Home | History | Annotate | Download | only in tutorial
      1 ============================================================
      2 Kaleidoscope: Extending the Language: User-defined Operators
      3 ============================================================
      4 
      5 .. contents::
      6    :local:
      7 
      8 Chapter 6 Introduction
      9 ======================
     10 
     11 Welcome to Chapter 6 of the "`Implementing a language with
     12 LLVM <index.html>`_" tutorial. At this point in our tutorial, we now
     13 have a fully functional language that is fairly minimal, but also
     14 useful. There is still one big problem with it, however. Our language
     15 doesn't have many useful operators (like division, logical negation, or
     16 even any comparisons besides less-than).
     17 
     18 This chapter of the tutorial takes a wild digression into adding
     19 user-defined operators to the simple and beautiful Kaleidoscope
     20 language. This digression now gives us a simple and ugly language in
     21 some ways, but also a powerful one at the same time. One of the great
     22 things about creating your own language is that you get to decide what
     23 is good or bad. In this tutorial we'll assume that it is okay to use
     24 this as a way to show some interesting parsing techniques.
     25 
     26 At the end of this tutorial, we'll run through an example Kaleidoscope
     27 application that `renders the Mandelbrot set <#kicking-the-tires>`_. This gives an
     28 example of what you can build with Kaleidoscope and its feature set.
     29 
     30 User-defined Operators: the Idea
     31 ================================
     32 
     33 The "operator overloading" that we will add to Kaleidoscope is more
     34 general than languages like C++. In C++, you are only allowed to
     35 redefine existing operators: you can't programatically change the
     36 grammar, introduce new operators, change precedence levels, etc. In this
     37 chapter, we will add this capability to Kaleidoscope, which will let the
     38 user round out the set of operators that are supported.
     39 
     40 The point of going into user-defined operators in a tutorial like this
     41 is to show the power and flexibility of using a hand-written parser.
     42 Thus far, the parser we have been implementing uses recursive descent
     43 for most parts of the grammar and operator precedence parsing for the
     44 expressions. See `Chapter 2 <LangImpl2.html>`_ for details. Without
     45 using operator precedence parsing, it would be very difficult to allow
     46 the programmer to introduce new operators into the grammar: the grammar
     47 is dynamically extensible as the JIT runs.
     48 
     49 The two specific features we'll add are programmable unary operators
     50 (right now, Kaleidoscope has no unary operators at all) as well as
     51 binary 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 
     79 Many languages aspire to being able to implement their standard runtime
     80 library in the language itself. In Kaleidoscope, we can implement
     81 significant parts of the language in the library!
     82 
     83 We will break down implementation of these features into two parts:
     84 implementing support for user-defined binary operators and adding unary
     85 operators.
     86 
     87 User-defined Binary Operators
     88 =============================
     89 
     90 Adding support for user-defined binary operators is pretty simple with
     91 our current framework. We'll first add support for the unary/binary
     92 keywords:
     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 
    115 This just adds lexer support for the unary and binary keywords, like we
    116 did in `previous chapters <LangImpl5.html#lexer-extensions-for-if-then-else>`_. One nice thing
    117 about our current AST, is that we represent binary operators with full
    118 generalisation by using their ASCII code as the opcode. For our extended
    119 operators, we'll use this same representation, so we don't need any new
    120 AST or parser support.
    121 
    122 On the other hand, we have to be able to represent the definitions of
    123 these new operators, in the "def binary\| 5" part of the function
    124 definition. In our grammar so far, the "name" for the function
    125 definition is parsed as the "prototype" production and into the
    126 ``PrototypeAST`` AST node. To represent our new user-defined operators
    127 as prototypes, we have to extend the ``PrototypeAST`` AST node like
    128 this:
    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       bool isUnaryOp() const { return IsOperator && Args.size() == 1; }
    147       bool isBinaryOp() const { return IsOperator && Args.size() == 2; }
    148 
    149       char getOperatorName() const {
    150         assert(isUnaryOp() || isBinaryOp());
    151         return Name[Name.size()-1];
    152       }
    153 
    154       unsigned getBinaryPrecedence() const { return Precedence; }
    155 
    156       Function *codegen();
    157     };
    158 
    159 Basically, in addition to knowing a name for the prototype, we now keep
    160 track of whether it was an operator, and if it was, what precedence
    161 level the operator is at. The precedence is only used for binary
    162 operators (as you'll see below, it just doesn't apply for unary
    163 operators). Now that we have a way to represent the prototype for a
    164 user-defined operator, we need to parse it:
    165 
    166 .. code-block:: c++
    167 
    168     /// prototype
    169     ///   ::= id '(' id* ')'
    170     ///   ::= binary LETTER number? (id, id)
    171     static std::unique_ptr<PrototypeAST> ParsePrototype() {
    172       std::string FnName;
    173 
    174       unsigned Kind = 0;  // 0 = identifier, 1 = unary, 2 = binary.
    175       unsigned BinaryPrecedence = 30;
    176 
    177       switch (CurTok) {
    178       default:
    179         return LogErrorP("Expected function name in prototype");
    180       case tok_identifier:
    181         FnName = IdentifierStr;
    182         Kind = 0;
    183         getNextToken();
    184         break;
    185       case tok_binary:
    186         getNextToken();
    187         if (!isascii(CurTok))
    188           return LogErrorP("Expected binary operator");
    189         FnName = "binary";
    190         FnName += (char)CurTok;
    191         Kind = 2;
    192         getNextToken();
    193 
    194         // Read the precedence if present.
    195         if (CurTok == tok_number) {
    196           if (NumVal < 1 || NumVal > 100)
    197             return LogErrorP("Invalid precedecnce: must be 1..100");
    198           BinaryPrecedence = (unsigned)NumVal;
    199           getNextToken();
    200         }
    201         break;
    202       }
    203 
    204       if (CurTok != '(')
    205         return LogErrorP("Expected '(' in prototype");
    206 
    207       std::vector<std::string> ArgNames;
    208       while (getNextToken() == tok_identifier)
    209         ArgNames.push_back(IdentifierStr);
    210       if (CurTok != ')')
    211         return LogErrorP("Expected ')' in prototype");
    212 
    213       // success.
    214       getNextToken();  // eat ')'.
    215 
    216       // Verify right number of names for operator.
    217       if (Kind && ArgNames.size() != Kind)
    218         return LogErrorP("Invalid number of operands for operator");
    219 
    220       return llvm::make_unique<PrototypeAST>(FnName, std::move(ArgNames), Kind != 0,
    221                                              BinaryPrecedence);
    222     }
    223 
    224 This is all fairly straightforward parsing code, and we have already
    225 seen a lot of similar code in the past. One interesting part about the
    226 code above is the couple lines that set up ``FnName`` for binary
    227 operators. This builds names like "binary@" for a newly defined "@"
    228 operator. This then takes advantage of the fact that symbol names in the
    229 LLVM symbol table are allowed to have any character in them, including
    230 embedded nul characters.
    231 
    232 The next interesting thing to add, is codegen support for these binary
    233 operators. Given our current structure, this is a simple addition of a
    234 default case for our existing binary operator node:
    235 
    236 .. code-block:: c++
    237 
    238     Value *BinaryExprAST::codegen() {
    239       Value *L = LHS->codegen();
    240       Value *R = RHS->codegen();
    241       if (!L || !R)
    242         return nullptr;
    243 
    244       switch (Op) {
    245       case '+':
    246         return Builder.CreateFAdd(L, R, "addtmp");
    247       case '-':
    248         return Builder.CreateFSub(L, R, "subtmp");
    249       case '*':
    250         return Builder.CreateFMul(L, R, "multmp");
    251       case '<':
    252         L = Builder.CreateFCmpULT(L, R, "cmptmp");
    253         // Convert bool 0/1 to double 0.0 or 1.0
    254         return Builder.CreateUIToFP(L, Type::getDoubleTy(LLVMContext),
    255                                     "booltmp");
    256       default:
    257         break;
    258       }
    259 
    260       // If it wasn't a builtin binary operator, it must be a user defined one. Emit
    261       // a call to it.
    262       Function *F = TheModule->getFunction(std::string("binary") + Op);
    263       assert(F && "binary operator not found!");
    264 
    265       Value *Ops[2] = { L, R };
    266       return Builder.CreateCall(F, Ops, "binop");
    267     }
    268 
    269 As you can see above, the new code is actually really simple. It just
    270 does a lookup for the appropriate operator in the symbol table and
    271 generates a function call to it. Since user-defined operators are just
    272 built as normal functions (because the "prototype" boils down to a
    273 function with the right name) everything falls into place.
    274 
    275 The final piece of code we are missing, is a bit of top-level magic:
    276 
    277 .. code-block:: c++
    278 
    279     Function *FunctionAST::codegen() {
    280       NamedValues.clear();
    281 
    282       Function *TheFunction = Proto->codegen();
    283       if (!TheFunction)
    284         return nullptr;
    285 
    286       // If this is an operator, install it.
    287       if (Proto->isBinaryOp())
    288         BinopPrecedence[Proto->getOperatorName()] = Proto->getBinaryPrecedence();
    289 
    290       // Create a new basic block to start insertion into.
    291       BasicBlock *BB = BasicBlock::Create(LLVMContext, "entry", TheFunction);
    292       Builder.SetInsertPoint(BB);
    293 
    294       if (Value *RetVal = Body->codegen()) {
    295         ...
    296 
    297 Basically, before codegening a function, if it is a user-defined
    298 operator, we register it in the precedence table. This allows the binary
    299 operator parsing logic we already have in place to handle it. Since we
    300 are working on a fully-general operator precedence parser, this is all
    301 we need to do to "extend the grammar".
    302 
    303 Now we have useful user-defined binary operators. This builds a lot on
    304 the previous framework we built for other operators. Adding unary
    305 operators is a bit more challenging, because we don't have any framework
    306 for it yet - lets see what it takes.
    307 
    308 User-defined Unary Operators
    309 ============================
    310 
    311 Since we don't currently support unary operators in the Kaleidoscope
    312 language, we'll need to add everything to support them. Above, we added
    313 simple support for the 'unary' keyword to the lexer. In addition to
    314 that, 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       virtual Value *codegen();
    327     };
    328 
    329 This AST node is very simple and obvious by now. It directly mirrors the
    330 binary operator AST node, except that it only has one child. With this,
    331 we need to add the parsing logic. Parsing a unary operator is pretty
    332 simple: we'll add a new function to do it:
    333 
    334 .. code-block:: c++
    335 
    336     /// unary
    337     ///   ::= primary
    338     ///   ::= '!' unary
    339     static std::unique_ptr<ExprAST> ParseUnary() {
    340       // If the current token is not an operator, it must be a primary expr.
    341       if (!isascii(CurTok) || CurTok == '(' || CurTok == ',')
    342         return ParsePrimary();
    343 
    344       // If this is a unary operator, read it.
    345       int Opc = CurTok;
    346       getNextToken();
    347       if (auto Operand = ParseUnary())
    348         return llvm::unique_ptr<UnaryExprAST>(Opc, std::move(Operand));
    349       return nullptr;
    350     }
    351 
    352 The grammar we add is pretty straightforward here. If we see a unary
    353 operator when parsing a primary operator, we eat the operator as a
    354 prefix and parse the remaining piece as another unary operator. This
    355 allows us to handle multiple unary operators (e.g. "!!x"). Note that
    356 unary operators can't have ambiguous parses like binary operators can,
    357 so there is no need for precedence information.
    358 
    359 The problem with this function, is that we need to call ParseUnary from
    360 somewhere. To do this, we change previous callers of ParsePrimary to
    361 call ParseUnary instead:
    362 
    363 .. code-block:: c++
    364 
    365     /// binoprhs
    366     ///   ::= ('+' unary)*
    367     static std::unique_ptr<ExprAST> ParseBinOpRHS(int ExprPrec,
    368                                                   std::unique_ptr<ExprAST> LHS) {
    369       ...
    370         // Parse the unary expression after the binary operator.
    371         auto RHS = ParseUnary();
    372         if (!RHS)
    373           return nullptr;
    374       ...
    375     }
    376     /// expression
    377     ///   ::= unary binoprhs
    378     ///
    379     static std::unique_ptr<ExprAST> ParseExpression() {
    380       auto LHS = ParseUnary();
    381       if (!LHS)
    382         return nullptr;
    383 
    384       return ParseBinOpRHS(0, std::move(LHS));
    385     }
    386 
    387 With these two simple changes, we are now able to parse unary operators
    388 and build the AST for them. Next up, we need to add parser support for
    389 prototypes, to parse the unary operator prototype. We extend the binary
    390 operator code above with:
    391 
    392 .. code-block:: c++
    393 
    394     /// prototype
    395     ///   ::= id '(' id* ')'
    396     ///   ::= binary LETTER number? (id, id)
    397     ///   ::= unary LETTER (id)
    398     static std::unique_ptr<PrototypeAST> ParsePrototype() {
    399       std::string FnName;
    400 
    401       unsigned Kind = 0;  // 0 = identifier, 1 = unary, 2 = binary.
    402       unsigned BinaryPrecedence = 30;
    403 
    404       switch (CurTok) {
    405       default:
    406         return LogErrorP("Expected function name in prototype");
    407       case tok_identifier:
    408         FnName = IdentifierStr;
    409         Kind = 0;
    410         getNextToken();
    411         break;
    412       case tok_unary:
    413         getNextToken();
    414         if (!isascii(CurTok))
    415           return LogErrorP("Expected unary operator");
    416         FnName = "unary";
    417         FnName += (char)CurTok;
    418         Kind = 1;
    419         getNextToken();
    420         break;
    421       case tok_binary:
    422         ...
    423 
    424 As with binary operators, we name unary operators with a name that
    425 includes the operator character. This assists us at code generation
    426 time. Speaking of, the final piece we need to add is codegen support for
    427 unary operators. It looks like this:
    428 
    429 .. code-block:: c++
    430 
    431     Value *UnaryExprAST::codegen() {
    432       Value *OperandV = Operand->codegen();
    433       if (!OperandV)
    434         return nullptr;
    435 
    436       Function *F = TheModule->getFunction(std::string("unary")+Opcode);
    437       if (!F)
    438         return LogErrorV("Unknown unary operator");
    439 
    440       return Builder.CreateCall(F, OperandV, "unop");
    441     }
    442 
    443 This code is similar to, but simpler than, the code for binary
    444 operators. It is simpler primarily because it doesn't need to handle any
    445 predefined operators.
    446 
    447 Kicking the Tires
    448 =================
    449 
    450 It is somewhat hard to believe, but with a few simple extensions we've
    451 covered in the last chapters, we have grown a real-ish language. With
    452 this, we can do a lot of interesting things, including I/O, math, and a
    453 bunch of other things. For example, we can now add a nice sequencing
    454 operator (printd is defined to print out the specified value and a
    455 newline):
    456 
    457 ::
    458 
    459     ready> extern printd(x);
    460     Read extern:
    461     declare double @printd(double)
    462 
    463     ready> def binary : 1 (x y) 0;  # Low-precedence operator that ignores operands.
    464     ..
    465     ready> printd(123) : printd(456) : printd(789);
    466     123.000000
    467     456.000000
    468     789.000000
    469     Evaluated to 0.000000
    470 
    471 We can also define a bunch of other "primitive" operations, such as:
    472 
    473 ::
    474 
    475     # Logical unary not.
    476     def unary!(v)
    477       if v then
    478         0
    479       else
    480         1;
    481 
    482     # Unary negate.
    483     def unary-(v)
    484       0-v;
    485 
    486     # Define > with the same precedence as <.
    487     def binary> 10 (LHS RHS)
    488       RHS < LHS;
    489 
    490     # Binary logical or, which does not short circuit.
    491     def binary| 5 (LHS RHS)
    492       if LHS then
    493         1
    494       else if RHS then
    495         1
    496       else
    497         0;
    498 
    499     # Binary logical and, which does not short circuit.
    500     def binary& 6 (LHS RHS)
    501       if !LHS then
    502         0
    503       else
    504         !!RHS;
    505 
    506     # Define = with slightly lower precedence than relationals.
    507     def binary = 9 (LHS RHS)
    508       !(LHS < RHS | LHS > RHS);
    509 
    510     # Define ':' for sequencing: as a low-precedence operator that ignores operands
    511     # and just returns the RHS.
    512     def binary : 1 (x y) y;
    513 
    514 Given the previous if/then/else support, we can also define interesting
    515 functions for I/O. For example, the following prints out a character
    516 whose "density" reflects the value passed in: the lower the value, the
    517 denser the character:
    518 
    519 ::
    520 
    521     ready>
    522 
    523     extern putchard(char)
    524     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 
    540 Based on these simple primitive operations, we can start to define more
    541 interesting things. For example, here's a little function that solves
    542 for the number of iterations it takes a function in the complex plane to
    543 converge:
    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 
    561 This "``z = z2 + c``" function is a beautiful little creature that is
    562 the basis for computation of the `Mandelbrot
    563 Set <http://en.wikipedia.org/wiki/Mandelbrot_set>`_. Our
    564 ``mandelconverge`` function returns the number of iterations that it
    565 takes for a complex orbit to escape, saturating to 255. This is not a
    566 very useful function by itself, but if you plot its value over a
    567 two-dimensional plane, you can see the Mandelbrot set. Given that we are
    568 limited to using putchard here, our amazing graphical output is limited,
    569 but 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 
    588 Given 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 
    723 At this point, you may be starting to realize that Kaleidoscope is a
    724 real and powerful language. It may not be self-similar :), but it can be
    725 used to plot things that are!
    726 
    727 With this, we conclude the "adding user-defined operators" chapter of
    728 the tutorial. We have successfully augmented our language, adding the
    729 ability to extend the language in the library, and we have shown how
    730 this can be used to build a simple but interesting end-user application
    731 in Kaleidoscope. At this point, Kaleidoscope can build a variety of
    732 applications that are functional and can call functions with
    733 side-effects, but it can't actually define and mutate a variable itself.
    734 
    735 Strikingly, variable mutation is an important feature of some languages,
    736 and it is not at all obvious how to `add support for mutable
    737 variables <LangImpl7.html>`_ without having to add an "SSA construction"
    738 phase to your front-end. In the next chapter, we will describe how you
    739 can add variable mutation without building SSA in your front-end.
    740 
    741 Full Code Listing
    742 =================
    743 
    744 Here is the complete code listing for our running example, enhanced with
    745 the if/then/else and for expressions.. 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 
    754 On some platforms, you will need to specify -rdynamic or
    755 -Wl,--export-dynamic when linking. This ensures that symbols defined in
    756 the main executable are exported to the dynamic linker and so are
    757 available for symbol resolution at run time. This is not needed if you
    758 compile your support code into a shared library, although doing that
    759 will cause problems on Windows.
    760 
    761 Here is the code:
    762 
    763 .. literalinclude:: ../../examples/Kaleidoscope/Chapter6/toy.cpp
    764    :language: c++
    765 
    766 `Next: Extending the language: mutable variables / SSA
    767 construction <LangImpl07.html>`_
    768 
    769