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1============================================================
2Kaleidoscope: Extending the Language: User-defined Operators
3============================================================
4
5.. contents::
6   :local:
7
8Chapter 6 Introduction
9======================
10
11Welcome to Chapter 6 of the "`Implementing a language with
12LLVM <index.html>`_" tutorial. At this point in our tutorial, we now
13have a fully functional language that is fairly minimal, but also
14useful. There is still one big problem with it, however. Our language
15doesn't have many useful operators (like division, logical negation, or
16even any comparisons besides less-than).
17
18This chapter of the tutorial takes a wild digression into adding
19user-defined operators to the simple and beautiful Kaleidoscope
20language. This digression now gives us a simple and ugly language in
21some ways, but also a powerful one at the same time. One of the great
22things about creating your own language is that you get to decide what
23is good or bad. In this tutorial we'll assume that it is okay to use
24this as a way to show some interesting parsing techniques.
25
26At the end of this tutorial, we'll run through an example Kaleidoscope
27application that `renders the Mandelbrot set <#kicking-the-tires>`_. This gives an
28example of what you can build with Kaleidoscope and its feature set.
29
30User-defined Operators: the Idea
31================================
32
33The "operator overloading" that we will add to Kaleidoscope is more
34general than in languages like C++. In C++, you are only allowed to
35redefine existing operators: you can't programmatically change the
36grammar, introduce new operators, change precedence levels, etc. In this
37chapter, we will add this capability to Kaleidoscope, which will let the
38user round out the set of operators that are supported.
39
40The point of going into user-defined operators in a tutorial like this
41is to show the power and flexibility of using a hand-written parser.
42Thus far, the parser we have been implementing uses recursive descent
43for most parts of the grammar and operator precedence parsing for the
44expressions. See `Chapter 2 <LangImpl02.html>`_ for details. By
45using operator precedence parsing, it is very easy to allow
46the programmer to introduce new operators into the grammar: the grammar
47is dynamically extensible as the JIT runs.
48
49The two specific features we'll add are programmable unary operators
50(right now, Kaleidoscope has no unary operators at all) as well as
51binary operators. An example of this is:
52
53::
54
55    # Logical unary not.
56    def unary!(v)
57      if v then
58        0
59      else
60        1;
61
62    # Define > with the same precedence as <.
63    def binary> 10 (LHS RHS)
64      RHS < LHS;
65
66    # Binary "logical or", (note that it does not "short circuit")
67    def binary| 5 (LHS RHS)
68      if LHS then
69        1
70      else if RHS then
71        1
72      else
73        0;
74
75    # Define = with slightly lower precedence than relationals.
76    def binary= 9 (LHS RHS)
77      !(LHS < RHS | LHS > RHS);
78
79Many languages aspire to being able to implement their standard runtime
80library in the language itself. In Kaleidoscope, we can implement
81significant parts of the language in the library!
82
83We will break down implementation of these features into two parts:
84implementing support for user-defined binary operators and adding unary
85operators.
86
87User-defined Binary Operators
88=============================
89
90Adding support for user-defined binary operators is pretty simple with
91our current framework. We'll first add support for the unary/binary
92keywords:
93
94.. code-block:: c++
95
96    enum Token {
97      ...
98      // operators
99      tok_binary = -11,
100      tok_unary = -12
101    };
102    ...
103    static int gettok() {
104    ...
105        if (IdentifierStr == "for")
106          return tok_for;
107        if (IdentifierStr == "in")
108          return tok_in;
109        if (IdentifierStr == "binary")
110          return tok_binary;
111        if (IdentifierStr == "unary")
112          return tok_unary;
113        return tok_identifier;
114
115This just adds lexer support for the unary and binary keywords, like we
116did in `previous chapters <LangImpl5.html#lexer-extensions-for-if-then-else>`_. One nice thing
117about our current AST, is that we represent binary operators with full
118generalisation by using their ASCII code as the opcode. For our extended
119operators, we'll use this same representation, so we don't need any new
120AST or parser support.
121
122On the other hand, we have to be able to represent the definitions of
123these new operators, in the "def binary\| 5" part of the function
124definition. In our grammar so far, the "name" for the function
125definition is parsed as the "prototype" production and into the
126``PrototypeAST`` AST node. To represent our new user-defined operators
127as prototypes, we have to extend the ``PrototypeAST`` AST node like
128this:
129
130.. code-block:: c++
131
132    /// PrototypeAST - This class represents the "prototype" for a function,
133    /// which captures its argument names as well as if it is an operator.
134    class PrototypeAST {
135      std::string Name;
136      std::vector<std::string> Args;
137      bool IsOperator;
138      unsigned Precedence;  // Precedence if a binary op.
139
140    public:
141      PrototypeAST(const std::string &name, std::vector<std::string> Args,
142                   bool IsOperator = false, unsigned Prec = 0)
143      : Name(name), Args(std::move(Args)), IsOperator(IsOperator),
144        Precedence(Prec) {}
145
146      Function *codegen();
147      const std::string &getName() const { return Name; }
148
149      bool isUnaryOp() const { return IsOperator && Args.size() == 1; }
150      bool isBinaryOp() const { return IsOperator && Args.size() == 2; }
151
152      char getOperatorName() const {
153        assert(isUnaryOp() || isBinaryOp());
154        return Name[Name.size() - 1];
155      }
156
157      unsigned getBinaryPrecedence() const { return Precedence; }
158    };
159
160Basically, in addition to knowing a name for the prototype, we now keep
161track of whether it was an operator, and if it was, what precedence
162level the operator is at. The precedence is only used for binary
163operators (as you'll see below, it just doesn't apply for unary
164operators). Now that we have a way to represent the prototype for a
165user-defined operator, we need to parse it:
166
167.. code-block:: c++
168
169    /// prototype
170    ///   ::= id '(' id* ')'
171    ///   ::= binary LETTER number? (id, id)
172    static std::unique_ptr<PrototypeAST> ParsePrototype() {
173      std::string FnName;
174
175      unsigned Kind = 0;  // 0 = identifier, 1 = unary, 2 = binary.
176      unsigned BinaryPrecedence = 30;
177
178      switch (CurTok) {
179      default:
180        return LogErrorP("Expected function name in prototype");
181      case tok_identifier:
182        FnName = IdentifierStr;
183        Kind = 0;
184        getNextToken();
185        break;
186      case tok_binary:
187        getNextToken();
188        if (!isascii(CurTok))
189          return LogErrorP("Expected binary operator");
190        FnName = "binary";
191        FnName += (char)CurTok;
192        Kind = 2;
193        getNextToken();
194
195        // Read the precedence if present.
196        if (CurTok == tok_number) {
197          if (NumVal < 1 || NumVal > 100)
198            return LogErrorP("Invalid precedence: must be 1..100");
199          BinaryPrecedence = (unsigned)NumVal;
200          getNextToken();
201        }
202        break;
203      }
204
205      if (CurTok != '(')
206        return LogErrorP("Expected '(' in prototype");
207
208      std::vector<std::string> ArgNames;
209      while (getNextToken() == tok_identifier)
210        ArgNames.push_back(IdentifierStr);
211      if (CurTok != ')')
212        return LogErrorP("Expected ')' in prototype");
213
214      // success.
215      getNextToken();  // eat ')'.
216
217      // Verify right number of names for operator.
218      if (Kind && ArgNames.size() != Kind)
219        return LogErrorP("Invalid number of operands for operator");
220
221      return llvm::make_unique<PrototypeAST>(FnName, std::move(ArgNames), Kind != 0,
222                                             BinaryPrecedence);
223    }
224
225This is all fairly straightforward parsing code, and we have already
226seen a lot of similar code in the past. One interesting part about the
227code above is the couple lines that set up ``FnName`` for binary
228operators. This builds names like "binary@" for a newly defined "@"
229operator. It then takes advantage of the fact that symbol names in the
230LLVM symbol table are allowed to have any character in them, including
231embedded nul characters.
232
233The next interesting thing to add, is codegen support for these binary
234operators. Given our current structure, this is a simple addition of a
235default case for our existing binary operator node:
236
237.. code-block:: c++
238
239    Value *BinaryExprAST::codegen() {
240      Value *L = LHS->codegen();
241      Value *R = RHS->codegen();
242      if (!L || !R)
243        return nullptr;
244
245      switch (Op) {
246      case '+':
247        return Builder.CreateFAdd(L, R, "addtmp");
248      case '-':
249        return Builder.CreateFSub(L, R, "subtmp");
250      case '*':
251        return Builder.CreateFMul(L, R, "multmp");
252      case '<':
253        L = Builder.CreateFCmpULT(L, R, "cmptmp");
254        // Convert bool 0/1 to double 0.0 or 1.0
255        return Builder.CreateUIToFP(L, Type::getDoubleTy(TheContext),
256                                    "booltmp");
257      default:
258        break;
259      }
260
261      // If it wasn't a builtin binary operator, it must be a user defined one. Emit
262      // a call to it.
263      Function *F = getFunction(std::string("binary") + Op);
264      assert(F && "binary operator not found!");
265
266      Value *Ops[2] = { L, R };
267      return Builder.CreateCall(F, Ops, "binop");
268    }
269
270As you can see above, the new code is actually really simple. It just
271does a lookup for the appropriate operator in the symbol table and
272generates a function call to it. Since user-defined operators are just
273built as normal functions (because the "prototype" boils down to a
274function with the right name) everything falls into place.
275
276The final piece of code we are missing, is a bit of top-level magic:
277
278.. code-block:: c++
279
280    Function *FunctionAST::codegen() {
281      // Transfer ownership of the prototype to the FunctionProtos map, but keep a
282      // reference to it for use below.
283      auto &P = *Proto;
284      FunctionProtos[Proto->getName()] = std::move(Proto);
285      Function *TheFunction = getFunction(P.getName());
286      if (!TheFunction)
287        return nullptr;
288
289      // If this is an operator, install it.
290      if (P.isBinaryOp())
291        BinopPrecedence[P.getOperatorName()] = P.getBinaryPrecedence();
292
293      // Create a new basic block to start insertion into.
294      BasicBlock *BB = BasicBlock::Create(TheContext, "entry", TheFunction);
295      ...
296
297Basically, before codegening a function, if it is a user-defined
298operator, we register it in the precedence table. This allows the binary
299operator parsing logic we already have in place to handle it. Since we
300are working on a fully-general operator precedence parser, this is all
301we need to do to "extend the grammar".
302
303Now we have useful user-defined binary operators. This builds a lot on
304the previous framework we built for other operators. Adding unary
305operators is a bit more challenging, because we don't have any framework
306for it yet - let's see what it takes.
307
308User-defined Unary Operators
309============================
310
311Since we don't currently support unary operators in the Kaleidoscope
312language, we'll need to add everything to support them. Above, we added
313simple support for the 'unary' keyword to the lexer. In addition to
314that, we need an AST node:
315
316.. code-block:: c++
317
318    /// UnaryExprAST - Expression class for a unary operator.
319    class UnaryExprAST : public ExprAST {
320      char Opcode;
321      std::unique_ptr<ExprAST> Operand;
322
323    public:
324      UnaryExprAST(char Opcode, std::unique_ptr<ExprAST> Operand)
325        : Opcode(Opcode), Operand(std::move(Operand)) {}
326
327      Value *codegen() override;
328    };
329
330This AST node is very simple and obvious by now. It directly mirrors the
331binary operator AST node, except that it only has one child. With this,
332we need to add the parsing logic. Parsing a unary operator is pretty
333simple: we'll add a new function to do it:
334
335.. code-block:: c++
336
337    /// unary
338    ///   ::= primary
339    ///   ::= '!' unary
340    static std::unique_ptr<ExprAST> ParseUnary() {
341      // If the current token is not an operator, it must be a primary expr.
342      if (!isascii(CurTok) || CurTok == '(' || CurTok == ',')
343        return ParsePrimary();
344
345      // If this is a unary operator, read it.
346      int Opc = CurTok;
347      getNextToken();
348      if (auto Operand = ParseUnary())
349        return llvm::make_unique<UnaryExprAST>(Opc, std::move(Operand));
350      return nullptr;
351    }
352
353The grammar we add is pretty straightforward here. If we see a unary
354operator when parsing a primary operator, we eat the operator as a
355prefix and parse the remaining piece as another unary operator. This
356allows us to handle multiple unary operators (e.g. "!!x"). Note that
357unary operators can't have ambiguous parses like binary operators can,
358so there is no need for precedence information.
359
360The problem with this function, is that we need to call ParseUnary from
361somewhere. To do this, we change previous callers of ParsePrimary to
362call ParseUnary instead:
363
364.. code-block:: c++
365
366    /// binoprhs
367    ///   ::= ('+' unary)*
368    static std::unique_ptr<ExprAST> ParseBinOpRHS(int ExprPrec,
369                                                  std::unique_ptr<ExprAST> LHS) {
370      ...
371        // Parse the unary expression after the binary operator.
372        auto RHS = ParseUnary();
373        if (!RHS)
374          return nullptr;
375      ...
376    }
377    /// expression
378    ///   ::= unary binoprhs
379    ///
380    static std::unique_ptr<ExprAST> ParseExpression() {
381      auto LHS = ParseUnary();
382      if (!LHS)
383        return nullptr;
384
385      return ParseBinOpRHS(0, std::move(LHS));
386    }
387
388With these two simple changes, we are now able to parse unary operators
389and build the AST for them. Next up, we need to add parser support for
390prototypes, to parse the unary operator prototype. We extend the binary
391operator code above with:
392
393.. code-block:: c++
394
395    /// prototype
396    ///   ::= id '(' id* ')'
397    ///   ::= binary LETTER number? (id, id)
398    ///   ::= unary LETTER (id)
399    static std::unique_ptr<PrototypeAST> ParsePrototype() {
400      std::string FnName;
401
402      unsigned Kind = 0;  // 0 = identifier, 1 = unary, 2 = binary.
403      unsigned BinaryPrecedence = 30;
404
405      switch (CurTok) {
406      default:
407        return LogErrorP("Expected function name in prototype");
408      case tok_identifier:
409        FnName = IdentifierStr;
410        Kind = 0;
411        getNextToken();
412        break;
413      case tok_unary:
414        getNextToken();
415        if (!isascii(CurTok))
416          return LogErrorP("Expected unary operator");
417        FnName = "unary";
418        FnName += (char)CurTok;
419        Kind = 1;
420        getNextToken();
421        break;
422      case tok_binary:
423        ...
424
425As with binary operators, we name unary operators with a name that
426includes the operator character. This assists us at code generation
427time. Speaking of, the final piece we need to add is codegen support for
428unary operators. It looks like this:
429
430.. code-block:: c++
431
432    Value *UnaryExprAST::codegen() {
433      Value *OperandV = Operand->codegen();
434      if (!OperandV)
435        return nullptr;
436
437      Function *F = getFunction(std::string("unary") + Opcode);
438      if (!F)
439        return LogErrorV("Unknown unary operator");
440
441      return Builder.CreateCall(F, OperandV, "unop");
442    }
443
444This code is similar to, but simpler than, the code for binary
445operators. It is simpler primarily because it doesn't need to handle any
446predefined operators.
447
448Kicking the Tires
449=================
450
451It is somewhat hard to believe, but with a few simple extensions we've
452covered in the last chapters, we have grown a real-ish language. With
453this, we can do a lot of interesting things, including I/O, math, and a
454bunch of other things. For example, we can now add a nice sequencing
455operator (printd is defined to print out the specified value and a
456newline):
457
458::
459
460    ready> extern printd(x);
461    Read extern:
462    declare double @printd(double)
463
464    ready> def binary : 1 (x y) 0;  # Low-precedence operator that ignores operands.
465    ...
466    ready> printd(123) : printd(456) : printd(789);
467    123.000000
468    456.000000
469    789.000000
470    Evaluated to 0.000000
471
472We can also define a bunch of other "primitive" operations, such as:
473
474::
475
476    # Logical unary not.
477    def unary!(v)
478      if v then
479        0
480      else
481        1;
482
483    # Unary negate.
484    def unary-(v)
485      0-v;
486
487    # Define > with the same precedence as <.
488    def binary> 10 (LHS RHS)
489      RHS < LHS;
490
491    # Binary logical or, which does not short circuit.
492    def binary| 5 (LHS RHS)
493      if LHS then
494        1
495      else if RHS then
496        1
497      else
498        0;
499
500    # Binary logical and, which does not short circuit.
501    def binary& 6 (LHS RHS)
502      if !LHS then
503        0
504      else
505        !!RHS;
506
507    # Define = with slightly lower precedence than relationals.
508    def binary = 9 (LHS RHS)
509      !(LHS < RHS | LHS > RHS);
510
511    # Define ':' for sequencing: as a low-precedence operator that ignores operands
512    # and just returns the RHS.
513    def binary : 1 (x y) y;
514
515Given the previous if/then/else support, we can also define interesting
516functions for I/O. For example, the following prints out a character
517whose "density" reflects the value passed in: the lower the value, the
518denser the character:
519
520::
521
522    ready> extern putchard(char);
523    ...
524    ready> def printdensity(d)
525      if d > 8 then
526        putchard(32)  # ' '
527      else if d > 4 then
528        putchard(46)  # '.'
529      else if d > 2 then
530        putchard(43)  # '+'
531      else
532        putchard(42); # '*'
533    ...
534    ready> printdensity(1): printdensity(2): printdensity(3):
535           printdensity(4): printdensity(5): printdensity(9):
536           putchard(10);
537    **++.
538    Evaluated to 0.000000
539
540Based on these simple primitive operations, we can start to define more
541interesting things. For example, here's a little function that determines
542the number of iterations it takes for a certain function in the complex
543plane to diverge:
544
545::
546
547    # Determine whether the specific location diverges.
548    # Solve for z = z^2 + c in the complex plane.
549    def mandelconverger(real imag iters creal cimag)
550      if iters > 255 | (real*real + imag*imag > 4) then
551        iters
552      else
553        mandelconverger(real*real - imag*imag + creal,
554                        2*real*imag + cimag,
555                        iters+1, creal, cimag);
556
557    # Return the number of iterations required for the iteration to escape
558    def mandelconverge(real imag)
559      mandelconverger(real, imag, 0, real, imag);
560
561This "``z = z2 + c``" function is a beautiful little creature that is
562the basis for computation of the `Mandelbrot
563Set <http://en.wikipedia.org/wiki/Mandelbrot_set>`_. Our
564``mandelconverge`` function returns the number of iterations that it
565takes for a complex orbit to escape, saturating to 255. This is not a
566very useful function by itself, but if you plot its value over a
567two-dimensional plane, you can see the Mandelbrot set. Given that we are
568limited to using putchard here, our amazing graphical output is limited,
569but we can whip together something using the density plotter above:
570
571::
572
573    # Compute and plot the mandelbrot set with the specified 2 dimensional range
574    # info.
575    def mandelhelp(xmin xmax xstep   ymin ymax ystep)
576      for y = ymin, y < ymax, ystep in (
577        (for x = xmin, x < xmax, xstep in
578           printdensity(mandelconverge(x,y)))
579        : putchard(10)
580      )
581
582    # mandel - This is a convenient helper function for plotting the mandelbrot set
583    # from the specified position with the specified Magnification.
584    def mandel(realstart imagstart realmag imagmag)
585      mandelhelp(realstart, realstart+realmag*78, realmag,
586                 imagstart, imagstart+imagmag*40, imagmag);
587
588Given this, we can try plotting out the mandelbrot set! Lets try it out:
589
590::
591
592    ready> mandel(-2.3, -1.3, 0.05, 0.07);
593    *******************************+++++++++++*************************************
594    *************************+++++++++++++++++++++++*******************************
595    **********************+++++++++++++++++++++++++++++****************************
596    *******************+++++++++++++++++++++.. ...++++++++*************************
597    *****************++++++++++++++++++++++.... ...+++++++++***********************
598    ***************+++++++++++++++++++++++.....   ...+++++++++*********************
599    **************+++++++++++++++++++++++....     ....+++++++++********************
600    *************++++++++++++++++++++++......      .....++++++++*******************
601    ************+++++++++++++++++++++.......       .......+++++++******************
602    ***********+++++++++++++++++++....                ... .+++++++*****************
603    **********+++++++++++++++++.......                     .+++++++****************
604    *********++++++++++++++...........                    ...+++++++***************
605    ********++++++++++++............                      ...++++++++**************
606    ********++++++++++... ..........                        .++++++++**************
607    *******+++++++++.....                                   .+++++++++*************
608    *******++++++++......                                  ..+++++++++*************
609    *******++++++.......                                   ..+++++++++*************
610    *******+++++......                                     ..+++++++++*************
611    *******.... ....                                      ...+++++++++*************
612    *******.... .                                         ...+++++++++*************
613    *******+++++......                                    ...+++++++++*************
614    *******++++++.......                                   ..+++++++++*************
615    *******++++++++......                                   .+++++++++*************
616    *******+++++++++.....                                  ..+++++++++*************
617    ********++++++++++... ..........                        .++++++++**************
618    ********++++++++++++............                      ...++++++++**************
619    *********++++++++++++++..........                     ...+++++++***************
620    **********++++++++++++++++........                     .+++++++****************
621    **********++++++++++++++++++++....                ... ..+++++++****************
622    ***********++++++++++++++++++++++.......       .......++++++++*****************
623    ************+++++++++++++++++++++++......      ......++++++++******************
624    **************+++++++++++++++++++++++....      ....++++++++********************
625    ***************+++++++++++++++++++++++.....   ...+++++++++*********************
626    *****************++++++++++++++++++++++....  ...++++++++***********************
627    *******************+++++++++++++++++++++......++++++++*************************
628    *********************++++++++++++++++++++++.++++++++***************************
629    *************************+++++++++++++++++++++++*******************************
630    ******************************+++++++++++++************************************
631    *******************************************************************************
632    *******************************************************************************
633    *******************************************************************************
634    Evaluated to 0.000000
635    ready> mandel(-2, -1, 0.02, 0.04);
636    **************************+++++++++++++++++++++++++++++++++++++++++++++++++++++
637    ***********************++++++++++++++++++++++++++++++++++++++++++++++++++++++++
638    *********************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++.
639    *******************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++...
640    *****************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++.....
641    ***************++++++++++++++++++++++++++++++++++++++++++++++++++++++++........
642    **************++++++++++++++++++++++++++++++++++++++++++++++++++++++...........
643    ************+++++++++++++++++++++++++++++++++++++++++++++++++++++..............
644    ***********++++++++++++++++++++++++++++++++++++++++++++++++++........        .
645    **********++++++++++++++++++++++++++++++++++++++++++++++.............
646    ********+++++++++++++++++++++++++++++++++++++++++++..................
647    *******+++++++++++++++++++++++++++++++++++++++.......................
648    ******+++++++++++++++++++++++++++++++++++...........................
649    *****++++++++++++++++++++++++++++++++............................
650    *****++++++++++++++++++++++++++++...............................
651    ****++++++++++++++++++++++++++......   .........................
652    ***++++++++++++++++++++++++.........     ......    ...........
653    ***++++++++++++++++++++++............
654    **+++++++++++++++++++++..............
655    **+++++++++++++++++++................
656    *++++++++++++++++++.................
657    *++++++++++++++++............ ...
658    *++++++++++++++..............
659    *+++....++++................
660    *..........  ...........
661    *
662    *..........  ...........
663    *+++....++++................
664    *++++++++++++++..............
665    *++++++++++++++++............ ...
666    *++++++++++++++++++.................
667    **+++++++++++++++++++................
668    **+++++++++++++++++++++..............
669    ***++++++++++++++++++++++............
670    ***++++++++++++++++++++++++.........     ......    ...........
671    ****++++++++++++++++++++++++++......   .........................
672    *****++++++++++++++++++++++++++++...............................
673    *****++++++++++++++++++++++++++++++++............................
674    ******+++++++++++++++++++++++++++++++++++...........................
675    *******+++++++++++++++++++++++++++++++++++++++.......................
676    ********+++++++++++++++++++++++++++++++++++++++++++..................
677    Evaluated to 0.000000
678    ready> mandel(-0.9, -1.4, 0.02, 0.03);
679    *******************************************************************************
680    *******************************************************************************
681    *******************************************************************************
682    **********+++++++++++++++++++++************************************************
683    *+++++++++++++++++++++++++++++++++++++++***************************************
684    +++++++++++++++++++++++++++++++++++++++++++++**********************************
685    ++++++++++++++++++++++++++++++++++++++++++++++++++*****************************
686    ++++++++++++++++++++++++++++++++++++++++++++++++++++++*************************
687    +++++++++++++++++++++++++++++++++++++++++++++++++++++++++**********************
688    +++++++++++++++++++++++++++++++++.........++++++++++++++++++*******************
689    +++++++++++++++++++++++++++++++....   ......+++++++++++++++++++****************
690    +++++++++++++++++++++++++++++.......  ........+++++++++++++++++++**************
691    ++++++++++++++++++++++++++++........   ........++++++++++++++++++++************
692    +++++++++++++++++++++++++++.........     ..  ...+++++++++++++++++++++**********
693    ++++++++++++++++++++++++++...........        ....++++++++++++++++++++++********
694    ++++++++++++++++++++++++.............       .......++++++++++++++++++++++******
695    +++++++++++++++++++++++.............        ........+++++++++++++++++++++++****
696    ++++++++++++++++++++++...........           ..........++++++++++++++++++++++***
697    ++++++++++++++++++++...........                .........++++++++++++++++++++++*
698    ++++++++++++++++++............                  ...........++++++++++++++++++++
699    ++++++++++++++++...............                 .............++++++++++++++++++
700    ++++++++++++++.................                 ...............++++++++++++++++
701    ++++++++++++..................                  .................++++++++++++++
702    +++++++++..................                      .................+++++++++++++
703    ++++++........        .                               .........  ..++++++++++++
704    ++............                                         ......    ....++++++++++
705    ..............                                                    ...++++++++++
706    ..............                                                    ....+++++++++
707    ..............                                                    .....++++++++
708    .............                                                    ......++++++++
709    ...........                                                     .......++++++++
710    .........                                                       ........+++++++
711    .........                                                       ........+++++++
712    .........                                                           ....+++++++
713    ........                                                             ...+++++++
714    .......                                                              ...+++++++
715                                                                        ....+++++++
716                                                                       .....+++++++
717                                                                        ....+++++++
718                                                                        ....+++++++
719                                                                        ....+++++++
720    Evaluated to 0.000000
721    ready> ^D
722
723At this point, you may be starting to realize that Kaleidoscope is a
724real and powerful language. It may not be self-similar :), but it can be
725used to plot things that are!
726
727With this, we conclude the "adding user-defined operators" chapter of
728the tutorial. We have successfully augmented our language, adding the
729ability to extend the language in the library, and we have shown how
730this can be used to build a simple but interesting end-user application
731in Kaleidoscope. At this point, Kaleidoscope can build a variety of
732applications that are functional and can call functions with
733side-effects, but it can't actually define and mutate a variable itself.
734
735Strikingly, variable mutation is an important feature of some languages,
736and it is not at all obvious how to `add support for mutable
737variables <LangImpl07.html>`_ without having to add an "SSA construction"
738phase to your front-end. In the next chapter, we will describe how you
739can add variable mutation without building SSA in your front-end.
740
741Full Code Listing
742=================
743
744Here is the complete code listing for our running example, enhanced with
745the support for user-defined operators. To build this example, use:
746
747.. code-block:: bash
748
749    # Compile
750    clang++ -g toy.cpp `llvm-config --cxxflags --ldflags --system-libs --libs core mcjit native` -O3 -o toy
751    # Run
752    ./toy
753
754On some platforms, you will need to specify -rdynamic or
755-Wl,--export-dynamic when linking. This ensures that symbols defined in
756the main executable are exported to the dynamic linker and so are
757available for symbol resolution at run time. This is not needed if you
758compile your support code into a shared library, although doing that
759will cause problems on Windows.
760
761Here is the code:
762
763.. literalinclude:: ../../examples/Kaleidoscope/Chapter6/toy.cpp
764   :language: c++
765
766`Next: Extending the language: mutable variables / SSA
767construction <LangImpl07.html>`_
768
769