ISO/IEC 14977:1996
(Main)Information technology — Syntactic metalanguage — Extended BNF
Information technology — Syntactic metalanguage — Extended BNF
Defines a notation, Extended BNF, for specifying the syntax of a linear sequence of symbols. It defines both the logical structure of the notation and its graphical representation.
Technologies de l'information — Métalangage syntaxique — BNF étendu
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Standards Content (Sample)
INTERNATIONAL
ISO/IEC
STANDARD
First edition
1996-l 2-l 5
Information technology - Syntactic
metalanguage - Extended BNF
Technologies de /‘information - Mbtalangage syntaxique - BNF &endu
Reference number
ISO/IEC 14977:1996(E)
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ISO/IEC 14977 : 1996(E)
Page
Contents
Foreword .
...........................................
Introduction
1 Scope .
..................................
2 Normative references
..........................................
3 Definitions
..........
4 The form of each syntactic element of Extended BNF
2
4.1 General .
2
Syntax .
4.2
2
Syntax-rule .
4.3
2
....................................
4.4 Definitions-list
2
Single-definition .
4.5
2
Syntactic-term .
4.6
2
................................
4.7 Syntactic exception
2
4.8 Syntactic-factor .
2
Integer .
4.9
2
..................................
4.10 Syntactic-primary
3
4.11 Optional-sequence .
3
Repeated sequence .
4.12
3
4.13 Grouped sequence .
3
4.14 Meta-identifier .
3
.............................
4.15 Meta-identifier-character
................................... 3
4.16 Terminal-string.
3
4.17 First-terminal-character .
3
............................
4.18 Second-terminal-character
3
..................................
4.19 Special-sequence
........................... 3
4.20 Special-sequence-character
3
4.21 Empty-sequence .
3
..................................
4.22 Further examples
@ ISO/IEC 1996
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Printed in Switzerland
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ISO/IEC 14977 : 1996(E)
........... 3
5 The symbols represented by each syntactic element.
......................................... 3
General
5.1
................................... 4
Terminal-string.
5.2
.................................... 4
5.3 Meta-identifier
................................. 4
5.4 Grouped-sequence
................................. 4
5.5 Optional-sequence
................................. 4
Repeated-sequence
5.6
................................... 4
5.7 Syntactic-factor
.................................... 4
5.8 Syntactic-term
...................................
5
5.9 Single-definition
....................................
5
5.10 Definitions-list
..................................
5
5.11 Special-sequence
................................... 5
5.12 Empty-sequence
.................................
6 Layout and Comments
6.1 General .
.................................
Terminal-character
6.2
..................................
6.3 Gap-free-symbol
....................................
6.4 Gap-separator
...............................
6.5 Commentless-symbol
..................................
Comment-symbol
6.6
...........................
Bracketed-textual-comment
6.7
7 The representation of each terminal-character in Extended BNF . .
.........................................
7.1 General
..................................
7.2 Letters and digits
............................
7.3 Other terminal characters
...........................
7.4 Alternative representations.
...................................
7.5 Other-character
....................................
7.6 Gap-separator
.......
7.7 Terminal-characters represented by a pair of characters
...........................
7.8 Invalid character sequences
8
8 Examples .
.........................
8
8.1 The syntax of Extended BNF
............. 10
8.2 Extended BNF used to define itself informally
...................... 10
8.3 Extended BNF defined informally
Annexes
................................... 11
A Two-level grammars
........................................
12
B Biblioeranhv
. . .
111
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Foreword
IS0 (the International Organization for Standardization) and IEC (the International
Electrotechnical Commission) form the specialized system for worldwide
standardization. National bodies that are members of IS0 or IEC participate
in the development of International Standards through technical committees
established by the respective organization to deal with particular fields of
technical activity. IS0 and IEC technical committees collaborate in fields
of mutual interest. Other international organizations, governmental and non-
governmental, in liaison with IS0 and IEC, also take part in the work.
In the field of information technology, IS0 and IEC have established a joint
technical committee ISO/IEC JTC 1. Draft International Standards adopted
by the joint technical committee are circulated to national bodies for voting.
Publication as an International Standard requires approval by at least 75% of
the national bodies casting a vote.
International Standard ISO/IEC 14977 was prepared by BSI (as BS 6154)
and was adopted, under a special “fast-track procedure”, by Joint Technical
Committee ISO/IEC JTC 1, Information technology, in parallel with its approval
by national bodies of IS0 and IEC.
Annexes A and B of this Internation .a1 Standard are for in
formation only.
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ISOJIEC 14977 : 1996(E)
Introduction
A syntactic metalanguage is an important tool of computer science. The
concepts are well known, but many slightly different notations are in use. As a
result syntactic metalanguages are still not widely used and understood, and the
advantages of rigorous notations are unappreciated by many people.
Extended BNF brings some order to the formal definition of a syntax and will
be useful not just for the definition of programming languages, but for many
other formal definitions.
Since the definition of the programming language Algol 60 (Naur, 1960) the
custom has been to define the syntax of a programming language formally.
Algol 60 was defined with a notation now known as BNF or Backus-Naur Form.
This notation has proved a suitable basis for subsequent languages but has
frequently been extended or slightly altered. The many different notations are
confusing and have prevented the advantages of formal unambiguous definitions
from being widely appreciated. The syntactic metalanguage Extended BNF
described in this standard is based on Backus-Naur Form and includes the most
widely adopted extensions.
Syntactic metalanguages
A syntactic metalanguage is a notation for defining the syntax of a language
by use of a number of rules. Each rule names part of the language (called a
non-terminal symbol of the language) and then defines its possible forms. A
terminal symbol of the language is an atom that cannot be split into smaller
components of the language. A syntactic metalanguage is useful whenever a
clear formal description and definition is required, e.g. the format for references
in papers submitted to a journal, or the instructions for performing a complicated
task.
A formal syntax definition has three distinct uses:
it names the various syntactic parts (i.e. non-terminal symbols) of the
a>
language;
it shows which sequences of symbols are valid sentences of the language;
b)
it shows the syntactic structure of any sentence of the language.
C>
The need for a standard syntactic metalanguage
Without a standard syntactic metalanguage every programming language definition
starts by specifying the metalanguage used to define its syntax. This causes
various problems:
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ISO/IEC 14977 : 1996(E)
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Many different notations - It is unusual for two different programming
languages to use the same metalanguage. Thus human readers are handicapped
by having to learn a new metalanguage before they can study a new language.
Concepts not widely understood - The lack of a standard notation hinders
the use of rigorous unambiguous definitions.
Imperfect notations - Because a metalanguage needs to be defined for
every programming language, almost inevitably, the metalanguage contains
defects. For example errors occurred in the drafting of RTL/2 (BS5904) and
CORAL 66 (BS5905) because the metalanguages could not be typed easily.
Special purpose notations - A metalanguage defined for a particular pro-
gramming language is often simplified by taking advantage of special features
in the language to be defined. However, the metalanguage is then unsuitable
for other programming languages.
Few general syntax processors - The multiplicity of syntactic meta-
languages has limited the availability of computer programs to analyse
and process syntaxes, e.g. to list a syntax neatly, to make an index of the
symbols used in the syntax, to produce a syntax-checker for programs written
in the language.
In practice experienced readers have little difficulty in picking up and learning
a new notation, but even so the differences obscure mutual understanding
and hinder communication. A standard metalanguage enables more people to
crystallize vague ideas into an unambiguous definition. It is also useful because
other people needing to provide formal definitions no longer need to reinvent
similar concepts.
The objectives to be satisfied
It is desirable that a standard syntactic metalanguage should be:
more easily
concise, so that languages can be defined briefly and thus be
a>
understood;
precise, so that the rules are unambiguous;
b)
formal, so that the rules can be parsed, or otherwise processed,
C> bY a
computer when required;
d) natural, so that the notation and format are relatively simple to learn and
understand, even for those who are not themselves language designers; (The
meaning of a symbol should not be surprising. It should also be possible to
define the syntax of a language in a way that helps to indicate the meaning
of the constructions.)
e) general, so that the notation is suitable for many purposes including the
description of many different languages;
simple in its character set and with a notation that avoids, as far as
f-l
is practicable, using characters that are not generally available on standard
keyboards (both typewriters and computer terminals) so that the rules can be
typed and can be processed by computer programs;
self describing, so that the notation is able to describe itself;
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0 ISO/IEC ISO/IEC 14977 : 1996(E)
h) linear, so that the syntax can be expressed as a single stream of characters.
(This simplifies printing a syntax.
Computer processing of a syntax is also
simpler.)
Some common syntactic metalanguages
Unfortunately n one of the existing sy ntactic metalanguages was suitable for
adoption as the standard, for example:
a) COBOL (IS0 1989:1985) lists alternatives vertically and uses brackets
spreading over many lines. This is inconvenient for computer processing and
cannot be prepared on typewriters.
b) Backus-Naur Form (used in ALGOL 60) has problems if the metasymbols
< > 1 ::= occur in the language being defined. Some common forms of
construction (e.g. comments) cannot be expressed naturally, other constructions
(e.g. repetition) are long-winded.
c) The obsolete FORTRAN 77 (IS0 1539: 1980) had ‘railroad tracks’. These
are easy to understand but difficult to prepare and to process on a computer
or typewriter. The current version, FORTRAN 90 (ISO/IEC 1539:1991), no
longer uses this notation.
Most other languages use a variant of one of these metalanguages. Most of
them cannot be candidates for standardization because they use characters not in
the language being defined as metasymbols of the metalanguage. This simplifies
the metalanguage but prevents it from being used generally.
POSIX (ISO/IEC 9945-2: 1993) includes two complementary facilities which
both assume an ISO/IEC 646: 1991 character set is applicable: LEX permits
the definition and lexical analysis of regular expressions, but is inadequate for
the description of an arbitrary context-free grammar, and YACC (Yet Another
Compiler Compiler) is a parser generator for an LALR(l) grammar.
The standard metalanguage Extended BNF
Extended BNF, the metalanguage defined in this International Standard, is based
on a suggestion by Niklaus Wirth (Wirth, 1977) that is based on Backus-Naur
Form and that contains the most common extensions, i.e.:
a) Terminal symbols of the language are quoted so that any character,
including one used in Extended BNF, can be defined as a terminal symbol of
the language being defined.
[ and I indicate optional symbols.
b)
{ and } indicate repetition.
d) Each rule has an explicit final character so that there is never any
ambiguity about where a rule ends.
items together. It is an obvious convenience to use ( and
Brackets group
e>
) in their ordinary mathematical sense.
The main differences in Extended BNF are further features that experience has
shown are often required when providing a formal definition:
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a) De$ning an explicit number of items. Fortran contains a rule that a label
field contains exactly five characters; an identifier in PWI or COBOL has up
to 32 characters: rules such as these can be expressed only with difficulty in
Backus-Naur Form. In practice, such definitions are often left incomplete and
the rules qualified informally in English.
b) DeJining something by specifying the few exceptional cases. An Algol
end-comment ends at the first end, else or semicolon. A rule like this cannot
be expressed concisely or clearly in Backus-Naur Form and is also usually
specified informally in English.
Including comments. Programming languages and other structures with
C>
a complicated syntax need many rules to define them. The syntax will
be clearer if explanations and cross-refe rences can be provided; accordingly
Extended BNF contains a comment facili ty so that ordinary text can be added
to a syntax for the benefit of a human reader without affecting the formal
meaning of the syntax.
d) Meta-identifier: A meta-identifier (the narne of a non-terminal symbol
in the language) need not be a single word or enclosed in brackets because
there is an explicit concatenate symbol. This also ensures that the layout of
a syntax (except in a terminal symbol) does not affect the language being
defined.
e) Extensions. A user may wish to extend Extended BNF. A special-sequence
is provided for this purpose, the format and meaning of which are not defined
in the standard except to ensure that the start and end of an extension
can always be seen easily. Various possible extensions are outlined in the
following paragraphs.
Limitations and extensions
The main limitation of Extended BNF is that the language being defined needs
to be linear, i.e. the symbols in a sentence of the language can be placed in
an ordered sequence. For example knitting patterns and recipes in cooking are
linear languages, but electric circuit diagrams are not.
A further limitation is that Extended BNF is inadequate for defining more
complex forms of grammars. Such facilities were not provided because it was
thought the main need was to define a notation sufficient for the simpler and
commoner requirements.
Instead Extended BNF has been designed so that various extensions can be
made in a natural way. There are two simple ways of extending the standard
metalanguage. Firstly, the special-sequence concept provides a basic framework
for any extension, the format between the special-sequence-characters being
almost completely arbitrary. This method would be suitable for an action
grammar, i.e. one specifying actions that are to take place as a sentence is
parsed. Secondly, a meta-identifier can never be followed immediately by a left
parenthesis in the standard metalanguage; thus another method of extending the
metalanguage is to define the syntax and meaning of a meta-identifier followed
by a sequence of parameters enclosed in parentheses. This would be reasonable
in an attribute grammar where the rules ensure consistency between different
parts of a sentence in the language being defined.
More complicated extensions are also possible. Annex A suggests how Extended
BNF might be extended to define a two-level grammar.
. . .
Vlll
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INTERNATIONAL STANDARD @ ISO/IEC ISOAEC 14977:1996(E)
Information technology - Syntactic metalanguage - Extended BNF
32 . subsequence: A sequence within a sequence.
1 Scope
This International Standard defines a notation, Extended
33 non-terminal symbol: A syntactic part of the lan-
BNF, for specifying the syntax of a linear sequence of
guage being defined.
symbols. It defines both the logical structure of the
notation and its graphical representation.
meta-identifier: The name of a non-terminal sym-
34
Extended BNF has applications in the definition of pro-
bol.
gramming and other languages, as well as in other formal
definitions, for example the commands to an operating
system, or the precise format of data and results.
3.5 start symbol: A non-terminal symbol that is defined
by one or more syntax rules but does not occur in any
Examples of Extended BNF are given in clause 8.
other syntax rule.
NOTE - Like many other notations, Extended BNF can still
be misused; thus it does not prevent someone from trying to
36 sentence: A sequence of symbols that represents
define an unparsable or ambiguous language.
the start symbol.
2 Normative references 3.7 terminal symbol: A sequence of one or more
characters forming an irreducible element of a language.
The following standards contain provisions which, through
NOTE - In this International Standard a terminal symbol of
reference in this text, constitute provisions of this Interna-
Extended BNF is called a terminal-character, and a terminal
tional Standard. At the time of publication, the editions
symbol of a language being defined by a syntax is represented
indicated were valid. All standards are subject to revi-
by a terminal-string.
sion, and parties to agreements based on this International
Standard are encouraged to investigate the possibility of
applying the most recent editions of the standards listed
4 The form of each syntactic element of Ex-
below. Members of IEC and IS0 maintain registers of
currently valid International Standards.
tended BNF
IS0 2382-15 : 1985, Data processing - kcabulary - NOTES
Part 15: Programming languages.
1 The following conventions are used:
ISO/IEC 646 : 1991, Information technology - IS0 7-bit
a) Each meta-identifier of Extended BNF is written as one
coded character set for information interchange.
or more words joined together by hyphens;
ISO/IEC 6429 : 1992, Information technology - Control
b) A meta-identifier ending with “-symbol” is the name of
functions for coded character sets.
a terminal symbol of Extended BNF.
BS 6154 : 198 1, Method of defining - Syntactic meta-
2 The normal character representing each operator of Extended
BNF and its implied precedence is (highest precedence at the
language.
top):
*
repetition-symbol
3 Definitions
-
except-symbol
concatenate-symbol
For the purposes of this International Standard, the
i definition-separator-symbol
in IS0 2382- 15 and the following
definitions given
=
defining-symbol
.
definitions apply. terminator-symbol
I
3 The normal precedence is over-ridden by the following
bracket pairs:
31 . sequence: An ordered list of zero or more items.
1
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ISO/IEC 14977 : 1996(E) @ ISO/IEC
/
first-quote-symbol first-quote-symbol ’
4.7 Syntactic exception
II
second-quote-symbol second-quote-symbol
*;
start-comment-symbol end-comment-symbol
t*
A syntactic-exception consists of a syntactic-factor subject
start-group-symbol end-group-symbol
( )
start-option-symbol end-option-symbol
[ 1 to the restriction that the sequences of symbols represented
start-repeat-symbol end-repeat-symbol
1 1
by the syntactic-exception could equally be represented by
? special-sequence special-sequence ?
a syntactic-factor containing no meta-identifiers.
-symbol -symbol
NOTE - If a syntactic-exception is permitted to be an arbitrary
syntactic-factor, Extended BNF could define a wider class of
languages than the context-free grammars, including attempts
4.1 General
which lead to Russell-like paradoxes, e.g.
= I’A” - xx;
Is ?“,I,
an example of xx? Such licence is undesirable
The logical structure of Extended BNF is defined in 4.2
and the form of a syntactic-exception is therefore restricted
to 4.21.
to cases that can be proved to be safe. Thus whereas a
syntactic-factor is in general equivalent to some context-free
a syntactic-exception is always equivalent to some
grammar,
regular grammar. It may be shown that the difference between a
4.2 Syntax context-free grammar and a regular grammar is always another
context-free grammar; hence a syntactic-term (and hence any
grammar defined according to this standard) is equivalent to
The syntax of a language consists of one or more
some context-free grammar.
syntax-rules.
4.8 Syntactic-factor
4.3 Syntax-rule
A syntactic-factor consists of either:
A syntax-rule consists of a meta-identifier (the name of
an integer followed by a repetition-symbol followed
a>
the non-terminal symbol being defined) followed by a
a syntactic-primary, or
bY
defining-symbol followed by a definitions-list followed by
a terminator-symbol.
a syntactic-primary.
b)
4.4 Definitions-list
4.9 Integer
A definitions-list consists of an ordered list of one or
An integer consists of an ordered list of one or more
more single-definitions separated from each other by a
decimal-digits.
definition-separator-symbol.
4.10 Syntactic-primary
4.5 Single-definition
A syntactic-primary consists of one of the following:
A single-definition consists of an ordered list of one
an optional-sequence;
a>
or more syntactic-terms separated from each other by a
concatenate-symbol.
b) a repeated-sequence;
a grouped-sequence;
4.6 Syntactic-term
d) a meta-identifier;
A syntactic-term consists of either:
a terminal-string;
e>
a syntactic-factor, or
a>
a special-sequence;
a syntactic-factor followed by an except-symbol
b)
followed by a syntactic-exception.
an empty-sequence.
g)
2
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ISOIIEC 14977 : 1996(E)
4.11 Optional-sequence 4.19 Special-sequence
An optional-sequence consists of a start-option-symbol
A special-sequence consists of a special-sequence-symbol
followed by a definitions-list followed by an end-option-
followed by a (possibly empty) sequence of special-
symbol.
sequence-characters followed by a special-sequence-
symbol.
4.12 Repeated sequence
4.20 Special .-sequence-character
A repeated-sequence consists of a start-repeat-symbol
followed by a definitions-list followed by an end-repeat-
A special-sequence-character is any terminal-character ex-
symbol.
cept a special-sequence-symbol.
4.13 Grouped sequence
Empty-sequence
4.21
A grouped-sequence consists of a start-group-symbol fol-
lowed by a definitions-list followed by an end-group-
An empty-sequence consists of the empty sequence of
symbol.
terminal-characters.
4.14 Meta-identifier
4.22 Further examples
A meta-identifier consists of an ordered list of one or more
The following example is a syntax-rule that states that a
meta-identifier-characters subject to the condition that the
Fortran 77 continuation line starts with 5 blanks, the sixth
first meta-identifier-character is a letter.
character must not be a blank or zero, and there must not
be more than 72 (= 5+1+66) characters altogether.
4.15 Meta-identifier-character
Fortran 77 continuation line = 5 * ' ",
(character - ('I 'I 1 "O")), 66 * [character] ;
A meta-identifier-character is a letter or a decimal-digit.
In Fortran 66, the definition of a continuation line is more
complicated. The following example is a syntax-rule that
4.16 Terminal-string
states that a continuation line must not start with C, there
must be at least 6 characters, the sixth character must not
A terminal-string consists of either:
be a blank or zero, and there must not be more than 72
(= 1+4+1+66) characters altogether.
a) A first-quote-symbol followed by a sequence of
one or more first-terminal-characters followed by a
Fortran 66 continuation line = character - "C",
first-quote-symbol, or
4 * character, character - (" " 1 " 0 " > ,
66 * [character] ;
b) A second-quote-symbol, followed by a sequence of
one or more second-terminal-characters followed by a
second-quote-symbol.
5 The symbols represented by each syntactic
element
4.17 First-terminal-character
5.1 General
A first-terminal-character is any terminal-character except
a first-quote-symbol.
Each syntax-rule is a syntax rule that defines (possibly
empty) sequences of terminal and non-terminal symbols.
4.18 Second-terminal-character
Each of these sequences of symbols is represented by the
non-terminal symbol named by the meta-identifier at the
A second-terminal-character is any terminal-character ex- start of the syntax-rule. 5.2 to 5.12 define the sequences
cept a second-quote-symbol. of symbols that are represented by any definitions-list.
3
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NOTES 5.7 Syntactic-factor
1 When the syntax of a complete language is defined there is:
A syntactic-factor represents an explicit number of subse-
quences where each subsequence is a sequence of symbols
a start symbol, and
a> represented by the syntactic-primary that is part of that
syntactic-factor. The required number of subsequences
b) at least one syntax-rule with each meta-identifier
starting
equals one when no integer is given and otherwise is equal
used as a syntactic-primary.
to the value of the integer.
2 It is more difficult to understand a language if there are
owing syntax-rules ill the
As examples the foll
several syntax-rules defining a meta-identifier and no indication
repetition.
facil ities for expressing
that each definition only partly defines the non-terminal symbol.
bb = 3 * aa, "B";
cc = 3 * [aa], IT";
5.2 Terminal-string
dd = {aa}, I'D";
ee = aa, {aa}, 92";
A termi nal-string represents either:
ff = 3 * aa, 3 * [aa], "F";
gg = 3 * {aa}, "D";
the sequence of first-terminal-characters between its
a>
defined these rules are as follows:
Termi nal-strings
bY
first-quote-symbols
? or
aa: A
the sequence of second-terminal-characters between
b)
bb: AAAB
its second-quote-symbols.
cc: c AC AAC MUX
etc.
dd: D AD AAD AAAD AAAAD
ee: AE AAE AAAE AAAAE AAAAAE etc.
ff: AAAF AAAAF AMAAF AAAAAAF
5.3 Meta-identifier
NOTE - The definition for gg, although syntactically valid,
is not sensible. The sequences of symbols represented by gg
are identical with those given by dd but cannot be parsed
unambiguously.
5.8 Syntactic-term
54 . Grouped-sequence
When a syntactic-term is a single syntactic-factor it
A grouped-sequence represents any sequence of symbols
represents any sequence of symbols represented by that
defined by the definitions-list enclosed by its start-group-
syntactic-factor.
symbol and end-group-symbol.
When a syntactic-term is a syntactic-factor followed by
an except-symbol followed by a syntactic-exception it
5.5 Optional-sequence
represents any sequence of symbols that satisfies both of
the conditions:
An optional -sequence represents either:
it is a sequence of symbols represented by the
a>
syntactic-factor,
the empty sequence of symbols, or
a>
it is not a sequence of symbols represented by the
b)
b) any sequence of symbols defined by the definitions-
syntac tic-ex .cepti on.
list enclosed by its start-option-symbol and end-option-
symbol.
As examples the following syntax-rules illustrate the
facilities provided by the except-symbol.
56 . Repeated-sequence
letter = 'IA" 1 IIBII 1 'ICI' 1 I'D" 1 "El' ) 'IF"
1 II G II 1 'I H II 1 II 1 II 1 II J II 1 II K II 1 'I L 'I 1 '1 M 1'
I II N II 1 II 0 II 1 II p II 1 II Q 'I 1 'I R 'I 1 1' S 11 1 11 T 11
A repeated-sequence represents a (possibly empty) se-
I'~" I I'~" I llwll I Ilxll I llyll I "z";
I
quence of subsequences where each subsequence is any
II E II 1 II 1 II 1 II 0 II 1 II U II ;
vowel = "A" I
sequence of symbols defined by the definitions-list enclosed
consonant = letter - vowel;
ee = {llAII}-, 'IElI;
by the start-repeat-symbol and end-repeat-symbol.
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CJ ISO/IEC ISO/IEC 14977 : 1996(E)
Terminal-strings defined by these rules are as follows: NOTES
1 It is much easier for
a person to read and understand a
...
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