bionic (3) pt_peg_language.3tcl.gz
NAME
pt::peg_language - PEG Language Tutorial
SYNOPSIS
package require Tcl 8.5 ________________________________________________________________________________________________________________
DESCRIPTION
Are you lost ? Do you have trouble understanding this document ? In that case please read the overview
provided by the Introduction to Parser Tools. This document is the entrypoint to the whole system the
current package is a part of.
Welcome to the tutorial / introduction for the PEG Specification Language. If you are already familiar
with the language we are about to discuss, and only wish to refresh your memory you can, of course, skip
ahead to the aforementioned section and just read the full formal specification.
WHAT IS IT?
peg, a language for the specification of parsing expression grammars is meant to be human readable, and
writable as well, yet strict enough to allow its processing by machine. Like any computer language. It
was defined to make writing the specification of a grammar easy, something the other formats found in the
Parser Tools do not lend themselves too.
THE ELEMENTS OF THE LANGUAGE
BASIC STRUCTURE
The general outline of a textual PEG is
PEG <<name>> (<<start-expression>>)
<<rules>>
END;
Note: We are using text in double angle-brackets as place-holders for things not yet explained.
NAMES
Names are mostly used to identify the nonterminal symbols of the grammar, i.e. that which occurs on the
left-hand side of a <rule>. The exception to that is the name given after the keyword PEG (see previous
section), which is the name of the whole grammar itself.
The structure of a name is simple:
[1] It begins with a letter, underscore, or colon, followed by
[2] zero or more letters, digits, underscores, or colons.
Or, in formal textual notation:
([_:] / <alpha>) ([_:] / <alnum>)*
Examples of names:
Hello
::world
_:submarine55_
Examples of text which are not names:
12
.bogus
0wrong
@location
RULES
The main body of the text of a grammar specification is taken up by the rules. Each rule defines the
sentence structure of one nonterminal symbol. Their basic structure is
<<name>> <- <<expression>> ;
The <name> specifies the nonterminal symbol to be defined, the <expression> after the arrow (<-) then
declares its structure.
Note that each rule ends in a single semicolon, even the last. I.e. the semicolon is a rule terminator,
not a separator.
We can have as many rules as we like, as long as we define each nonterminal symbol at most once, and have
at least one rule for each nonterminal symbol which occured in an expression, i.e. in either the start
expression of the grammar, or the right-hande side of a rule.
EXPRESSIONS
The parsing expressions are the meat of any specification. They declare the structure of the whole
document (<<start-expression>>), and of all nonterminal symbols.
All expressions are made up out of atomic expressions and operators combining them. We have operators for
choosing between alternatives, repetition of parts, and for look-ahead constraints. There is no explicit
operator for the sequencing (also known as concatenation) of parts however. This is specified by simply
placing the parts adjacent to each other.
Here are the operators, from highest to lowest priority (i.e. strength of binding):
# Binary operators.
<<expression-1>> <<expression-2>> # sequence. parse 1, then 2.
<<expression-1>> / <<expression-2>> # alternative. try to parse 1, and parse 2 if 1 failed to parse.
# Prefix operators. Lookahead constraints. Same priority.
& <<expression>> # Parse expression, ok on successful parse.
! <<expression>> # Ditto, except ok on failure to parse.
# Suffix operators. Repetition. Same priority.
<<expression>> ? # Parse expression none, or once (repeat 0 or 1).
<<expression>> * # Parse expression zero or more times.
<<expression>> + # Parse expression one or more times.
# Expression nesting
( <<expression>> ) # Put an expression in parens to change its priority.
With this we can now deconstruct the formal expression for names given in section Names:
([_:] / <alpha>) ([_:] / <alnum>)*
It is a sequence of two parts,
[_:] / <alpha>
and
([_:] / <alnum>)*
The parentheses around the parts kept their inner alternatives bound together against the normally higher
priority of the sequence. Each of the two parts is an alternative, with the second part additionally
repeated zero or more times, leaving us with the three atomic expressions
[_:]
<alpha>
<alnum>
And atomic expressions are our next topic. They fall into three classes:
[1] names, i.e. nonterminal symbols,
[2] string literals, and
[3] character classes.
Names we know about already, or see section Names for a refresher.
String literals are simple. They are delimited by (i.e. start and end with) either a single or double-
apostroph, and in between the delimiters we can have any character but the delimiter itself. They can be
empty as well. Examples of strings are
''
""
'hello'
"umbra"
"'"
'"'
The last two examples show how to place any of the delimiters into a string.
For the last, but not least of our atomic expressions, character classes, we have a number of predefined
classes, shown below, and the ability to construct or own. The predefined classes are:
<alnum> # Any unicode alphabet or digit character (string is alnum).
<alpha> # Any unicode alphabet character (string is alpha).
<ascii> # Any unicode character below codepoint 0x80 (string is ascii).
<control> # Any unicode control character (string is control).
<ddigit> # The digit characters [0-9].
<digit> # Any unicode digit character (string is digit).
<graph> # Any unicode printing character, except space (string is graph).
<lower> # Any unicode lower-case alphabet character (string is lower).
<print> # Any unicode printing character, incl. space (string is print).
<punct> # Any unicode punctuation character (string is punct).
<space> # Any unicode space character (string is space).
<upper> # Any unicode upper-case alphabet character (string is upper).
<wordchar> # Any unicode word character (string is wordchar).
<xdigit> # The hexadecimal digit characters [0-9a-fA-F].
. # Any character, except end of input.
And the syntax of custom-defined character classes is
[ <<range>>* ]
where each range is either a single character, or of the form
<<character>> - <character>>
Examples for character classes we have seen already in the course of this introduction are
[_:]
[0-9]
[0-9a-fA-F]
We are nearly done with expressions. The only piece left is to tell how the characters in character
classes and string literals are specified.
Basically characters in the input stand for themselves, and in addition to that we several types of
escape syntax to to repesent control characters, or characters outside of the encoding the text is in.
All the escaped forms are started with a backslash character ('\', unicode codepoint 0x5C). This is then
followed by a series of octal digits, or 'u' and hexedecimal digits, or a regular character from a fixed
set for various control characters. Some examples:
\n \r \t \' \" \[ \] \\ #
\000 up to \277 # octal escape, all ascii character, leading 0's can be removed.
\u2CA7 # hexadecimal escape, all unicode characters.
# # Here 2ca7 <=> Koptic Small Letter Tau
WHITESPACE AND COMMENTS
One issue not touched upon so far is whitespace and comments.
Whitespace is any unicode space character, i.e. anything in the character class <space>, and comments.
The latter are sequences of characters starting with a '#' (hash, unicode codepoint 0x23) and ending at
the next end-of-line.
Whitespace can be freely used between all syntactical elements of a grammar specification. It cannot be
used inside of syntactical elements, like names, string literals, predefined character classes, etc.
NONTERMINAL ATTRIBUTES
Lastly, a more advanced topic. In the section Rules we gave the structure of a rule as
<<name>> <- <<expression>> ;
This is not quite true. It is possible to associate a semantic mode with the nonterminal in the rule, by
writing it before the name, separated from it by a colon, i.e. writing
<<mode>> : <<name>> <- <<expression>> ;
is also allowed. This mode is optional. The known modes and their meanings are:
value The semantic value of the nonterminal symbol is an abstract syntax tree consisting of a single
node node for the nonterminal itself, which has the ASTs of the symbol's right hand side as its
children.
leaf The semantic value of the nonterminal symbol is an abstract syntax tree consisting of a single
node node for the nonterminal, without any children. Any ASTs generated by the symbol's right hand
side are discarded.
void The nonterminal has no semantic value. Any ASTs generated by the symbol's right hand side are
discarded (as well).
Of these three modes only leaf and void can be specified directly. value is implicitly specified by the
absence of a mode before the nonterminal.
Now, with all the above under our belt it should be possible to not only read, but understand the formal
specification of the text representation shown in the next section, written in itself.
PEG SPECIFICATION LANGUAGE
peg, a language for the specification of parsing expression grammars is meant to be human readable, and
writable as well, yet strict enough to allow its processing by machine. Like any computer language. It
was defined to make writing the specification of a grammar easy, something the other formats found in the
Parser Tools do not lend themselves too.
It is formally specified by the grammar shown below, written in itself. For a tutorial / introduction to
the language please go and read the PEG Language Tutorial.
PEG pe-grammar-for-peg (Grammar)
# --------------------------------------------------------------------
# Syntactical constructs
Grammar <- WHITESPACE Header Definition* Final EOF ;
Header <- PEG Identifier StartExpr ;
Definition <- Attribute? Identifier IS Expression SEMICOLON ;
Attribute <- (VOID / LEAF) COLON ;
Expression <- Sequence (SLASH Sequence)* ;
Sequence <- Prefix+ ;
Prefix <- (AND / NOT)? Suffix ;
Suffix <- Primary (QUESTION / STAR / PLUS)? ;
Primary <- ALNUM / ALPHA / ASCII / CONTROL / DDIGIT / DIGIT
/ GRAPH / LOWER / PRINTABLE / PUNCT / SPACE / UPPER
/ WORDCHAR / XDIGIT
/ Identifier
/ OPEN Expression CLOSE
/ Literal
/ Class
/ DOT
;
Literal <- APOSTROPH (!APOSTROPH Char)* APOSTROPH WHITESPACE
/ DAPOSTROPH (!DAPOSTROPH Char)* DAPOSTROPH WHITESPACE ;
Class <- OPENB (!CLOSEB Range)* CLOSEB WHITESPACE ;
Range <- Char TO Char / Char ;
StartExpr <- OPEN Expression CLOSE ;
void: Final <- "END" WHITESPACE SEMICOLON WHITESPACE ;
# --------------------------------------------------------------------
# Lexing constructs
Identifier <- Ident WHITESPACE ;
leaf: Ident <- ([_:] / <alpha>) ([_:] / <alnum>)* ;
Char <- CharSpecial / CharOctalFull / CharOctalPart
/ CharUnicode / CharUnescaped
;
leaf: CharSpecial <- "\\" [nrt'"\[\]\\] ;
leaf: CharOctalFull <- "\\" [0-2][0-7][0-7] ;
leaf: CharOctalPart <- "\\" [0-7][0-7]? ;
leaf: CharUnicode <- "\\" 'u' HexDigit (HexDigit (HexDigit HexDigit?)?)? ;
leaf: CharUnescaped <- !"\\" . ;
void: HexDigit <- [0-9a-fA-F] ;
void: TO <- '-' ;
void: OPENB <- "[" ;
void: CLOSEB <- "]" ;
void: APOSTROPH <- "'" ;
void: DAPOSTROPH <- '"' ;
void: PEG <- "PEG" !([_:] / <alnum>) WHITESPACE ;
void: IS <- "<-" WHITESPACE ;
leaf: VOID <- "void" WHITESPACE ; # Implies that definition has no semantic value.
leaf: LEAF <- "leaf" WHITESPACE ; # Implies that definition has no terminals.
void: SEMICOLON <- ";" WHITESPACE ;
void: COLON <- ":" WHITESPACE ;
void: SLASH <- "/" WHITESPACE ;
leaf: AND <- "&" WHITESPACE ;
leaf: NOT <- "!" WHITESPACE ;
leaf: QUESTION <- "?" WHITESPACE ;
leaf: STAR <- "*" WHITESPACE ;
leaf: PLUS <- "+" WHITESPACE ;
void: OPEN <- "(" WHITESPACE ;
void: CLOSE <- ")" WHITESPACE ;
leaf: DOT <- "." WHITESPACE ;
leaf: ALNUM <- "<alnum>" WHITESPACE ;
leaf: ALPHA <- "<alpha>" WHITESPACE ;
leaf: ASCII <- "<ascii>" WHITESPACE ;
leaf: CONTROL <- "<control>" WHITESPACE ;
leaf: DDIGIT <- "<ddigit>" WHITESPACE ;
leaf: DIGIT <- "<digit>" WHITESPACE ;
leaf: GRAPH <- "<graph>" WHITESPACE ;
leaf: LOWER <- "<lower>" WHITESPACE ;
leaf: PRINTABLE <- "<print>" WHITESPACE ;
leaf: PUNCT <- "<punct>" WHITESPACE ;
leaf: SPACE <- "<space>" WHITESPACE ;
leaf: UPPER <- "<upper>" WHITESPACE ;
leaf: WORDCHAR <- "<wordchar>" WHITESPACE ;
leaf: XDIGIT <- "<xdigit>" WHITESPACE ;
void: WHITESPACE <- (" " / "\t" / EOL / COMMENT)* ;
void: COMMENT <- '#' (!EOL .)* EOL ;
void: EOL <- "\n\r" / "\n" / "\r" ;
void: EOF <- !. ;
# --------------------------------------------------------------------
END;
EXAMPLE
Our example specifies the grammar for a basic 4-operation calculator.
PEG calculator (Expression)
Digit <- '0'/'1'/'2'/'3'/'4'/'5'/'6'/'7'/'8'/'9' ;
Sign <- '-' / '+' ;
Number <- Sign? Digit+ ;
Expression <- Term (AddOp Term)* ;
MulOp <- '*' / '/' ;
Term <- Factor (MulOp Factor)* ;
AddOp <- '+'/'-' ;
Factor <- '(' Expression ')' / Number ;
END;
Using higher-level features of the notation, i.e. the character classes (predefined and custom), this
example can be rewritten as
PEG calculator (Expression)
Sign <- [-+] ;
Number <- Sign? <ddigit>+;
Expression <- '(' Expression ')' / (Factor (MulOp Factor)*);
MulOp <- [*/];
Factor <- Term (AddOp Term)*;
AddOp <- [-+];
Term <- Number;
END;
BUGS, IDEAS, FEEDBACK
This document, and the package it describes, will undoubtedly contain bugs and other problems. Please
report such in the category pt of the Tcllib Trackers [http://core.tcl.tk/tcllib/reportlist]. Please
also report any ideas for enhancements you may have for either package and/or documentation.
When proposing code changes, please provide unified diffs, i.e the output of diff -u.
Note further that attachments are strongly preferred over inlined patches. Attachments can be made by
going to the Edit form of the ticket immediately after its creation, and then using the left-most button
in the secondary navigation bar.
KEYWORDS
EBNF, LL(k), PEG, TDPL, context-free languages, expression, grammar, matching, parser, parsing
expression, parsing expression grammar, push down automaton, recursive descent, state, top-down parsing
languages, transducer
CATEGORY
Parsing and Grammars
COPYRIGHT
Copyright (c) 2009 Andreas Kupries <andreas_kupries@users.sourceforge.net>