LALR-1 Parser Generator

An LALR-1 parser generator for Erlang, similar to yacc. Takes a BNF grammar definition as input, and produces Erlang code for a parser.

To understand this text, you also have to look at the yacc documentation in the UNIX(TM) manual. This is most probably necessary in order to understand the idea of a parser generator, and the principle and problems of LALR parsing with finite look-ahead.

An nice introduction to yacc can be found in chapter 8 of "The UNIX Programming Environment" by Brian W. Kernighan and Rob Pike.

Default Yecc Options

The (host operating system) environment variable ERL_COMPILER_OPTIONS can be used to give default Yecc options. Its value must be a valid Erlang term. If the value is a list, it is used as is. If it is not a list, it is put into a list.

The list is appended to any options given to file/2.

The list can be retrieved with compile:env_compiler_options/0.

Pre-Processing

A scanner to pre-process the text (program) to be parsed is not provided in the yecc module. The scanner serves as a kind of lexicon look-up routine. It is possible to write a grammar that uses only character tokens as terminal symbols, thereby eliminating the need for a scanner, but this would make the parser larger and slower.

The user should implement a scanner that segments the input text, and turns it into one or more lists of tokens. Each token should be a tuple containing information about syntactic category, position in the text (for example line number), and the actual terminal symbol found in the text: {Category, Position, Symbol}.

If a terminal symbol is the only member of a category, and the symbol name is identical to the category name, the token format can be {Symbol, Position}.

A list of tokens produced by the scanner should end with a special end_of_input tuple which the parser is looking for. The format of this tuple should be {Endsymbol, EndPosition}, where Endsymbol is an identifier that is distinguished from all the terminal and non-terminal categories of the syntax rules. The Endsymbol can be declared in the grammar file.

The simplest case is to segment the input string into a list of identifiers (atoms) and use those atoms both as categories and values of the tokens. For example, the input string aaa bbb 777, X may be scanned (tokenized) as:

[{aaa, 1}, {bbb, 1}, {777, 1}, {',' , 1}, {'X', 1},
 {'$end', 1}].

This assumes that this is the first line of the input text, and that '$end' is the distinguished end_of_input symbol.

The Erlang scanner in the io module can be used as a starting point when writing a new scanner. Study yeccscan.erl in order to see how a filter can be added on top of io:scan_erl_form/3 to provide a scanner for Yecc that tokenizes grammar files before parsing them with the Yecc parser. A more general approach to scanner implementation is to use a scanner generator such as leex.

Grammar Definition Format

Erlang style comments, starting with a '%', are allowed in grammar files.

Each declaration or rule ends with a dot (the character '.').

The grammar starts with an optional header section. The header is put first in the generated file, before the module declaration. The purpose of the header is to provide a means to make the documentation generated by EDoc look nicer. Each header line should be enclosed in double quotes, and newlines will be inserted between the lines. For example:

Header "%% Copyright (C)"
"%% @private"
"%% @Author John".

Next comes a declaration of the nonterminal categories to be used in the rules. For example:

Nonterminals sentence nounphrase verbphrase.

A non-terminal category can be used at the left-hand side (= lhs, or head) of a grammar rule. It can also appear at the right-hand side of rules.

Next comes a declaration of the terminal categories, which are the categories of tokens produced by the scanner. For example:

Terminals article adjective noun verb.

Terminal categories may only appear in the right hand sides (= rhs) of grammar rules.

Next comes a declaration of the rootsymbol, or start category of the grammar. For example:

Rootsymbol sentence.

This symbol should appear in the lhs of at least one grammar rule. This is the most general syntactic category which the parser ultimately will parse every input string into.

After the rootsymbol declaration comes an optional declaration of the end_of_input symbol that your scanner is expected to use. For example:

Endsymbol '$end'.

Next comes one or more declarations of operator precedences, if needed. These are used to resolve shift/reduce conflicts (see yacc documentation).

Examples of operator declarations:

Right 100 '='.
Nonassoc 200 '==' '=/='.
Left 300 '+'.
Left 400 '*'.
Unary 500 '-'.

These declarations mean that '=' is defined as a right associative binary operator with precedence 100, '==' and '=/=' are operators with no associativity, '+' and '*' are left associative binary operators, where '*' takes precedence over '+' (the normal case), and '-' is a unary operator of higher precedence than '*'. The fact that '==' has no associativity means that an expression like a == b == c is considered a syntax error.

Certain rules are assigned precedence: each rule gets its precedence from the last terminal symbol mentioned in the right hand side of the rule. It is also possible to declare precedence for non-terminals, "one level up". This is practical when an operator is overloaded (see also example 3 below).

Next come the grammar rules. Each rule has the general form

Left_hand_side -> Right_hand_side : Associated_code.

The left hand side is a non-terminal category. The right hand side is a sequence of one or more non-terminal or terminal symbols with spaces between. The associated code is a sequence of zero or more Erlang expressions (with commas ',' as separators). If the associated code is empty, the separating colon ':' is also omitted. A final dot marks the end of the rule.

Symbols such as '{', '.', and so on, have to be enclosed in single quotes when used as terminal or non-terminal symbols in grammar rules. The use of the symbols '$empty', '$end', and '$undefined' should be avoided.

The last part of the grammar file is an optional section with Erlang code (= function definitions) which is included 'as is' in the resulting parser file. This section must start with the pseudo declaration, or key words

Erlang code.

No syntax rule definitions or other declarations must follow this section. To avoid conflicts with internal variables, do not use variable names beginning with two underscore characters ('__') in the Erlang code in this section, or in the code associated with the individual syntax rules.

The optional expect declaration can be placed anywhere before the last optional section with Erlang code. It is used for suppressing the warning about conflicts that is ordinarily given if the grammar is ambiguous. An example:

Expect 2.

The warning is given if the number of shift/reduce conflicts differs from 2, or if there are reduce/reduce conflicts.

Examples

A grammar to parse list expressions (with empty associated code):

Nonterminals list elements element.
Terminals atom '(' ')'.
Rootsymbol list.
list -> '(' ')'.
list -> '(' elements ')'.
elements -> element.
elements -> element elements.
element -> atom.
element -> list.

This grammar can be used to generate a parser which parses list expressions, such as (), (a), (peter charles), (a (b c) d (())), ... provided that your scanner tokenizes, for example, the input (peter charles) as follows:

[{'(', 1} , {atom, 1, peter}, {atom, 1, charles}, {')', 1},
 {'$end', 1}]

When a grammar rule is used by the parser to parse (part of) the input string as a grammatical phrase, the associated code is evaluated, and the value of the last expression becomes the value of the parsed phrase. This value may be used by the parser later to build structures that are values of higher phrases of which the current phrase is a part. The values initially associated with terminal category phrases, i.e. input tokens, are the token tuples themselves.

Below is an example of the grammar above with structure building code added:

list -> '(' ')' : nil.
list -> '(' elements ')' : '$2'.
elements -> element : {cons, '$1', nil}.
elements -> element elements : {cons, '$1', '$2'}.
element -> atom : '$1'.
element -> list : '$1'.

With this code added to the grammar rules, the parser produces the following value (structure) when parsing the input string (a b c).. This still assumes that this was the first input line that the scanner tokenized:

{cons, {atom, 1, a}, {cons, {atom, 1, b},
                            {cons, {atom, 1, c}, nil}}}

The associated code contains pseudo variables '$1', '$2', '$3', and so on. which refer to (are bound to) the values associated previously by the parser with the symbols of the right-hand side of the rule. When these symbols are terminal categories, the values are token tuples of the input string (see above).

The associated code may not only be used to build structures associated with phrases, but may also be used for syntactic and semantic tests, printout actions (for example for tracing), and so on during the parsing process. Since tokens contain positional (line number) information, it is possible to produce error messages which contain line numbers. If there is no associated code after the right-hand side of the rule, the value '$undefined' is associated with the phrase.

The right-hand side of a grammar rule can be empty. This is indicated by using the special symbol '$empty' as rhs. Then the list grammar above can be simplified to:

list -> '(' elements ')' : '$2'.
elements -> element elements : {cons, '$1', '$2'}.
elements -> '$empty' : nil.
element -> atom : '$1'.
element -> list : '$1'.

Generating a Parser

To call the parser generator, use the following command:

yecc:file(Grammarfile).

An error message from Yecc will be shown if the grammar is not of the LALR type (for example too ambiguous). Shift/reduce conflicts are resolved in favor of shifting if there are no operator precedence declarations. Refer to the yacc documentation on the use of operator precedence.

The output file contains Erlang source code for a parser module with module name equal to the Parserfile parameter. After compilation, the parser can be called as follows (the module name is assumed to be myparser):

myparser:parse(myscanner:scan(Inport))

The call format can be different if a customized prologue file has been included when generating the parser instead of the default file lib/parsetools/include/yeccpre.hrl.

With the standard prologue, this call will return either {ok, Result}, where Result is a structure that the Erlang code of the grammar file has built, or {error, {Position, Module, Message}} if there was a syntax error in the input.

Message is something which may be converted into a string by calling Module:format_error(Message) and printed with io:format/3.

Note

By default, the parser that was generated will not print out error messages to the screen. The user will have to do this either by printing the returned error messages, or by inserting tests and print instructions in the Erlang code associated with the syntax rules of the grammar file.

It is also possible to make the parser ask for more input tokens when needed if the following call format is used:

myparser:parse_and_scan({Function, Args})
myparser:parse_and_scan({Mod, Tokenizer, Args})

The tokenizer Function is either a fun or a tuple {Mod, Tokenizer}. The call apply(Function, Args) or apply({Mod, Tokenizer}, Args) is executed whenever a new token is needed. This, for example, makes it possible to parse from a file, token by token.

The tokenizer used above has to be implemented so as to return one of the following:

{ok, Tokens, EndPosition}
{eof, EndPosition}
{error, Error_description, EndPosition}

This conforms to the format used by the scanner in the Erlang io library module.

If {eof, EndPosition} is returned immediately, the call to parse_and_scan/1 returns {ok, eof}. If {eof, EndPosition} is returned before the parser expects end of input, parse_and_scan/1 will, of course, return an error message (see above). Otherwise {ok, Result} is returned.

More Examples

1. A grammar for parsing infix arithmetic expressions into prefix notation, without operator precedence:

Nonterminals E T F.
Terminals '+' '*' '(' ')' number.
Rootsymbol E.
E -> E '+' T: {'$2', '$1', '$3'}.
E -> T : '$1'.
T -> T '*' F: {'$2', '$1', '$3'}.
T -> F : '$1'.
F -> '(' E ')' : '$2'.
F -> number : '$1'.

2. The same with operator precedence becomes simpler:

Nonterminals E.
Terminals '+' '*' '(' ')' number.
Rootsymbol E.
Left 100 '+'.
Left 200 '*'.
E -> E '+' E : {'$2', '$1', '$3'}.
E -> E '*' E : {'$2', '$1', '$3'}.
E -> '(' E ')' : '$2'.
E -> number : '$1'.

3. An overloaded minus operator:

Nonterminals E uminus.
Terminals '*' '-' number.
Rootsymbol E.

Left 100 '-'.
Left 200 '*'.
Unary 300 uminus.

E -> E '-' E.
E -> E '*' E.
E -> uminus.
E -> number.

uminus -> '-' E.

4. The Yecc grammar that is used for parsing grammar files, including itself:

Nonterminals
grammar declaration rule head symbol symbols attached_code
token tokens.
Terminals
atom float integer reserved_symbol reserved_word string char var
'->' ':' dot.
Rootsymbol grammar.
Endsymbol '$end'.
grammar -> declaration : '$1'.
grammar -> rule : '$1'.
declaration -> symbol symbols dot: {'$1', '$2'}.
rule -> head '->' symbols attached_code dot: {rule, ['$1' | '$3'],
        '$4'}.
head -> symbol : '$1'.
symbols -> symbol : ['$1'].
symbols -> symbol symbols : ['$1' | '$2'].
attached_code -> ':' tokens : {erlang_code, '$2'}.
attached_code -> '$empty' : {erlang_code,
                 [{atom, 0, '$undefined'}]}.
tokens -> token : ['$1'].
tokens -> token tokens : ['$1' | '$2'].
symbol -> var : value_of('$1').
symbol -> atom : value_of('$1').
symbol -> integer : value_of('$1').
symbol -> reserved_word : value_of('$1').
token -> var : '$1'.
token -> atom : '$1'.
token -> float : '$1'.
token -> integer : '$1'.
token -> string : '$1'.
token -> char : '$1'.
token -> reserved_symbol : {value_of('$1'), line_of('$1')}.
token -> reserved_word : {value_of('$1'), line_of('$1')}.
token -> '->' : {'->', line_of('$1')}.
token -> ':' : {':', line_of('$1')}.
Erlang code.
value_of(Token) ->
    element(3, Token).
line_of(Token) ->
    element(2, Token).

Note

The symbols '->', and ':' have to be treated in a special way, as they are meta symbols of the grammar notation, as well as terminal symbols of the Yecc grammar.

5. The file erl_parse.yrl in the lib/stdlib/src directory contains the grammar for Erlang.

Note

Syntactic tests are used in the code associated with some rules, and an error is thrown (and caught by the generated parser to produce an error message) when a test fails. The same effect can be achieved with a call to return_error(ErrorPosition, Message_string), which is defined in the yeccpre.hrl default header file.

Files

lib/parsetools/include/yeccpre.hrl

See Also

• Aho & Johnson: 'LR Parsing', ACM Computing Surveys, vol. 6:2, 1974.

• Kernighan & Pike: The UNIX programming environment, 1984.