[comment {-*- tcl -*- doctools manpage}]
[manpage_begin grammar::peg n 0.3]
[keywords {context-free languages}]
[keywords expression]
[keywords grammar]
[keywords LL(k)]
[keywords parsing]
[keywords {parsing expression}]
[keywords {parsing expression grammar}]
[keywords {push down automaton}]
[keywords {recursive descent}]
[keywords state]
[keywords TDPL]
[keywords {top-down parsing languages}]
[keywords transducer]
[copyright {2005 Andreas Kupries <andreas_kupries@users.sourceforge.net>}]
[moddesc   {Grammar operations and usage}]
[titledesc {Create and manipulate parsing expression grammars}]
[category  {Grammars and finite automata}]
[require Tcl "8.5 9"]
[require snit]
[require grammar::peg [opt 0.3]]
[description]
[para]

This package provides a container class for
[term {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 [package grammar::mengine] and
[package 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.

[subsection {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
[sectref {PARSING EXPRESSION GRAMMARS}].

[para]

In short, we have [term {terminal symbols}], which are the most basic
building blocks for [term sentences], and [term {nonterminal symbols}]
with associated [term {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 [term symbols].

[para]

Here the set of [term {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.

[para]

A pair of [term nonterminal] and [term {parsing expression}] is also
called a [term {grammatical rule}], or [term 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).

[para]

The [term {start expression}] of a grammar is a parsing expression
from which all the sentences contained in the language specified by
the grammar are [term 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

[para][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
}][para]

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

[para]

Some definitions for nonterminals and expressions:

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

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

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

[enum]
The [term {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
[term left-recursive].

[enum]
The [term {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
[term right-recursive].

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

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

[list_end]
[para]

And based on the above definitions for grammars:

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

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

[enum]
A grammar is [term wellformed] if it is not left-recursive. Such
grammars are also [term 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.

[enum]
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 [term invalid].

We cannot use the term [term incomplete] as this term is already
taken, see the last item.

[list_end]
[para]

[subsection {CONTAINER CLASS API}]

The package exports the API described here.

[list_begin definitions]

[call [cmd ::grammar::peg] [arg pegName] \
	[opt "[const =]|[const :=]|[const <--]|[const as]|[const deserialize] [arg 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 [sectref {CONTAINER OBJECT API}]. It may be used to invoke
various operations on the container and the grammar within.

[para]

The new container, i.e. grammar will be empty if no [arg src] is
specified. Otherwise it will contain a copy of the grammar contained
in the [arg src].

The [arg src] has to be a container object reference for all operators
except [const deserialize].

The [const deserialize] operator requires [arg src] to be the
serialization of a parsing expression grammar instead.

[para]

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

[list_end]

[subsection {CONTAINER OBJECT API}]
[para]

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

[list_begin definitions]

[call [arg pegName] [method destroy]]

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

[call [arg pegName] [method clear]]

Clears out the definition of the grammar contained in [arg pegName],
but does [emph not] destroy the object.

[call [arg pegName] [method =] [arg srcPEG]]

Assigns the contents of the grammar contained in [arg srcPEG] to
[arg pegName], overwriting any existing definition.

This is the assignment operator for grammars. It copies the grammar
contained in the grammar object [arg srcPEG] over the grammar
definition in [arg pegName]. The old contents of [arg pegName] are
deleted by this operation.

[para]

This operation is in effect equivalent to
[para]
[example_begin]
    [arg pegName] [method deserialize] [lb][arg srcPEG] [method serialize][rb]
[example_end]

[call [arg pegName] [method -->] [arg dstPEG]]

This is the reverse assignment operator for grammars. It copies the
automation contained in the object [arg pegName] over the grammar
definition in the object [arg dstPEG].

The old contents of [arg dstPEG] are deleted by this operation.

[para]

This operation is in effect equivalent to
[para]
[example_begin]
    [arg dstPEG] [method deserialize] [lb][arg pegName] [method serialize][rb]
[example_end]

[call [arg pegName] [method serialize]]

This method serializes the grammar stored in [arg pegName]. In other
words it returns a tcl [emph 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.

[para]

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

[para]

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

[list_begin enumerated]
[enum]
The constant string [const grammar::peg].

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

[enum]
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.

[enum]
The last item is a parsing expression, the [term {start expression}]
of the grammar.

[list_end]
[para]

Assuming the following PEG for simple mathematical expressions

[para]
[example {
    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
}]
[para]

a possible serialization is

[para]
[example {
    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
}]
[para]

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

[call [arg pegName] [method deserialize] [arg serialization]]

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

[call [arg pegName] [method {is valid}]]

A predicate. It tests whether the PEG in [arg pegName] is [term valid].
See section [sectref {TERMS & CONCEPTS}] for the definition of this
grammar property.

The result is a boolean value. It will be set to [const true] if
the PEG has the tested property, and [const false] otherwise.

[call [arg pegName] [method start] [opt [arg pe]]]

This method defines the [term {start expression}] of the grammar. It
replaces the previously defined start expression with the parsing
expression [arg pe].

The method fails and throws an error if [arg pe] does not contain a
valid parsing expression as specified in the section
[sectref {PARSING EXPRESSIONS}]. In that case the existing start
expression is not changed.

The method returns the empty string as its result.

[para]

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

[call [arg pegName] [method nonterminals]]

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

[call [arg pegName] [method {nonterminal add}] [arg nt] [arg pe]]

This method adds the nonterminal [arg nt] and its associated parsing
expression [arg pe] to the set of nonterminal symbols and rules of the
PEG contained in the object [arg pegName].

The method fails and throws an error if either the string [arg nt] is
already known as a symbol of the grammar, or if [arg pe] does not
contain a valid parsing expression as specified in the section
[sectref {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.

[call [arg pegName] [method {nonterminal delete}] [arg nt1] [opt "[arg nt2] ..."]]

This method removes the named symbols [arg nt1], [arg nt2] from the
set of nonterminal symbols of the PEG contained in the object
[arg 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.

[para]

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

[call [arg pegName] [method {nonterminal exists}] [arg nt]]

A predicate. It tests whether the nonterminal symbol [arg nt] is known
to the PEG in [arg pegName].

The result is a boolean value. It will be set to [const true] if the
symbol [arg nt] is known, and [const false] otherwise.

[call [arg pegName] [method {nonterminal rename}] [arg nt] [arg ntnew]]

This method renames the nonterminal symbol [arg nt] to [arg ntnew].

The method fails and throws an error if either [arg nt] is not known
as a nonterminal, or if [arg ntnew] is a known symbol.

The method returns the empty string as its result.

[call [arg pegName] [method {nonterminal mode}] [arg nt] [opt [arg mode]]]

This mode returns or sets the semantic mode associated with the
nonterminal symbol [arg nt]. If no [arg mode] is specified the
current mode of the nonterminal is returned. Otherwise the current
mode is set to [arg mode].

The method fails and throws an error if [arg nt] is not known as a
nonterminal.

The grammar interpreter implemented by the package
[package grammar::peg::interpreter] recognizes the
following modes:

[list_begin definitions]
[def 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.

[def 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.

[def 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.

[def discard]

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

[list_end]

[call [arg pegName] [method {nonterminal rule}] [arg nt]]

This method returns the parsing expression associated with the
nonterminal [arg nt].

The method fails and throws an error if [arg nt] is not known as a
nonterminal.

[call [arg pegName] [method {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.

[list_end]

[para]

[subsection {PARSING EXPRESSIONS}]
[para]

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.

[para]

[list_begin enumerated]
[enum]
The string [const epsilon] is an atomic parsing expression. It matches
the empty string.

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

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

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

[enum]
The expression
    [lb]list t [var x][rb]
is an atomic parsing expression. It matches the terminal string [var x].

[enum]
The expression
    [lb]list n [var A][rb]
is an atomic parsing expression. It matches the nonterminal [var A].

[enum]
For parsing expressions [var e1], [var e2], ... the result of

    [lb]list / [var e1] [var e2] ... [rb]

is a parsing expression as well.

This is the [term {ordered choice}], aka [term {prioritized choice}].

[enum]
For parsing expressions [var e1], [var e2], ... the result of

    [lb]list x [var e1] [var e2] ... [rb]

is a parsing expression as well.

This is the [term {sequence}].

[enum]
For a parsing expression [var e] the result of

    [lb]list * [var e][rb]

is a parsing expression as well.

This is the [term {kleene closure}], describing zero or more
repetitions.

[enum]
For a parsing expression [var e] the result of

    [lb]list + [var e][rb]

is a parsing expression as well.

This is the [term {positive kleene closure}], describing one or more
repetitions.

[enum]
For a parsing expression [var e] the result of

    [lb]list & [var e][rb]

is a parsing expression as well.

This is the [term {and lookahead predicate}].

[enum]
For a parsing expression [var e] the result of

    [lb]list ! [var e][rb]

is a parsing expression as well.

This is the [term {not lookahead predicate}].

[enum]
For a parsing expression [var e] the result of

    [lb]list ? [var e][rb]

is a parsing expression as well.

This is the [term {optional input}].

[list_end]
[para]

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

[section {PARSING EXPRESSION GRAMMARS}]
[para]

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

[list_begin itemized]
[item]
VN is a set of [term {nonterminal symbols}],

[item]
VT is a set of [term {terminal symbols}],

[item]
R is a finite set of rules, where each rule is a pair (A,e), A in VN,
and [term e] a [term {parsing expression}].

[item]
eS is a parsing expression, the [term {start expression}].

[list_end]
[para]

Further constraints are

[list_begin itemized]
[item]
The intersection of VN and VT is empty.

[item]
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.

[list_end]
[para]

Parsing expression are inductively defined via

[list_begin itemized]
[item]
The empty string (epsilon) is a parsing expression.

[item]
A terminal symbol [term a] is a parsing expression.

[item]
A nonterminal symbol [term A] is a parsing expression.

[item]
[term e1][term e2] is a parsing expression for parsing expressions
[term e1] and [term 2]. This is called [term sequence].

[item]
[term e1]/[term e2] is a parsing expression for parsing expressions
[term e1] and [term 2]. This is called [term {ordered choice}].

[item]
[term e]* is a parsing expression for parsing expression
[term e]. This is called [term {zero-or-more repetitions}], also known
as [term {kleene closure}].

[item]
[term e]+ is a parsing expression for parsing expression
[term e]. This is called [term {one-or-more repetitions}], also known
as [term {positive kleene closure}].

[item]
![term e] is a parsing expression for parsing expression
[term e1]. This is called a [term {not lookahead predicate}].

[item]
&[term e] is a parsing expression for parsing expression
[term e1]. This is called an [term {and lookahead predicate}].

[list_end]
[para]

[para]

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).

[para]

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

[section REFERENCES]

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

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

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

[vset CATEGORY grammar_peg]
[include ../common-text/feedback.inc]
[manpage_end]