Provided by: libmarpa-r2-perl_2.086000~dfsg-10_amd64 
NAME
Marpa::R2::Vocabulary - Standard parsing terms as used within Marpa
Description
The definitions in this document are of standard parsing terms as they are used in the Marpa context. I
put defining uses of terms in boldface, for easy skimming. Where a narrow or specialized sense of the
term is the one that applies within Marpa, that is the only definition given. Marpa also sometimes uses
a standard term with a definition which is slightly different from the standard one. ("Ambiguous
grammar" is one example, and "grammar" itself is another.) When this is the case, it is explicitly
pointed out.
A reader totally new to parsing will find this document too terse to act as a textbook or tutorial. They
will need to look elsewhere first. As an introduction, I recommend Mark Jason Dominus's excellent
chapter on parsing in the Perl context. It's available on-line. Wikipedia is also an excellent place to
start.
Basic
A grammar is a set of rules, associated with a set of symbols, one of which is distinguished as the start
symbol. A symbol string, or simply string where the meaning is clear, is an ordered series of symbols.
The length of a string is the number of symbols in it.
A language is a set of symbol strings. A grammar defines a language, as will be described later.
It is important to note that the term language, as it is used in parsing theory, means something very
different from what it means in ordinary use. The meaning of the strings is an essential part of the
ordinary idea of what a language is. In ordinary use, the word "language" means far more than a
unordered list of its sentences. In parsing terminology, meaning (or semantics as it is called) is a
separate issue. For parsing theory a language is exactly a set of strings -- that and nothing more.
The Marpa definition of a grammar differs slightly from the various standard ones. Standard definitions
usually sharply distinguish terminal symbols from non-terminals. Marpa does not.
Stages of parsing
A recognizer is a program that determines whether its input is in the language of a grammar and a start
symbol. A parser is a program which finds the structure of that input.
The term parsing is used in a strict and a loose sense. Parsing in the loose sense is all phases of
finding a grammar's structure, including a separate recognition phase if the parser has one. (Marpa
does.) If a parser has phases, parsing in the strict sense refers specifically to the phase that finds
the structure of the input. When the Marpa documents use the term parsing in its strict sense, they will
speak explicitly of "parsing in the strict sense". Otherwise, parsing will mean parsing in the loose
sense.
Parsers often use a lexical analyzer to convert raw input, usually input text, into a token stream, which
is a series of tokens. Each token represents a symbol of the grammar and has a value. A lexical
analyzer is often called a lexer or a scanner, and lexical analysis is often called lexing or scanning.
The series of symbols represented by the series of tokens becomes the symbol string input seen by the
recognizer. The symbol string input is more often called the input sentence.
By default, Marpa uses the token stream model of input. Marpa also allows alternative input models.
These are new to Marpa, so that their terminology is of necessity non-standard. The terminology needed
for alternative input models is explained in the document that introduces them.
Rules
A standard way of describing rules is Backus-Naur Form, or BNF. A rule of a grammar is also often called
a production. In one common way of writing BNF, a production looks like this:
Expression ::= Term Factor
In the production above, "Expression", "Term" and "Factor" are symbols. A production consists of a left
hand side and a right hand side. In a context-free grammar, like those Marpa parses, the left hand side
of a production is always a symbol string of length 1. The right hand side of a production is a symbol
string of zero or more symbols. In the example, "Expression" is the left hand side, and "Term" and
"Factor" are right hand side symbols.
Left hand side and right hand side are often abbreviated as RHS and LHS. If the RHS of a production has
no symbols, the production is called an empty production or an empty rule.
Any symbol which is allowed to occur in the symbol string input is called a terminal symbol. If the
symbols in a symbol string are all terminals, that symbol string is also called a sentence.
Derivations
A step of a derivation, or derivation step, is a change made to a symbol string by applying one of the
productions from the grammar. The production must be one of those with a LHS that occurs in the symbol
string. The result of the derivation step is another symbol string, one in which every occurence of the
LHS symbol from the production is replaced by the RHS of the production. For example, if "A", "B", "C",
"D", and "X" are symbols, and
X ::= B C
is a production, then
A X D -> A B C D
is a derivation step, with ""A X D"" as its beginning and ""A B C D"" as its end or result. We say that
the symbol string ""A X D"" derives the symbol string ""A B C D"".
A derivation is a sequence of derivation steps. The length of a derivation is its length in steps.
• We say that a first symbol string directly derives a second symbol string if and only if there is a
derivation of length 1 from the first symbol string to the second symbol string.
• Every symbol string is said to derive itself in a derivation of length 0. A zero length derivation
is a trivial derivation.
• A derivation which is not trivial (that is, a derivation which has one or more steps) is a non-
trivial derivation.
• A non-trivial derivation of a symbol string from itself is called a cycle. Grammars which contain
cycles are traditionally considered useless, but Marpa will parse with such grammars.
• If a derivation is not trivial or direct, that is, if it has more than one step, then it is an
indirect derivation.
Technically, a symbol "X" and a string that consists of only that symbol are two different things. But
we often say "the symbol "X"" as shorthand for "the string of length 1 whose only symbol is "X"". For
example, if the string containing only the symbol "X" derives a string "Y", we will usually say simply
that ""X" derives "Y"".
Wherever symbol or string "X" derives "Y", we may also say "X" produces "Y". Derivations are often
described as symbol matches. Wherever symbol or string "X" derives "Y", we may also say that "Y" matches
"X" or that "X" matches "Y". It is particularly common to say that "X" matches "Y" when "X" or "Y" is a
sentence.
The parse of an input by a grammar is successful if and only if, according to the grammar, the start
symbol produces the input sentence. The set of all input sentences that a grammar will successfully
parse is the language of the grammar.
Nulling
The zero length symbol string is called the empty string. The empty string can be considered to be a
sentence, in which case it is the empty sentence. A string of one or more symbols is non-empty. A
derivation which produces the empty string is a null derivation. A derivation from the start symbol
which produces the empty string is a null parse.
If in a particular grammar, a symbol has a null derivation, it is a nullable symbol. If, in a particular
grammar, the only sentence produced by a symbol is the empty sentence, it is a nulling symbol. All
nulling symbols are nullable symbols.
If a symbol is not nullable, it is non-nullable. If a symbol is not nulling, it is non-nulling. In any
instance where a symbol produces the empty string, it is said to be nulled, or to be a null symbol.
Useless rules
If any derivation from the start symbol uses a rule, that rule is called reachable or accessible. A rule
that is not accessible is called unreachable or inaccessible. If any derivation which results in a
sentence uses a rule, that rule is said to be productive. A rule that is not productive is called
unproductive. For example, a rule is unproductive unless every symbol on its RHS either is a terminal or
is the LHS of some other rule. A rule which is inaccessible or unproductive is called a useless rule.
Marpa can handle grammars with useless rules.
A symbol is reachable or accessible if it appears in a reachable production. If a symbol is not
reachable, it is unreachable or inaccessible. A symbol is productive if it appears on the LHS of a
productive rule, or if it is a nullable symbol. If a symbol is not productive, it is unproductive. A
symbol which is inaccessible or unproductive is called a useless symbol. Marpa can handle grammars with
useless symbols.
Recursion and cycles
If any symbol in the grammar non-trivially produces a symbol string containing itself, the grammar is
said to be recursive. If any symbol non-trivially produces a symbol string with itself on the left, the
grammar is said to be left-recursive. If any symbol non-trivially produces a symbol string with itself
on the right, the grammar is said to be right-recursive. Marpa can handle all recursive grammars,
including grammars which are left-recursive, grammars which are right-recursive, and grammars which
contain both left- and right-recursion.
A cycle is a non-trivial derivation of a string of symbols from itself. If it is not possible for any
derivation using a grammar to contain a cycle, then that grammar is said to be cycle-free.
Traditionally, a grammar is considered useless if it is not cycle-free.
The traditional deprecation of cycles is well-founded. A cycle is the parsing equivalent of an infinite
loop. Once a cycle appears, it can be repeated over and over again. Even a very short input sentence
can have an infinite number of parses when the grammar is not cycle-free.
For that reason, a grammar which contains a cycle is also called infinitely ambiguous. Marpa can parse
with grammars which are not cycle-free, and will even parse inputs that cause cycles. When a parse is
infinitely ambiguous, Marpa limits cycles to a single loop, so that only a finite number of parses is
returned.
Parse structure
The structure of a parse can be represented as a series of derivation steps from the start symbol to the
input. Another way to represent structure is as a parse tree. Every symbol used in the parse is
represented by a node of the parse tree. Wherever a production is used in the parse, its LHS is
represented by a parent node and the RHS symbols are represented by child nodes. The start symbol is the
root of the tree. The node at the root of the tree is called the start node.
Traditionally, grammars divide all symbols sharply into terminals and non-terminals. A terminal symbol
must ALWAYS be used as a terminal. A non-terminal symbol can NEVER be used as a terminal.
Marpa's use of terminals is non-traditional, and its terminology is different accordingly. As in the
traditional approach, Marpa's non-terminals can never be used as terminals. But Marpa terminals can be
used anywhere, even in places where the traditional approach requires a a non-terminal symbol. In
particular, a Marpa terminal can be the LHS of a rule.
Traditionally, and in Marpa as well, every node is either a inner node or a leaf node. In Marpa, leaf
nodes are of two kinds:
• Nodes for nulled symbols. A node for a nulled symbol is called a nulled node.
• Nodes for symbols being used as terminals.
Ambiguity
Marpa allows ambiguous grammars. Traditionally we say that a parse is ambiguous if, for a given grammar
and a given input, more than one derivation tree is possible. However, Marpa allows ambiguous input
tokens, which the traditional definition does not take into account. If Marpa used the traditional
definition, all grammars would be ambiguous except those grammars which allowed only the null parse.
It is easiest if the Marpa definition and the traditional definition were extensionally equivalent ---
that is, if Marpa's set of ambiguous grammars was exactly the same as the set of traditionally ambiguous
grammars. This can be accomplished by using a slightly altered definition. In the Marpa context, a
grammar is ambiguous if and only if, for some UNAMBIGUOUS stream of input tokens, that grammar produces
more than one parse tree.
Semantics
In real life, the structure of a parse is usually a means to an end. Grammars usually have a semantics
associated with them, and what the user actually wants is the value of the parse according to the
semantics.
The tree representation is especially useful when evaluating a parse. In the traditional method of
evaluating a parse tree, every node which represents a terminal symbol has a value associated with it on
input. Non-null inner nodes take their semantics from the production whose LHS they represent. Nulled
nodes are dealt with as special cases.
The semantics for a production describe how to calculate the value of the node which represents the LHS
(the parent node) from the values of zero or more of the nodes which represent the RHS symbols (child
nodes). Values are computed recursively, bottom-up. The value of a parse is the value of its start
symbol.
Copyright and License
Copyright 2014 Jeffrey Kegler
This file is part of Marpa::R2. Marpa::R2 is free software: you can
redistribute it and/or modify it under the terms of the GNU Lesser
General Public License as published by the Free Software Foundation,
either version 3 of the License, or (at your option) any later version.
Marpa::R2 is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser
General Public License along with Marpa::R2. If not, see
http://www.gnu.org/licenses/.
perl v5.40.0 2024-12-07 Marpa::R2::Vocabulary(3pm)