EBNF parser and generic parser generator.

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This is a Ruby implementation of an EBNF and [BNF][] parser and parser generator. It parses EBNF grammars to [BNF][], generates First/Follow and Branch tables for LL(1) grammars, which can be used with the stream Tokenizer and LL(1) Parser.

As LL(1) grammars operate using alt and seq primitives, allowing for a match on alternative productions or a sequence of productions, generating a parser requires turning the EBNF rules into BNF:

  • Transform a ::= b? into a ::= _empty | b
  • Transform a ::= b+ into a ::= b b*
  • Transform a ::= b* into a ::= _empty | (b a)
  • Transform a ::= op1 (op2) into two rules: a ::= op1 _a_1 _a_1_ ::= op2

Of note in this implementation is that the tokenizer and parser are streaming, so that they can process inputs of arbitrary size.


Parsing an LL(1) Grammar

require 'ebnf'

ebnf = EBNF.parse(File.open('./etc/ebnf.ebnf'))

Output rules and terminals as S-Expressions, Turtle, HTML or BNF

puts ebnf.to_sxp
puts ebnf.to_ttl
puts ebnf.to_html
puts ebnf.to_s

Transform EBNF to BNF (generates sub-productions using alt or seq from plus, star or opt)


Generate First/Follow rules for BNF grammars


Generate Terminal, First/Follow, Cleanup and Branch tables as Ruby for parsing grammars


Generate formatted grammar using HTML (requires Haml gem)


Parser S-Expressions

Intermediate representations of the grammar may be serialized to Lisp-like S-Expressions. For example, the rule [1] ebnf ::= (declaration | rule)* is serialized as (rule ebnf "1" (star (alt declaration rule))).

Once the LL(1) conversion is made, the First/Follow table is generated, this rule expands as follows:

 (rule ebnf "1"
  (start #t)
  (first "@pass" "@terminals" LHS _eps)
  (follow _eof)
  (cleanup star)
  (alt _empty _ebnf_2))
 (rule _ebnf_1 "1.1"
  (first "@pass" "@terminals" LHS)
  (follow "@pass" "@terminals" LHS _eof)
  (alt declaration rule))
 (rule _ebnf_2 "1.2"
  (first "@pass" "@terminals" LHS)
  (follow _eof)
  (cleanup merge)
  (seq _ebnf_1 ebnf))
 (rule _ebnf_3 "1.3" (first "@pass" "@terminals" LHS _eps) (follow _eof) (seq ebnf))

Creating terminal definitions and parser rules to parse generated grammars

The parser is initialized to callbacks invoked on entry and exit to each terminal and production. A trivial parser loop can be described as follows:

require 'ebnf/ll1/parser'
require 'meta'

class Parser
  include Meta

  terminal(:SYMBOL, /([a-z]|[A-Z]|[0-9]|_)+/) do |prod, token, input|
    # Add data based on scanned token to input
    input[:symbol] = token.value

  start_production(:rule) do |input, current, callback|
    # Process on start of production
    # Set state for entry into recursed rules through current

    # Callback to parser loop with callback

  production(:rule) do |input, current, callback|
    # Process on end of production
    # return results in input, retrieve results from recursed rules in current

    # Callback to parser loop with callback

  def initialize(input)
    parser_options = {
      branch: BRANCH,
      first: FIRST,
      follow: FOLLOW,
      cleanup: CLEANUP
    parse(input, start_symbol, parser_options) do |context, *data|
      # Process calls from callback from productions

    rescue ArgumentError, RDF::LL1::Parser::Error => e
      progress("Parsing completed with errors:\n\t#{e.message}")
      raise RDF::ReaderError, e.message if validate?

Branch Table

The Branch table is a hash mapping production rules to a hash relating terminals appearing in input to sequence of productions to follow when the corresponding input terminal is found. This allows either the seq primitive, where all terminals map to the same sequence of productions, or the alt primitive, where each terminal may map to a different production.

  :alt => {
    "(" => [:seq, :_alt_1],
    :ENUM => [:seq, :_alt_1],
    :HEX => [:seq, :_alt_1],
    :O_ENUM => [:seq, :_alt_1],
    :O_RANGE => [:seq, :_alt_1],
    :RANGE => [:seq, :_alt_1],
    :STRING1 => [:seq, :_alt_1],
    :STRING2 => [:seq, :_alt_1],
    :SYMBOL => [:seq, :_alt_1],
  :declaration => {
    "@pass" => [:pass],
    "@terminals" => ["@terminals"],

In this case the alt rule is seq ('|' seq)* can happen when any of the specified tokens appears on the input stream. The all cause the same token to be passed to the seq rule and follow with _alt_1, which handles the ('|' seq)* portion of the rule, after the first sequence is matched.

The declaration rule is @terminals' | pass using the alt primitive determining the production to run based on the terminal appearing on the input stream. Eventually, a terminal production is found and the token is consumed.

First/Follow Table

The First/Follow table is a hash mapping production rules to the terminals that may proceed or follow the rule. For example:

  :alt => [

Terminals Table

This table is a simple list of the terminal productions found in the grammar. For example:

TERMINALS = ["(", ")", "-",
  "@pass", "@terminals",

Cleanup Table

This table identifies productions which used EBNF rules, which are transformed to BNF for actual parsing. This allows the parser, in some cases, to reproduce star, plus, and opt rule matches. For example:

  :_alt_1 => :star,
  :_alt_3 => :merge,
  :_diff_1 => :opt,
  :ebnf => :star,
  :_ebnf_2 => :merge,
  :_postfix_1 => :opt,
  :seq => :plus,
  :_seq_1 => :star,
  :_seq_2 => :merge,

In this case the ebnf rule was (declaration | rule)*. As BNF does not support a star operator, this is decomposed into a set of rules using alt and seq primitives:

ebnf    ::= _empty _ebnf_2
_ebnf_1 ::= declaration | rule
_ebnf_2 ::= _ebnf_1 ebnf
_ebnf_3 ::= ebnf

The _empty production matches an empty string, so allows for now value. _ebnf_2 matches declaration | rule (using the alt primitive) followed by ebnf, creating a sequence of zero or more declaration or alt members.

EBNF Grammar

The EBNF variant used here is based on W3C EBNF (see EBNF grammar) as defined in the XML 1.0 recommendation, with minor extensions:

  • Comments include \\ and # through end of line (other than hex character) and /* ... */ (* ... *) which may cross lines
  • All rules MAY start with an identifier, contained within square brackets. For example [1] rule, where the value within the brackets is a symbol ([a-z] | [A-Z] | [0-9] | "_" | ".")+
  • @terminals causes following rules to be treated as terminals. Any terminal which are entirely upper-case are also treated as terminals
  • @pass defines the expression used to detect whitespace, which is removed in processing.
  • No support for wfc (well-formedness constraint) or vc (validity constraint).

Parsing this grammar yields an S-Expression version: ebnf.ll1.

Example parser

For an example parser built using this gem, see EBNF Parser example. This example creates a parser for the EBNF grammar which generates the same Abstract Syntax Tree as the built-in parser in the gem.


Much of this work, particularly the generic parser, is inspired by work originally done by Tim Berners-Lee's Python predictive parser.

The EBNF parser was inspired by Dan Connolly's EBNF to Turtle processor, EBNF to BNF Notation-3 rules, and First Follow Notation-3 rules.


Full documentation available on Rubydoc.info.

Future Work



This repository uses Git Flow to mange development and release activity. All submissions must be on a feature branch based on the develop branch to ease staging and integration.

  • Do your best to adhere to the existing coding conventions and idioms.
  • Don't use hard tabs, and don't leave trailing whitespace on any line.
  • Do document every method you add using YARD annotations. Read the tutorial or just look at the existing code for examples.
  • Don't touch the .gemspec, VERSION or AUTHORS files. If you need to change them, do so on your private branch only.
  • Do feel free to add yourself to the CREDITS file and the corresponding list in the the README. Alphabetical order applies.
  • Do note that in order for us to merge any non-trivial changes (as a rule of thumb, additions larger than about 15 lines of code), we need an explicit public domain dedication on record from you.


This is free and unencumbered public domain software. For more information, see http://unlicense.org/ or the accompanying UNLICENSE file.

A copy of the Turtle EBNF and derived parser files are included in the repository, which are not covered under the UNLICENSE. These files are covered via the W3C Document License.