Welcome to the "Implementing a language with LLVM" tutorial. This tutorial +runs through the implementation of a simple language, showing how fun and +easy it can be. This tutorial will get you up and started as well as help to +build a framework you can extend to other languages. The code in this tutorial +can also be used as a playground to hack on other LLVM specific things. +
+ ++The goal of this tutorial is to progressively unveil our language, describing +how it is built up over time. This will let us cover a fairly broad range of +language design and LLVM-specific usage issues, showing and explaining the code +for it all along the way, without overwhelming you with tons of details up +front.
+ +It is useful to point out ahead of time that this tutorial is really about +teaching compiler techniques and LLVM specifically, not about teaching +modern and sane software engineering principles. In practice, this means that +we'll take a number of shortcuts to simplify the exposition. For example, the +code leaks memory, uses global variables all over the place, doesn't use nice +design patterns like visitors, etc... but it +is very simple. If you dig in and use the code as a basis for future projects, +fixing these deficiencies shouldn't be hard.
+ +I've tried to put this tutorial together in a way that makes chapters easy to +skip over if you are already familiar with or are uninterested in the various +pieces. The structure of the tutorial is: +
+ +By the end of the tutorial, we'll have written a bit less than 700 lines of +non-comment, non-blank, lines of code. With this small amount of code, we'll +have built up a very reasonable compiler for a non-trivial language including +a hand-written lexer, parser, AST, as well as code generation support with a JIT +compiler. While other systems may have interesting "hello world" tutorials, +I think the breadth of this tutorial is a great testament to the strengths of +LLVM and why you should consider it if you're interested in language or compiler +design.
+ +A note about this tutorial: we expect you to extend the language and play +with it on your own. Take the code and go crazy hacking away at it, compilers +don't need to be scary creatures - it can be a lot of fun to play with +languages!
+ +This tutorial will be illustrated with a toy language that we'll call +"Kaleidoscope" (derived +from "meaning beautiful, form, and view"). +Kaleidoscope is a procedural language that allows you to define functions, use +conditionals, math, etc. Over the course of the tutorial, we'll extend +Kaleidoscope to support the if/then/else construct, a for loop, user defined +operators, JIT compilation with a simple command line interface, etc.
+ +Because we want to keep things simple, the only datatype in Kaleidoscope is a +64-bit floating point type (aka 'float' in O'Caml parlance). As such, all +values are implicitly double precision and the language doesn't require type +declarations. This gives the language a very nice and simple syntax. For +example, the following simple example computes Fibonacci numbers:
+ ++# Compute the x'th fibonacci number. +def fib(x) + if x < 3 then + 1 + else + fib(x-1)+fib(x-2) + +# This expression will compute the 40th number. +fib(40) ++
We also allow Kaleidoscope to call into standard library functions (the LLVM +JIT makes this completely trivial). This means that you can use the 'extern' +keyword to define a function before you use it (this is also useful for mutually +recursive functions). For example:
+ ++extern sin(arg); +extern cos(arg); +extern atan2(arg1 arg2); + +atan2(sin(.4), cos(42)) ++
A more interesting example is included in Chapter 6 where we write a little +Kaleidoscope application that displays +a Mandelbrot Set at various levels of magnification.
+ +Lets dive into the implementation of this language!
+ +When it comes to implementing a language, the first thing needed is +the ability to process a text file and recognize what it says. The traditional +way to do this is to use a "lexer" (aka 'scanner') +to break the input up into "tokens". Each token returned by the lexer includes +a token code and potentially some metadata (e.g. the numeric value of a number). +First, we define the possibilities: +
+ ++(* 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 ++
Each token returned by our lexer will be one of the token variant values. +An unknown character like '+' will be returned as Kwd '+'. If the +curr token is an identifier, the value will be Ident s. If the +current token is a numeric literal (like 1.0), the value will be +Number 1.0. +
+ +The actual implementation of the lexer is a collection of functions driven +by a function named lex. The lex function is called to +return the next token from standard input. We will use +Camlp4 +to simplify the tokenization of the standard input. Its definition starts +as:
+ +
+(*===----------------------------------------------------------------------===
+ * Lexer
+ *===----------------------------------------------------------------------===*)
+
+let rec lex = parser
+ (* Skip any whitespace. *)
+ | [< ' (' ' | '\n' | '\r' | '\t'); stream >] -> lex stream
+
++lex works by recursing over a char Stream.t to read +characters one at a time from the standard input. It eats them as it recognizes +them and stores them in in a token variant. The first thing that it +has to do is ignore whitespace between tokens. This is accomplished with the +recursive call above.
+ +The next thing lex needs to do is recognize identifiers and +specific keywords like "def". Kaleidoscope does this with this a pattern match +and a helper function.
+ +
+ (* 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
+
+...
+
+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 >]
+ | id -> [< 'Token.Ident id; stream >]
+
+
+ (* number: [0-9.]+ *)
+ | [< ' ('0' .. '9' as c); stream >] ->
+ let buffer = Buffer.create 1 in
+ Buffer.add_char buffer c;
+ lex_number buffer 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 >]
+
+This is all pretty straight-forward code for processing input. When reading +a numeric value from input, we use the ocaml float_of_string function +to convert it to a numeric value that we store in NumVal. Note that +this isn't doing sufficient error checking: it will raise Failure +if the string "1.23.45.67". Feel free to extend it :). Next we handle +comments: +
+ +
+ (* Comment until end of line. *)
+ | [< ' ('#'); stream >] ->
+ lex_comment stream
+
+...
+
+and lex_comment = parser
+ | [< ' ('\n'); stream=lex >] -> stream
+ | [< 'c; e=lex_comment >] -> e
+ | [< >] -> [< >]
+
+We handle comments by skipping to the end of the line and then return the +next token. Finally, if the input doesn't match one of the above cases, it is +either an operator character like '+' or the end of the file. These are handled +with this code:
+ ++ (* Otherwise, just return the character as its ascii value. *) + | [< 'c; stream >] -> + [< 'Token.Kwd c; lex stream >] + + (* end of stream. *) + | [< >] -> [< >] ++
With this, we have the complete lexer for the basic Kaleidoscope language +(the full code listing for the Lexer is +available in the next chapter of the +tutorial). Next we'll build a simple parser that +uses this to build an Abstract Syntax Tree. When we have that, we'll +include a driver so that you can use the lexer and parser together. +
+ +Next: Implementing a Parser and AST +
+ Welcome to Chapter 2 of the "Implementing a language +with LLVM in Objective Caml" tutorial. This chapter shows you how to use +the lexer, built in Chapter 1, to build a +full parser for our +Kaleidoscope language. Once we have a parser, we'll define and build an Abstract Syntax +Tree (AST).
+ +The parser we will build uses a combination of Recursive Descent +Parsing and Operator-Precedence +Parsing to parse the Kaleidoscope language (the latter for +binary expressions and the former for everything else). Before we get to +parsing though, lets talk about the output of the parser: the Abstract Syntax +Tree.
+ +The AST for a program captures its behavior in such a way that it is easy for +later stages of the compiler (e.g. code generation) to interpret. We basically +want one object for each construct in the language, and the AST should closely +model the language. In Kaleidoscope, we have expressions, a prototype, and a +function object. We'll start with expressions first:
+ ++(* expr - Base type for all expression nodes. *) +type expr = + (* variant for numeric literals like "1.0". *) + | Number of float ++
The code above shows the definition of the base ExprAST class and one +subclass which we use for numeric literals. The important thing to note about +this code is that the Number variant captures the numeric value of the +literal as an instance variable. This allows later phases of the compiler to +know what the stored numeric value is.
+ +Right now we only create the AST, so there are no useful functions on +them. It would be very easy to add a function to pretty print the code, +for example. Here are the other expression AST node definitions that we'll use +in the basic form of the Kaleidoscope language: +
+ ++ (* variant for referencing a variable, like "a". *) + | Variable of string + + (* variant for a binary operator. *) + | Binary of char * expr * expr + + (* variant for function calls. *) + | Call of string * expr array ++
This is all (intentionally) rather straight-forward: variables capture the +variable name, binary operators capture their opcode (e.g. '+'), and calls +capture a function name as well as a list of any argument expressions. One thing +that is nice about our AST is that it captures the language features without +talking about the syntax of the language. Note that there is no discussion about +precedence of binary operators, lexical structure, etc.
+ +For our basic language, these are all of the expression nodes we'll define. +Because it doesn't have conditional control flow, it isn't Turing-complete; +we'll fix that in a later installment. The two things we need next are a way +to talk about the interface to a function, and a way to talk about functions +themselves:
+ ++(* 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 + +(* func - This type represents a function definition itself. *) +type func = Function of proto * expr ++
In Kaleidoscope, functions are typed with just a count of their arguments. +Since all values are double precision floating point, the type of each argument +doesn't need to be stored anywhere. In a more aggressive and realistic +language, the "expr" variants would probably have a type field.
+ +With this scaffolding, we can now talk about parsing expressions and function +bodies in Kaleidoscope.
+ +Now that we have an AST to build, we need to define the parser code to build +it. The idea here is that we want to parse something like "x+y" (which is +returned as three tokens by the lexer) into an AST that could be generated with +calls like this:
+ +
+ let x = Variable "x" in
+ let y = Variable "y" in
+ let result = Binary ('+', x, y) in
+ ...
+
++The error handling routines make use of the builtin Stream.Failure and +Stream.Errors. Stream.Failure is raised when the parser is +unable to find any matching token in the first position of a pattern. +Stream.Error is raised when the first token matches, but the rest do +not. The error recovery in our parser will not be the best and is not +particular user-friendly, but it will be enough for our tutorial. These +exceptions make it easier to handle errors in routines that have various return +types.
+ +With these basic types and exceptions, we can implement the first +piece of our grammar: numeric literals.
+ +We start with numeric literals, because they are the simplest to process. +For each production in our grammar, we'll define a function which parses that +production. We call this class of expressions "primary" expressions, for +reasons that will become more clear +later in the tutorial. In order to parse an arbitrary primary expression, +we need to determine what sort of expression it is. For numeric literals, we +have:
+ ++(* primary + * ::= identifier + * ::= numberexpr + * ::= parenexpr *) +parse_primary = parser + (* numberexpr ::= number *) + | [< 'Token.Number n >] -> Ast.Number n ++
This routine is very simple: it expects to be called when the current token +is a Token.Number token. It takes the current number value, creates +a Ast.Number node, advances the lexer to the next token, and finally +returns.
+ +There are some interesting aspects to this. The most important one is that +this routine eats all of the tokens that correspond to the production and +returns the lexer buffer with the next token (which is not part of the grammar +production) ready to go. This is a fairly standard way to go for recursive +descent parsers. For a better example, the parenthesis operator is defined like +this:
+ +
+ (* parenexpr ::= '(' expression ')' *)
+ | [< 'Token.Kwd '('; e=parse_expr; 'Token.Kwd ')' ?? "expected ')'" >] -> e
+
+This function illustrates a number of interesting things about the +parser:
+ ++1) It shows how we use the Stream.Error exception. When called, this +function expects that the current token is a '(' token, but after parsing the +subexpression, it is possible that there is no ')' waiting. For example, if +the user types in "(4 x" instead of "(4)", the parser should emit an error. +Because errors can occur, the parser needs a way to indicate that they +happened. In our parser, we use the camlp4 shortcut syntax token ?? "parse +error", where if the token before the ?? does not match, then +Stream.Error "parse error" will be raised.
+ +2) Another interesting aspect of this function is that it uses recursion by +calling parse_primary (we will soon see that parse_primary can +call parse_primary). This is powerful because it allows us to handle +recursive grammars, and keeps each production very simple. Note that +parentheses do not cause construction of AST nodes themselves. While we could +do it this way, the most important role of parentheses are to guide the parser +and provide grouping. Once the parser constructs the AST, parentheses are not +needed.
+ +The next simple production is for handling variable references and function +calls:
+ +
+ (* 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
+
+This routine follows the same style as the other routines. (It expects to be +called if the current token is a Token.Ident token). It also has +recursion and error handling. One interesting aspect of this is that it uses +look-ahead to determine if the current identifier is a stand alone +variable reference or if it is a function call expression. It handles this by +checking to see if the token after the identifier is a '(' token, constructing +either a Ast.Variable or Ast.Call node as appropriate. +
+ +We finish up by raising an exception if we received a token we didn't +expect:
+ ++ | [< >] -> raise (Stream.Error "unknown token when expecting an expression.") ++
Now that basic expressions are handled, we need to handle binary expressions. +They are a bit more complex.
+ +Binary expressions are significantly harder to parse because they are often +ambiguous. For example, when given the string "x+y*z", the parser can choose +to parse it as either "(x+y)*z" or "x+(y*z)". With common definitions from +mathematics, we expect the later parse, because "*" (multiplication) has +higher precedence than "+" (addition).
+ +There are many ways to handle this, but an elegant and efficient way is to +use Operator-Precedence +Parsing. This parsing technique uses the precedence of binary operators to +guide recursion. To start with, we need a table of precedences:
+ ++(* 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 + +... + +let main () = + (* Install standard binary operators. + * 1 is the lowest precedence. *) + Hashtbl.add Parser.binop_precedence '<' 10; + Hashtbl.add Parser.binop_precedence '+' 20; + Hashtbl.add Parser.binop_precedence '-' 20; + Hashtbl.add Parser.binop_precedence '*' 40; (* highest. *) + ... ++
For the basic form of Kaleidoscope, we will only support 4 binary operators +(this can obviously be extended by you, our brave and intrepid reader). The +precedence function returns the precedence for the current token, +or -1 if the token is not a binary operator. Having a Hashtbl.t makes +it easy to add new operators and makes it clear that the algorithm doesn't +depend on the specific operators involved, but it would be easy enough to +eliminate the Hashtbl.t and do the comparisons in the +precedence function. (Or just use a fixed-size array).
+ +With the helper above defined, we can now start parsing binary expressions. +The basic idea of operator precedence parsing is to break down an expression +with potentially ambiguous binary operators into pieces. Consider ,for example, +the expression "a+b+(c+d)*e*f+g". Operator precedence parsing considers this +as a stream of primary expressions separated by binary operators. As such, +it will first parse the leading primary expression "a", then it will see the +pairs [+, b] [+, (c+d)] [*, e] [*, f] and [+, g]. Note that because parentheses +are primary expressions, the binary expression parser doesn't need to worry +about nested subexpressions like (c+d) at all. +
+ ++To start, an expression is a primary expression potentially followed by a +sequence of [binop,primaryexpr] pairs:
+ ++(* expression + * ::= primary binoprhs *) +and parse_expr = parser + | [< lhs=parse_primary; stream >] -> parse_bin_rhs 0 lhs stream ++
parse_bin_rhs is the function that parses the sequence of pairs for +us. It takes a precedence and a pointer to an expression for the part that has been +parsed so far. Note that "x" is a perfectly valid expression: As such, "binoprhs" is +allowed to be empty, in which case it returns the expression that is passed into +it. In our example above, the code passes the expression for "a" into +ParseBinOpRHS and the current token is "+".
+ +The precedence value passed into parse_bin_rhs indicates the +minimal operator precedence that the function is allowed to eat. For +example, if the current pair stream is [+, x] and parse_bin_rhs is +passed in a precedence of 40, it will not consume any tokens (because the +precedence of '+' is only 20). With this in mind, parse_bin_rhs starts +with:
+ +
+(* binoprhs
+ * ::= ('+' primary)* *)
+and parse_bin_rhs expr_prec lhs stream =
+ match Stream.peek stream with
+ (* If this is a binop, find its precedence. *)
+ | Some (Token.Kwd c) when Hashtbl.mem binop_precedence c ->
+ let token_prec = precedence c in
+
+ (* If this is a binop that binds at least as tightly as the current binop,
+ * consume it, otherwise we are done. *)
+ if token_prec < expr_prec then lhs else begin
+
+This code gets the precedence of the current token and checks to see if if is +too low. Because we defined invalid tokens to have a precedence of -1, this +check implicitly knows that the pair-stream ends when the token stream runs out +of binary operators. If this check succeeds, we know that the token is a binary +operator and that it will be included in this expression:
+ ++ (* Eat the binop. *) + Stream.junk stream; + + (* Okay, we know this is a binop. *) + let rhs = + match Stream.peek stream with + | Some (Token.Kwd c2) -> ++
As such, this code eats (and remembers) the binary operator and then parses +the primary expression that follows. This builds up the whole pair, the first of +which is [+, b] for the running example.
+ +Now that we parsed the left-hand side of an expression and one pair of the +RHS sequence, we have to decide which way the expression associates. In +particular, we could have "(a+b) binop unparsed" or "a + (b binop unparsed)". +To determine this, we look ahead at "binop" to determine its precedence and +compare it to BinOp's precedence (which is '+' in this case):
+ ++ (* If BinOp binds less tightly with rhs than the operator after + * rhs, let the pending operator take rhs as its lhs. *) + let next_prec = precedence c2 in + if token_prec < next_prec ++
If the precedence of the binop to the right of "RHS" is lower or equal to the +precedence of our current operator, then we know that the parentheses associate +as "(a+b) binop ...". In our example, the current operator is "+" and the next +operator is "+", we know that they have the same precedence. In this case we'll +create the AST node for "a+b", and then continue parsing:
+ ++ ... if body omitted ... + in + + (* Merge lhs/rhs. *) + let lhs = Ast.Binary (c, lhs, rhs) in + parse_bin_rhs expr_prec lhs stream + end ++
In our example above, this will turn "a+b+" into "(a+b)" and execute the next +iteration of the loop, with "+" as the current token. The code above will eat, +remember, and parse "(c+d)" as the primary expression, which makes the +current pair equal to [+, (c+d)]. It will then evaluate the 'if' conditional above with +"*" as the binop to the right of the primary. In this case, the precedence of "*" is +higher than the precedence of "+" so the if condition will be entered.
+ +The critical question left here is "how can the if condition parse the right +hand side in full"? In particular, to build the AST correctly for our example, +it needs to get all of "(c+d)*e*f" as the RHS expression variable. The code to +do this is surprisingly simple (code from the above two blocks duplicated for +context):
+ ++ match Stream.peek stream with + | Some (Token.Kwd c2) -> + (* If BinOp binds less tightly with rhs than the operator after + * rhs, let the pending operator take rhs as its lhs. *) + if token_prec < precedence c2 + then parse_bin_rhs (token_prec + 1) rhs stream + else rhs + | _ -> rhs + in + + (* Merge lhs/rhs. *) + let lhs = Ast.Binary (c, lhs, rhs) in + parse_bin_rhs expr_prec lhs stream + end ++
At this point, we know that the binary operator to the RHS of our primary +has higher precedence than the binop we are currently parsing. As such, we know +that any sequence of pairs whose operators are all higher precedence than "+" +should be parsed together and returned as "RHS". To do this, we recursively +invoke the parse_bin_rhs function specifying "token_prec+1" as the +minimum precedence required for it to continue. In our example above, this will +cause it to return the AST node for "(c+d)*e*f" as RHS, which is then set as the +RHS of the '+' expression.
+ +Finally, on the next iteration of the while loop, the "+g" piece is parsed +and added to the AST. With this little bit of code (14 non-trivial lines), we +correctly handle fully general binary expression parsing in a very elegant way. +This was a whirlwind tour of this code, and it is somewhat subtle. I recommend +running through it with a few tough examples to see how it works. +
+ +This wraps up handling of expressions. At this point, we can point the +parser at an arbitrary token stream and build an expression from it, stopping +at the first token that is not part of the expression. Next up we need to +handle function definitions, etc.
+ ++The next thing missing is handling of function prototypes. In Kaleidoscope, +these are used both for 'extern' function declarations as well as function body +definitions. The code to do this is straight-forward and not very interesting +(once you've survived expressions): +
+ +
+(* prototype
+ * ::= id '(' id* ')' *)
+let parse_prototype =
+ let rec parse_args accumulator = parser
+ | [< 'Token.Ident id; e=parse_args (id::accumulator) >] -> e
+ | [< >] -> accumulator
+ 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))
+
+ | [< >] ->
+ raise (Stream.Error "expected function name in prototype")
+
+Given this, a function definition is very simple, just a prototype plus +an expression to implement the body:
+ ++(* definition ::= 'def' prototype expression *) +let parse_definition = parser + | [< 'Token.Def; p=parse_prototype; e=parse_expr >] -> + Ast.Function (p, e) ++
In addition, we support 'extern' to declare functions like 'sin' and 'cos' as +well as to support forward declaration of user functions. These 'extern's are just +prototypes with no body:
+ ++(* external ::= 'extern' prototype *) +let parse_extern = parser + | [< 'Token.Extern; e=parse_prototype >] -> e ++
Finally, we'll also let the user type in arbitrary top-level expressions and +evaluate them on the fly. We will handle this by defining anonymous nullary +(zero argument) functions for them:
+ +
+(* toplevelexpr ::= expression *)
+let parse_toplevel = parser
+ | [< e=parse_expr >] ->
+ (* Make an anonymous proto. *)
+ Ast.Function (Ast.Prototype ("", [||]), e)
+
+Now that we have all the pieces, let's build a little driver that will let us +actually execute this code we've built!
+ +The driver for this simply invokes all of the parsing pieces with a top-level +dispatch loop. There isn't much interesting here, so I'll just include the +top-level loop. See below for full code in the "Top-Level +Parsing" section.
+ ++(* top ::= definition | external | expression | ';' *) +let rec main_loop stream = + match Stream.peek stream with + | None -> () + + (* ignore top-level semicolons. *) + | Some (Token.Kwd ';') -> + Stream.junk stream; + main_loop stream + + | Some token -> + begin + try match token with + | Token.Def -> + ignore(Parser.parse_definition stream); + print_endline "parsed a function definition."; + | Token.Extern -> + ignore(Parser.parse_extern stream); + print_endline "parsed an extern."; + | _ -> + (* Evaluate a top-level expression into an anonymous function. *) + ignore(Parser.parse_toplevel stream); + print_endline "parsed a top-level expr"; + with Stream.Error s -> + (* Skip token for error recovery. *) + Stream.junk stream; + print_endline s; + end; + print_string "ready> "; flush stdout; + main_loop stream ++
The most interesting part of this is that we ignore top-level semicolons. +Why is this, you ask? The basic reason is that if you type "4 + 5" at the +command line, the parser doesn't know whether that is the end of what you will type +or not. For example, on the next line you could type "def foo..." in which case +4+5 is the end of a top-level expression. Alternatively you could type "* 6", +which would continue the expression. Having top-level semicolons allows you to +type "4+5;", and the parser will know you are done.
+ +With just under 300 lines of commented code (240 lines of non-comment, +non-blank code), we fully defined our minimal language, including a lexer, +parser, and AST builder. With this done, the executable will validate +Kaleidoscope code and tell us if it is grammatically invalid. For +example, here is a sample interaction:
+ ++$ ./toy.byte +ready> def foo(x y) x+foo(y, 4.0); +Parsed a function definition. +ready> def foo(x y) x+y y; +Parsed a function definition. +Parsed a top-level expr +ready> def foo(x y) x+y ); +Parsed a function definition. +Error: unknown token when expecting an expression +ready> extern sin(a); +ready> Parsed an extern +ready> ^D +$ ++
There is a lot of room for extension here. You can define new AST nodes, +extend the language in many ways, etc. In the +next installment, we will describe how to generate LLVM Intermediate +Representation (IR) from the AST.
+ ++Here is the complete code listing for this and the previous chapter. +Note that it is fully self-contained: you don't need LLVM or any external +libraries at all for this. (Besides the ocaml standard libraries, of +course.) To build this, just compile with:
+ ++# Compile +ocamlbuild toy.byte +# Run +./toy ++
Here is the code:
+ +
+<{lexer,parser}.ml>: use_camlp4, pp(camlp4of)
+
++(*===----------------------------------------------------------------------=== + * 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 ++
+(*===----------------------------------------------------------------------===
+ * 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 >]
+ | id -> [< 'Token.Ident id; stream >]
+
+and lex_comment = parser
+ | [< ' ('\n'); stream=lex >] -> stream
+ | [< 'c; e=lex_comment >] -> e
+ | [< >] -> [< >]
+
++(*===----------------------------------------------------------------------=== + * 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 binary operator. *) + | Binary of char * expr * expr + + (* variant for function calls. *) + | Call of string * expr array + +(* 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 + +(* func - This type represents a function definition itself. *) +type func = Function of proto * expr ++
+(*===---------------------------------------------------------------------===
+ * 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 *)
+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
+
+ | [< >] -> raise (Stream.Error "unknown token when expecting an expression.")
+
+(* binoprhs
+ * ::= ('+' primary)* *)
+and parse_bin_rhs expr_prec lhs stream =
+ match Stream.peek stream with
+ (* If this is a binop, find its precedence. *)
+ | Some (Token.Kwd c) when Hashtbl.mem binop_precedence c ->
+ let token_prec = precedence c in
+
+ (* If this is a binop that binds at least as tightly as the current binop,
+ * consume it, otherwise we are done. *)
+ if token_prec < expr_prec then lhs else begin
+ (* Eat the binop. *)
+ Stream.junk stream;
+
+ (* Parse the primary expression after the binary operator. *)
+ let rhs = parse_primary stream in
+
+ (* Okay, we know this is a binop. *)
+ let rhs =
+ match Stream.peek stream with
+ | Some (Token.Kwd c2) ->
+ (* If BinOp binds less tightly with rhs than the operator after
+ * rhs, let the pending operator take rhs as its lhs. *)
+ let next_prec = precedence c2 in
+ if token_prec < next_prec
+ then parse_bin_rhs (token_prec + 1) rhs stream
+ else rhs
+ | _ -> rhs
+ in
+
+ (* Merge lhs/rhs. *)
+ let lhs = Ast.Binary (c, lhs, rhs) in
+ parse_bin_rhs expr_prec lhs stream
+ end
+ | _ -> lhs
+
+(* expression
+ * ::= primary binoprhs *)
+and parse_expr = parser
+ | [< lhs=parse_primary; stream >] -> parse_bin_rhs 0 lhs stream
+
+(* prototype
+ * ::= id '(' id* ')' *)
+let parse_prototype =
+ let rec parse_args accumulator = parser
+ | [< 'Token.Ident id; e=parse_args (id::accumulator) >] -> e
+ | [< >] -> accumulator
+ 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))
+
+ | [< >] ->
+ raise (Stream.Error "expected function name in prototype")
+
+(* definition ::= 'def' prototype expression *)
+let parse_definition = parser
+ | [< 'Token.Def; p=parse_prototype; e=parse_expr >] ->
+ Ast.Function (p, e)
+
+(* toplevelexpr ::= expression *)
+let parse_toplevel = parser
+ | [< e=parse_expr >] ->
+ (* Make an anonymous proto. *)
+ Ast.Function (Ast.Prototype ("", [||]), e)
+
+(* external ::= 'extern' prototype *)
+let parse_extern = parser
+ | [< 'Token.Extern; e=parse_prototype >] -> e
+
++(*===----------------------------------------------------------------------=== + * Top-Level parsing and JIT Driver + *===----------------------------------------------------------------------===*) + +(* top ::= definition | external | expression | ';' *) +let rec main_loop stream = + match Stream.peek stream with + | None -> () + + (* ignore top-level semicolons. *) + | Some (Token.Kwd ';') -> + Stream.junk stream; + main_loop stream + + | Some token -> + begin + try match token with + | Token.Def -> + ignore(Parser.parse_definition stream); + print_endline "parsed a function definition."; + | Token.Extern -> + ignore(Parser.parse_extern stream); + print_endline "parsed an extern."; + | _ -> + (* Evaluate a top-level expression into an anonymous function. *) + ignore(Parser.parse_toplevel stream); + print_endline "parsed a top-level expr"; + with Stream.Error s -> + (* Skip token for error recovery. *) + Stream.junk stream; + print_endline s; + end; + print_string "ready> "; flush stdout; + main_loop stream ++
+(*===----------------------------------------------------------------------=== + * Main driver code. + *===----------------------------------------------------------------------===*) + +let main () = + (* Install standard binary operators. + * 1 is the lowest precedence. *) + Hashtbl.add Parser.binop_precedence '<' 10; + Hashtbl.add Parser.binop_precedence '+' 20; + Hashtbl.add Parser.binop_precedence '-' 20; + Hashtbl.add Parser.binop_precedence '*' 40; (* highest. *) + + (* Prime the first token. *) + print_string "ready> "; flush stdout; + let stream = Lexer.lex (Stream.of_channel stdin) in + + (* Run the main "interpreter loop" now. *) + Toplevel.main_loop stream; +;; + +main () ++
+