Lexer and parser generators (ocamllex, ocamlyacc)

# Chapter 12 Lexer and parser generators (ocamllex, ocamlyacc)

- Overview of `ocamllex`
- Syntax of lexer definitions
- Overview of `ocamlyacc`
- Syntax of grammar definitions
- Options
- A complete example
- Common errors

This chapter describes two program generators: `ocamllex`, that produces a lexical analyzer from a set of regular expressions with associated semantic actions, and `ocamlyacc`, that produces a parser from a grammar with associated semantic actions.

These program generators are very close to the well-known `lex` and `yacc` commands that can be found in most C programming environments. This chapter assumes a working knowledge of `lex` and `yacc`: while it describes the input syntax for `ocamllex` and `ocamlyacc` and the main differences with `lex` and `yacc`, it does not explain the basics of writing a lexer or parser description in `lex` and `yacc`. Readers unfamiliar with `lex` and `yacc` are referred to “Compilers: principles, techniques, and tools” by Aho, Sethi and Ullman (Addison-Wesley, 1986), or “Lex & Yacc”, by Levine, Mason and Brown (O’Reilly, 1992).

## 12.1 Overview of `ocamllex`

The `ocamllex` command produces a lexical analyzer from a set of regular expressions with attached semantic actions, in the style of `lex`. Assuming the input file is lexer`.mll`, executing

            ocamllex lexer.mll

produces Caml code for a lexical analyzer in file lexer`.ml`. This file defines one lexing function per entry point in the lexer definition. These functions have the same names as the entry points. Lexing functions take as argument a lexer buffer, and return the semantic attribute of the corresponding entry point.

Lexer buffers are an abstract data type implemented in the standard library module `Lexing`. The functions `Lexing.from_channel`, `Lexing.from_string` and `Lexing.from_function` create lexer buffers that read from an input channel, a character string, or any reading function, respectively. (See the description of module `Lexing` in chapter 20.)

When used in conjunction with a parser generated by `ocamlyacc`, the semantic actions compute a value belonging to the type `token` defined by the generated parsing module. (See the description of `ocamlyacc` below.)

### 12.1.1 Options

The following command-line options are recognized by `ocamllex`.

`-ml`
  Output code that does not use OCaml’s built-in automata interpreter. Instead, the automaton is encoded by Caml functions. This option mainly is useful for debugging `ocamllex`, using it for production lexers is not recommended.
`-o` output-file
  Specify the name of the output file produced by `ocamllex`. The default is the input file name with its extension replaced by `.ml`.
`-q`
  Quiet mode. `ocamllex` normally outputs informational messages to standard output. They are suppressed if option `-q` is used.
`-v` or `-version`
  Print version string and exit.
`-vnum`
  Print short version number and exit.
`-help` or `--help`
  Display a short usage summary and exit.

## 12.2 Syntax of lexer definitions

The format of lexer definitions is as follows:

    { header }
    let ident = regexp …
    rule entrypoint [arg1… argn] =
      parse regexp { action }
          | …
          | regexp { action }
    and entrypoint [arg1… argn] =
      parse …
    and …
    { trailer }

Comments are delimited by `(*` and `*)`, as in Caml. The `parse` keyword, can be replaced by the `shortest` keyword, with the semantic consequences explained below.

### 12.2.1 Header and trailer

The header and trailer sections are arbitrary Caml text enclosed in curly braces. Either or both can be omitted. If present, the header text is copied as is at the beginning of the output file and the trailer text at the end. Typically, the header section contains the `open` directives required by the actions, and possibly some auxiliary functions used in the actions.

### 12.2.2 Naming regular expressions

Between the header and the entry points, one can give names to frequently-occurring regular expressions. This is written `let` ident `=` regexp. In regular expressions that follow this declaration, the identifier ident can be used as shorthand for regexp.

### 12.2.3 Entry points

The names of the entry points must be valid identifiers for Caml values (starting with a lowercase letter). Similarily, the arguments `arg1… argn` must be valid identifiers for Caml. Each entry point becomes a Caml function that takes n+1 arguments, the extra implicit last argument being of type `Lexing.lexbuf`. Characters are read from the `Lexing.lexbuf` argument and matched against the regular expressions provided in the rule, until a prefix of the input matches one of the rule. The corresponding action is then evaluated and returned as the result of the function.

If several regular expressions match a prefix of the input, the “longest match” rule applies: the regular expression that matches the longest prefix of the input is selected. In case of tie, the regular expression that occurs earlier in the rule is selected.

However, if lexer rules are introduced with the `shortest` keyword in place of the `parse` keyword, then the “shortest match” rule applies: the shortest prefix of the input is selected. In case of tie, the regular expression that occurs earlier in the rule is still selected. This feature is not intended for use in ordinary lexical analyzers, it may facilitate the use of `ocamllex` as a simple text processing tool.

### 12.2.4 Regular expressions

The regular expressions are in the style of `lex`, with a more Caml-like syntax.

regexp | ::= | …

`'` regular-char ∣ escape-sequence `'`
  A character constant, with the same syntax as OCaml character constants. Match the denoted character.
`_`
  (Underscore.) Match any character.
`eof`
  Match the end of the lexer input.
  Note: On some systems, with interactive input, an end-of-file may be followed by more characters. However, `ocamllex` will not correctly handle regular expressions that contain `eof` followed by something else.
`"` { string-character } `"`
  A string constant, with the same syntax as OCaml string constants. Match the corresponding sequence of characters.
`[` character-set `]`
  Match any single character belonging to the given character set. Valid character sets are: single character constants `'` c `'`; ranges of characters `'` c1 `'` `-` `'` c2 `'` (all characters between c1 and c2, inclusive); and the union of two or more character sets, denoted by concatenation.
`[` `^` character-set `]`
  Match any single character not belonging to the given character set.
regexp1 `#` regexp2
  (Difference of character sets). Regular expressions regexp1 and regexp2 must be character sets defined with `[`… `]` (or a a single character expression or underscore `_`). Match the difference of the two specified character sets.
regexp `*`
  (Repetition.) Match the concatenation of zero or more strings that match regexp.
regexp `+`
  (Strict repetition.) Match the concatenation of one or more strings that match regexp.
regexp `?`
  (Option.) Match either the empty string, or a string matching regexp.
regexp1 `|` regexp2
  (Alternative.) Match any string that matches either regexp1 or regexp2
regexp1 regexp2
  (Concatenation.) Match the concatenation of two strings, the first matching regexp1, the second matching regexp2.
`(` regexp `)`
  Match the same strings as regexp.
ident
  Reference the regular expression bound to ident by an earlier `let` ident `=` regexp definition.
regexp `as` ident
  Bind the substring matched by regexp to identifier ident.

Concerning the precedences of operators, `#` has the highest precedence, followed by `*`, `+` and `?`, then concatenation, then `|` (alternation), then `as`.

### 12.2.5 Actions

The actions are arbitrary Caml expressions. They are evaluated in a context where the identifiers defined by using the `as` construct are bound to subparts of the matched string. Additionally, `lexbuf` is bound to the current lexer buffer. Some typical uses for `lexbuf`, in conjunction with the operations on lexer buffers provided by the `Lexing` standard library module, are listed below.

`Lexing.lexeme lexbuf`
  Return the matched string.
`Lexing.lexeme_char lexbuf` n
  Return the nth character in the matched string. The first character corresponds to n = 0.
`Lexing.lexeme_start lexbuf`
  Return the absolute position in the input text of the beginning of the matched string (i.e. the offset of the first character of the matched string). The first character read from the input text has offset 0.
`Lexing.lexeme_end lexbuf`
  Return the absolute position in the input text of the end of the matched string (i.e. the offset of the first character after the matched string). The first character read from the input text has offset 0.
entrypoint [exp1… expn] `lexbuf`
  (Where entrypoint is the name of another entry point in the same lexer definition.) Recursively call the lexer on the given entry point. Notice that `lexbuf` is the last argument. Useful for lexing nested comments, for example.

### 12.2.6 Variables in regular expressions

The `as` construct is similar to “groups” as provided by numerous regular expression packages. The type of these variables can be `string`, `char`, `string option` or `char option`.

We first consider the case of linear patterns, that is the case when all `as` bound variables are distinct. In regexp `as` ident, the type of ident normally is `string` (or `string option`) except when regexp is a character constant, an underscore, a string constant of length one, a character set specification, or an alternation of those. Then, the type of ident is `char` (or `char option`). Option types are introduced when overall rule matching does not imply matching of the bound sub-pattern. This is in particular the case of `(` regexp `as` ident `)` `?` and of regexp1 `|` `(` regexp2 `as` ident `)`.

There is no linearity restriction over `as` bound variables. When a variable is bound more than once, the previous rules are to be extended as follows:

- A variable is a `char` variable when all its occurrences bind `char` occurrences in the previous sense.
- A variable is an `option` variable when the overall expression can be matched without binding this variable.

For instance, in `('a' as x) | ( 'a' (_ as x) )` the variable `x` is of type `char`, whereas in `("ab" as x) | ( 'a' (_ as x) ? )` the variable `x` is of type `string option`.

In some cases, a sucessful match may not yield a unique set of bindings. For instance the matching of `aba` by the regular expression `(('a'|"ab") as x) (("ba"|'a') as y)` may result in binding either `x` to `"ab"` and `y` to `"a"`, or `x` to `"a"` and `y` to `"ba"`. The automata produced `ocamllex` on such ambiguous regular expressions will select one of the possible resulting sets of bindings. The selected set of bindings is purposely left unspecified.

### 12.2.7 Reserved identifiers

All identifiers starting with `__ocaml_lex` are reserved for use by `ocamllex`; do not use any such identifier in your programs.

## 12.3 Overview of `ocamlyacc`

The `ocamlyacc` command produces a parser from a context-free grammar specification with attached semantic actions, in the style of `yacc`. Assuming the input file is grammar`.mly`, executing

            ocamlyacc options grammar.mly

produces Caml code for a parser in the file grammar`.ml`, and its interface in file grammar`.mli`.

The generated module defines one parsing function per entry point in the grammar. These functions have the same names as the entry points. Parsing functions take as arguments a lexical analyzer (a function from lexer buffers to tokens) and a lexer buffer, and return the semantic attribute of the corresponding entry point. Lexical analyzer functions are usually generated from a lexer specification by the `ocamllex` program. Lexer buffers are an abstract data type implemented in the standard library module `Lexing`. Tokens are values from the concrete type `token`, defined in the interface file grammar`.mli` produced by `ocamlyacc`.

## 12.4 Syntax of grammar definitions

Grammar definitions have the following format:

    %{
      header
    %}
      declarations
    %%
      rules
    %%
      trailer

Comments are enclosed between `/*` and `*/` (as in C) in the “declarations” and “rules” sections, and between `(*` and `*)` (as in Caml) in the “header” and “trailer” sections.

### 12.4.1 Header and trailer

The header and the trailer sections are Caml code that is copied as is into file grammar`.ml`. Both sections are optional. The header goes at the beginning of the output file; it usually contains `open` directives and auxiliary functions required by the semantic actions of the rules. The trailer goes at the end of the output file.

### 12.4.2 Declarations

Declarations are given one per line. They all start with a `%` sign.

`%token` constr … constr
  Declare the given symbols constr … constr as tokens (terminal symbols). These symbols are added as constant constructors for the `token` concrete type.
`%token` `<` typexpr `>` constr … constr
  Declare the given symbols constr … constr as tokens with an attached attribute of the given type. These symbols are added as constructors with arguments of the given type for the `token` concrete type. The typexpr part is an arbitrary Caml type expression, except that all type constructor names must be fully qualified (e.g. `Modname.typename`) for all types except standard built-in types, even if the proper `open` directives (e.g. `open Modname`) were given in the header section. That’s because the header is copied only to the `.ml` output file, but not to the `.mli` output file, while the typexpr part of a `%token` declaration is copied to both.
`%start` symbol … symbol
  Declare the given symbols as entry points for the grammar. For each entry point, a parsing function with the same name is defined in the output module. Non-terminals that are not declared as entry points have no such parsing function. Start symbols must be given a type with the `%type` directive below.
`%type` `<` typexpr `>` symbol … symbol
  Specify the type of the semantic attributes for the given symbols. This is mandatory for start symbols only. Other nonterminal symbols need not be given types by hand: these types will be inferred when running the output files through the OCaml compiler (unless the `-s` option is in effect). The typexpr part is an arbitrary Caml type expression, except that all type constructor names must be fully qualified, as explained above for `%token`.
`%left` symbol … symbol
`%right` symbol … symbol
`%nonassoc` symbol … symbol

  Associate precedences and associativities to the given symbols. All symbols on the same line are given the same precedence. They have higher precedence than symbols declared before in a `%left`, `%right` or `%nonassoc` line. They have lower precedence than symbols declared after in a `%left`, `%right` or `%nonassoc` line. The symbols are declared to associate to the left (`%left`), to the right (`%right`), or to be non-associative (`%nonassoc`). The symbols are usually tokens. They can also be dummy nonterminals, for use with the `%prec` directive inside the rules.

  The precedence declarations are used in the following way to resolve reduce/reduce and shift/reduce conflicts:

  - Tokens and rules have precedences. By default, the precedence of a rule is the precedence of its rightmost terminal. You can override this default by using the `%prec` directive in the rule.
  - A reduce/reduce conflict is resolved in favor of the first rule (in the order given by the source file), and `ocamlyacc` outputs a warning.
  - A shift/reduce conflict is resolved by comparing the precedence of the rule to be reduced with the precedence of the token to be shifted. If the precedence of the rule is higher, then the rule will be reduced; if the precedence of the token is higher, then the token will be shifted.
  - A shift/reduce conflict between a rule and a token with the same precedence will be resolved using the associativity: if the token is left-associative, then the parser will reduce; if the token is right-associative, then the parser will shift. If the token is non-associative, then the parser will declare a syntax error.
  - When a shift/reduce conflict cannot be resolved using the above method, then `ocamlyacc` will output a warning and the parser will always shift.

### 12.4.3 Rules

The syntax for rules is as usual:

    nonterminal :
        symbol … symbol { semantic-action }
      | …
      | symbol … symbol { semantic-action }
    ;

Rules can also contain the `%prec` symbol directive in the right-hand side part, to override the default precedence and associativity of the rule with the precedence and associativity of the given symbol.

Semantic actions are arbitrary Caml expressions, that are evaluated to produce the semantic attribute attached to the defined nonterminal. The semantic actions can access the semantic attributes of the symbols in the right-hand side of the rule with the `$` notation: `$1` is the attribute for the first (leftmost) symbol, `$2` is the attribute for the second symbol, etc.

The rules may contain the special symbol `error` to indicate resynchronization points, as in `yacc`.

Actions occurring in the middle of rules are not supported.

Nonterminal symbols are like regular Caml symbols, except that they cannot end with `’` (single quote).

### 12.4.4 Error handling

Error recovery is supported as follows: when the parser reaches an error state (no grammar rules can apply), it calls a function named `parse_error` with the string `"syntax error"` as argument. The default `parse_error` function does nothing and returns, thus initiating error recovery (see below). The user can define a customized `parse_error` function in the header section of the grammar file.

The parser also enters error recovery mode if one of the grammar actions raises the `Parsing.Parse_error` exception.

In error recovery mode, the parser discards states from the stack until it reaches a place where the error token can be shifted. It then discards tokens from the input until it finds three successive tokens that can be accepted, and starts processing with the first of these. If no state can be uncovered where the error token can be shifted, then the parser aborts by raising the `Parsing.Parse_error` exception.

Refer to documentation on `yacc` for more details and guidance in how to use error recovery.

## 12.5 Options

The `ocamlyacc` command recognizes the following options:

`-b`prefix
  Name the output files prefix`.ml`, prefix`.mli`, prefix`.output`, instead of the default naming convention.
`-q`
  This option has no effect.
`-v`
  Generate a description of the parsing tables and a report on conflicts resulting from ambiguities in the grammar. The description is put in file grammar`.output`.
`-version`
  Print version string and exit.
`-vnum`
  Print short version number and exit.
`-`
  Read the grammar specification from standard input. The default output file names are `stdin.ml` and `stdin.mli`.
`--` file
  Process file as the grammar specification, even if its name starts with a dash (-) character. This option must be the last on the command line.

At run-time, the `ocamlyacc`-generated parser can be debugged by setting the `p` option in the `OCAMLRUNPARAM` environment variable (see section 10.2). This causes the pushdown automaton executing the parser to print a trace of its action (tokens shifted, rules reduced, etc). The trace mentions rule numbers and state numbers that can be interpreted by looking at the file grammar`.output` generated by `ocamlyacc -v`.

## 12.6 A complete example

The all-time favorite: a desk calculator. This program reads arithmetic expressions on standard input, one per line, and prints their values. Here is the grammar definition:

            /* File parser.mly */
            %token <int> INT
            %token PLUS MINUS TIMES DIV
            %token LPAREN RPAREN
            %token EOL
            %left PLUS MINUS        /* lowest precedence */
            %left TIMES DIV         /* medium precedence */
            %nonassoc UMINUS        /* highest precedence */
            %start main             /* the entry point */
            %type <int> main
            %%
            main:
                expr EOL                { $1 }
            ;
            expr:
                INT                     { $1 }
              | LPAREN expr RPAREN      { $2 }
              | expr PLUS expr          { $1 + $3 }
              | expr MINUS expr         { $1 - $3 }
              | expr TIMES expr         { $1 * $3 }
              | expr DIV expr           { $1 / $3 }
              | MINUS expr %prec UMINUS { - $2 }
            ;

Here is the definition for the corresponding lexer:

            (* File lexer.mll *)
            {
            open Parser        (* The type token is defined in parser.mli *)
            exception Eof
            }
            rule token = parse
                [' ' '\t']     { token lexbuf }     (* skip blanks *)
              | ['\n' ]        { EOL }
              | ['0'-'9']+ as lxm { INT(int_of_string lxm) }
              | '+'            { PLUS }
              | '-'            { MINUS }
              | '*'            { TIMES }
              | '/'            { DIV }
              | '('            { LPAREN }
              | ')'            { RPAREN }
              | eof            { raise Eof }

Here is the main program, that combines the parser with the lexer:

            (* File calc.ml *)
            let _ =
              try
                let lexbuf = Lexing.from_channel stdin in
                while true do
                  let result = Parser.main Lexer.token lexbuf in
                    print_int result; print_newline(); flush stdout
                done
              with Lexer.Eof ->
                exit 0

To compile everything, execute:

            ocamllex lexer.mll       # generates lexer.ml
            ocamlyacc parser.mly     # generates parser.ml and parser.mli
            ocamlc -c parser.mli
            ocamlc -c lexer.ml
            ocamlc -c parser.ml
            ocamlc -c calc.ml
            ocamlc -o calc lexer.cmo parser.cmo calc.cmo

## 12.7 Common errors

ocamllex: transition table overflow, automaton is too big

  The deterministic automata generated by `ocamllex` are limited to at most 32767 transitions. The message above indicates that your lexer definition is too complex and overflows this limit. This is commonly caused by lexer definitions that have separate rules for each of the alphabetic keywords of the language, as in the following example.

      rule token = parse
        "keyword1"   { KWD1 }
      | "keyword2"   { KWD2 }
      | ...
      | "keyword100" { KWD100 }
      | ['A'-'Z' 'a'-'z'] ['A'-'Z' 'a'-'z' '0'-'9' '_'] * as id
                     { IDENT id}

  To keep the generated automata small, rewrite those definitions with only one general “identifier” rule, followed by a hashtable lookup to separate keywords from identifiers:

      { let keyword_table = Hashtbl.create 53
        let _ =
          List.iter (fun (kwd, tok) -> Hashtbl.add keyword_table kwd tok)
                    [ "keyword1", KWD1;
                      "keyword2", KWD2; ...
                      "keyword100", KWD100 ]
      }
      rule token = parse
        ['A'-'Z' 'a'-'z'] ['A'-'Z' 'a'-'z' '0'-'9' '_'] * as id
                     { try
                         Hashtbl.find keyword_table id
                       with Not_found ->
                         IDENT id }

ocamllex: Position memory overflow, too many bindings
  The deterministic automata generated by `ocamllex` maintains a table of positions inside the scanned lexer buffer. The size of this table is limited to at most 255 cells. This error should not show up in normal situations.