grammar::peg(n) Grammar operations and usage grammar::peg(n) ______________________________________________________________________________
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 pro-
vides complex operations on the grammar, nor has it the ability to exe-
cute 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 pars-
ing 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 mathemati-
cal 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 implic-
itly 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 grammati-
cal 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 expres-
sion, 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 non-
terminal 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 nontermi-
nal 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 gram-
mars 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 expres-
sion 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 spec-
ified. 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 peg-
Name, overwriting any existing definition. This is the assign-
ment operator for grammars. It copies the grammar contained in
the grammar object srcPEG over the grammar definition in peg-
Name. 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 arbi-
trary 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 implementa-
tions of the same interface.
The result is a list of four elements with the following struc-
ture:
[1] The constant string grammar::peg.
[2] A dictionary. Its keys are the names of all known nonter-
minal symbols, and their associated values are the pars-
ing expressions describing their sentennial structure.
[3] A dictionary. Its keys are the names of all known nonter-
minal 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 expres-
sion 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 serial-
ization 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 pars-
ing 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 nontermi-
nal 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 nontermi-
nal 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
o VN is a set of nonterminal symbols,
o VT is a set of terminal symbols,
o R is a finite set of rules, where each rule is a pair (A,e), A
in VN, and e a parsing expression.
o eS is a parsing expression, the start expression.
Further constraints are
o The intersection of VN and VT is empty.
o 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
o The empty string (epsilon) is a parsing expression.
o A terminal symbol a is a parsing expression.
o A nonterminal symbol A is a parsing expression.
o e1e2 is a parsing expression for parsing expressions e1 and 2.
This is called sequence.
o e1/e2 is a parsing expression for parsing expressions e1 and 2.
This is called ordered choice.
o e* is a parsing expression for parsing expression e. This is
called zero-or-more repetitions, also known as kleene closure.
o e+ is a parsing expression for parsing expression e. This is
called one-or-more repetitions, also known as positive kleene
closure.
o !e is a parsing expression for parsing expression e1. This is
called a not lookahead predicate.
o &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 back-
tracking. 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 applicabili-
ties, including error recovery techniques.
[3] Compilers and Compiler Generators [http://scifac.ru.ac.za/com-
pilers/], 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 gram-
mar_peg of the Tcllib SF Trackers [http://source-
forge.net/tracker/?group_id=12883]. Please also report any ideas for
enhancements you may have for either package and/or documentation.
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
CATEGORY
Grammars and finite automata
COPYRIGHT
Copyright (c) 2005 Andreas Kupries <andreas_kupries@users.sourceforge.net>
grammar_peg 0.1 grammar::peg(n)
Mac OS X 10.8 - Generated Mon Sep 10 18:02:40 CDT 2012