the computed
+value.  Returning a value allows for chained assignments like "X = (Y = Z)".</p>
+
+<p>Now that we have an assignment operator, we can mutate loop variables and
+arguments.  For example, we can now run code like this:</p>
+
+<div class="doc_code">
+<pre>
+# Function to print a double.
+extern printd(x);
+
+# Define ':' for sequencing: as a low-precedence operator that ignores operands
+# and just returns the RHS.
+def binary : 1 (x y) y;
+
+def test(x)
+  printd(x) :
+  x = 4 :
+  printd(x);
+
+test(123);
+</pre>
+</div>
+
+<p>When run, this example prints "123" and then "4", showing that we did
+actually mutate the value!  Okay, we have now officially implemented our goal:
+getting this to work requires SSA construction in the general case.  However,
+to be really useful, we want the ability to define our own local variables, lets
+add this next!
+</p>
+
+</div>
+
+<!-- *********************************************************************** -->
+<div class="doc_section"><a name="localvars">User-defined Local
+Variables</a></div>
+<!-- *********************************************************************** -->
+
+<div class="doc_text">
+
+<p>Adding var/in is just like any other other extensions we made to
+Kaleidoscope: we extend the lexer, the parser, the AST and the code generator.
+The first step for adding our new 'var/in' construct is to extend the lexer.
+As before, this is pretty trivial, the code looks like this:</p>
+
+<div class="doc_code">
+<pre>
+type token =
+  ...
+  <b>(* var definition *)
+  | Var</b>
+
+...
+
+and lex_ident buffer = parser
+      ...
+      | "in" -&gt; [&lt; 'Token.In; stream &gt;]
+      | "binary" -&gt; [&lt; 'Token.Binary; stream &gt;]
+      | "unary" -&gt; [&lt; 'Token.Unary; stream &gt;]
+      <b>| "var" -&gt; [&lt; 'Token.Var; stream &gt;]</b>
+      ...
+</pre>
+</div>
+
+<p>The next step is to define the AST node that we will construct.  For var/in,
+it looks like this:</p>
+
+<div class="doc_code">
+<pre>
+type expr =
+  ...
+  (* variant for var/in. *)
+  | Var of (string * expr option) array * expr
+  ...
+</pre>
+</div>
+
+<p>var/in allows a list of names to be defined all at once, and each name can
+optionally have an initializer value.  As such, we capture this information in
+the VarNames vector.  Also, var/in has a body, this body is allowed to access
+the variables defined by the var/in.</p>
+
+<p>With this in place, we can define the parser pieces.  The first thing we do
+is add it as a primary expression:</p>
+
+<div class="doc_code">
+<pre>
+(* primary
+ *   ::= identifier
+ *   ::= numberexpr
+ *   ::= parenexpr
+ *   ::= ifexpr
+ *   ::= forexpr
+ <b>*   ::= varexpr</b> *)
+let rec parse_primary = parser
+  ...
+  <b>(* varexpr
+   *   ::= 'var' identifier ('=' expression?
+   *             (',' identifier ('=' expression)?)* 'in' expression *)
+  | [&lt; 'Token.Var;
+       (* At least one variable name is required. *)
+       'Token.Ident id ?? "expected identifier after var";
+       init=parse_var_init;
+       var_names=parse_var_names [(id, init)];
+       (* At this point, we have to have 'in'. *)
+       'Token.In ?? "expected 'in' keyword after 'var'";
+       body=parse_expr &gt;] -&gt;
+      Ast.Var (Array.of_list (List.rev var_names), body)</b>
+
+...
+
+and parse_var_init = parser
+  (* read in the optional initializer. *)
+  | [&lt; 'Token.Kwd '='; e=parse_expr &gt;] -&gt; Some e
+  | [&lt; &gt;] -&gt; None
+
+and parse_var_names accumulator = parser
+  | [&lt; 'Token.Kwd ',';
+       'Token.Ident id ?? "expected identifier list after var";
+       init=parse_var_init;
+       e=parse_var_names ((id, init) :: accumulator) &gt;] -&gt; e
+  | [&lt; &gt;] -&gt; accumulator
+</pre>
+</div>
+
+<p>Now that we can parse and represent the code, we need to support emission of
+LLVM IR for it.  This code starts out with:</p>
+
+<div class="doc_code">
+<pre>
+let rec codegen_expr = function
+  ...
+  | Ast.Var (var_names, body)
+      let old_bindings = ref [] in
+
+      let the_function = block_parent (insertion_block builder) in
+
+      (* Register all variables and emit their initializer. *)
+      Array.iter (fun (var_name, init) -&gt;
+</pre>
+</div>
+
+<p>Basically it loops over all the variables, installing them one at a time.
+For each variable we put into the symbol table, we remember the previous value
+that we replace in OldBindings.</p>
+
+<div class="doc_code">
+<pre>
+        (* Emit the initializer before adding the variable to scope, this
+         * prevents the initializer from referencing the variable itself, and
+         * permits stuff like this:
+         *   var a = 1 in
+         *     var a = a in ...   # refers to outer 'a'. *)
+        let init_val =
+          match init with
+          | Some init -&gt; codegen_expr init
+          (* If not specified, use 0.0. *)
+          | None -&gt; const_float double_type 0.0
+        in
+
+        let alloca = create_entry_block_alloca the_function var_name in
+        ignore(build_store init_val alloca builder);
+
+        (* Remember the old variable binding so that we can restore the binding
+         * when we unrecurse. *)
+
+        begin
+          try
+            let old_value = Hashtbl.find named_values var_name in
+            old_bindings := (var_name, old_value) :: !old_bindings;
+          with Not_found &gt; ()
+        end;
+
+        (* Remember this binding. *)
+        Hashtbl.add named_values var_name alloca;
+      ) var_names;
+</pre>
+</div>
+
+<p>There are more comments here than code.  The basic idea is that we emit the
+initializer, create the alloca, then update the symbol table to point to it.
+Once all the variables are installed in the symbol table, we evaluate the body
+of the var/in expression:</p>
+
+<div class="doc_code">
+<pre>
+      (* Codegen the body, now that all vars are in scope. *)
+      let body_val = codegen_expr body in
+</pre>
+</div>
+
+<p>Finally, before returning, we restore the previous variable bindings:</p>
+
+<div class="doc_code">
+<pre>
+      (* Pop all our variables from scope. *)
+      List.iter (fun (var_name, old_value) -&gt;
+        Hashtbl.add named_values var_name old_value
+      ) !old_bindings;
+
+      (* Return the body computation. *)
+      body_val
+</pre>
+</div>
+
+<p>The end result of all of this is that we get properly scoped variable
+definitions, and we even (trivially) allow mutation of them :).</p>
+
+<p>With this, we completed what we set out to do.  Our nice iterative fib
+example from the intro compiles and runs just fine.  The mem2reg pass optimizes
+all of our stack variables into SSA registers, inserting PHI nodes where needed,
+and our front-end remains simple: no "iterated dominance frontier" computation
+anywhere in sight.</p>
+
+</div>
+
+<!-- *********************************************************************** -->
+<div class="doc_section"><a name="code">Full Code Listing</a></div>
+<!-- *********************************************************************** -->
+
+<div class="doc_text">
+
+<p>
+Here is the complete code listing for our running example, enhanced with mutable
+variables and var/in support.  To build this example, use:
+</p>
+
+<div class="doc_code">
+<pre>
+# Compile
+ocamlbuild toy.byte
+# Run
+./toy.byte
+</pre>
+</div>
+
+<p>Here is the code:</p>
+
+<dl>
+<dt>_tags:</dt>
+<dd class="doc_code">
+<pre>
+&lt;{lexer,parser}.ml&gt;: use_camlp4, pp(camlp4of)
+&lt;*.{byte,native}&gt;: g++, use_llvm, use_llvm_analysis
+&lt;*.{byte,native}&gt;: use_llvm_executionengine, use_llvm_target
+&lt;*.{byte,native}&gt;: use_llvm_scalar_opts, use_bindings
+</pre>
+</dd>
+
+<dt>myocamlbuild.ml:</dt>
+<dd class="doc_code">
+<pre>
+open Ocamlbuild_plugin;;
+
+ocaml_lib ~extern:true "llvm";;
+ocaml_lib ~extern:true "llvm_analysis";;
+ocaml_lib ~extern:true "llvm_executionengine";;
+ocaml_lib ~extern:true "llvm_target";;
+ocaml_lib ~extern:true "llvm_scalar_opts";;
+
+flag ["link"; "ocaml"; "g++"] (S[A"-cc"; A"g++"]);;
+dep ["link"; "ocaml"; "use_bindings"] ["bindings.o"];;
+</pre>
+</dd>
+
+<dt>token.ml:</dt>
+<dd class="doc_code">
+<pre>
+(*===----------------------------------------------------------------------===
+ * Lexer Tokens
+ *===----------------------------------------------------------------------===*)
+
+(* The lexer returns these 'Kwd' if it is an unknown character, otherwise one of
+ * these others for known things. *)
+type token =
+  (* commands *)
+  | Def | Extern
+
+  (* primary *)
+  | Ident of string | Number of float
+
+  (* unknown *)
+  | Kwd of char
+
+  (* control *)
+  | If | Then | Else
+  | For | In
+
+  (* operators *)
+  | Binary | Unary
+
+  (* var definition *)
+  | Var
+</pre>
+</dd>
+
+<dt>lexer.ml:</dt>
+<dd class="doc_code">
+<pre>
+(*===----------------------------------------------------------------------===
+ * Lexer
+ *===----------------------------------------------------------------------===*)
+
+let rec lex = parser
+  (* Skip any whitespace. *)
+  | [&lt; ' (' ' | '\n' | '\r' | '\t'); stream &gt;] -&gt; lex stream
+
+  (* identifier: [a-zA-Z][a-zA-Z0-9] *)
+  | [&lt; ' ('A' .. 'Z' | 'a' .. 'z' as c); stream &gt;] -&gt;
+      let buffer = Buffer.create 1 in
+      Buffer.add_char buffer c;
+      lex_ident buffer stream
+
+  (* number: [0-9.]+ *)
+  | [&lt; ' ('0' .. '9' as c); stream &gt;] -&gt;
+      let buffer = Buffer.create 1 in
+      Buffer.add_char buffer c;
+      lex_number buffer stream
+
+  (* Comment until end of line. *)
+  | [&lt; ' ('#'); stream &gt;] -&gt;
+      lex_comment stream
+
+  (* Otherwise, just return the character as its ascii value. *)
+  | [&lt; 'c; stream &gt;] -&gt;
+      [&lt; 'Token.Kwd c; lex stream &gt;]
+
+  (* end of stream. *)
+  | [&lt; &gt;] -&gt; [&lt; &gt;]
+
+and lex_number buffer = parser
+  | [&lt; ' ('0' .. '9' | '.' as c); stream &gt;] -&gt;
+      Buffer.add_char buffer c;
+      lex_number buffer stream
+  | [&lt; stream=lex &gt;] -&gt;
+      [&lt; 'Token.Number (float_of_string (Buffer.contents buffer)); stream &gt;]
+
+and lex_ident buffer = parser
+  | [&lt; ' ('A' .. 'Z' | 'a' .. 'z' | '0' .. '9' as c); stream &gt;] -&gt;
+      Buffer.add_char buffer c;
+      lex_ident buffer stream
+  | [&lt; stream=lex &gt;] -&gt;
+      match Buffer.contents buffer with
+      | "def" -&gt; [&lt; 'Token.Def; stream &gt;]
+      | "extern" -&gt; [&lt; 'Token.Extern; stream &gt;]
+      | "if" -&gt; [&lt; 'Token.If; stream &gt;]
+      | "then" -&gt; [&lt; 'Token.Then; stream &gt;]
+      | "else" -&gt; [&lt; 'Token.Else; stream &gt;]
+      | "for" -&gt; [&lt; 'Token.For; stream &gt;]
+      | "in" -&gt; [&lt; 'Token.In; stream &gt;]
+      | "binary" -&gt; [&lt; 'Token.Binary; stream &gt;]
+      | "unary" -&gt; [&lt; 'Token.Unary; stream &gt;]
+      | "var" -&gt; [&lt; 'Token.Var; stream &gt;]
+      | id -&gt; [&lt; 'Token.Ident id; stream &gt;]
+
+and lex_comment = parser
+  | [&lt; ' ('\n'); stream=lex &gt;] -&gt; stream
+  | [&lt; 'c; e=lex_comment &gt;] -&gt; e
+  | [&lt; &gt;] -&gt; [&lt; &gt;]
+</pre>
+</dd>
+
+<dt>ast.ml:</dt>
+<dd class="doc_code">
+<pre>
+(*===----------------------------------------------------------------------===
+ * Abstract Syntax Tree (aka Parse Tree)
+ *===----------------------------------------------------------------------===*)
+
+(* expr - Base type for all expression nodes. *)
+type expr =
+  (* variant for numeric literals like "1.0". *)
+  | Number of float
+
+  (* variant for referencing a variable, like "a". *)
+  | Variable of string
+
+  (* variant for a unary operator. *)
+  | Unary of char * expr
+
+  (* variant for a binary operator. *)
+  | Binary of char * expr * expr
+
+  (* variant for function calls. *)
+  | Call of string * expr array
+
+  (* variant for if/then/else. *)
+  | If of expr * expr * expr
+
+  (* variant for for/in. *)
+  | For of string * expr * expr * expr option * expr
+
+  (* variant for var/in. *)
+  | Var of (string * expr option) array * expr
+
+(* proto - This type represents the "prototype" for a function, which captures
+ * its name, and its argument names (thus implicitly the number of arguments the
+ * function takes). *)
+type proto =
+  | Prototype of string * string array
+  | BinOpPrototype of string * string array * int
+
+(* func - This type represents a function definition itself. *)
+type func = Function of proto * expr
+</pre>
+</dd>
+
+<dt>parser.ml:</dt>
+<dd class="doc_code">
+<pre>
+(*===---------------------------------------------------------------------===
+ * Parser
+ *===---------------------------------------------------------------------===*)
+
+(* binop_precedence - This holds the precedence for each binary operator that is
+ * defined *)
+let binop_precedence:(char, int) Hashtbl.t = Hashtbl.create 10
+
+(* precedence - Get the precedence of the pending binary operator token. *)
+let precedence c = try Hashtbl.find binop_precedence c with Not_found -&gt; -1
+
+(* primary
+ *   ::= identifier
+ *   ::= numberexpr
+ *   ::= parenexpr
+ *   ::= ifexpr
+ *   ::= forexpr
+ *   ::= varexpr *)
+let rec parse_primary = parser
+  (* numberexpr ::= number *)
+  | [&lt; 'Token.Number n &gt;] -&gt; Ast.Number n
+
+  (* parenexpr ::= '(' expression ')' *)
+  | [&lt; 'Token.Kwd '('; e=parse_expr; 'Token.Kwd ')' ?? "expected ')'" &gt;] -&gt; e
+
+  (* identifierexpr
+   *   ::= identifier
+   *   ::= identifier '(' argumentexpr ')' *)
+  | [&lt; 'Token.Ident id; stream &gt;] -&gt;
+      let rec parse_args accumulator = parser
+        | [&lt; e=parse_expr; stream &gt;] -&gt;
+            begin parser
+              | [&lt; 'Token.Kwd ','; e=parse_args (e :: accumulator) &gt;] -&gt; e
+              | [&lt; &gt;] -&gt; e :: accumulator
+            end stream
+        | [&lt; &gt;] -&gt; accumulator
+      in
+      let rec parse_ident id = parser
+        (* Call. *)
+        | [&lt; 'Token.Kwd '(';
+             args=parse_args [];
+             'Token.Kwd ')' ?? "expected ')'"&gt;] -&gt;
+            Ast.Call (id, Array.of_list (List.rev args))
+
+        (* Simple variable ref. *)
+        | [&lt; &gt;] -&gt; Ast.Variable id
+      in
+      parse_ident id stream
+
+  (* ifexpr ::= 'if' expr 'then' expr 'else' expr *)
+  | [&lt; 'Token.If; c=parse_expr;
+       'Token.Then ?? "expected 'then'"; t=parse_expr;
+       'Token.Else ?? "expected 'else'"; e=parse_expr &gt;] -&gt;
+      Ast.If (c, t, e)
+
+  (* forexpr
+        ::= 'for' identifier '=' expr ',' expr (',' expr)? 'in' expression *)
+  | [&lt; 'Token.For;
+       'Token.Ident id ?? "expected identifier after for";
+       'Token.Kwd '=' ?? "expected '=' after for";
+       stream &gt;] -&gt;
+      begin parser
+        | [&lt;
+             start=parse_expr;
+             'Token.Kwd ',' ?? "expected ',' after for";
+             end_=parse_expr;
+             stream &gt;] -&gt;
+            let step =
+              begin parser
+              | [&lt; 'Token.Kwd ','; step=parse_expr &gt;] -&gt; Some step
+              | [&lt; &gt;] -&gt; None
+              end stream
+            in
+            begin parser
+            | [&lt; 'Token.In; body=parse_expr &gt;] -&gt;
+                Ast.For (id, start, end_, step, body)
+            | [&lt; &gt;] -&gt;
+                raise (Stream.Error "expected 'in' after for")
+            end stream
+        | [&lt; &gt;] -&gt;
+            raise (Stream.Error "expected '=' after for")
+      end stream
+
+  (* varexpr
+   *   ::= 'var' identifier ('=' expression?
+   *             (',' identifier ('=' expression)?)* 'in' expression *)
+  | [&lt; 'Token.Var;
+       (* At least one variable name is required. *)
+       'Token.Ident id ?? "expected identifier after var";
+       init=parse_var_init;
+       var_names=parse_var_names [(id, init)];
+       (* At this point, we have to have 'in'. *)
+       'Token.In ?? "expected 'in' keyword after 'var'";
+       body=parse_expr &gt;] -&gt;
+      Ast.Var (Array.of_list (List.rev var_names), body)
+
+  | [&lt; &gt;] -&gt; raise (Stream.Error "unknown token when expecting an expression.")
+
+(* unary
+ *   ::= primary
+ *   ::= '!' unary *)
+and parse_unary = parser
+  (* If this is a unary operator, read it. *)
+  | [&lt; 'Token.Kwd op when op != '(' &amp;&amp; op != ')'; operand=parse_expr &gt;] -&gt;
+      Ast.Unary (op, operand)
+
+  (* If the current token is not an operator, it must be a primary expr. *)
+  | [&lt; stream &gt;] -&gt; parse_primary stream
+
+(* binoprhs
+ *   ::= ('+' primary)* *)
+and parse_bin_rhs expr_prec lhs stream =
+  match Stream.peek stream with
+  (* If this is a binop, find its precedence. *)
+  | Some (Token.Kwd c) when Hashtbl.mem binop_precedence c -&gt;
+      let token_prec = precedence c in
+
+      (* If this is a binop that binds at least as tightly as the current binop,
+       * consume it, otherwise we are done. *)
+      if token_prec &lt; expr_prec then lhs else begin
+        (* Eat the binop. *)
+        Stream.junk stream;
+
+        (* Parse the primary expression after the binary operator. *)
+        let rhs = parse_unary stream in
+
+        (* Okay, we know this is a binop. *)
+        let rhs =
+          match Stream.peek stream with
+          | Some (Token.Kwd c2) -&gt;
+              (* If BinOp binds less tightly with rhs than the operator after
+               * rhs, let the pending operator take rhs as its lhs. *)
+              let next_prec = precedence c2 in
+              if token_prec &lt; next_prec
+              then parse_bin_rhs (token_prec + 1) rhs stream
+              else rhs
+          | _ -&gt; rhs
+        in
+
+        (* Merge lhs/rhs. *)
+        let lhs = Ast.Binary (c, lhs, rhs) in
+        parse_bin_rhs expr_prec lhs stream
+      end
+  | _ -&gt; lhs
+
+and parse_var_init = parser
+  (* read in the optional initializer. *)
+  | [&lt; 'Token.Kwd '='; e=parse_expr &gt;] -&gt; Some e
+  | [&lt; &gt;] -&gt; None
+
+and parse_var_names accumulator = parser
+  | [&lt; 'Token.Kwd ',';
+       'Token.Ident id ?? "expected identifier list after var";
+       init=parse_var_init;
+       e=parse_var_names ((id, init) :: accumulator) &gt;] -&gt; e
+  | [&lt; &gt;] -&gt; accumulator
+
+(* expression
+ *   ::= primary binoprhs *)
+and parse_expr = parser
+  | [&lt; lhs=parse_unary; stream &gt;] -&gt; parse_bin_rhs 0 lhs stream
+
+(* prototype
+ *   ::= id '(' id* ')'
+ *   ::= binary LETTER number? (id, id)
+ *   ::= unary LETTER number? (id) *)
+let parse_prototype =
+  let rec parse_args accumulator = parser
+    | [&lt; 'Token.Ident id; e=parse_args (id::accumulator) &gt;] -&gt; e
+    | [&lt; &gt;] -&gt; accumulator
+  in
+  let parse_operator = parser
+    | [&lt; 'Token.Unary &gt;] -&gt; "unary", 1
+    | [&lt; 'Token.Binary &gt;] -&gt; "binary", 2
+  in
+  let parse_binary_precedence = parser
+    | [&lt; 'Token.Number n &gt;] -&gt; int_of_float n
+    | [&lt; &gt;] -&gt; 30
+  in
+  parser
+  | [&lt; 'Token.Ident id;
+       'Token.Kwd '(' ?? "expected '(' in prototype";
+       args=parse_args [];
+       'Token.Kwd ')' ?? "expected ')' in prototype" &gt;] -&gt;
+      (* success. *)
+      Ast.Prototype (id, Array.of_list (List.rev args))
+  | [&lt; (prefix, kind)=parse_operator;
+       'Token.Kwd op ?? "expected an operator";
+       (* Read the precedence if present. *)
+       binary_precedence=parse_binary_precedence;
+       'Token.Kwd '(' ?? "expected '(' in prototype";
+        args=parse_args [];
+       'Token.Kwd ')' ?? "expected ')' in prototype" &gt;] -&gt;
+      let name = prefix ^ (String.make 1 op) in
+      let args = Array.of_list (List.rev args) in
+
+      (* Verify right number of arguments for operator. *)
+      if Array.length args != kind
+      then raise (Stream.Error "invalid number of operands for operator")
+      else
+        if kind == 1 then
+          Ast.Prototype (name, args)
+        else
+          Ast.BinOpPrototype (name, args, binary_precedence)
+  | [&lt; &gt;] -&gt;
+      raise (Stream.Error "expected function name in prototype")
+
+(* definition ::= 'def' prototype expression *)
+let parse_definition = parser
+  | [&lt; 'Token.Def; p=parse_prototype; e=parse_expr &gt;] -&gt;
+      Ast.Function (p, e)
+
+(* toplevelexpr ::= expression *)
+let parse_toplevel = parser
+  | [&lt; e=parse_expr &gt;] -&gt;
+      (* Make an anonymous proto. *)
+      Ast.Function (Ast.Prototype ("", [||]), e)
+
+(*  external ::= 'extern' prototype *)
+let parse_extern = parser
+  | [&lt; 'Token.Extern; e=parse_prototype &gt;] -&gt; e
+</pre>
+</dd>
+
+<dt>codegen.ml:</dt>
+<dd class="doc_code">
+<pre>
+(*===----------------------------------------------------------------------===
+ * Code Generation
+ *===----------------------------------------------------------------------===*)
+
+open Llvm
+
+exception Error of string
+
+let the_module = create_module "my cool jit"
+let builder = builder ()
+let named_values:(string, llvalue) Hashtbl.t = Hashtbl.create 10
+
+(* Create an alloca instruction in the entry block of the function. This
+ * is used for mutable variables etc. *)
+let create_entry_block_alloca the_function var_name =
+  let builder = builder_at (instr_begin (entry_block the_function)) in
+  build_alloca double_type var_name builder
+
+let rec codegen_expr = function
+  | Ast.Number n -&gt; const_float double_type n
+  | Ast.Variable name -&gt;
+      let v = try Hashtbl.find named_values name with
+        | Not_found -&gt; raise (Error "unknown variable name")
+      in
+      (* Load the value. *)
+      build_load v name builder
+  | Ast.Unary (op, operand) -&gt;
+      let operand = codegen_expr operand in
+      let callee = "unary" ^ (String.make 1 op) in
+      let callee =
+        match lookup_function callee the_module with
+        | Some callee -&gt; callee
+        | None -&gt; raise (Error "unknown unary operator")
+      in
+      build_call callee [|operand|] "unop" builder
+  | Ast.Binary (op, lhs, rhs) -&gt;
+      begin match op with
+      | '=' -&gt;
+          (* Special case '=' because we don't want to emit the LHS as an
+           * expression. *)
+          let name =
+            match lhs with
+            | Ast.Variable name -&gt; name
+            | _ -&gt; raise (Error "destination of '=' must be a variable")
+          in
+
+          (* Codegen the rhs. *)
+          let val_ = codegen_expr rhs in
+
+          (* Lookup the name. *)
+          let variable = try Hashtbl.find named_values name with
+          | Not_found -&gt; raise (Error "unknown variable name")
+          in
+          ignore(build_store val_ variable builder);
+          val_
+      | _ -&gt;
+          let lhs_val = codegen_expr lhs in
+          let rhs_val = codegen_expr rhs in
+          begin
+            match op with
+            | '+' -&gt; build_add lhs_val rhs_val "addtmp" builder
+            | '-' -&gt; build_sub lhs_val rhs_val "subtmp" builder
+            | '*' -&gt; build_mul lhs_val rhs_val "multmp" builder
+            | '&lt;' -&gt;
+                (* Convert bool 0/1 to double 0.0 or 1.0 *)
+                let i = build_fcmp Fcmp.Ult lhs_val rhs_val "cmptmp" builder in
+                build_uitofp i double_type "booltmp" builder
+            | _ -&gt;
+                (* If it wasn't a builtin binary operator, it must be a user defined
+                 * one. Emit a call to it. *)
+                let callee = "binary" ^ (String.make 1 op) in
+                let callee =
+                  match lookup_function callee the_module with
+                  | Some callee -&gt; callee
+                  | None -&gt; raise (Error "binary operator not found!")
+                in
+                build_call callee [|lhs_val; rhs_val|] "binop" builder
+          end
+      end
+  | Ast.Call (callee, args) -&gt;
+      (* Look up the name in the module table. *)
+      let callee =
+        match lookup_function callee the_module with
+        | Some callee -&gt; callee
+        | None -&gt; raise (Error "unknown function referenced")
+      in
+      let params = params callee in
+
+      (* If argument mismatch error. *)
+      if Array.length params == Array.length args then () else
+        raise (Error "incorrect # arguments passed");
+      let args = Array.map codegen_expr args in
+      build_call callee args "calltmp" builder
+  | Ast.If (cond, then_, else_) -&gt;
+      let cond = codegen_expr cond in
+
+      (* Convert condition to a bool by comparing equal to 0.0 *)
+      let zero = const_float double_type 0.0 in
+      let cond_val = build_fcmp Fcmp.One cond zero "ifcond" builder in
+
+      (* Grab the first block so that we might later add the conditional branch
+       * to it at the end of the function. *)
+      let start_bb = insertion_block builder in
+      let the_function = block_parent start_bb in
+
+      let then_bb = append_block "then" the_function in
+
+      (* Emit 'then' value. *)
+      position_at_end then_bb builder;
+      let then_val = codegen_expr then_ in
+
+      (* Codegen of 'then' can change the current block, update then_bb for the
+       * phi. We create a new name because one is used for the phi node, and the
+       * other is used for the conditional branch. *)
+      let new_then_bb = insertion_block builder in
+
+      (* Emit 'else' value. *)
+      let else_bb = append_block "else" the_function in
+      position_at_end else_bb builder;
+      let else_val = codegen_expr else_ in
+
+      (* Codegen of 'else' can change the current block, update else_bb for the
+       * phi. *)
+      let new_else_bb = insertion_block builder in
+
+      (* Emit merge block. *)
+      let merge_bb = append_block "ifcont" the_function in
+      position_at_end merge_bb builder;
+      let incoming = [(then_val, new_then_bb); (else_val, new_else_bb)] in
+      let phi = build_phi incoming "iftmp" builder in
+
+      (* Return to the start block to add the conditional branch. *)
+      position_at_end start_bb builder;
+      ignore (build_cond_br cond_val then_bb else_bb builder);
+
+      (* Set a unconditional branch at the end of the 'then' block and the
+       * 'else' block to the 'merge' block. *)
+      position_at_end new_then_bb builder; ignore (build_br merge_bb builder);
+      position_at_end new_else_bb builder; ignore (build_br merge_bb builder);
+
+      (* Finally, set the builder to the end of the merge block. *)
+      position_at_end merge_bb builder;
+
+      phi
+  | Ast.For (var_name, start, end_, step, body) -&gt;
+      (* Output this as:
+       *   var = alloca double
+       *   ...
+       *   start = startexpr
+       *   store start -&gt; var
+       *   goto loop
+       * loop:
+       *   ...
+       *   bodyexpr
+       *   ...
+       * loopend:
+       *   step = stepexpr
+       *   endcond = endexpr
+       *
+       *   curvar = load var
+       *   nextvar = curvar + step
+       *   store nextvar -&gt; var
+       *   br endcond, loop, endloop
+       * outloop: *)
+
+      let the_function = block_parent (insertion_block builder) in
+
+      (* Create an alloca for the variable in the entry block. *)
+      let alloca = create_entry_block_alloca the_function var_name in
+
+      (* Emit the start code first, without 'variable' in scope. *)
+      let start_val = codegen_expr start in
+
+      (* Store the value into the alloca. *)
+      ignore(build_store start_val alloca builder);
+
+      (* Make the new basic block for the loop header, inserting after current
+       * block. *)
+      let loop_bb = append_block "loop" the_function in
+
+      (* Insert an explicit fall through from the current block to the
+       * loop_bb. *)
+      ignore (build_br loop_bb builder);
+
+      (* Start insertion in loop_bb. *)
+      position_at_end loop_bb builder;
+
+      (* Within the loop, the variable is defined equal to the PHI node. If it
+       * shadows an existing variable, we have to restore it, so save it
+       * now. *)
+      let old_val =
+        try Some (Hashtbl.find named_values var_name) with Not_found -&gt; None
+      in
+      Hashtbl.add named_values var_name alloca;
+
+      (* Emit the body of the loop.  This, like any other expr, can change the
+       * current BB.  Note that we ignore the value computed by the body, but
+       * don't allow an error *)
+      ignore (codegen_expr body);
+
+      (* Emit the step value. *)
+      let step_val =
+        match step with
+        | Some step -&gt; codegen_expr step
+        (* If not specified, use 1.0. *)
+        | None -&gt; const_float double_type 1.0
+      in
+
+      (* Compute the end condition. *)
+      let end_cond = codegen_expr end_ in
+
+      (* Reload, increment, and restore the alloca. This handles the case where
+       * the body of the loop mutates the variable. *)
+      let cur_var = build_load alloca var_name builder in
+      let next_var = build_add cur_var step_val "nextvar" builder in
+      ignore(build_store next_var alloca builder);
+
+      (* Convert condition to a bool by comparing equal to 0.0. *)
+      let zero = const_float double_type 0.0 in
+      let end_cond = build_fcmp Fcmp.One end_cond zero "loopcond" builder in
+
+      (* Create the "after loop" block and insert it. *)
+      let after_bb = append_block "afterloop" the_function in
+
+      (* Insert the conditional branch into the end of loop_end_bb. *)
+      ignore (build_cond_br end_cond loop_bb after_bb builder);
+
+      (* Any new code will be inserted in after_bb. *)
+      position_at_end after_bb builder;
+
+      (* Restore the unshadowed variable. *)
+      begin match old_val with
+      | Some old_val -&gt; Hashtbl.add named_values var_name old_val
+      | None -&gt; ()
+      end;
+
+      (* for expr always returns 0.0. *)
+      const_null double_type
+  | Ast.Var (var_names, body) -&gt;
+      let old_bindings = ref [] in
+
+      let the_function = block_parent (insertion_block builder) in
+
+      (* Register all variables and emit their initializer. *)
+      Array.iter (fun (var_name, init) -&gt;
+        (* Emit the initializer before adding the variable to scope, this
+         * prevents the initializer from referencing the variable itself, and
+         * permits stuff like this:
+         *   var a = 1 in
+         *     var a = a in ...   # refers to outer 'a'. *)
+        let init_val =
+          match init with
+          | Some init -&gt; codegen_expr init
+          (* If not specified, use 0.0. *)
+          | None -&gt; const_float double_type 0.0
+        in
+
+        let alloca = create_entry_block_alloca the_function var_name in
+        ignore(build_store init_val alloca builder);
+
+        (* Remember the old variable binding so that we can restore the binding
+         * when we unrecurse. *)
+        begin
+          try
+            let old_value = Hashtbl.find named_values var_name in
+            old_bindings := (var_name, old_value) :: !old_bindings;
+          with Not_found -&gt; ()
+        end;
+
+        (* Remember this binding. *)
+        Hashtbl.add named_values var_name alloca;
+      ) var_names;
+
+      (* Codegen the body, now that all vars are in scope. *)
+      let body_val = codegen_expr body in
+
+      (* Pop all our variables from scope. *)
+      List.iter (fun (var_name, old_value) -&gt;
+        Hashtbl.add named_values var_name old_value
+      ) !old_bindings;
+
+      (* Return the body computation. *)
+      body_val
+
+let codegen_proto = function
+  | Ast.Prototype (name, args) | Ast.BinOpPrototype (name, args, _) -&gt;
+      (* Make the function type: double(double,double) etc. *)
+      let doubles = Array.make (Array.length args) double_type in
+      let ft = function_type double_type doubles in
+      let f =
+        match lookup_function name the_module with
+        | None -&gt; declare_function name ft the_module
+
+        (* If 'f' conflicted, there was already something named 'name'. If it
+         * has a body, don't allow redefinition or reextern. *)
+        | Some f -&gt;
+            (* If 'f' already has a body, reject this. *)
+            if block_begin f &lt;&gt; At_end f then
+              raise (Error "redefinition of function");
+
+            (* If 'f' took a different number of arguments, reject. *)
+            if element_type (type_of f) &lt;&gt; ft then
+              raise (Error "redefinition of function with different # args");
+            f
+      in
+
+      (* Set names for all arguments. *)
+      Array.iteri (fun i a -&gt;
+        let n = args.(i) in
+        set_value_name n a;
+        Hashtbl.add named_values n a;
+      ) (params f);
+      f
+
+(* Create an alloca for each argument and register the argument in the symbol
+ * table so that references to it will succeed. *)
+let create_argument_allocas the_function proto =
+  let args = match proto with
+    | Ast.Prototype (_, args) | Ast.BinOpPrototype (_, args, _) -&gt; args
+  in
+  Array.iteri (fun i ai -&gt;
+    let var_name = args.(i) in
+    (* Create an alloca for this variable. *)
+    let alloca = create_entry_block_alloca the_function var_name in
+
+    (* Store the initial value into the alloca. *)
+    ignore(build_store ai alloca builder);
+
+    (* Add arguments to variable symbol table. *)
+    Hashtbl.add named_values var_name alloca;
+  ) (params the_function)
+
+let codegen_func the_fpm = function
+  | Ast.Function (proto, body) -&gt;
+      Hashtbl.clear named_values;
+      let the_function = codegen_proto proto in
+
+      (* If this is an operator, install it. *)
+      begin match proto with
+      | Ast.BinOpPrototype (name, args, prec) -&gt;
+          let op = name.[String.length name - 1] in
+          Hashtbl.add Parser.binop_precedence op prec;
+      | _ -&gt; ()
+      end;
+
+      (* Create a new basic block to start insertion into. *)
+      let bb = append_block "entry" the_function in
+      position_at_end bb builder;
+
+      try
+        (* Add all arguments to the symbol table and create their allocas. *)
+        create_argument_allocas the_function proto;
+
+        let ret_val = codegen_expr body in
+
+        (* Finish off the function. *)
+        let _ = build_ret ret_val builder in
+
+        (* Validate the generated code, checking for consistency. *)
+        Llvm_analysis.assert_valid_function the_function;
+
+        (* Optimize the function. *)
+        let _ = PassManager.run_function the_function the_fpm in
+
+        the_function
+      with e -&gt;
+        delete_function the_function;
+        raise e
+</pre>
+</dd>
+
+<dt>toplevel.ml:</dt>
+<dd class="doc_code">
+<pre>
+(*===----------------------------------------------------------------------===
+ * Top-Level parsing and JIT Driver
+ *===----------------------------------------------------------------------===*)
+
+open Llvm
+open Llvm_executionengine
+
+(* top ::= definition | external | expression | ';' *)
+let rec main_loop the_fpm the_execution_engine stream =
+  match Stream.peek stream with
+  | None -&gt; ()
+
+  (* ignore top-level semicolons. *)
+  | Some (Token.Kwd ';') -&gt;
+      Stream.junk stream;
+      main_loop the_fpm the_execution_engine stream
+
+  | Some token -&gt;
+      begin
+        try match token with
+        | Token.Def -&gt;
+            let e = Parser.parse_definition stream in
+            print_endline "parsed a function definition.";
+            dump_value (Codegen.codegen_func the_fpm e);
+        | Token.Extern -&gt;
+            let e = Parser.parse_extern stream in
+            print_endline "parsed an extern.";
+            dump_value (Codegen.codegen_proto e);
+        | _ -&gt;
+            (* Evaluate a top-level expression into an anonymous function. *)
+            let e = Parser.parse_toplevel stream in
+            print_endline "parsed a top-level expr";
+            let the_function = Codegen.codegen_func the_fpm e in
+            dump_value the_function;
+
+            (* JIT the function, returning a function pointer. *)
+            let result = ExecutionEngine.run_function the_function [||]
+              the_execution_engine in
+
+            print_string "Evaluated to ";
+            print_float (GenericValue.as_float double_type result);
+            print_newline ();
+        with Stream.Error s | Codegen.Error s -&gt;
+          (* Skip token for error recovery. *)
+          Stream.junk stream;
+          print_endline s;
+      end;
+      print_string "ready&gt; "; flush stdout;
+      main_loop the_fpm the_execution_engine stream
+</pre>
+</dd>
+
+<dt>toy.ml:</dt>
+<dd class="doc_code">
+<pre>
+(*===----------------------------------------------------------------------===
+ * Main driver code.
+ *===----------------------------------------------------------------------===*)
+
+open Llvm
+open Llvm_executionengine
+open Llvm_target
+open Llvm_scalar_opts
+
+let main () =
+  (* Install standard binary operators.
+   * 1 is the lowest precedence. *)
+  Hashtbl.add Parser.binop_precedence '=' 2;
+  Hashtbl.add Parser.binop_precedence '&lt;' 10;
+  Hashtbl.add Parser.binop_precedence '+' 20;
+  Hashtbl.add Parser.binop_precedence '-' 20;
+  Hashtbl.add Parser.binop_precedence '*' 40;    (* highest. *)
+
+  (* Prime the first token. *)
+  print_string "ready&gt; "; flush stdout;
+  let stream = Lexer.lex (Stream.of_channel stdin) in
+
+  (* Create the JIT. *)
+  let the_module_provider = ModuleProvider.create Codegen.the_module in
+  let the_execution_engine = ExecutionEngine.create the_module_provider in
+  let the_fpm = PassManager.create_function the_module_provider in
+
+  (* Set up the optimizer pipeline.  Start with registering info about how the
+   * target lays out data structures. *)
+  TargetData.add (ExecutionEngine.target_data the_execution_engine) the_fpm;
+
+  (* Promote allocas to registers. *)
+  add_memory_to_register_promotion the_fpm;
+
+  (* Do simple "peephole" optimizations and bit-twiddling optzn. *)
+  add_instruction_combining the_fpm;
+
+  (* reassociate expressions. *)
+  add_reassociation the_fpm;
+
+  (* Eliminate Common SubExpressions. *)
+  add_gvn the_fpm;
+
+  (* Simplify the control flow graph (deleting unreachable blocks, etc). *)
+  add_cfg_simplification the_fpm;
+
+  (* Run the main "interpreter loop" now. *)
+  Toplevel.main_loop the_fpm the_execution_engine stream;
+
+  (* Print out all the generated code. *)
+  dump_module Codegen.the_module
+;;
+
+main ()
+</pre>
+</dd>
+
+<dt>bindings.c</dt>
+<dd class="doc_code">
+<pre>
+#include &lt;stdio.h&gt;
+
+/* putchard - putchar that takes a double and returns 0. */
+extern double putchard(double X) {
+  putchar((char)X);
+  return 0;
+}
+
+/* printd - printf that takes a double prints it as "%f\n", returning 0. */
+extern double printd(double X) {
+  printf("%f\n", X);
+  return 0;
+}
+</pre>
+</dd>
+</dl>
+
+<a href="LangImpl8.html">Next: Conclusion and other useful LLVM tidbits</a>
+</div>
+
+<!-- *********************************************************************** -->
+<hr>
+<address>
+  <a href="http://jigsaw.w3.org/css-validator/check/referer"><img
+  src="http://jigsaw.w3.org/css-validator/images/vcss" alt="Valid CSS!"></a>
+  <a href="http://validator.w3.org/check/referer"><img
+  src="http://www.w3.org/Icons/valid-html401" alt="Valid HTML 4.01!"></a>
+
+  <a href="mailto:sabre@nondot.org">Chris Lattner</a><br>
+  <a href="http://llvm.org">The LLVM Compiler Infrastructure</a><br>
+  <a href="mailto:idadesub@users.sourceforge.net">Erick Tryzelaar</a><br>
+  Last modified: $Date: 2007-10-17 11:05:13 -0700 (Wed, 17 Oct 2007) $
+</address>
+</body>
+</html>