Tcl Library Source Code

EuroTcl/OpenACS 11 - 12 JULY 2024, VIENNA

[ Main Table Of Contents | Table Of Contents | Keyword Index | Categories | Modules | Applications ]


pt::peg_language - PEG Language Tutorial

Table Of Contents


package require Tcl 8.5 9


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>>)

Note: We are using text in double angle-brackets as place-holders for things not yet explained.


Names are mostly used to identify the nonterminal symbols of the grammar, i.e. that which occurs on the left-hand side of a . 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:


Examples of text which are not names:



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 specifies the nonterminal symbol to be defined, the 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.


The parsing expressions are the meat of any specification. They declare the structure of the whole document (<>), 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>


([_:] / <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


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


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


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 , 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:

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
        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   <- "\\" [0-3][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             <- !. ;

        # --------------------------------------------------------------------


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                   ;

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 <- Term (AddOp Term)*                            ;
    MulOp      <- [*/]						;
    Term       <- Factor (MulOp Factor)*                        ;
    AddOp      <- [-+]						;
    Factor     <- '(' Expression ')' / Number                   ;

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. 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.


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


Parsing and Grammars


Copyright © 2009 Andreas Kupries