Ubuntu Manpage: grammar::peg - Create and manipulate parsing expression grammars

NAME

       grammar::peg - Create and manipulate parsing expression grammars

SYNOPSIS

       package require Tcl  8.4

       package require snit

       package require grammar::peg  ?0.1?

       ::grammar::peg pegName ?=|:=|<--|as|deserialize src?

       pegName destroy

       pegName clear

       pegName = srcPEG

       pegName --> dstPEG

       pegName serialize

       pegName deserialize serialization

       pegName is valid

       pegName start ?pe?

       pegName nonterminals

       pegName nonterminal add nt pe

       pegName nonterminal delete nt1 ?nt2 ...?

       pegName nonterminal exists nt

       pegName nonterminal rename nt ntnew

       pegName nonterminal mode nt ?mode?

       pegName nonterminal rule nt

       pegName unknown nonterminals

________________________________________________________________________________________________________________

DESCRIPTION

This package provides a container class for parsing expression grammars (Short: PEG). It allows the
incremental definition of the grammar, its manipulation and querying of the definition. The package
neither provides complex operations on the grammar, nor has it the ability to execute a grammar
definition for a stream of symbols. Two packages related to this one are grammar::mengine and
grammar::peg::interpreter. The first of them defines a general virtual machine for the matching of a
character stream, and the second implements an interpreter for parsing expression grammars on top of that
virtual machine.

TERMS & CONCEPTS
PEGs are similar to context-free grammars, but not equivalent; in some cases PEGs are strictly more
powerful than context-free grammars (there exist PEGs for some non-context-free languages). The formal
mathematical definition of parsing expressions and parsing expression grammars can be found in section
PARSING EXPRESSION GRAMMARS.

In short, we have terminal symbols, which are the most basic building blocks for sentences, and
nonterminal symbols with associated parsing expressions, defining the grammatical structure of the
sentences. The two sets of symbols are distinctive, and do not overlap. When speaking about symbols the
word "symbol" is often left out. The union of the sets of terminal and nonterminal symbols is called the
set of symbols.

Here the set of terminal symbols is not explicitly managed, but implicitly defined as the set of all
characters. Note that this means that we inherit from Tcl the ability to handle all of Unicode.

A pair of nonterminal and parsing expression is also called a grammatical rule, or rule for short. In the
context of a rule the nonterminal is often called the left-hand-side (LHS), and the parsing expression
the right-hand-side (RHS).

The start expression of a grammar is a parsing expression from which all the sentences contained in the
language specified by the grammar are derived. To make the understanding of this term easier let us
assume for a moment that the RHS of each rule, and the start expression, is either a sequence of symbols,
or a series of alternate parsing expressions. In the latter case the rule can be seen as a set of rules,
each providing one alternative for the nonterminal. A parsing expression A' is now a derivation of a
parsing expression A if we pick one of the nonterminals N in the expression, and one of the alternative
rules R for N, and then replace the nonterminal in A with the RHS of the chosen rule. Here we can see why
the terminal symbols are called such. They cannot be expanded any further, thus terminate the process of
deriving new expressions. An example

Rules
(1) A <- a B c
(2a) B <- d B
(2b) B <- e

Some derivations, using starting expression A.

A -/1/-> a B c -/2a/-> a d B c -/2b/-> a d e c

A derived expression containing only terminal symbols is a sentence. The set of all sentences which can
be derived from the start expression is the language of the grammar.

Some definitions for nonterminals and expressions:

[1] A nonterminal A is called reachable if it is possible to derive a parsing expression from the
start expression which contains A.

[2] A nonterminal A is called useful if it is possible to derive a sentence from it.

[3] A nonterminal A is called recursive if it is possible to derive a parsing expression from it which
contains A, again.

[4] The FIRST set of a nonterminal A contains all the symbols which can occur of as the leftmost
symbol in a parsing expression derived from A. If the FIRST set contains A itself then that
nonterminal is called left-recursive.

[5] The LAST set of a nonterminal A contains all the symbols which can occur of as the rightmost
symbol in a parsing expression derived from A. If the LAST set contains A itself then that
nonterminal is called right-recursive.

[6] The FOLLOW set of a nonterminal A contains all the symbols which can occur after A in a parsing
expression derived from the start expression.

[7] A nonterminal (or parsing expression) is called nullable if the empty sentence can be derived from
it.

And based on the above definitions for grammars:

[1] A grammar G is recursive if and only if it contains a nonterminal A which is recursive. The terms
left- and right-recursive, and useful are analogously defined.

[2] A grammar is minimal if it contains only reachable and useful nonterminals.

[3] A grammar is wellformed if it is not left-recursive. Such grammars are also complete, which means
that they always succeed or fail on all input sentences. For an incomplete grammar on the other
hand input sentences exist for which an attempt to match them against the grammar will not
terminate.

[4] As we wish to allow ourselves to build a grammar incrementally in a container object we will
encounter stages where the RHS of one or more rules reference symbols which are not yet known to
the container. Such a grammar we call invalid. We cannot use the term incomplete as this term is
already taken, see the last item.

CONTAINER CLASS API
The package exports the API described here.

::grammar::peg pegName ?=|:=|<--|as|deserialize src?
The command creates a new container object for a parsing expression grammar and returns the fully
qualified name of the object command as its result. The API the returned command is following is
described in the section CONTAINER OBJECT API. It may be used to invoke various operations on the
container and the grammar within.

The new container, i.e. grammar will be empty if no src is specified. Otherwise it will contain a
copy of the grammar contained in the src. The src has to be a container object reference for all
operators except deserialize. The deserialize operator requires src to be the serialization of a
parsing expression grammar instead.

An empty grammar has no nonterminal symbols, and the start expression is the empty expression,
i.e. epsilon. It is valid, but not useful.

CONTAINER OBJECT API
All grammar container objects provide the following methods for the manipulation of their contents:

pegName destroy
Destroys the grammar, including its storage space and associated command.

pegName clear
Clears out the definition of the grammar contained in pegName, but does not destroy the object.

pegName = srcPEG
Assigns the contents of the grammar contained in srcPEG to pegName, overwriting any existing
definition. This is the assignment operator for grammars. It copies the grammar contained in the
grammar object srcPEG over the grammar definition in pegName. The old contents of pegName are
deleted by this operation.

This operation is in effect equivalent to

pegName deserialize [srcPEG serialize]

pegName --> dstPEG
This is the reverse assignment operator for grammars. It copies the automation contained in the
object pegName over the grammar definition in the object dstPEG. The old contents of dstPEG are
deleted by this operation.

This operation is in effect equivalent to

dstPEG deserialize [pegName serialize]

pegName serialize
This method serializes the grammar stored in pegName. In other words it returns a tcl value
completely describing that grammar. This allows, for example, the transfer of grammars over
arbitrary channels, persistence, etc. This method is also the basis for both the copy constructor
and the assignment operator.

The result of this method has to be semantically identical over all implementations of the
grammar::peg interface. This is what will enable us to copy grammars between different
implementations of the same interface.

The result is a list of four elements with the following structure:

[1] The constant string grammar::peg.

[2] A dictionary. Its keys are the names of all known nonterminal symbols, and their associated
values are the parsing expressions describing their sentennial structure.

[3] A dictionary. Its keys are the names of all known nonterminal symbols, and their associated
values hints to a matcher regarding the semantic values produced by the symbol.

[4] The last item is a parsing expression, the start expression of the grammar.

Assuming the following PEG for simple mathematical expressions

Digit <- '0'/'1'/'2'/'3'/'4'/'5'/'6'/'7'/'8'/'9'
Sign <- '+' / '-'
Number <- Sign? Digit+
Expression <- '(' Expression ')' / (Factor (MulOp Factor)*)
MulOp <- '*' / '/'
Factor <- Term (AddOp Term)*
AddOp <- '+'/'-'
Term <- Number

a possible serialization is

grammar::peg \
{Expression {/ {x ( Expression )} {x Factor {* {x MulOp Factor}}}} \
Factor {x Term {* {x AddOp Term}}} \
Term Number \
MulOp {/ * /} \
AddOp {/ + -} \
Number {x {? Sign} {+ Digit}} \
Sign {/ + -} \
Digit {/ 0 1 2 3 4 5 6 7 8 9} \
} \
{Expression value Factor value \
Term value MulOp value \
AddOp value Number value \
Sign value Digit value \
}
Expression

A possible one, because the order of the nonterminals in the dictionary is not relevant.

pegName deserialize serialization
This is the complement to serialize. It replaces the grammar definition in pegName with the
grammar described by the serialization value. The old contents of pegName are deleted by this
operation.

pegName is valid
A predicate. It tests whether the PEG in pegName is valid. See section TERMS & CONCEPTS for the
definition of this grammar property. The result is a boolean value. It will be set to true if the
PEG has the tested property, and false otherwise.

pegName start ?pe?
This method defines the start expression of the grammar. It replaces the previously defined start
expression with the parsing expression pe. The method fails and throws an error if pe does not
contain a valid parsing expression as specified in the section PARSING EXPRESSIONS. In that case
the existing start expression is not changed. The method returns the empty string as its result.

If the method is called without an argument it will return the currently defined start expression.

pegName nonterminals
Returns the set of all nonterminal symbols known to the grammar.

pegName nonterminal add nt pe
This method adds the nonterminal nt and its associated parsing expression pe to the set of
nonterminal symbols and rules of the PEG contained in the object pegName. The method fails and
throws an error if either the string nt is already known as a symbol of the grammar, or if pe does
not contain a valid parsing expression as specified in the section PARSING EXPRESSIONS. In that
case the current set of nonterminal symbols and rules is not changed. The method returns the
empty string as its result.

pegName nonterminal delete nt1 ?nt2 ...?
This method removes the named symbols nt1, nt2 from the set of nonterminal symbols of the PEG
contained in the object pegName. The method fails and throws an error if any of the strings is
not known as a nonterminal symbol. In that case the current set of nonterminal symbols is not
changed. The method returns the empty string as its result.

The stored grammar becomes invalid if the deleted nonterminals are referenced by the RHS of still-
known rules.

pegName nonterminal exists nt
A predicate. It tests whether the nonterminal symbol nt is known to the PEG in pegName. The
result is a boolean value. It will be set to true if the symbol nt is known, and false otherwise.

pegName nonterminal rename nt ntnew
This method renames the nonterminal symbol nt to ntnew. The method fails and throws an error if
either nt is not known as a nonterminal, or if ntnew is a known symbol. The method returns the
empty string as its result.

pegName nonterminal mode nt ?mode?
This mode returns or sets the semantic mode associated with the nonterminal symbol nt. If no mode
is specified the current mode of the nonterminal is returned. Otherwise the current mode is set to
mode. The method fails and throws an error if nt is not known as a nonterminal. The grammar
interpreter implemented by the package grammar::peg::interpreter recognizes the following modes:

value The semantic value of the nonterminal is the abstract syntax tree created from the AST's of
the RHS and a node for the nonterminal itself.

match The semantic value of the nonterminal is an the abstract syntax tree consisting of single a
node for the string matched by the RHS. The ASTs generated by the RHS are discarded.

leaf The semantic value of the nonterminal is an the abstract syntax tree consisting of single a
node for the nonterminal itself. The ASTs generated by the RHS are discarded.

discard
The nonterminal has no semantic value. The ASTs generated by the RHS are discarded (as
well).

pegName nonterminal rule nt
This method returns the parsing expression associated with the nonterminal nt. The method fails
and throws an error if nt is not known as a nonterminal.

pegName unknown nonterminals
This method returns a list containing the names of all nonterminal symbols which are referenced on
the RHS of a grammatical rule, but have no rule definining their structure. In other words, a list
of the nonterminal symbols which make the grammar invalid. The grammar is valid if this list is
empty.

PARSING EXPRESSIONS
Various methods of PEG container objects expect a parsing expression as their argument, or will return
such. This section specifies the format such parsing expressions are in.

[1] The string epsilon is an atomic parsing expression. It matches the empty string.

[2] The string alnum is an atomic parsing expression. It matches any alphanumeric character.

[3] The string alpha is an atomic parsing expression. It matches any alphabetical character.

[4] The string dot is an atomic parsing expression. It matches any character.

[5] The expression [list t x] is an atomic parsing expression. It matches the terminal string x.

[6] The expression [list n A] is an atomic parsing expression. It matches the nonterminal A.

[7] For parsing expressions e1, e2, ... the result of [list / e1 e2 ... ] is a parsing expression as
well. This is the ordered choice, aka prioritized choice.

[8] For parsing expressions e1, e2, ... the result of [list x e1 e2 ... ] is a parsing expression as
well. This is the sequence.

[9] For a parsing expression e the result of [list * e] is a parsing expression as well. This is the
kleene closure, describing zero or more repetitions.

[10] For a parsing expression e the result of [list + e] is a parsing expression as well. This is the
positive kleene closure, describing one or more repetitions.

[11] For a parsing expression e the result of [list & e] is a parsing expression as well. This is the
and lookahead predicate.

[12] For a parsing expression e the result of [list ! e] is a parsing expression as well. This is the
not lookahead predicate.

[13] For a parsing expression e the result of [list ? e] is a parsing expression as well. This is the
optional input.

Examples of parsing expressions where already shown, in the description of the method serialize.

PARSING EXPRESSION GRAMMARS

For the mathematically inclined, a PEG is a 4-tuple (VN,VT,R,eS) where

• VN is a set of nonterminal symbols,

• VT is a set of terminal symbols,

• R is a finite set of rules, where each rule is a pair (A,e), A in VN, and e a parsing expression.

• eS is a parsing expression, the start expression.

Further constraints are

• The intersection of VN and VT is empty.

• For all A in VT exists exactly one pair (A,e) in R. In other words, R is a function from
nonterminal symbols to parsing expressions.

Parsing expression are inductively defined via

• The empty string (epsilon) is a parsing expression.

• A terminal symbol a is a parsing expression.

• A nonterminal symbol A is a parsing expression.

• e1e2 is a parsing expression for parsing expressions e1 and 2. This is called sequence.

• e1/e2 is a parsing expression for parsing expressions e1 and 2. This is called ordered choice.

• e* is a parsing expression for parsing expression e. This is called zero-or-more repetitions, also
known as kleene closure.

• e+ is a parsing expression for parsing expression e. This is called one-or-more repetitions, also
known as positive kleene closure.

• !e is a parsing expression for parsing expression e1. This is called a not lookahead predicate.

• &e is a parsing expression for parsing expression e1. This is called an and lookahead predicate.

PEGs are used to define a grammatical structure for streams of symbols over VT. They are a modern
phrasing of older formalisms invented by Alexander Birham. These formalisms were called TS (TMG
recognition scheme), and gTS (generalized TS). Later they were renamed to TPDL (Top-Down Parsing
Languages) and gTPDL (generalized TPDL).

They can be easily implemented by recursive descent parsers with backtracking. This makes them relatives
of LL(k) Context-Free Grammars.

REFERENCES

       [1]    The       Packrat       Parsing       and       Parsing       Expression       Grammars       Page
              [http://www.pdos.lcs.mit.edu/~baford/packrat/],  by  Bryan  Ford,   Massachusetts   Institute   of
              Technology. This is the main entry page to PEGs, and their realization through Packrat Parsers.

       [2]    Parsing  Techniques  -  A  Practical Guide  [http://www.cs.vu.nl/~dick/PTAPG.html], an online book
              offering a clear, accessible, and thorough discussion of many different  parsing  techniques  with
              their interrelations and applicabilities, including error recovery techniques.

       [3]    Compilers  and  Compiler  Generators  [http://scifac.ru.ac.za/compilers/],  an  online  book using
              CoCo/R, a generator for recursive descent parsers.

BUGS, IDEAS, FEEDBACK

       This document, and the package it describes, will undoubtedly contain bugs and  other  problems.   Please
       report  such  in  the category grammar_peg 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

       LL(k), TDPL, context-free languages, expression, grammar, parsing, parsing expression, parsing expression
       grammar, push down automaton, recursive descent, state, top-down parsing languages, transducer

COPYRIGHT

       Copyright (c) 2005 Andreas Kupries <andreas_kupries@users.sourceforge.net>