Recursive Descent Parsing for XML Developers Roger L. Costello 15 October 2014 1.

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Recursive Descent Parsing for XML

Developers

Roger L. Costello15 October 2014

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Table of Contents

• Introduction to parsing in general, recursive descent parsing in particular

• Example #1: How to do recursive descent parsing on Book data• Example #2: How to do recursive descent parsing for a grammar that

contains alternatives • Limitations of recursive descent parsing

Flat XML Document

You might receive an XML document that has no structure. For example, this XML document contains a flat (linear) list of Book data:

<input> <Title>Parsing Techniques</Title> <Author>Dick Grune</Author> <Author> Ceriel J.H. Jacobs</Author> <Date>2007</Date> <ISBN>978-0-387-20248-8</ISBN> <Publisher>Springer</Publisher> <Title>Introduction to Graph Theory</Title> <Author>Richard J. Trudeau</Author> <Date>1993</Date> <ISBN>0-486-67870-9</ISBN> <Publisher>Dover Publications</Publisher> <Title>Introduction to Formal Languages</Title> <Author>Gyorgy E. Revesz</Author> <Date>2012</Date> <ISBN>0-486-66697-2</ISBN> <Publisher>Dover Publications</Publisher></input> 2

Give it structure to facilitate processing

<input> <Title>Parsing Techniques</Title> <Author>Dick Grune</Author> <Author> Ceriel J.H. Jacobs</Author> <Date>2007</Date> <ISBN>978-0-387-20248-8</ISBN> <Publisher>Springer</Publisher> <Title>Introduction to Graph Theory</Title> <Author>Richard J. Trudeau</Author> <Date>1993</Date> <ISBN>0-486-67870-9</ISBN> <Publisher>Dover Publications</Publisher> <Title>Introduction to Formal Languages</Title> <Author>Gyorgy E. Revesz</Author> <Date>2012</Date> <ISBN>0-486-66697-2</ISBN> <Publisher>Dover Publications</Publisher></input>

<Books> <Book> <Title>Parsing Techniques</Title> <Authors> <Author>Dick Grune</Author> <Author> Ceriel J.H. Jacobs</Author> </Authors> <Date>2007</Date> <ISBN>978-0-387-20248-8</ISBN> <Publisher>Springer</Publisher> </Book> <Book> <Title>Introduction to Graph Theory</Title> <Authors> <Author>Richard J. Trudeau</Author> </Authors> <Date>1993</Date> <ISBN>0-486-67870-9</ISBN> <Publisher>Dover Publications</Publisher> </Book> <Book> <Title>Introduction to Formal Languages</Title> <Authors> <Author>Gyorgy E. Revesz</Author> </Authors> <Date>2012</Date> <ISBN>0-486-66697-2</ISBN> <Publisher>Dover Publications</Publisher> </Book></Books> 3

That’s parsing!

Parsing is taking a flat (linear) sequence of items and adding structure so that the result conforms to a grammar.

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Parsing


<Books> <Book> <Title>Parsing Techniques</Title> <Authors> <Author>Dick Grune</Author> <Author> Ceriel J.H. Jacobs</Author> </Authors> <Date>2007</Date> <ISBN>978-0-387-20248-8</ISBN> <Publisher>Springer</Publisher> </Book> <Book> <Title>Introduction to Graph Theory</Title> <Authors> <Author>Richard J. Trudeau</Author> </Authors> <Date>1993</Date> <ISBN>0-486-67870-9</ISBN> <Publisher>Dover Publications</Publisher> </Book> <Book> <Title>Introduction to Formal Languages</Title> <Authors> <Author>Gyorgy E. Revesz</Author> </Authors> <Date>2012</Date> <ISBN>0-486-66697-2</ISBN> <Publisher>Dover Publications</Publisher> </Book></Books>

parse

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From the book: “Parsing Techniques”

• Parsing is the process of structuring a linear representation in accordance with a given grammar.

• The “linear representation” may be:• a flat sequence of XML elements• a sentence• a computer program• a knitting pattern• a sequence of geological strata• a piece of music• actions of ritual behavior

Grammar

• A grammar is a succinct description of the structure.• Here is a grammar for Books:

Books → Book+Book → Title Authors Date ISBN PublisherAuthors → Author+Title → textAuthor → textDate → textISBN → textPublisher → text

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Parsing

parser



Grammar

Linear representation


Structured representation

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Alternate view of the parser output

parser



Grammar

Linear representation

Parse tree

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Books

Book

Title Authors Date ISBN Publisher

Book

Title Authors

Author

Date ISBN Publisher

Book

Title Authors

Author

Date ISBN Publisher

Author Author

Parsing Techniques

Dick Grune Ceriel J.H. Jacobs

2007 978-0-387-20248-8 Springer Introduction to Graph Theory

Richard J. Trudeau

1993 0-486-67870-9 Dover Publications Introduction to Formal Languages

Gyorgy E. Revesz

2012 0-486-66697-2 Dover Publications

Parsing Techniques

• Over the last 50 years many parsing techniques have been created.• Some parsing techniques work from the starting grammar rule to the

bottom. Those are called top-down parsing techniques.• Other parsing techniques work from the bottom grammar rules to the

starting grammar rule. Those are called bottom-up parsing techniques.

• The following slides explain the “recursive descent parsing technique.” It is a top-down parsing technique.

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Terminology: Token

• A token is an atomic (indivisible) unit.• Each item in the input is a token.• After parsing the tokens will be leaf nodes.

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The input consists of a sequence of tokens


Each of these are tokens. This input consists of 16 tokens.

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After parsing the tokens will be leaf nodes


tokens (terminal symbols)

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Another view of the tokens, after parsing

Books

Book

Title Authors Date ISBN Publisher

Book

Title Authors

Author

Date ISBN Publisher

Book

Title Authors

Author

Date ISBN Publisher

Author Author

Parsing Techniques

Dick Grune Ceriel J.H. Jacobs

2007 978-0-387-20248-8 Springer Introduction to Graph Theory

Richard J. Trudeau

1993 0-486-67870-9 Dover Publications Introduction to Formal Languages

Gyorgy E. Revesz

2012 0-486-66697-2 Dover Publications

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Parsing structures the input by wrapping the tokens in non-terminal symbols


non-terminal symbols

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Recursive descent parsing

Recursive descent parsing works like this:• Start at the grammar’s start symbol and output it. In our grammar, the start

symbol is <Books>, so output it.• Progress through each grammar rule. For a non-terminal symbol, output it.

For a terminal symbol (i.e., token), check the token in the input stream for match with the terminal symbol; if it matches, output it.

Initial


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<Title>Parsing Techniques</Title><Author>Dick Grune</Author><Author> Ceriel J.H. Jacobs</Author><Date>2007</Date><ISBN>978-0-387-20248-8</ISBN><Publisher>Springer</Publisher><Title>Introduction to Graph Theory</Title><Author>Richard J. Trudeau</Author><Date>1993</Date><ISBN>0-486-67870-9</ISBN><Publisher>Dover Publications</Publisher><Title>Introduction to Formal Languages</Title><Author>Gyorgy E. Revesz</Author><Date>2012</Date><ISBN>0-486-66697-2</ISBN><Publisher>Dover Publications</Publisher>

Start with the grammar’s start symbol and the first token in the input stream.

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Output the start symbol



<Books>

</Books>

Output:

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Grammar says there must be at least one Book


So the input stream must contain all the tokens for at least one Book. Let’s process the grammar rule for Book.

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Output <Book>



<Books> <Book>

<Book></Books>

Output:

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Grammar says the token in the input stream must be Title


<Title>Parsing Techniques</Title><Author>Dick Grune</Author><Author> Ceriel J.H. Jacobs</Author><Date>2007</Date><ISBN>978-0-387-20248-8</ISBN><Publisher>Springer</Publisher><Title>Introduction to Graph Theory</Title><Author>Richard J. Trudeau</Author><Date>1993</Date><ISBN>0-486-67870-9</ISBN><Publisher>Dover Publications</Publisher><Title>Introduction to Formal Languages</Title><Author>Gyorgy E. Revesz</Author><Date>2012</Date><ISBN>0-486-66697-2</ISBN><Publisher>Dover Publications</Publisher><Books>

<Book> <Title>Parsing Techniques</Title>

<Book></Books>

Output:

Yea, the input token matches the

grammar rule

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Grammar: after Title must be Authors


So the input stream must contain Author tokens. Let’s process the rule for Authors.

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Output <Authors>


<Title>Parsing Techniques</Title><Author>Dick Grune</Author><Author> Ceriel J.H. Jacobs</Author><Date>2007</Date><ISBN>978-0-387-20248-8</ISBN><Publisher>Springer</Publisher><Title>Introduction to Graph Theory</Title><Author>Richard J. Trudeau</Author><Date>1993</Date><ISBN>0-486-67870-9</ISBN><Publisher>Dover Publications</Publisher><Title>Introduction to Formal Languages</Title><Author>Gyorgy E. Revesz</Author><Date>2012</Date><ISBN>0-486-66697-2</ISBN><Publisher>Dover Publications</Publisher><Books>

<Book> <Authors>

<Authors>

<Book></Books>

Output:

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Grammar says the next token in the input stream must be an Author token




grammar rule

<Books> <Book> <Authors> <Author>Dick Grune</Author>

<Authors>

<Book></Books>

Output:

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Grammar says the next token in the input stream may be an Author token



Another Author match

<Books> <Book> <Authors> <Author>Dick Grune</Author> <Author> Ceriel J.H. Jacobs</Author> <Authors>

<Book></Books>

Output:

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The next token in the input stream is not an Author token



So, return to the caller (i.e., return to the Book rule).

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Grammar says the input stream token must be a Date token




grammar rule

<Books> <Book> <Authors> <Author>Dick Grune</Author> <Author> Ceriel J.H. Jacobs</Author> <Authors> <Date>2007</Date>

<Book></Books>

Output:

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Grammar says the input stream token must be an ISBN token




grammar rule

<Books> <Book> <Authors> <Author>Dick Grune</Author> <Author> Ceriel J.H. Jacobs</Author> <Authors> <Date>2007</Date> <ISBN>978-0-387-20248-8</ISBN>

<Book></Books>

Output:

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Grammar says the input stream token must be a Publisher token




grammar rule

<Books> <Book> <Authors> <Author>Dick Grune</Author> <Author> Ceriel J.H. Jacobs</Author> <Authors> <Date>2007</Date> <ISBN>978-0-387-20248-8</ISBN> <Publisher>Springer</Publisher> <Book></Books>

Output:

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We’ve completed structuring the first 6 input tokens



<Books> <Book> <Authors> <Author>Dick Grune</Author> <Author> Ceriel J.H. Jacobs</Author> <Authors> <Date>2007</Date> <ISBN>978-0-387-20248-8</ISBN> <Publisher>Springer</Publisher> <Book></Books>

Output:

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Completed the Book rule



We’ve finished processing the Book rule, so return to the caller (i.e., the Books rule).

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Begin work on structuring the next Book



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Implementation

The following slides show, in a step-by-step manner, how to implement a recursive descent parser

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Step 1

Create a function for each non-terminal symbol in the grammar:

Books() { …} Book() { …} Authors() { …}

Books → Book+Book → Title Authors Date ISBN PublisherAuthors → Author+

Functions

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Step 2

Create a global element, Token, that is used to identify the current position in the input stream. Initialize Token to 0:

Token = 0

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Step 3

Create a function, get_next_token(). When it is called, it increments the current position in the input stream:

get_next_token() { Token = Token + 1}

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Step 4

Create a function, token(), and pass it a name, tk. The purpose of this function is to answer the question: “Does the token at the current position in the input stream match tk?”

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Example of using the token() functionSuppose that during recursive descent parsing the grammar indicates that the next token in the input stream must be “Title.” Suppose the global variable, Token, indicates that we are here in the input stream:


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Example (cont.)

The token() function determines that there is a match, so it calls get_next_token() to increment the position in the input stream and returns the token:


return

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The token() function

token(string tk) { if (tk != input[position() = Token]) then return () else { get_next_token() return input[position() = Token]) }}

Notice that token() returns empty if there is not a match.

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Motivation for Step 5

Suppose that during recursive descent parsing we are in the Book() function. The Book() function first checks—by calling the token() function—to see if the current position of the input stream contains “Title.” Suppose it does. Then, according to the grammar, there must be Authors, Date, ISBN, and then Publisher:

Book → Title Authors Date ISBN Publisher

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Step 5

Create a function, require(), and pass it a token, found. If the token is empty (i.e., the token() function returned empty because there was not a match) then call the error() function. Otherwise, return the token.

require(element found) { if empty(found) then error(‘Invalid input’) else return found}

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Step 6

Create an error function, error(). Pass it a string. It outputs the string and then halts the parser.

error(string s) { output s stop}

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The complete implementation

• Recursive descent has been around a long time and people have developed beautiful code for it.

• The following two slides collects all the code from the previous slides. I recommend spending some time studying it to appreciate its beauty.

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Token = 0

main() { get_next_token() require(input())}

input() { return require(Books())} Books() { <Books> return (require(Book()), optional_additional_Books()) </Books>} optional_additional_Books() { book = Book() if exists(book) then return (book, optional_additional_Books())} Book() { title = token('Title') if exists(title) then <Book> return (title, require(Authors(), require(token('Date')), require(token(‘ISBN')), require(token(‘Publisher')) </Book> } Authors() { <Authors> return (require(Author()), optional_additional_Authors()) </Authors>}

Code for a Recursive Descent Parser

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optional_additional_Authors() { author = token(‘Author') if exists(author) then return (author, optional_additional_Authors())}

token(string tk) { if (tk != input[position() = Token]) then return () else { get_next_token() return input[position() = Token]) }}

require(element found) { if empty(found) then error(‘Invalid input’) else return found}

get_next_token() { Token = Token + 1}

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XSLT Implementation

• I created an XSLT implementation. I tried to mirror the beautiful code shown on the previous slides.

• If you would like to give my implementation a go, here is the XSLT program and a sample flat (linear) input XML document:

• http://www.xfront.com/parsing-techniques/recursive-descent-parser/books-parser.xsl

• http://www.xfront.com/parsing-techniques/recursive-descent-parser/books-test.xml

http://www.xfront.com/parsing-techniques/recursive-descent-parser/books-parser.xsl



http://www.xfront.com/parsing-techniques/recursive-descent-parser/books.xml



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Richer example

• The Books example shown on the previous slides was fine for introducing recursive descent parsing.

• But it glossed over an important problem: grammar rules with alternatives.

• The following example shows how to do recursive descent parsing with a grammar that has alternatives.

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Expressions

• Let’s parse a simple expression language that has these tokens: IDENTIFIER, addition, parentheses, and EoF.

• Here are a few examples of expressions:

IDENTIFIER EoF(IDENTIFIER) EoFIDENTIFIER + IDENTIFIER EoF(IDENTIFIER + IDENTIFIER) EoFIDENTIFIER + (IDENTIFIER + IDENTIFIER) EoF(IDENTIFIER + IDENTIFIER) + IDENTIFIER EoFIDENTIFIER + (IDENTIFIER + (IDENTIFIER + IDENTIFIER)) EoF

Each expression ends with an end-of-file (EoF) token.

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Expression grammar

input → expression EoFexpression → term rest_expressionterm → IDENTIFIER | parenthesized_expressionparenthesized_expression → '(' expression ')'rest_expression → '+' expression | ε

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Parse tree for: IDENTIFIER EoF


input

expression EoF

term rest_expression

IDENTIFIER ε

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Parser selects the first alternative


input

expression EoF


IDENTIFIER ε

term has two alternatives. The parser selected the first alternative.

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Parse tree for: (IDENTIFIER) EoFinput

expression EoF


parenthesized_expression ε( expression )


IDENTIFIER εinput → expression EoFexpression → term rest_expressionterm → IDENTIFIER | parenthesized_expressionparenthesized_expression → '(' expression ')'rest_expression → '+' expression | ε

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Parser selects the second alternative


input

expression EoF


parenthesized_expression ε( expression )


IDENTIFIER ε term’s second alternative is selected

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Question

How does a recursive descent parser know that it should select the first or second alternative?

term → IDENTIFIER | parenthesized_expression

How does the parser know which alternative to select?

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Answer

• The parser doesn’t know.• It tries the first alternative. If that fails it tries the second alternative

(i.e., the parser backtracks and tries the next alternative). It repeats until it finds an alternative that succeeds.

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Processing the first token in the input stream


input

expression

term

IDENTIFIER

Try the first alternative, which says the input token must be IDENTIFIER. However, the input token is ( so we must back up and try the next alternative

1

2

3

Input tokens:(IDENTIFIER)EoF

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Implementation of the term() function

term() { <term> identifier = token('IDENTIFIER') if exists(identifier) then return (identifier) else return (require(parenthesized_expression())) </term> }

Check the current token in the input stream to see if it is IDENTIFIER.

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term() function (cont.)


If there is a match, return the token.

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term() function (cont.)


Otherwise try the other alternative, it must succeed.

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Let’s represent each expression as XML

Instead of this input: IDENTIFIER EoF

our input will be this:

<input> <IDENTIFIER /> <EoF /></input>

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XML representation (cont.)

Instead of this input: (IDENTIFIER) EoF


<input> <LP /> <IDENTIFIER /> <RP /> <EoF /></input>

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Instead of this input: IDENTIFIER + IDENTIFIER EoF


<input> <IDENTIFIER /> <PLUS /> <IDENTIFIER /> <EoF /></input>

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Instead of this input: IDENTIFIER + (IDENTIFIER + IDENTIFIER) EoF

our input will be this XML input:

<input> <IDENTIFIER /> <PLUS /> <LP /> <IDENTIFIER /> <PLUS /> <IDENTIFIER /> <RP /> <EoF /></input>

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Parsing

<input> <IDENTIFIER /> <EoF /></input>

Parser


<output> <expression> <term> <IDENTIFIER/> </term> <rest_expression/> </expression> <EoF/></output>

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Parsing (cont.)

<input> <LP /> <IDENTIFIER /> <RP /> <EoF /></input>

Parser


<output> <expression> <term> <parenthesized_expression> <LP/> <expression> <term> <IDENTIFIER/> </term> <rest_expression/> </expression> <RP/> </parenthesized_expression> </term> <rest_expression/> </expression> <EoF/></output>

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Parsing (cont.)

<input> <IDENTIFIER /> <PLUS /> <IDENTIFIER /> <EoF /></input>

Parser


<output> <expression> <term> <IDENTIFIER/> </term> <rest_expression> <PLUS/> <expression> <term> <IDENTIFIER/> </term> <rest_expression/> </expression> </rest_expression> </expression> <EoF/></output>

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Parsing (cont.)

<input> <IDENTIFIER /> <PLUS /> <LP /> <IDENTIFIER /> <PLUS /> <IDENTIFIER /> <RP /> <EoF /></input>

Parser


<output> <expression> <term> <IDENTIFIER/> </term> <rest_expression> <PLUS/> <expression> <term> <parenthesized_expression> <LP/> <expression> <term> <IDENTIFIER/> </term> <rest_expression> <PLUS/> <expression> <term> <IDENTIFIER/> </term> <rest_expression/> </expression> </rest_expression> </expression> <RP/> </parenthesized_expression> </term> <rest_expression/> </expression> </rest_expression> </expression> <EoF/></output>

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XSLT Implementation

• I created an XSLT implementation of a recursive descent parser for the expression language.

• If you would like to give my implementation a go, here is the XSLT program and a sample flat (linear) input XML document:

• http://www.xfront.com/parsing-techniques/recursive-descent-parser/expression-parser.xsl

• http://www.xfront.com/parsing-techniques/recursive-descent-parser/expression-test.xml

http://www.xfront.com/parsing-techniques/recursive-descent-parser/expression-parser.xsl







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Limitations of Recursive Descent ParsersRecall that in a rule containing alternatives we tried the first alternative, if it failed we backtracked and tried the second alternative. Searching the alternatives is time-consuming.

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Limitations (cont.)

Recursive descent parsers can’t handle left-recursive grammar rules. The parser goes into an infinite loop.Example: suppose the grammar has this rule: expression → expression '-' termThat is a “left-recursive” rule: on the rule’s right-hand side it starts with the same symbol as on the left-hand side (i.e., expression). The recursive descent routine for this rule is:

expression() { return expression() and require(token(‘-’)) and require(term)}

(infinite) recursion!

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Limitations (cont.)

Suppose we add an array element as a term: term → IDENTIFIER | indexed_element | parenthesized_expression indexed_element → IDENTIFIER '[' expression ']'

and create a recursive descent parser for the new grammar. The routine for indexed_element will never be tried: when the sequence IDENTIFIER '[' occurs in the input, the first alternative of term will succeed, consume the identifier, and leave the indigestible part '[' expression ']' in the input.

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References – Great Books

Modern Compiler Design (http://www.amazon.com/Modern-Compiler-Design-Dick-Grune/dp/1461446988/ref=sr_1_1?s=books&ie=UTF8&qid=1413408458&sr=1-1&keywords=modern+compiler+design)Parsing Techniques (http://www.amazon.com/Parsing-Techniques-Practical-Monographs-Computer/dp/038720248X/ref=sr_1_1?s=books&ie=UTF8&qid=1413408496&sr=1-1&keywords=parsing+techniques)

http://www.amazon.com/Modern-Compiler-Design-Dick-Grune/dp/1461446988/ref=sr_1_1?s=books&ie=UTF8&qid=1413408458&sr=1-1&keywords=modern+compiler+design




http://www.amazon.com/Parsing-Techniques-Practical-Monographs-Computer/dp/038720248X/ref=sr_1_1?s=books&ie=UTF8&qid=1413408496&sr=1-1&keywords=parsing+techniques



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Recursive Descent Parsing for XML Developers Roger L. Costello 15 October 2014 1.

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