aboutsummaryrefslogtreecommitdiffstats
path: root/docs/tutorial/LangImpl6.rst
blob: cdceb03fb92eba44c465a001ba2c9099aa26d790 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
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
635
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
678
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
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
============================================================
Kaleidoscope: Extending the Language: User-defined Operators
============================================================

.. contents::
   :local:

Chapter 6 Introduction
======================

Welcome to Chapter 6 of the "`Implementing a language with
LLVM <index.html>`_" 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).

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.

At the end of this tutorial, we'll run through an example Kaleidoscope
application that `renders the Mandelbrot set <#example>`_. This gives an
example of what you can build with Kaleidoscope and its feature set.

User-defined Operators: the Idea
================================

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.

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 `Chapter 2 <LangImpl2.html>`_ 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.

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:

::

    # Logical unary not.
    def unary!(v)
      if v then
        0
      else
        1;

    # Define > with the same precedence as <.
    def binary> 10 (LHS RHS)
      RHS < 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 < RHS | LHS > RHS);

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!

We will break down implementation of these features into two parts:
implementing support for user-defined binary operators and adding unary
operators.

User-defined Binary Operators
=============================

Adding support for user-defined binary operators is pretty simple with
our current framework. We'll first add support for the unary/binary
keywords:

.. code-block:: c++

    enum Token {
      ...
      // operators
      tok_binary = -11, tok_unary = -12
    };
    ...
    static int gettok() {
    ...
        if (IdentifierStr == "for") return tok_for;
        if (IdentifierStr == "in") return tok_in;
        if (IdentifierStr == "binary") return tok_binary;
        if (IdentifierStr == "unary") return tok_unary;
        return tok_identifier;

This just adds lexer support for the unary and binary keywords, like we
did in `previous chapters <LangImpl5.html#iflexer>`_. 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.

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
``PrototypeAST`` AST node. To represent our new user-defined operators
as prototypes, we have to extend the ``PrototypeAST`` AST node like
this:

.. code-block:: c++

    /// PrototypeAST - This class represents the "prototype" for a function,
    /// which captures its argument names as well as if it is an operator.
    class PrototypeAST {
      std::string Name;
      std::vector<std::string> Args;
      bool isOperator;
      unsigned Precedence;  // Precedence if a binary op.
    public:
      PrototypeAST(const std::string &name, const std::vector<std::string> &args,
                   bool isoperator = false, unsigned prec = 0)
      : Name(name), Args(args), isOperator(isoperator), Precedence(prec) {}

      bool isUnaryOp() const { return isOperator && Args.size() == 1; }
      bool isBinaryOp() const { return isOperator && Args.size() == 2; }

      char getOperatorName() const {
        assert(isUnaryOp() || isBinaryOp());
        return Name[Name.size()-1];
      }

      unsigned getBinaryPrecedence() const { return Precedence; }

      Function *Codegen();
    };

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:

.. code-block:: c++

    /// prototype
    ///   ::= id '(' id* ')'
    ///   ::= binary LETTER number? (id, id)
    static PrototypeAST *ParsePrototype() {
      std::string FnName;

      unsigned Kind = 0;  // 0 = identifier, 1 = unary, 2 = binary.
      unsigned BinaryPrecedence = 30;

      switch (CurTok) {
      default:
        return ErrorP("Expected function name in prototype");
      case tok_identifier:
        FnName = IdentifierStr;
        Kind = 0;
        getNextToken();
        break;
      case tok_binary:
        getNextToken();
        if (!isascii(CurTok))
          return ErrorP("Expected binary operator");
        FnName = "binary";
        FnName += (char)CurTok;
        Kind = 2;
        getNextToken();

        // Read the precedence if present.
        if (CurTok == tok_number) {
          if (NumVal < 1 || NumVal > 100)
            return ErrorP("Invalid precedecnce: must be 1..100");
          BinaryPrecedence = (unsigned)NumVal;
          getNextToken();
        }
        break;
      }

      if (CurTok != '(')
        return ErrorP("Expected '(' in prototype");

      std::vector<std::string> ArgNames;
      while (getNextToken() == tok_identifier)
        ArgNames.push_back(IdentifierStr);
      if (CurTok != ')')
        return ErrorP("Expected ')' in prototype");

      // success.
      getNextToken();  // eat ')'.

      // Verify right number of names for operator.
      if (Kind && ArgNames.size() != Kind)
        return ErrorP("Invalid number of operands for operator");

      return new PrototypeAST(FnName, ArgNames, Kind != 0, BinaryPrecedence);
    }

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 ``FnName`` 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.

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:

.. code-block:: c++

    Value *BinaryExprAST::Codegen() {
      Value *L = LHS->Codegen();
      Value *R = RHS->Codegen();
      if (L == 0 || R == 0) return 0;

      switch (Op) {
      case '+': return Builder.CreateFAdd(L, R, "addtmp");
      case '-': return Builder.CreateFSub(L, R, "subtmp");
      case '*': return Builder.CreateFMul(L, R, "multmp");
      case '<':
        L = Builder.CreateFCmpULT(L, R, "cmptmp");
        // Convert bool 0/1 to double 0.0 or 1.0
        return Builder.CreateUIToFP(L, Type::getDoubleTy(getGlobalContext()),
                                    "booltmp");
      default: break;
      }

      // If it wasn't a builtin binary operator, it must be a user defined one. Emit
      // a call to it.
      Function *F = TheModule->getFunction(std::string("binary")+Op);
      assert(F && "binary operator not found!");

      Value *Ops[2] = { L, R };
      return Builder.CreateCall(F, Ops, "binop");
    }

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.

The final piece of code we are missing, is a bit of top-level magic:

.. code-block:: c++

    Function *FunctionAST::Codegen() {
      NamedValues.clear();

      Function *TheFunction = Proto->Codegen();
      if (TheFunction == 0)
        return 0;

      // If this is an operator, install it.
      if (Proto->isBinaryOp())
        BinopPrecedence[Proto->getOperatorName()] = Proto->getBinaryPrecedence();

      // Create a new basic block to start insertion into.
      BasicBlock *BB = BasicBlock::Create(getGlobalContext(), "entry", TheFunction);
      Builder.SetInsertPoint(BB);

      if (Value *RetVal = Body->Codegen()) {
        ...

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".

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.

User-defined Unary Operators
============================

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:

.. code-block:: c++

    /// UnaryExprAST - Expression class for a unary operator.
    class UnaryExprAST : public ExprAST {
      char Opcode;
      ExprAST *Operand;
    public:
      UnaryExprAST(char opcode, ExprAST *operand)
        : Opcode(opcode), Operand(operand) {}
      virtual Value *Codegen();
    };

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:

.. code-block:: c++

    /// unary
    ///   ::= primary
    ///   ::= '!' unary
    static ExprAST *ParseUnary() {
      // If the current token is not an operator, it must be a primary expr.
      if (!isascii(CurTok) || CurTok == '(' || CurTok == ',')
        return ParsePrimary();

      // If this is a unary operator, read it.
      int Opc = CurTok;
      getNextToken();
      if (ExprAST *Operand = ParseUnary())
        return new UnaryExprAST(Opc, Operand);
      return 0;
    }

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.

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 ParseUnary instead:

.. code-block:: c++

    /// binoprhs
    ///   ::= ('+' unary)*
    static ExprAST *ParseBinOpRHS(int ExprPrec, ExprAST *LHS) {
      ...
        // Parse the unary expression after the binary operator.
        ExprAST *RHS = ParseUnary();
        if (!RHS) return 0;
      ...
    }
    /// expression
    ///   ::= unary binoprhs
    ///
    static ExprAST *ParseExpression() {
      ExprAST *LHS = ParseUnary();
      if (!LHS) return 0;

      return ParseBinOpRHS(0, LHS);
    }

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:

.. code-block:: c++

    /// prototype
    ///   ::= id '(' id* ')'
    ///   ::= binary LETTER number? (id, id)
    ///   ::= unary LETTER (id)
    static PrototypeAST *ParsePrototype() {
      std::string FnName;

      unsigned Kind = 0;  // 0 = identifier, 1 = unary, 2 = binary.
      unsigned BinaryPrecedence = 30;

      switch (CurTok) {
      default:
        return ErrorP("Expected function name in prototype");
      case tok_identifier:
        FnName = IdentifierStr;
        Kind = 0;
        getNextToken();
        break;
      case tok_unary:
        getNextToken();
        if (!isascii(CurTok))
          return ErrorP("Expected unary operator");
        FnName = "unary";
        FnName += (char)CurTok;
        Kind = 1;
        getNextToken();
        break;
      case tok_binary:
        ...

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:

.. code-block:: c++

    Value *UnaryExprAST::Codegen() {
      Value *OperandV = Operand->Codegen();
      if (OperandV == 0) return 0;

      Function *F = TheModule->getFunction(std::string("unary")+Opcode);
      if (F == 0)
        return ErrorV("Unknown unary operator");

      return Builder.CreateCall(F, OperandV, "unop");
    }

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.

Kicking the Tires
=================

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):

::

    ready> extern printd(x);
    Read extern:
    declare double @printd(double)

    ready> def binary : 1 (x y) 0;  # Low-precedence operator that ignores operands.
    ..
    ready> printd(123) : printd(456) : printd(789);
    123.000000
    456.000000
    789.000000
    Evaluated to 0.000000

We can also define a bunch of other "primitive" operations, such as:

::

    # Logical unary not.
    def unary!(v)
      if v then
        0
      else
        1;

    # Unary negate.
    def unary-(v)
      0-v;

    # Define > with the same precedence as <.
    def binary> 10 (LHS RHS)
      RHS < 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& 6 (LHS RHS)
      if !LHS then
        0
      else
        !!RHS;

    # Define = with slightly lower precedence than relationals.
    def binary = 9 (LHS RHS)
      !(LHS < RHS | LHS > RHS);

    # Define ':' for sequencing: as a low-precedence operator that ignores operands
    # and just returns the RHS.
    def binary : 1 (x y) y;

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:

::

    ready>

    extern putchard(char)
    def printdensity(d)
      if d > 8 then
        putchard(32)  # ' '
      else if d > 4 then
        putchard(46)  # '.'
      else if d > 2 then
        putchard(43)  # '+'
      else
        putchard(42); # '*'
    ...
    ready> printdensity(1): printdensity(2): printdensity(3):
           printdensity(4): printdensity(5): printdensity(9):
           putchard(10);
    **++.
    Evaluated to 0.000000

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:

::

    # 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 > 255 | (real*real + imag*imag > 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);

This "``z = z2 + c``" function is a beautiful little creature that is
the basis for computation of the `Mandelbrot
Set <http://en.wikipedia.org/wiki/Mandelbrot_set>`_. Our
``mandelconverge`` 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:

::

    # 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 < ymax, ystep in (
        (for x = xmin, x < 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);

Given this, we can try plotting out the mandlebrot set! Lets try it out:

::

    ready> mandel(-2.3, -1.3, 0.05, 0.07);
    *******************************+++++++++++*************************************
    *************************+++++++++++++++++++++++*******************************
    **********************+++++++++++++++++++++++++++++****************************
    *******************+++++++++++++++++++++.. ...++++++++*************************
    *****************++++++++++++++++++++++.... ...+++++++++***********************
    ***************+++++++++++++++++++++++.....   ...+++++++++*********************
    **************+++++++++++++++++++++++....     ....+++++++++********************
    *************++++++++++++++++++++++......      .....++++++++*******************
    ************+++++++++++++++++++++.......       .......+++++++******************
    ***********+++++++++++++++++++....                ... .+++++++*****************
    **********+++++++++++++++++.......                     .+++++++****************
    *********++++++++++++++...........                    ...+++++++***************
    ********++++++++++++............                      ...++++++++**************
    ********++++++++++... ..........                        .++++++++**************
    *******+++++++++.....                                   .+++++++++*************
    *******++++++++......                                  ..+++++++++*************
    *******++++++.......                                   ..+++++++++*************
    *******+++++......                                     ..+++++++++*************
    *******.... ....                                      ...+++++++++*************
    *******.... .                                         ...+++++++++*************
    *******+++++......                                    ...+++++++++*************
    *******++++++.......                                   ..+++++++++*************
    *******++++++++......                                   .+++++++++*************
    *******+++++++++.....                                  ..+++++++++*************
    ********++++++++++... ..........                        .++++++++**************
    ********++++++++++++............                      ...++++++++**************
    *********++++++++++++++..........                     ...+++++++***************
    **********++++++++++++++++........                     .+++++++****************
    **********++++++++++++++++++++....                ... ..+++++++****************
    ***********++++++++++++++++++++++.......       .......++++++++*****************
    ************+++++++++++++++++++++++......      ......++++++++******************
    **************+++++++++++++++++++++++....      ....++++++++********************
    ***************+++++++++++++++++++++++.....   ...+++++++++*********************
    *****************++++++++++++++++++++++....  ...++++++++***********************
    *******************+++++++++++++++++++++......++++++++*************************
    *********************++++++++++++++++++++++.++++++++***************************
    *************************+++++++++++++++++++++++*******************************
    ******************************+++++++++++++************************************
    *******************************************************************************
    *******************************************************************************
    *******************************************************************************
    Evaluated to 0.000000
    ready> mandel(-2, -1, 0.02, 0.04);
    **************************+++++++++++++++++++++++++++++++++++++++++++++++++++++
    ***********************++++++++++++++++++++++++++++++++++++++++++++++++++++++++
    *********************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++.
    *******************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++...
    *****************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++.....
    ***************++++++++++++++++++++++++++++++++++++++++++++++++++++++++........
    **************++++++++++++++++++++++++++++++++++++++++++++++++++++++...........
    ************+++++++++++++++++++++++++++++++++++++++++++++++++++++..............
    ***********++++++++++++++++++++++++++++++++++++++++++++++++++........        .
    **********++++++++++++++++++++++++++++++++++++++++++++++.............
    ********+++++++++++++++++++++++++++++++++++++++++++..................
    *******+++++++++++++++++++++++++++++++++++++++.......................
    ******+++++++++++++++++++++++++++++++++++...........................
    *****++++++++++++++++++++++++++++++++............................
    *****++++++++++++++++++++++++++++...............................
    ****++++++++++++++++++++++++++......   .........................
    ***++++++++++++++++++++++++.........     ......    ...........
    ***++++++++++++++++++++++............
    **+++++++++++++++++++++..............
    **+++++++++++++++++++................
    *++++++++++++++++++.................
    *++++++++++++++++............ ...
    *++++++++++++++..............
    *+++....++++................
    *..........  ...........
    *
    *..........  ...........
    *+++....++++................
    *++++++++++++++..............
    *++++++++++++++++............ ...
    *++++++++++++++++++.................
    **+++++++++++++++++++................
    **+++++++++++++++++++++..............
    ***++++++++++++++++++++++............
    ***++++++++++++++++++++++++.........     ......    ...........
    ****++++++++++++++++++++++++++......   .........................
    *****++++++++++++++++++++++++++++...............................
    *****++++++++++++++++++++++++++++++++............................
    ******+++++++++++++++++++++++++++++++++++...........................
    *******+++++++++++++++++++++++++++++++++++++++.......................
    ********+++++++++++++++++++++++++++++++++++++++++++..................
    Evaluated to 0.000000
    ready> mandel(-0.9, -1.4, 0.02, 0.03);
    *******************************************************************************
    *******************************************************************************
    *******************************************************************************
    **********+++++++++++++++++++++************************************************
    *+++++++++++++++++++++++++++++++++++++++***************************************
    +++++++++++++++++++++++++++++++++++++++++++++**********************************
    ++++++++++++++++++++++++++++++++++++++++++++++++++*****************************
    ++++++++++++++++++++++++++++++++++++++++++++++++++++++*************************
    +++++++++++++++++++++++++++++++++++++++++++++++++++++++++**********************
    +++++++++++++++++++++++++++++++++.........++++++++++++++++++*******************
    +++++++++++++++++++++++++++++++....   ......+++++++++++++++++++****************
    +++++++++++++++++++++++++++++.......  ........+++++++++++++++++++**************
    ++++++++++++++++++++++++++++........   ........++++++++++++++++++++************
    +++++++++++++++++++++++++++.........     ..  ...+++++++++++++++++++++**********
    ++++++++++++++++++++++++++...........        ....++++++++++++++++++++++********
    ++++++++++++++++++++++++.............       .......++++++++++++++++++++++******
    +++++++++++++++++++++++.............        ........+++++++++++++++++++++++****
    ++++++++++++++++++++++...........           ..........++++++++++++++++++++++***
    ++++++++++++++++++++...........                .........++++++++++++++++++++++*
    ++++++++++++++++++............                  ...........++++++++++++++++++++
    ++++++++++++++++...............                 .............++++++++++++++++++
    ++++++++++++++.................                 ...............++++++++++++++++
    ++++++++++++..................                  .................++++++++++++++
    +++++++++..................                      .................+++++++++++++
    ++++++........        .                               .........  ..++++++++++++
    ++............                                         ......    ....++++++++++
    ..............                                                    ...++++++++++
    ..............                                                    ....+++++++++
    ..............                                                    .....++++++++
    .............                                                    ......++++++++
    ...........                                                     .......++++++++
    .........                                                       ........+++++++
    .........                                                       ........+++++++
    .........                                                           ....+++++++
    ........                                                             ...+++++++
    .......                                                              ...+++++++
                                                                        ....+++++++
                                                                       .....+++++++
                                                                        ....+++++++
                                                                        ....+++++++
                                                                        ....+++++++
    Evaluated to 0.000000
    ready> ^D

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!

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.

Strikingly, variable mutation is an important feature of some languages,
and it is not at all obvious how to `add support for mutable
variables <LangImpl7.html>`_ 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.

Full Code Listing
=================

Here is the complete code listing for our running example, enhanced with
the if/then/else and for expressions.. To build this example, use:

.. code-block:: bash

    # Compile
    clang++ -g toy.cpp `llvm-config --cxxflags --ldflags --system-libs --libs core jit native` -O3 -o toy
    # Run
    ./toy

On some platforms, you will need to specify -rdynamic or
-Wl,--export-dynamic when linking. This ensures that symbols defined in
the main executable are exported to the dynamic linker and so are
available for symbol resolution at run time. This is not needed if you
compile your support code into a shared library, although doing that
will cause problems on Windows.

Here is the code:

.. literalinclude:: ../../examples/Kaleidoscope/Chapter6/toy.cpp
   :language: c++

`Next: Extending the language: mutable variables / SSA
construction <LangImpl7.html>`_