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+============================================================
+Kaleidoscope: Extending the Language: User-defined Operators
+============================================================
+
+.. contents::
+ :local:
+
+Written by `Chris Lattner <mailto:sabre@nondot.org>`_ and `Erick
+Tryzelaar <mailto:idadesub@users.sourceforge.net>`_
+
+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 <OCamlLangImpl2.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:: ocaml
+
+ type token =
+ ...
+ (* operators *)
+ | Binary | Unary
+
+ ...
+
+ and lex_ident buffer = parser
+ ...
+ | "for" -> [< 'Token.For; stream >]
+ | "in" -> [< 'Token.In; stream >]
+ | "binary" -> [< 'Token.Binary; stream >]
+ | "unary" -> [< 'Token.Unary; stream >]
+
+This just adds lexer support for the unary and binary keywords, like we
+did in `previous chapters <OCamlLangImpl5.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
+``Ast.Prototype`` AST node. To represent our new user-defined operators
+as prototypes, we have to extend the ``Ast.Prototype`` AST node like
+this:
+
+.. code-block:: ocaml
+
+ (* proto - This type represents the "prototype" for a function, which captures
+ * its name, and its argument names (thus implicitly the number of arguments the
+ * function takes). *)
+ type proto =
+ | Prototype of string * string array
+ | BinOpPrototype of string * string array * int
+
+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:: ocaml
+
+ (* prototype
+ * ::= id '(' id* ')'
+ * ::= binary LETTER number? (id, id)
+ * ::= unary LETTER number? (id) *)
+ let parse_prototype =
+ let rec parse_args accumulator = parser
+ | [< 'Token.Ident id; e=parse_args (id::accumulator) >] -> e
+ | [< >] -> accumulator
+ in
+ let parse_operator = parser
+ | [< 'Token.Unary >] -> "unary", 1
+ | [< 'Token.Binary >] -> "binary", 2
+ in
+ let parse_binary_precedence = parser
+ | [< 'Token.Number n >] -> int_of_float n
+ | [< >] -> 30
+ in
+ parser
+ | [< 'Token.Ident id;
+ 'Token.Kwd '(' ?? "expected '(' in prototype";
+ args=parse_args [];
+ 'Token.Kwd ')' ?? "expected ')' in prototype" >] ->
+ (* success. *)
+ Ast.Prototype (id, Array.of_list (List.rev args))
+ | [< (prefix, kind)=parse_operator;
+ 'Token.Kwd op ?? "expected an operator";
+ (* Read the precedence if present. *)
+ binary_precedence=parse_binary_precedence;
+ 'Token.Kwd '(' ?? "expected '(' in prototype";
+ args=parse_args [];
+ 'Token.Kwd ')' ?? "expected ')' in prototype" >] ->
+ let name = prefix ^ (String.make 1 op) in
+ let args = Array.of_list (List.rev args) in
+
+ (* Verify right number of arguments for operator. *)
+ if Array.length args != kind
+ then raise (Stream.Error "invalid number of operands for operator")
+ else
+ if kind == 1 then
+ Ast.Prototype (name, args)
+ else
+ Ast.BinOpPrototype (name, args, binary_precedence)
+ | [< >] ->
+ raise (Stream.Error "expected function name in prototype")
+
+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 ``name`` 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:: ocaml
+
+ let codegen_expr = function
+ ...
+ | Ast.Binary (op, lhs, rhs) ->
+ let lhs_val = codegen_expr lhs in
+ let rhs_val = codegen_expr rhs in
+ begin
+ match op with
+ | '+' -> build_add lhs_val rhs_val "addtmp" builder
+ | '-' -> build_sub lhs_val rhs_val "subtmp" builder
+ | '*' -> build_mul lhs_val rhs_val "multmp" builder
+ | '<' ->
+ (* Convert bool 0/1 to double 0.0 or 1.0 *)
+ let i = build_fcmp Fcmp.Ult lhs_val rhs_val "cmptmp" builder in
+ build_uitofp i double_type "booltmp" builder
+ | _ ->
+ (* If it wasn't a builtin binary operator, it must be a user defined
+ * one. Emit a call to it. *)
+ let callee = "binary" ^ (String.make 1 op) in
+ let callee =
+ match lookup_function callee the_module with
+ | Some callee -> callee
+ | None -> raise (Error "binary operator not found!")
+ in
+ build_call callee [|lhs_val; rhs_val|] "binop" builder
+ end
+
+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:: ocaml
+
+ let codegen_func the_fpm = function
+ | Ast.Function (proto, body) ->
+ Hashtbl.clear named_values;
+ let the_function = codegen_proto proto in
+
+ (* If this is an operator, install it. *)
+ begin match proto with
+ | Ast.BinOpPrototype (name, args, prec) ->
+ let op = name.[String.length name - 1] in
+ Hashtbl.add Parser.binop_precedence op prec;
+ | _ -> ()
+ end;
+
+ (* Create a new basic block to start insertion into. *)
+ let bb = append_block context "entry" the_function in
+ position_at_end bb builder;
+ ...
+
+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:: ocaml
+
+ type expr =
+ ...
+ (* variant for a unary operator. *)
+ | Unary of char * expr
+ ...
+
+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:: ocaml
+
+ (* unary
+ * ::= primary
+ * ::= '!' unary *)
+ and parse_unary = parser
+ (* If this is a unary operator, read it. *)
+ | [< 'Token.Kwd op when op != '(' && op != ')'; operand=parse_expr >] ->
+ Ast.Unary (op, operand)
+
+ (* If the current token is not an operator, it must be a primary expr. *)
+ | [< stream >] -> parse_primary stream
+
+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 ``parse_unary`` instead:
+
+.. code-block:: ocaml
+
+ (* binoprhs
+ * ::= ('+' primary)* *)
+ and parse_bin_rhs expr_prec lhs stream =
+ ...
+ (* Parse the unary expression after the binary operator. *)
+ let rhs = parse_unary stream in
+ ...
+
+ ...
+
+ (* expression
+ * ::= primary binoprhs *)
+ and parse_expr = parser
+ | [< lhs=parse_unary; stream >] -> parse_bin_rhs 0 lhs stream
+
+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:: ocaml
+
+ (* prototype
+ * ::= id '(' id* ')'
+ * ::= binary LETTER number? (id, id)
+ * ::= unary LETTER number? (id) *)
+ let parse_prototype =
+ let rec parse_args accumulator = parser
+ | [< 'Token.Ident id; e=parse_args (id::accumulator) >] -> e
+ | [< >] -> accumulator
+ in
+ let parse_operator = parser
+ | [< 'Token.Unary >] -> "unary", 1
+ | [< 'Token.Binary >] -> "binary", 2
+ in
+ let parse_binary_precedence = parser
+ | [< 'Token.Number n >] -> int_of_float n
+ | [< >] -> 30
+ in
+ parser
+ | [< 'Token.Ident id;
+ 'Token.Kwd '(' ?? "expected '(' in prototype";
+ args=parse_args [];
+ 'Token.Kwd ')' ?? "expected ')' in prototype" >] ->
+ (* success. *)
+ Ast.Prototype (id, Array.of_list (List.rev args))
+ | [< (prefix, kind)=parse_operator;
+ 'Token.Kwd op ?? "expected an operator";
+ (* Read the precedence if present. *)
+ binary_precedence=parse_binary_precedence;
+ 'Token.Kwd '(' ?? "expected '(' in prototype";
+ args=parse_args [];
+ 'Token.Kwd ')' ?? "expected ')' in prototype" >] ->
+ let name = prefix ^ (String.make 1 op) in
+ let args = Array.of_list (List.rev args) in
+
+ (* Verify right number of arguments for operator. *)
+ if Array.length args != kind
+ then raise (Stream.Error "invalid number of operands for operator")
+ else
+ if kind == 1 then
+ Ast.Prototype (name, args)
+ else
+ Ast.BinOpPrototype (name, args, binary_precedence)
+ | [< >] ->
+ raise (Stream.Error "expected function name in prototype")
+
+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:: ocaml
+
+ let rec codegen_expr = function
+ ...
+ | Ast.Unary (op, operand) ->
+ let operand = codegen_expr operand in
+ let callee = "unary" ^ (String.make 1 op) in
+ let callee =
+ match lookup_function callee the_module with
+ | Some callee -> callee
+ | None -> raise (Error "unknown unary operator")
+ in
+ build_call callee [|operand|] "unop" builder
+
+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);
+
+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 = z\ :sup:`2`\ + 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 <OCamlLangImpl7.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
+ ocamlbuild toy.byte
+ # Run
+ ./toy.byte
+
+Here is the code:
+
+\_tags:
+ ::
+
+ <{lexer,parser}.ml>: use_camlp4, pp(camlp4of)
+ <*.{byte,native}>: g++, use_llvm, use_llvm_analysis
+ <*.{byte,native}>: use_llvm_executionengine, use_llvm_target
+ <*.{byte,native}>: use_llvm_scalar_opts, use_bindings
+
+myocamlbuild.ml:
+ .. code-block:: ocaml
+
+ open Ocamlbuild_plugin;;
+
+ ocaml_lib ~extern:true "llvm";;
+ ocaml_lib ~extern:true "llvm_analysis";;
+ ocaml_lib ~extern:true "llvm_executionengine";;
+ ocaml_lib ~extern:true "llvm_target";;
+ ocaml_lib ~extern:true "llvm_scalar_opts";;
+
+ flag ["link"; "ocaml"; "g++"] (S[A"-cc"; A"g++"; A"-cclib"; A"-rdynamic"]);;
+ dep ["link"; "ocaml"; "use_bindings"] ["bindings.o"];;
+
+token.ml:
+ .. code-block:: ocaml
+
+ (*===----------------------------------------------------------------------===
+ * Lexer Tokens
+ *===----------------------------------------------------------------------===*)
+
+ (* The lexer returns these 'Kwd' if it is an unknown character, otherwise one of
+ * these others for known things. *)
+ type token =
+ (* commands *)
+ | Def | Extern
+
+ (* primary *)
+ | Ident of string | Number of float
+
+ (* unknown *)
+ | Kwd of char
+
+ (* control *)
+ | If | Then | Else
+ | For | In
+
+ (* operators *)
+ | Binary | Unary
+
+lexer.ml:
+ .. code-block:: ocaml
+
+ (*===----------------------------------------------------------------------===
+ * Lexer
+ *===----------------------------------------------------------------------===*)
+
+ let rec lex = parser
+ (* Skip any whitespace. *)
+ | [< ' (' ' | '\n' | '\r' | '\t'); stream >] -> lex stream
+
+ (* identifier: [a-zA-Z][a-zA-Z0-9] *)
+ | [< ' ('A' .. 'Z' | 'a' .. 'z' as c); stream >] ->
+ let buffer = Buffer.create 1 in
+ Buffer.add_char buffer c;
+ lex_ident buffer stream
+
+ (* number: [0-9.]+ *)
+ | [< ' ('0' .. '9' as c); stream >] ->
+ let buffer = Buffer.create 1 in
+ Buffer.add_char buffer c;
+ lex_number buffer stream
+
+ (* Comment until end of line. *)
+ | [< ' ('#'); stream >] ->
+ lex_comment stream
+
+ (* Otherwise, just return the character as its ascii value. *)
+ | [< 'c; stream >] ->
+ [< 'Token.Kwd c; lex stream >]
+
+ (* end of stream. *)
+ | [< >] -> [< >]
+
+ and lex_number buffer = parser
+ | [< ' ('0' .. '9' | '.' as c); stream >] ->
+ Buffer.add_char buffer c;
+ lex_number buffer stream
+ | [< stream=lex >] ->
+ [< 'Token.Number (float_of_string (Buffer.contents buffer)); stream >]
+
+ and lex_ident buffer = parser
+ | [< ' ('A' .. 'Z' | 'a' .. 'z' | '0' .. '9' as c); stream >] ->
+ Buffer.add_char buffer c;
+ lex_ident buffer stream
+ | [< stream=lex >] ->
+ match Buffer.contents buffer with
+ | "def" -> [< 'Token.Def; stream >]
+ | "extern" -> [< 'Token.Extern; stream >]
+ | "if" -> [< 'Token.If; stream >]
+ | "then" -> [< 'Token.Then; stream >]
+ | "else" -> [< 'Token.Else; stream >]
+ | "for" -> [< 'Token.For; stream >]
+ | "in" -> [< 'Token.In; stream >]
+ | "binary" -> [< 'Token.Binary; stream >]
+ | "unary" -> [< 'Token.Unary; stream >]
+ | id -> [< 'Token.Ident id; stream >]
+
+ and lex_comment = parser
+ | [< ' ('\n'); stream=lex >] -> stream
+ | [< 'c; e=lex_comment >] -> e
+ | [< >] -> [< >]
+
+ast.ml:
+ .. code-block:: ocaml
+
+ (*===----------------------------------------------------------------------===
+ * Abstract Syntax Tree (aka Parse Tree)
+ *===----------------------------------------------------------------------===*)
+
+ (* expr - Base type for all expression nodes. *)
+ type expr =
+ (* variant for numeric literals like "1.0". *)
+ | Number of float
+
+ (* variant for referencing a variable, like "a". *)
+ | Variable of string
+
+ (* variant for a unary operator. *)
+ | Unary of char * expr
+
+ (* variant for a binary operator. *)
+ | Binary of char * expr * expr
+
+ (* variant for function calls. *)
+ | Call of string * expr array
+
+ (* variant for if/then/else. *)
+ | If of expr * expr * expr
+
+ (* variant for for/in. *)
+ | For of string * expr * expr * expr option * expr
+
+ (* proto - This type represents the "prototype" for a function, which captures
+ * its name, and its argument names (thus implicitly the number of arguments the
+ * function takes). *)
+ type proto =
+ | Prototype of string * string array
+ | BinOpPrototype of string * string array * int
+
+ (* func - This type represents a function definition itself. *)
+ type func = Function of proto * expr
+
+parser.ml:
+ .. code-block:: ocaml
+
+ (*===---------------------------------------------------------------------===
+ * Parser
+ *===---------------------------------------------------------------------===*)
+
+ (* binop_precedence - This holds the precedence for each binary operator that is
+ * defined *)
+ let binop_precedence:(char, int) Hashtbl.t = Hashtbl.create 10
+
+ (* precedence - Get the precedence of the pending binary operator token. *)
+ let precedence c = try Hashtbl.find binop_precedence c with Not_found -> -1
+
+ (* primary
+ * ::= identifier
+ * ::= numberexpr
+ * ::= parenexpr
+ * ::= ifexpr
+ * ::= forexpr *)
+ let rec parse_primary = parser
+ (* numberexpr ::= number *)
+ | [< 'Token.Number n >] -> Ast.Number n
+
+ (* parenexpr ::= '(' expression ')' *)
+ | [< 'Token.Kwd '('; e=parse_expr; 'Token.Kwd ')' ?? "expected ')'" >] -> e
+
+ (* identifierexpr
+ * ::= identifier
+ * ::= identifier '(' argumentexpr ')' *)
+ | [< 'Token.Ident id; stream >] ->
+ let rec parse_args accumulator = parser
+ | [< e=parse_expr; stream >] ->
+ begin parser
+ | [< 'Token.Kwd ','; e=parse_args (e :: accumulator) >] -> e
+ | [< >] -> e :: accumulator
+ end stream
+ | [< >] -> accumulator
+ in
+ let rec parse_ident id = parser
+ (* Call. *)
+ | [< 'Token.Kwd '(';
+ args=parse_args [];
+ 'Token.Kwd ')' ?? "expected ')'">] ->
+ Ast.Call (id, Array.of_list (List.rev args))
+
+ (* Simple variable ref. *)
+ | [< >] -> Ast.Variable id
+ in
+ parse_ident id stream
+
+ (* ifexpr ::= 'if' expr 'then' expr 'else' expr *)
+ | [< 'Token.If; c=parse_expr;