aboutsummaryrefslogtreecommitdiff
path: root/docs/tutorial/OCamlLangImpl6.html
diff options
context:
space:
mode:
Diffstat (limited to 'docs/tutorial/OCamlLangImpl6.html')
-rw-r--r--docs/tutorial/OCamlLangImpl6.html1574
1 files changed, 0 insertions, 1574 deletions
diff --git a/docs/tutorial/OCamlLangImpl6.html b/docs/tutorial/OCamlLangImpl6.html
deleted file mode 100644
index 56883d539b..0000000000
--- a/docs/tutorial/OCamlLangImpl6.html
+++ /dev/null
@@ -1,1574 +0,0 @@
-<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN"
- "http://www.w3.org/TR/html4/strict.dtd">
-
-<html>
-<head>
- <title>Kaleidoscope: Extending the Language: User-defined Operators</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="../_static/llvm.css" type="text/css">
-</head>
-
-<body>
-
-<h1>Kaleidoscope: Extending the Language: User-defined Operators</h1>
-
-<ul>
-<li><a href="index.html">Up to Tutorial Index</a></li>
-<li>Chapter 6
- <ol>
- <li><a href="#intro">Chapter 6 Introduction</a></li>
- <li><a href="#idea">User-defined Operators: the Idea</a></li>
- <li><a href="#binary">User-defined Binary Operators</a></li>
- <li><a href="#unary">User-defined Unary Operators</a></li>
- <li><a href="#example">Kicking the Tires</a></li>
- <li><a href="#code">Full Code Listing</a></li>
- </ol>
-</li>
-<li><a href="OCamlLangImpl7.html">Chapter 7</a>: Extending the Language: Mutable
-Variables / SSA Construction</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>
-
-<!-- *********************************************************************** -->
-<h2><a name="intro">Chapter 6 Introduction</a></h2>
-<!-- *********************************************************************** -->
-
-<div>
-
-<p>Welcome to Chapter 6 of the "<a href="index.html">Implementing a language
-with LLVM</a>" tutorial. At this point in our tutorial, we now have a fully
-functional language that is fairly minimal, but also useful. There
-is still one big problem with it, however. Our language doesn't have many
-useful operators (like division, logical negation, or even any comparisons
-besides less-than).</p>
-
-<p>This chapter of the tutorial takes a wild digression into adding user-defined
-operators to the simple and beautiful Kaleidoscope language. This digression now
-gives us a simple and ugly language in some ways, but also a powerful one at the
-same time. One of the great things about creating your own language is that you
-get to decide what is good or bad. In this tutorial we'll assume that it is
-okay to use this as a way to show some interesting parsing techniques.</p>
-
-<p>At the end of this tutorial, we'll run through an example Kaleidoscope
-application that <a href="#example">renders the Mandelbrot set</a>. This gives
-an example of what you can build with Kaleidoscope and its feature set.</p>
-
-</div>
-
-<!-- *********************************************************************** -->
-<h2><a name="idea">User-defined Operators: the Idea</a></h2>
-<!-- *********************************************************************** -->
-
-<div>
-
-<p>
-The "operator overloading" that we will add to Kaleidoscope is more general than
-languages like C++. In C++, you are only allowed to redefine existing
-operators: you can't programatically change the grammar, introduce new
-operators, change precedence levels, etc. In this chapter, we will add this
-capability to Kaleidoscope, which will let the user round out the set of
-operators that are supported.</p>
-
-<p>The point of going into user-defined operators in a tutorial like this is to
-show the power and flexibility of using a hand-written parser. Thus far, the parser
-we have been implementing uses recursive descent for most parts of the grammar and
-operator precedence parsing for the expressions. See <a
-href="OCamlLangImpl2.html">Chapter 2</a> for details. Without using operator
-precedence parsing, it would be very difficult to allow the programmer to
-introduce new operators into the grammar: the grammar is dynamically extensible
-as the JIT runs.</p>
-
-<p>The two specific features we'll add are programmable unary operators (right
-now, Kaleidoscope has no unary operators at all) as well as binary operators.
-An example of this is:</p>
-
-<div class="doc_code">
-<pre>
-# Logical unary not.
-def unary!(v)
- if v then
- 0
- else
- 1;
-
-# Define &gt; with the same precedence as &lt;.
-def binary&gt; 10 (LHS RHS)
- RHS &lt; LHS;
-
-# Binary "logical or", (note that it does not "short circuit")
-def binary| 5 (LHS RHS)
- if LHS then
- 1
- else if RHS then
- 1
- else
- 0;
-
-# Define = with slightly lower precedence than relationals.
-def binary= 9 (LHS RHS)
- !(LHS &lt; RHS | LHS &gt; RHS);
-</pre>
-</div>
-
-<p>Many languages aspire to being able to implement their standard runtime
-library in the language itself. In Kaleidoscope, we can implement significant
-parts of the language in the library!</p>
-
-<p>We will break down implementation of these features into two parts:
-implementing support for user-defined binary operators and adding unary
-operators.</p>
-
-</div>
-
-<!-- *********************************************************************** -->
-<h2><a name="binary">User-defined Binary Operators</a></h2>
-<!-- *********************************************************************** -->
-
-<div>
-
-<p>Adding support for user-defined binary operators is pretty simple with our
-current framework. We'll first add support for the unary/binary keywords:</p>
-
-<div class="doc_code">
-<pre>
-type token =
- ...
- <b>(* operators *)
- | Binary | Unary</b>
-
-...
-
-and lex_ident buffer = parser
- ...
- | "for" -&gt; [&lt; 'Token.For; stream &gt;]
- | "in" -&gt; [&lt; 'Token.In; stream &gt;]
- <b>| "binary" -&gt; [&lt; 'Token.Binary; stream &gt;]
- | "unary" -&gt; [&lt; 'Token.Unary; stream &gt;]</b>
-</pre>
-</div>
-
-<p>This just adds lexer support for the unary and binary keywords, like we
-did in <a href="OCamlLangImpl5.html#iflexer">previous chapters</a>. One nice
-thing about our current AST, is that we represent binary operators with full
-generalisation by using their ASCII code as the opcode. For our extended
-operators, we'll use this same representation, so we don't need any new AST or
-parser support.</p>
-
-<p>On the other hand, we have to be able to represent the definitions of these
-new operators, in the "def binary| 5" part of the function definition. In our
-grammar so far, the "name" for the function definition is parsed as the
-"prototype" production and into the <tt>Ast.Prototype</tt> AST node. To
-represent our new user-defined operators as prototypes, we have to extend
-the <tt>Ast.Prototype</tt> AST node like this:</p>
-
-<div class="doc_code">
-<pre>
-(* 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
- <b>| BinOpPrototype of string * string array * int</b>
-</pre>
-</div>
-
-<p>Basically, in addition to knowing a name for the prototype, we now keep track
-of whether it was an operator, and if it was, what precedence level the operator
-is at. The precedence is only used for binary operators (as you'll see below,
-it just doesn't apply for unary operators). Now that we have a way to represent
-the prototype for a user-defined operator, we need to parse it:</p>
-
-<div class="doc_code">
-<pre>
-(* prototype
- * ::= id '(' id* ')'
- <b>* ::= binary LETTER number? (id, id)
- * ::= unary LETTER number? (id) *)</b>
-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))
- <b>| [&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)</b>
- | [&lt; &gt;] -&gt;
- raise (Stream.Error "expected function name in prototype")
-</pre>
-</div>
-
-<p>This is all fairly straightforward parsing code, and we have already seen
-a lot of similar code in the past. One interesting part about the code above is
-the couple lines that set up <tt>name</tt> for binary operators. This builds
-names like "binary@" for a newly defined "@" operator. This then takes
-advantage of the fact that symbol names in the LLVM symbol table are allowed to
-have any character in them, including embedded nul characters.</p>
-
-<p>The next interesting thing to add, is codegen support for these binary
-operators. Given our current structure, this is a simple addition of a default
-case for our existing binary operator node:</p>
-
-<div class="doc_code">
-<pre>
-let codegen_expr = function
- ...
- | Ast.Binary (op, lhs, rhs) -&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
- <b>| _ -&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</b>
- end
-</pre>
-</div>
-
-<p>As you can see above, the new code is actually really simple. It just does
-a lookup for the appropriate operator in the symbol table and generates a
-function call to it. Since user-defined operators are just built as normal
-functions (because the "prototype" boils down to a function with the right
-name) everything falls into place.</p>
-
-<p>The final piece of code we are missing, is a bit of top level magic:</p>
-
-<div class="doc_code">
-<pre>
-let codegen_func the_fpm = function
- | Ast.Function (proto, body) -&gt;
- Hashtbl.clear named_values;
- let the_function = codegen_proto proto in
-
- <b>(* 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;</b>
-
- (* Create a new basic block to start insertion into. *)
- let bb = append_block context "entry" the_function in
- position_at_end bb builder;
- ...
-</pre>
-</div>
-
-<p>Basically, before codegening a function, if it is a user-defined operator, we
-register it in the precedence table. This allows the binary operator parsing
-logic we already have in place to handle it. Since we are working on a
-fully-general operator precedence parser, this is all we need to do to "extend
-the grammar".</p>
-
-<p>Now we have useful user-defined binary operators. This builds a lot
-on the previous framework we built for other operators. Adding unary operators
-is a bit more challenging, because we don't have any framework for it yet - lets
-see what it takes.</p>
-
-</div>
-
-<!-- *********************************************************************** -->
-<h2><a name="unary">User-defined Unary Operators</a></h2>
-<!-- *********************************************************************** -->
-
-<div>
-
-<p>Since we don't currently support unary operators in the Kaleidoscope
-language, we'll need to add everything to support them. Above, we added simple
-support for the 'unary' keyword to the lexer. In addition to that, we need an
-AST node:</p>
-
-<div class="doc_code">
-<pre>
-type expr =
- ...
- (* variant for a unary operator. *)
- | Unary of char * expr
- ...
-</pre>
-</div>
-
-<p>This AST node is very simple and obvious by now. It directly mirrors the
-binary operator AST node, except that it only has one child. With this, we
-need to add the parsing logic. Parsing a unary operator is pretty simple: we'll
-add a new function to do it:</p>
-
-<div class="doc_code">
-<pre>
-(* 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
-</pre>
-</div>
-
-<p>The grammar we add is pretty straightforward here. If we see a unary
-operator when parsing a primary operator, we eat the operator as a prefix and
-parse the remaining piece as another unary operator. This allows us to handle
-multiple unary operators (e.g. "!!x"). Note that unary operators can't have
-ambiguous parses like binary operators can, so there is no need for precedence
-information.</p>
-
-<p>The problem with this function, is that we need to call ParseUnary from
-somewhere. To do this, we change previous callers of ParsePrimary to call
-<tt>parse_unary</tt> instead:</p>
-
-<div class="doc_code">
-<pre>
-(* binoprhs
- * ::= ('+' primary)* *)
-and parse_bin_rhs expr_prec lhs stream =
- ...
- <b>(* Parse the unary expression after the binary operator. *)
- let rhs = parse_unary stream in</b>
- ...
-
-...
-
-(* expression
- * ::= primary binoprhs *)
-and parse_expr = parser
- | [&lt; lhs=<b>parse_unary</b>; stream &gt;] -&gt; parse_bin_rhs 0 lhs stream
-</pre>
-</div>
-
-<p>With these two simple changes, we are now able to parse unary operators and build the
-AST for them. Next up, we need to add parser support for prototypes, to parse
-the unary operator prototype. We extend the binary operator code above
-with:</p>
-
-<div class="doc_code">
-<pre>
-(* prototype
- * ::= id '(' id* ')'
- * ::= binary LETTER number? (id, id)
- <b>* ::= unary LETTER number? (id)</b> *)
-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
- <b>let parse_operator = parser
- | [&lt; 'Token.Unary &gt;] -&gt; "unary", 1
- | [&lt; 'Token.Binary &gt;] -&gt; "binary", 2
- in</b>
- 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))
- <b>| [&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)</b>
- | [&lt; &gt;] -&gt;
- raise (Stream.Error "expected function name in prototype")
-</pre>
-</div>
-
-<p>As with binary operators, we name unary operators with a name that includes
-the operator character. This assists us at code generation time. Speaking of,
-the final piece we need to add is codegen support for unary operators. It looks
-like this:</p>
-
-<div class="doc_code">
-<pre>
-let rec codegen_expr = function
- ...
- | 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
-</pre>
-</div>
-
-<p>This code is similar to, but simpler than, the code for binary operators. It
-is simpler primarily because it doesn't need to handle any predefined operators.
-</p>
-
-</div>
-
-<!-- *********************************************************************** -->
-<h2><a name="example">Kicking the Tires</a></h2>
-<!-- *********************************************************************** -->
-
-<div>
-
-<p>It is somewhat hard to believe, but with a few simple extensions we've
-covered in the last chapters, we have grown a real-ish language. With this, we
-can do a lot of interesting things, including I/O, math, and a bunch of other
-things. For example, we can now add a nice sequencing operator (printd is
-defined to print out the specified value and a newline):</p>
-
-<div class="doc_code">
-<pre>
-ready&gt; <b>extern printd(x);</b>
-Read extern: declare double @printd(double)
-ready&gt; <b>def binary : 1 (x y) 0; # Low-precedence operator that ignores operands.</b>
-..
-ready&gt; <b>printd(123) : printd(456) : printd(789);</b>
-123.000000
-456.000000
-789.000000
-Evaluated to 0.000000
-</pre>
-</div>
-
-<p>We can also define a bunch of other "primitive" operations, such as:</p>
-
-<div class="doc_code">
-<pre>
-# Logical unary not.
-def unary!(v)
- if v then
- 0
- else
- 1;
-
-# Unary negate.
-def unary-(v)
- 0-v;
-
-# Define &gt; with the same precedence as &lt;.
-def binary&gt; 10 (LHS RHS)
- RHS &lt; LHS;
-
-# Binary logical or, which does not short circuit.
-def binary| 5 (LHS RHS)
- if LHS then
- 1
- else if RHS then
- 1
- else
- 0;
-
-# Binary logical and, which does not short circuit.
-def binary&amp; 6 (LHS RHS)
- if !LHS then
- 0
- else
- !!RHS;
-
-# Define = with slightly lower precedence than relationals.
-def binary = 9 (LHS RHS)
- !(LHS &lt; RHS | LHS &gt; RHS);
-
-</pre>
-</div>
-
-
-<p>Given the previous if/then/else support, we can also define interesting
-functions for I/O. For example, the following prints out a character whose
-"density" reflects the value passed in: the lower the value, the denser the
-character:</p>
-
-<div class="doc_code">
-<pre>
-ready&gt;
-<b>
-extern putchard(char)
-def printdensity(d)
- if d &gt; 8 then
- putchard(32) # ' '
- else if d &gt; 4 then
- putchard(46) # '.'
- else if d &gt; 2 then
- putchard(43) # '+'
- else
- putchard(42); # '*'</b>
-...
-ready&gt; <b>printdensity(1): printdensity(2): printdensity(3) :
- printdensity(4): printdensity(5): printdensity(9): putchard(10);</b>
-*++..
-Evaluated to 0.000000
-</pre>
-</div>
-
-<p>Based on these simple primitive operations, we can start to define more
-interesting things. For example, here's a little function that solves for the
-number of iterations it takes a function in the complex plane to
-converge:</p>
-
-<div class="doc_code">
-<pre>
-# determine whether the specific location diverges.
-# Solve for z = z^2 + c in the complex plane.
-def mandleconverger(real imag iters creal cimag)
- if iters &gt; 255 | (real*real + imag*imag &gt; 4) then
- iters
- else
- mandleconverger(real*real - imag*imag + creal,
- 2*real*imag + cimag,
- iters+1, creal, cimag);
-
-# return the number of iterations required for the iteration to escape
-def mandleconverge(real imag)
- mandleconverger(real, imag, 0, real, imag);
-</pre>
-</div>
-
-<p>This "z = z<sup>2</sup> + c" function is a beautiful little creature that is the basis
-for computation of the <a
-href="http://en.wikipedia.org/wiki/Mandelbrot_set">Mandelbrot Set</a>. Our
-<tt>mandelconverge</tt> function returns the number of iterations that it takes
-for a complex orbit to escape, saturating to 255. This is not a very useful
-function by itself, but if you plot its value over a two-dimensional plane,
-you can see the Mandelbrot set. Given that we are limited to using putchard
-here, our amazing graphical output is limited, but we can whip together
-something using the density plotter above:</p>
-
-<div class="doc_code">
-<pre>
-# compute and plot the mandlebrot set with the specified 2 dimensional range
-# info.
-def mandelhelp(xmin xmax xstep ymin ymax ystep)
- for y = ymin, y &lt; ymax, ystep in (
- (for x = xmin, x &lt; xmax, xstep in
- printdensity(mandleconverge(x,y)))
- : putchard(10)
- )
-
-# mandel - This is a convenient helper function for plotting the mandelbrot set
-# from the specified position with the specified Magnification.
-def mandel(realstart imagstart realmag imagmag)
- mandelhelp(realstart, realstart+realmag*78, realmag,
- imagstart, imagstart+imagmag*40, imagmag);
-</pre>
-</div>
-
-<p>Given this, we can try plotting out the mandlebrot set! Lets try it out:</p>
-
-<div class="doc_code">
-<pre>
-ready&gt; <b>mandel(-2.3, -1.3, 0.05, 0.07);</b>
-*******************************+++++++++++*************************************
-*************************+++++++++++++++++++++++*******************************
-**********************+++++++++++++++++++++++++++++****************************
-*******************+++++++++++++++++++++.. ...++++++++*************************
-*****************++++++++++++++++++++++.... ...+++++++++***********************
-***************+++++++++++++++++++++++..... ...+++++++++*********************
-**************+++++++++++++++++++++++.... ....+++++++++********************
-*************++++++++++++++++++++++...... .....++++++++*******************
-************+++++++++++++++++++++....... .......+++++++******************
-***********+++++++++++++++++++.... ... .+++++++*****************
-**********+++++++++++++++++....... .+++++++****************
-*********++++++++++++++........... ...+++++++***************
-********++++++++++++............ ...++++++++**************
-********++++++++++... .......... .++++++++**************
-*******+++++++++..... .+++++++++*************
-*******++++++++...... ..+++++++++*************
-*******++++++....... ..+++++++++*************
-*******+++++...... ..+++++++++*************
-*******.... .... ...+++++++++*************
-*******.... . ...+++++++++*************
-*******+++++...... ...+++++++++*************
-*******++++++....... ..+++++++++*************
-*******++++++++...... .+++++++++*************
-*******+++++++++..... ..+++++++++*************
-********++++++++++... .......... .++++++++**************
-********++++++++++++............ ...++++++++**************
-*********++++++++++++++.......... ...+++++++***************
-**********++++++++++++++++........ .+++++++****************
-**********++++++++++++++++++++.... ... ..+++++++****************
-***********++++++++++++++++++++++....... .......++++++++*****************
-************+++++++++++++++++++++++...... ......++++++++******************
-**************+++++++++++++++++++++++.... ....++++++++********************
-***************+++++++++++++++++++++++..... ...+++++++++*********************
-*****************++++++++++++++++++++++.... ...++++++++***********************
-*******************+++++++++++++++++++++......++++++++*************************
-*********************++++++++++++++++++++++.++++++++***************************
-*************************+++++++++++++++++++++++*******************************
-******************************+++++++++++++************************************
-*******************************************************************************
-*******************************************************************************
-*******************************************************************************
-Evaluated to 0.000000
-ready&gt; <b>mandel(-2, -1, 0.02, 0.04);</b>
-**************************+++++++++++++++++++++++++++++++++++++++++++++++++++++
-***********************++++++++++++++++++++++++++++++++++++++++++++++++++++++++
-*********************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++.
-*******************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++...
-*****************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++.....
-***************++++++++++++++++++++++++++++++++++++++++++++++++++++++++........
-**************++++++++++++++++++++++++++++++++++++++++++++++++++++++...........
-************+++++++++++++++++++++++++++++++++++++++++++++++++++++..............
-***********++++++++++++++++++++++++++++++++++++++++++++++++++........ .
-**********++++++++++++++++++++++++++++++++++++++++++++++.............
-********+++++++++++++++++++++++++++++++++++++++++++..................
-*******+++++++++++++++++++++++++++++++++++++++.......................
-******+++++++++++++++++++++++++++++++++++...........................
-*****++++++++++++++++++++++++++++++++............................
-*****++++++++++++++++++++++++++++...............................
-****++++++++++++++++++++++++++...... .........................
-***++++++++++++++++++++++++......... ...... ...........
-***++++++++++++++++++++++............
-**+++++++++++++++++++++..............
-**+++++++++++++++++++................
-*++++++++++++++++++.................
-*++++++++++++++++............ ...
-*++++++++++++++..............
-*+++....++++................
-*.......... ...........
-*
-*.......... ...........
-*+++....++++................
-*++++++++++++++..............
-*++++++++++++++++............ ...
-*++++++++++++++++++.................
-**+++++++++++++++++++................
-**+++++++++++++++++++++..............
-***++++++++++++++++++++++............
-***++++++++++++++++++++++++......... ...... ...........
-****++++++++++++++++++++++++++...... .........................
-*****++++++++++++++++++++++++++++...............................
-*****++++++++++++++++++++++++++++++++............................
-******+++++++++++++++++++++++++++++++++++...........................
-*******+++++++++++++++++++++++++++++++++++++++.......................
-********+++++++++++++++++++++++++++++++++++++++++++..................
-Evaluated to 0.000000
-ready&gt; <b>mandel(-0.9, -1.4, 0.02, 0.03);</b>
-*******************************************************************************
-*******************************************************************************
-*******************************************************************************
-**********+++++++++++++++++++++************************************************
-*+++++++++++++++++++++++++++++++++++++++***************************************
-+++++++++++++++++++++++++++++++++++++++++++++**********************************
-++++++++++++++++++++++++++++++++++++++++++++++++++*****************************
-++++++++++++++++++++++++++++++++++++++++++++++++++++++*************************
-+++++++++++++++++++++++++++++++++++++++++++++++++++++++++**********************
-+++++++++++++++++++++++++++++++++.........++++++++++++++++++*******************
-+++++++++++++++++++++++++++++++.... ......+++++++++++++++++++****************
-+++++++++++++++++++++++++++++....... ........+++++++++++++++++++**************
-++++++++++++++++++++++++++++........ ........++++++++++++++++++++************
-+++++++++++++++++++++++++++......... .. ...+++++++++++++++++++++**********
-++++++++++++++++++++++++++........... ....++++++++++++++++++++++********
-++++++++++++++++++++++++............. .......++++++++++++++++++++++******
-+++++++++++++++++++++++............. ........+++++++++++++++++++++++****
-++++++++++++++++++++++........... ..........++++++++++++++++++++++***
-++++++++++++++++++++........... .........++++++++++++++++++++++*
-++++++++++++++++++............ ...........++++++++++++++++++++
-++++++++++++++++............... .............++++++++++++++++++
-++++++++++++++................. ...............++++++++++++++++
-++++++++++++.................. .................++++++++++++++
-+++++++++.................. .................+++++++++++++
-++++++........ . ......... ..++++++++++++
-++............ ...... ....++++++++++
-.............. ...++++++++++
-.............. ....+++++++++
-.............. .....++++++++
-............. ......++++++++
-........... .......++++++++
-......... ........+++++++
-......... ........+++++++
-......... ....+++++++
-........ ...+++++++
-....... ...+++++++
- ....+++++++
- .....+++++++
- ....+++++++
- ....+++++++
- ....+++++++
-Evaluated to 0.000000
-ready&gt; <b>^D</b>
-</pre>
-</div>
-
-<p>At this point, you may be starting to realize that Kaleidoscope is a real
-and powerful language. It may not be self-similar :), but it can be used to
-plot things that are!</p>
-
-<p>With this, we conclude the "adding user-defined operators" chapter of the
-tutorial. We have successfully augmented our language, adding the ability to
-extend the language in the library, and we have shown how this can be used to
-build a simple but interesting end-user application in Kaleidoscope. At this
-point, Kaleidoscope can build a variety of applications that are functional and
-can call functions with side-effects, but it can't actually define and mutate a
-variable itself.</p>
-
-<p>Strikingly, variable mutation is an important feature of some
-languages, and it is not at all obvious how to <a href="OCamlLangImpl7.html">add
-support for mutable variables</a> without having to add an "SSA construction"
-phase to your front-end. In the next chapter, we will describe how you can
-add variable mutation without building SSA in your front-end.</p>
-
-</div>
-
-
-<!-- *********************************************************************** -->
-<h2><a name="code">Full Code Listing</a></h2>
-<!-- *********************************************************************** -->
-
-<div>
-
-<p>
-Here is the complete code listing for our running example, enhanced with the
-if/then/else and for expressions.. 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++"; A"-cclib"; A"-rdynamic"]);;
-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
-</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;]
- | id -&gt; [&lt; 'Token.Ident id; stream &gt;