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.

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>