PEG GrammarExplorer

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Introduction

This is the first part of a series of articles which cover the parsing technique Parsing

Expression Grammars. This part introduces a support library and a parser generator for C# 3.0 .

The support library consists of the classes PegCharParser and PegByteParser which are for

parsing text and binary sources and which support user defined error handling, direct evaluationduring parsing, parse tree generation and abstract syntax tree generation. Using these base

classes results in fast, easy to understand and to extend Parsers, which are well integrated into the

hosting C# program.

The underlying parsing methodologycalled Parsing Expression Grammar[1][2][3]is

relatively new (first described 2004), but has already many implementations. Parsing

Expressions Grammars (PEG) can be easily implemented in any programming language, but fitespecially well into languages with a rich expression syntax like functional languages and

functionally enhanced imperative languages (like C# 3.0) because PEG concepts have a closerelationship to mutually recursive function calls, short-circuit boolean expressions and in-place

defined functions (lambdas).

A new trend in parsing is integration of parsers into a host language so that the semantic gap

between grammar notation and implementation in the host language is as small as possible (Perl

6 and boost::sprit are forerunners of this trend). Parsing Expression Grammars areescpecially well suited when striving for this goal. Earlier Grammars were not so easy toimplement, so that one grammar rule could result in dozens of code lines. In some parsing

strategies, the relationship between grammar rule and implementation code was even lost. This is

the reason, that until recently generators were used to build parsers.

This article shows how the C# 3.0 lambda facility can be used to implement a support library for

Parsing Expression Grammars, which makes parsing with the PEG technique easy. When usingthis library, a PEG grammar is mapped to a C# grammar class which inherits basic functionality

from a PEG base class and each PEG grammar rule is mapped to a method in the C# grammar

class. Parsers implemented with this libary should be fast (provided the C# compiler inlinesmethods whenever possible), easy to understand and to extend. Error Diagnosis, generation of a

parse tree and addition of semantic actions are also supported by this library.

The most striking property of PEG and especially this library is the small footprint and the lack

of any administrative overhead.

The main emphasis of this article is on explaining the PEG framework and on studying concrete

application samples. One of the sample applications is a PEG parser generator, which generatesC# source code. The PEG parser generator is the only sample parser which has been written

manually, all other sample parsers were generated by the parser generator.

Contents

Introduction
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Parsing Expression Grammar Tutorialo Parsing Expression Grammars Basicso Parsing Expression Grammars partiularities and idiomso Integrating semantic actions into a PEG frameworko Parsing Expression Grammars exposed

Parsing Expression Grammar Implementationso General implementation strategy for PEG

o Parsing Expression Grammars mapped to C#1.0o Parsing Expression Grammars mapped to C#3.0

Parsing Expression Grammar Exampleso Json Checker (Recognize only)o Json Tree (Build Tree)o Basic Encode Rules (Direct Evaluation + Build Tree)o Scientific Calculator (Build Tree + Evaluate Tree)

PEG Parser Generatoro A PEG Generator implemented with PEGo

PEG Parser Generator Grammaro The PEG Parser Generator's handling of semantic blocks

Parsing Expression Grammars in perspectiveo Parsing Expression Grammars Tuningo Comparison of PEG parsing with other parsing techniqueso Translating LR grammars to PEG grammars

Future Developments

Parsing Expression Grammar Tutorial

Parsing Expression Grammars are a kind of executable grammars. Execution of a PEG grammar

means, that grammar patterns matching the input string advance the current input positionaccordingly. Mismatches are handled by going back to a previous input string position whereparsing eventually continues with an alternative. The following subchapters explain PEGs in

detail and introduce the basic PEG constructs, which have been extended by the author in order

to support error diagnosis, direct evaluation and tree generation.

Parsing Expression Grammars Basics

The following PEG grammar rule

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EnclosedDigits: [0-9]+ / '(' EnclosedDigits ')' ;

introduces a so called Nonterminal EnclosedDigits and a right hand side consisting of two

alternatives.

The first alternative ([0-9]+) describes a sequence of digits, the second ( '(' EnclosedDigits ')')

something enclosed in parentheses. Executing EnclosedDigits with the string ((123))+5 as input

would result in a match and move the input position to just before +5.
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Developmentshttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Future%20Developmentshttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Translating%20LR%20grammars%20to%20PEG%20grammarshttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Comparison%20of%20PEG%20parsing%20with%20other%20parsing%20techniqueshttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammars%20Tuninghttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammars%20in%20perspectivehttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#The%20PEG%20Parser%20Generator%27s%20handling%20of%20semantic%20blockshttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#PEG%20Parser%20Generator%20Grammarhttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#A%20PEG%20Generator%20implemented%20with%20PEGhttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#PEG%20Parser%20Generatorhttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Scientific%20Calculator%20%20%28Build%20Tree%20+%20Evaluate%20Tree%29http://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Basic%20Encode%20Rules%20%28Direct%20Evaluation%20+%20Build%20Tree%29http://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Json%20Tree%20%20%28Build%20Tree%29http://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Json%20Checker%20%28Recognize%20only%29http://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammar%20Exampleshttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammars%20mapped%20to%20C#3.0http://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammars%20mapped%20to%20C#1.0http://www.codeproject.com/KB/recipes/grammar_support_1.aspx#General%20implementation%20strategy%20for%20PEGhttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammar%20Implementationhttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammars%20exposedhttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Integrating%20semantic%20actions%20into%20a%20PEG%20frameworkhttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammars%20particularities%20and%20idiomshttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammars%20Basicshttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammar%20Tutorial


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This sample also shows the potential for recursive definitions, since EnclosedDigits uses itself as

soon as it recognizes an opening parentheses. The following table shows the outcome ofapplying the above grammar for some other input strings. The | character is an artifical character

which visualizes the input position before and after the match.

Input Match Position Match Result|((123))+5 ((123))|+5 true

|123 123| true

|5+123 |5+123 false

|((1)] |((1)] false

For people familiar with regular expressions, it may help to think of a parsing expression

grammar as a generalized regular expression which always matches the beginning of an input

string (regexp prefixed with ^). Whereas a regular expression consists of a single expression, a

PEG consists of set of rules; each rule can use other rules to help in parsing. The starting rule

matches the whole input and uses the other rules to match subparts of the input. During parsingone has always a current input position and the input string starting at this position must match

against the rest of the PEG grammar. Like regular expressions PEG supports the postfixoperators * + ? , the dot . and character sets enclosed in [].

Unique to PEG are the prefix operators & (peek) and ! (not), which are used to look aheadwithout consuming input. Alternatives in a PEG are not separated by | but by/to indicate that

alternatives are strictly tried in sequential order. What makes PEG grammars powerful and at the

same time a potential memory hogg is unlimited backtracking, meaning that the input position

can be set back to any of the previously visited input positions in case an alternative fails. Agood and detailed explanation of PEG can be found in the wikipedia[2]. The following table

gives an overview of the PEG constructs (and some homegrown extensions) which are supportedby the library class described in this article. The following terminology is used

Notion Meaning

Nonterminal

Name of a grammar rule. In PEG, there must be exactly one grammar rule having a

nonterminal on the left hand side. The right hand side of the grammar rule provides

the definition of the grammar rule. A nonterminal on the right hand side of a

grammar rule must reference an existing grammar rule definition.;

Input string string which is parsed.

Input

positionIndicates the next input character to be read.

MatchA grammar element can match a stretch of the input. The match starts at the current

input position.

Success/

FailurePossible outcome of matching a PEG element against the input

e, e1, e2 e, e1 and e2 stand each for arbitrary PEG expressions.
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The extended PEG constructs supported by this library are listed in the following table

(|indicates the input position, italics like in name indicate a placeholder):

PEG element Notation Meaning

CodePoint

#32 (decimal)

#x3A0 (hex)

#b111 (binary)

Match input against the specified unicode character.

PEG Success Failure

#x25 %|1 |1%

Literal 'literal'

Match input against quoted string.

PEG Success Failure

'for' for|tran |afordable

Escapes take the same form as in the "C" syntax

family.

CaseInsensitive

Literal'literal'\i

Same as for Literal but compares case insensitive. \i

must follow a Literal

PEG Success Failure'FOR'\i FoR|TraN |affordable

CharacterSet [chars]

Same meaning as in regular expressions. Supported

are ranges as in [A-Za-z0-9], single characters andescapes sequences.

Any .

increment the input position except when being at the

end of the input.

PEG Success Failure

'this is the end'

.

this is the

end!||this is the

end

BITS

BITS

BITS

Interprets the Bit bitNo/Bitsequence [low-high] of thecurrent input byte as integer which must match is used

as input for the PegElement.

PEG Success Failure

&BITS

|11010101 |01010101

Sequence e1 e2

Match input against e1 and then -in case of success-against e2.

PEG Success Failure

'#'[0-9] #5| |#A

Sequentially

executed

alternatives

e1 /e2

Match input against e1 and then - in case of failure -against e2.

PEG Success Failure

'


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'-'? -|42 |+42

Greedy repeat

zero or more

occurrences

e*

Match input repeated against e until the match fails.

PEG Success Success

[0-9]* 42|b |-42

Greedy repeat

one or more

occurrences

e+

Shorthand for e e*

PEG Success Failure

[0-9]* 42|b |-42

Greedy repeatbetween

minimum and

maximum

occurrences

e{min}

e{min,max}

e{,max}e{min,}

Match input at least min times but not more than maxtimes against e.

PEG Success Failure

('.'[0-9]*){2,3} .12.36.42|.18b |.42b

Peek &e

Match e without changing input position.

PEG Success Failure

&'42' |42 |-42

Not !e

Like Peek but SuccessFailure

PEG Success Failure

!'42' |-42 |42

FATALFATAL

Prints the message and error location to the error

stream and quits the parsing process afterwards

(throws an exception).

WARNINGWARNING

WARNING Prints the message and

location to the error stream.Success:

Mandatory @e Same as (e/FATAL )

Tree Node ^ê

ife is matched, a tree node will be added to the parse

tree. This tree node will hold the starting and ending

match positions for e

Ast Node êlike ^ê, but node will be replaced by the child node ifthere is only one child

Rule N: e;Nis the nonterminal; e the right hand side which is

terminated by a semicolon.

Rule with id [id]N: e;idmust be a positive integer,e.g. [1] Int:[0-9]+;The id will be assigned to the the tree/ast node id.

Tree building

rule[id] ^ N: e; Nwill be allocated as tree node having the id

Ast buildingrule

[id] N: e;Nwill be allocated as tree node and is eventuallyreplaced by a child if the node forNhas only one


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child which has no siblings.

Parametrized

Rule

N: e;

Ntakes the PEG epressionspeg1,peg2 ... as

parameter. This parameters cant then be used in e.

Into variable e:variableName

Set the host language variable (a string, byte[],

int, double or PegBegEnd) to the matched inputstretch. The language variable must be declared eitherin the semantic block of the corresponding rule or in

the semantic block of the grammar (see below).

Bits Into

variable

BITS

BITS

Interpret the Bit bitNo or the Bitsequence [low-high]

as integer and store it in the host variable.

Semantic

Function_

call host language functionf_ in a semantic block (see

below). A semantic function has the signature bool

_();. A return value of true is handled as successwhereas a return value of false is handled as fail.

Semantic Block(Grammar

level)

BlockName{ //host

//language

//statements

}

TheBlockName can be missing in which case a localclass named _Top will be created. Functions and data

of a grammar-level semantic block can be accessed

from any other rule-level semantic block. Functions in

the grammar-level semantic block can be used assemantic functions at any place in the grammar.

CREATE

Semantic Block

(Grammar

level)

CREATE{ //host

//language

//statements

}

This kind of block is used in conjunction withcustomized tree nodes as described at the very end of

this table

Semantic Block

(Rule level)

RuleName { //host

//language

//statements}: e;

Functions and data of a rule-level semantic block are

only available from within the associated rule.

Functions in the rule associated semantic block can beused as semantic functions on the right hand side of

the rule.

Using semanticblock

(which is

elsewhere

defined)

RuleName

usingNameOfSemanticBlock:e;

The using directive supports reusing the same

semantic block when several rules need the same local

semantic block.

Custom Node

Creation

^^CREATEN: e;

^CREATEN: e;

Custom Node creation allows to create a user definedNode (which must be derived from the library node

PegNode). The CreaFunc must be defined in a

CREATE semantic block (see above) and must havethe following overall structure

CollapsePegNode CreaFuncName(ECreatorPhase phase,


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PegNode parentOrCreated, int id){

if (phase == ECreatorPhase.eCreate ||phase == ECreatorPhase.eCreateAndComplete)

{ // create and return the custom

node; ifphase==ECreatorPhase.eCreateAndComplete

// this will be the only call}else{// finish the custom node and return

parentOrCreated; one only gets here// after successful parsing of the

subrules}

}

Parsing Expression Grammars Particularities and Idioms

PEG's behave in some respects similar to regular expressions: The application of a PEG to an

input string can be explained by a pattern matching process which assigns matching parts of theinput string to rules of the grammar (much like with groups in regexes) and which backtracks in

case of a mismatch. The most important difference between a PEG and regexes is the fact, that

PEG support recursivenesss and that PEG patterns are greedy. Compared to most othertraditional language parsing techniques, PEG is surprisingly different. The most striking

differences are:

Parsing Expression Grammars are deterministic and never ambigous, thereby removing aproblem of most other parsing techniques. Ambiguity means that the same input string

can be parsed with different sets of rules of a given grammar and that there is no policy

saying which of the competing rules should be used. This is in most cases a seriousproblem, since if this gets undetected it results in different parse trees for the same input.

The lack of ambiguity is a big plus for PEG. But the fact, that the order of alternatives in

a PEG rule matters, takes getting used to.

The following PEG rule e.g. rel_operator: '='; will never

succeed in recognizing > which can be a right shift operator or the closingof two template brackets.


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Parsing Expression Grammars can backtrack to an arbitrary location at the beginning ofthe input string. PEG does not require that a file which has to be parsed must be readcompletely into memory, but it prohibits to give free any part of the file which has

already been parsed. This means that a file which foreseeably will be parsed to the end,

should be read into memory completely before parsing starts. Fortunately memory is not

anymore a scarce resource. In a direct evaluation scenario (semantic actions are executedas soon as the corresponding syntax element is recognized) backtracking can also cause

problems, since already executed semantic actions are in most cases not so easily undone.

Semantic actions should therefore be placed at points where backtracking cannotanymore occur or where backtracking would indicate a fatal error. Fatal errors in PEG

parsing are best handled by throwing an exception.

For many common problems idiomatic solution exist within the PEG framework asshown in the following table

Goal Idiomatic solution Sample

Avoid that

white spacescanning

clutters up the

grammar

White Space scanning

should be done

immediately after reading a terminal,but not in any other place.

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//to avoid[3]prod: val S ([*/] S valS)*;[4]val : [0-9]+ / '(' Sexpr ')' S;//to prefer[3]prod: val ([*/] S val)*;[4]val: ([0-9]+ / '(' Sexpr ')') S;

Reuse Nonterminal

when only a subset

is applicable

!oneOfExceptions

reusedNonterminal

Java spec SingleCharacter:

InputCharacter but not ' or \

Peg specCollapse

SingleCharacter: !['\\]InputCharacter

Test for end of

input!.

Collapse(!./FATAL )

Generic rule

for quoting situation

GenericQuote

:

BegQuote QuoteContent EndQuote;

CollapseGenericQuote

Order alternatives

having the same

start

longer_choice / shorter_choiceCollapse


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Goal Idiomatic solution Sample

expressive errormessages

peeking at next symbol //poor error handling[4]object: '{' S members?@'}' S;[5]members: (str/num)(','S @(str/num))*;

//better error handling[4]object: '{' S(&'}'/members) @'}' S;[5]members: @(str/num)(','S @(str/num))*;

PEG Idioms Applied to Real Word Grammar Problems

Most modern programming languages are based on grammars, which can be almost parsed by

the predominant parsing technique (LALR(1) parsing). The emphasis here is on almost, meaning

that there are often grammar rules which require special handling outside of the grammarframework. The PEG framework can handle this exceptional cases far better as will be shown for

the C++ and C# grammar.

TheC# Language Specification V3.0 e.g. has the following wording for its cast-

expression/parenthized-expression disambiguation rule:

CollapseA sequence of one or more tokens (2.3.3) enclosed in parentheses isconsideredthe start of a cast-expression only if at least one of the following aretrue:

1) The sequence of tokens is correct grammar for a type,and the token immediately following the closing parentheses isthe token ~, the token !, the token (, an identifier (2.4.1),a literal (2.4.4), or any keyword (2.4.3) except as and is.

2) The sequence of tokens is correct grammar for a type, but not for anexpression.

This can be expressed in PEG with

Collapsecast_expression:/*1)*/ ('(' S type ')' S &([~!(]/identifier/literal/!('as' B/'is' B)

keyword B)/*2)*/ / !parenthesized_expression '(' S type ')' ) S unary_expression;B: ![a-zA-Z_0-9];S: (comment/whitespace/new_line/pp_directive )*;

The C++ standard has the following wording for its expression-statement/declaration

disambiguation rule

Collapse
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An expression-statement ... can be indistinguishable from a declaration ...In those cases the statement is a declaration.

This can be expressed in PEG with

Collapsestatement: declaration / expression_statement;

Integrating Semantic Actions into a PEG Framework

A PEG grammar can only recognize an input string, which gives you just two results, a booleanvalue indicating match success or match failure and an input position pointing to the end of the

matched string part. But in most cases, the grammar is only a means to give the input string a

structure. This structure is then used to associate the input string with a meaning (a semantic) and

to execute statements based on this meaning. These statements executed during parsing arecalled semantic actions. The executable nature of PEG grammars makes integration of semantic

actions easy. Assuming a sequence of grammar symbols e1 e2 and a semantic action es_ which

should be performed after recognition ofe1 we just get the sequence e1es_e2 where es_ is afunction of the host language.

From the grammar view point es_ has to conform to the same interface as e1 and e2 or any other

PEG component, what means that es_ is a function returning a bool value as result, where true

means success and false failure. The semantic function es_ can be defined either local to the

rule which uses (calls) es_ or in the global environment of the grammar. A bundling of semanticfunctions, into-variables, helper data values and helper functions forms then a semantic block.

Semantic actions face one big problem in PEG grammars, namely backtracking. In most cases,

backtracking should not occur anymore after a semantic function (e.g. computation of a result of

an arithemtic subexpression) has been performed. The simplest way to guard against

backtracking in such a case is to handle any attempt to backtrack as fatal error. TheFATAL construct presented here aborts parsing (by raising an exception).

Embedding semantic actions into the grammar enables direct evaluation of the parsed construct.

A typical application is the stepwise computation of an arithmetical expression during the parse

phase. Direct evaluation is fast but very limiting since it can only use information present at the

current parse point. In many cases embedded semantic actions are therefore used to collectinformation during parsing for processing after parsing has completed.

The collected data can have many forms, but the most important one is a tree. Optimizing parsers

and compilers delay semantic actions until the end of the parsing phase and just create a physicalparse tree during parsing (our PEG framework supports tree generating by the prefixes ^ and ^^).

A tree walking process then checks and optimizes the tree. Finally the tree is intrerpreted atruntime or it is just used to generate virtual or real machine code. The most important evaluation

options are shown below

CollapseParsing -> Direct Evaluation


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-> Collecting Information during Parsing-> User defined datastructure

->User defined evaluation-> Tree Structure

->Interpretation of generated tree->Generation of VM or machine code

In a PEG implementation, tree generation must cope with backtracking by deleting tree parts

which were built after the backtrack restore point. Furthermore, no tree nodes should be created

when a Peek or Not production is active. In this implementation this is handled by tree

generation aware code in the implemenations for And, Peek, Not and ForRepeat productions.

Parsing Expression Grammars Exposed

The following sample grammar is also taken from the wikipedia article on PEG [2] (but with a

sligthly different notation).

CollapseExpr: S Sum;Sum: Product ([+-] S Product)*;Product: Value ([*/] S Value)*;Value: [0-9]+ ('.' [0-9]+)? S / '(' S Sum ')' S;S: [ \n\r\t\v]*;

During the application of a grammar to an input string, each grammar rule is called from some

parent grammar rule and matches a subpart of the input string which is matched by the parentrule. This results in a parse tree. The grammar rule Expr would associate the arithmetical

expressions 2.5 * (3 + 5/7) with the following parse tree:

CollapseExpr

The above parse tree is not a physical tree but an implicit tree which only exists during the parse

process. The natural implementation for a PEG parser associates each grammar rule with amethod (function). The right hand side of the grammar rule corresponds to the function body and

each nonterminal on the right hand side of the rule is mapped to a function call. When a rule

function is called, it tries to match the input string at the current input position against the righthand side of the rule. If it succeeds it advances the input position accordingly and returns true

otherwise the input position is unchanged and the result is false. The above parse tree can

therefore be regarded as a stack trace. The location marked with [*] in the above parse tree

corresponds to the function stackValue


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/'/' S Value div_)* store_ ;Value: Number S / '(' S Sum ')' S ;Number{ //semantic rule related block using C# as host language

string sNumber;bool store_(){double.TryParse(sNumber,out result);return true;}

}: ([0-9]+ ('.' [0-9]+)?):sNumber store_ ;

S: [ \n\r\t\v]* ;

In many cases on the fly evaluation during parsing is not sufficient and one needs a physical

parse tree or an abstract syntax tree (abbreviated AST). An AST is a parse tree shrinked to the

essential nodes thereby saving space and providing a view better suited for evaluation. Suchphysical trees typically need at least 10 times the memory space of the input string and reduce

the parsing speed by a factor of 3 to 10.

The following PEG grammar uses the symbol ^ to indicate an abstract snytax node and the

symbol ^^ to indicate a parse tree node. The grammar presented below is furthermore enhancedwith the error handling item Fatal< errMsg>. Fatal leaves the parsing process immediately with

the result fail but the input position set to the place where the fatal error occurred.

Collapse[1] ^^Expr: S Sum (!./FATAL) ;[2] ^Sum: Product (^[+-] S Product)* ;[3] ^Product: Value (^[*/] S Value)* ;[4] Value: Number S / '(' S Sum ')' S /

FATAL;[5] ^^Number: [0-9]+ ('.' [0-9]+)? ;[6] S: [ \n\r\t\v]* ;

With this grammar the arithmetical expression 2.5 * (3 + 5/7) would result in the followingphysical tree:

CollapseExpr>

With a physical parse tree, much more options for evaluation are possible, e.g. one can generatecode for a virtual machine after first optimizing the tree.

Parsing Expression Grammar Implementation


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In this chapter I first show how to implement all the PEG constructs one by one. This will be

expressed in pseudo code. Then I will try to find the best interface for this basic PEG functionsin C#1.0 and C#3.0.

General Implementation Strategy for PEG

The natural representation of a PEG is a top down recursive parser with backtracking. PEG rules

are implemented as functions/methods which call each other when needed and return true in caseof a match and false in case of a mismatch. Backtracking is implemented by saving the input

position before calling a parsing function and restoring the input position to the saved one in case

the parsing function returns false.

Backtracking can be limited to the the PEG sequence construct and the e repetitions

if the input position is only moved forward after successful matching in all other cases. In the

following pseudo code we use strings and integer variables, short circuit conditional expressions(using && for AND and || for OR) and exceptions. s stands for the input string and i refers to the

current input position. bTreeBuild is an instance variable which inhibits tree build operationswhen set to false.

PEG construct sample pseudo code to implement sample

CodePoint#

#x

#x

#32 (decimal)

#x3A0 (hex)

(binary)

Collapseif i


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else {return false;}

BITS BITS

Collapseif i=low


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message > PrintMsg(message); return true;

Into e :variableName

Collapseint i0=i;bool b= e();

variableName= s.substring(i0,i-i0);return b;

Bits Into variable BITS

Collapseint i0=i;if i


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//[0-9]+if( !In('0', '9') ){return false;}while (In('0', '9')) ;

for(;;){//(S [+-] S [0-9]+)*int pos= pos_;if( S() && OneOfChars('+','-') && S() ){

//[0-9]+if( !In('0', '9') ){pos_=pos; break;}while (In('0', '9')) ;

}else{pos_= pos; break;

}}S();return true;

}bool S()//S: [ \n\r\t\v]* ;{

while (OneOfChars(' ', '\n', '\r', '\t', '\v')) ;

return true;}

}

To execute the Grammar we must just call the method Sum of an object of the above class. Butwe cannot be happy and satisfied with this solution. Compared with the original grammar rule,

the method Sum in the above class InSum_C1 is large and in its use of loops and helper variables

quite confusing. But it is perhaps the best of what is possible in C#1.0. Many traditional parsergenerators even produce worse code.

Parsing Expression Grammars Mapped to C#3.0

PEG operators like Sequence, Repeat, Into, Tree Build, Peek and Not can be regarded as

operators or functions which take a function as parameter. This maps in C# to a method with adelegate parameter. The Peg Sequence operator e.g can be implemented as a function with the

following interface public bool And(Matcher pegSequence); where Matcher is the

following delegate public delegate bool Matcher();.

In older C# versions, passing a function as a parameter required some code lines, but with C#3.0

this changed. C#3.0 supports lambdas, which are anonymous functions with a very low

syntactical overhead. Lambdas enable a functional implementation of PEG in C#. The PEG

Sequence e1 e2 can now be mapped to the C# term And(()=>e1() && e2()). ()=>e1()&&

e2() looks like a normal expression, but is in effect a fullfledged function with zero parameters(hence ()=>) and the function body {return e1() && e2();}. With this facility, the Grammarfor integer sums

CollapseSum: S [0-9]+ ([+-] S [0-9]+)* S ;S: [ \n\r\t\v]* ;


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results in the following C#3.0 implementation (PegCharParser is a not shown base class with

methods And,PlusRepeat,OptRepeat, In and OneOfChars)

Collapseclass IntSum_C3 : PegCharParser{

public IntSum_C3(string s) : base(s) { }public bool Sum()//Sum: S [0-9]+ (S [+-] S [0-9]+)* S ;{

returnAnd(()=>

S()&& PlusRepeat(()=>In('0','9'))&& OptRepeat(()=> S() && OneOfChars('+','-') && S() &&

PlusRepeat(()=>In('0','9')))&& S());

}public bool S()//S: [ \n\r\t\v]* ;

{return OptRepeat(()=>OneOfChars(' ', '\n', '\r', '\t', '\v'));

}}

Compared to the C#1.0 implementation this parser class is a huge improvement. We have

eliminated all loops and helper variables. The correctness (accordance with the grammar rule) is

also much easier to check. The methods And, PlusRepeat, OptRepeat, In and OneOfChars are

all implemented in both the PegCharParser and PegByteParser base classes.

The following table shows most of the PEG methods available in the base library delivered withthis article.

PEG element C# methods sample usage

CodePoint Char(char) Char('\u0023')

LiteralChar(char c0,char c1,...)Char(string s)

Char("ab")

CaseInsensitiveLiteral

IChar(char c0,char c1,...)IChar(string s)

IChar("ab")

Char Set

[]

OneOf(char c0,char c1,...)

OneOf(string s)OneOf("ab")

Char Set[]

In(char c0,char c1,...)In(string s) In('A','Z','a'-'z','0'-'9')

Any

.Any() Any()

BITSBits(char cLow,char

cHigh,byte toMatch)Bits(1,5,31)

Sequencee1 e2 ...

And(MatcherDelegate m) And(() => S() && top_element())


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Alternativee1 / e2 / ...

e1 || e2 || ... @object() || array()

Greedy Option

e?

Option(MatcherDelegate

m)Option(() => Char('-'))

Greedy repeat 0+e*

OptRepeat(MatcherDelegate m)

OptRepeat(() => OneOf(' ', '\t', '\r', '\n'))

Greedy repeat 1+

e+

PlusRepeat(MatcherDeleg

ate m)PlusRepeat(() => In('0', '9'))

Greedy repeatn0..n1

e{low,high}

PlusRepeat(MatcherDeleg

ate m)ForRepeat(4, 4, () => In('0', '9', 'A', 'F', 'a', 'f'))

Peek

&ePeek(MatcherDelegate m) Peek(() => Char('}'))

Not

!e Not(MatcherDelegate m) Not(()=>OneOf('"','\\'))

FATAL

FATALFatal("") Fatal(" expected")

WARNING

WARNING

Warning("") Warning("non-json stuff before end of file")

Into

e :variableName

Into(out string

varName,MatcherDelegat

e m)

Into(out intvarName,MatcherDelegat

e m)

Into(out PegBegEnd

varName,MatcherDelegate m)

Into(out top.n, () => Any())

Bits Into

BITSvariableNa

me

BitsInto(int lowBitNo, int

highBitNo,out int

varName)

BitsInto(1, 5,out top.tag)

Build Tree Node

[id]^^RuleName:

TreeNT(int nRuleId,

PegBaseParser.MatchertoMatch);

TreeNT((int)Ejson_tree.json_text,()=>...)

Build Ast Node[id] RuleName:

TreeAST(int

id,PegBaseParser.Matcher

Delegate m)

TreeAST((int)EC_KernighanRitchie2.external_declaration,()=>...)

ParametrizedRule

RuleName(MatcherDelegate a,

binary(()=> relational_expression(),()=>TreeChars(


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RuleNameMatcherDelegate b,...) ()=>Char('=','=') || Char('!','=') )

Expression Grammar ExamplesThe following examples show uses of the PegGrammar class for all supported use cases:

1. Recognition only: The result is just match or does not match, in which case an errormessage is issued.

2. Build of a physical parse tree: The result is a physical tree.3. Direct evaluation: Semantic actions executed during parsing.4. Build tree, interpret tree: The generated Tree is traversed and evaluated.

JSON Checker (Recognize only)

JSON (JavaScript Object Notation)[5][6]is an exchange format suited for

serializing/deserializing program data. Compared to XML it is featherweight and therefore a

good testing candidate for parsing techniques. The JSON Checker presented here gives an error

message and error location in case the file does not conform to the JSON grammar. The

following PEG grammar is the basis ofjson_check.

Collapse

[1]json_text: S top_element expect_file_end ;

[2]expect_file_end: !./ WARNING;[3]top_element: object / array /

FATAL ;[4]object: '{' S (&'}'/members) @'}' S ;[5]members: pair S (',' S pair S)* ;[6]pair: @string S @':' S value ;[7]array: '[' S (&']'/elements) @']' S ;[8]elements: value S (','S value S)* ;[9]value: @(string / number / object /

array / 'true' / 'false' / 'null') ;[10]string: '"' char* @'"' ;[11]char: escape / !(["\\]/control_chars)unicode_char ;[12]escape: '\\' ( ["\\/bfnrt] /

'u' ([0-9A-Fa-f]{4}/FATAL)/FATAL);[13]number: '-'? int frac? exp? ;[14]int: '0'/ [1-9][0-9]* ;[15]frac: '.' [0-9]+ ;[16]exp: [eE] [-+] [0-9]+ ;[17]control_chars: [#x0-#x1F] ;[18]unicode_char: [#x0-#xFFFF] ;[19]S: [ \t\r\n]* ;


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The translation of the above grammar to C#3.0 is straightforward and results in the followingcode (only the translation of the first 4 rules are reproduced).

Collapsepublic bool json_text()

{return And(()=> S() && top_element() && expect_file_end() );}public bool expect_file_end(){ return

Not(()=> Any() )|| Warning("non-json stuff before end of file");

}public bool top_element(){ return

@object()|| array()|| Fatal("json file must start with '{' or '['");

}public bool @object(){

return And(()=>Char('{')

&& S()&& ( Peek(()=> Char('}') ) || members())&& ( Char('}') || Fatal(" expected"))&& S() );

}

JSON Tree (Build Tree)

With a few changes of the JSON checker grammar we get a grammar which generates a physical

tree for a JSON file. In order to have unique nodes for the JSON values true, false, null weadd corresponding rules. Furthermore, we add a rule which matches the content of a string (the

string without the enclosing double quotes). This gives us the following grammar:

Collapse

[1]^^json_text: (object / array) ;[2]^^object: S '{' S (&'}'/members) S @'}' S ;[3]members: pair S (',' S @pair S)* ;

[4]^^pair: @string S ':' S value ;[5]^^array: S '[' S (&']'/elements) S @']' S ;[6]elements: value S (','S @value S)* ;[7]value: @(string / number / object /

array / true / false / null) ;[8]string: '"' string_content '"' ;[9]^^string_content: ( '\\'

( 'u'([0-9A-Fa-f]{4}/FATAL)


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/ ["\\/bfnrt]/FATAL)

/ [#x20-#x21#x23-#xFFFF])* ;

[10]^^number: '-'? '0'/ [1-9][0-9]* ('.' [0-9]+)? ([eE] [-+] [0-9]+)?;[11]S: [ \t\r\n]* ;[12]^^true: 'true' ;[13]^^false: 'false' ;[14]^^null: 'null' ;

The following table shows on the left hand side a JSON input file and on the right hand side the

tree generated by the TreePrint helper class of our parser library.

JSON Sample File TreePrint Output

Collapse{

"ImageDescription": {"Width": 800,"Height": 600,"Title": "View from 15th

Floor","IDs": [116, 943, 234,

38793]}

}

Collapse

json_text>

>>

Basic Encode Rules (Direct Evaluation + Build Tree)

BER (Basic Encoding Rules) is the most commonly used format for encoding ASN.1 data. LikeXML, ASN.1 serves the purpose of representing hierarchical data, but unlike XML, ASN.1 is

traditionally encoded in compact binary formats and BER is one of the these formats (albeit the

least compact one). The Internet standards SNMP and LDAP are examples of ASN.1 protocols

using BER as encoding. The following PEG grammar for reading a BER file into a treerepresentation uses semantic blocks to store information necessary for further parsing. This kind

of dynamic parsing which uses data read during the parsing process to decode data furtherdownstreams is typical for parsing of binary formats. The grammar rules for BER[4]as shown

below express the following facts:

1. BER nodes consist of the triple Tag Length Value (abbreviated as TLV) where Value iseither a primitive value or a list of TLV nodes.

2. The Tag identifies the element (like the start tag in XML).


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3. The Tag contains a flag whether the element is primitive or constructed. Constructedmeans that there are children.

4. The Length is either the length of the Value in bytes or it is the special pattern 0x80 (onlyallowed for elements with children), in which case the sequence of childrens ends with

two zero bytes (0x0000).

5.

The Value is either a primitive value or -if the constructed flag is set- it is a sequence ofTag Length Value triples. The sequence of TLV triples ends when the length given in the

Length part of the TLV tripple is used up or in the case where the length is given as 0x80,

when the end marker 0x0000 has been reached.

Collapse

{int tag,length,n,@byte;bool init_() {tag=0;length=0; return true;}bool add_Tag_() {tag*=128;tag+=n; return true;}

bool addLength_(){length*=256;length+=@byte;return true;}}[1] ProtocolDataUnit: TLV;[2] ^^TLV: init_

( &BITS Tag ( #x80 CompositeDelimValue #0#0 / LengthCompositeValue )

/ Tag Length PrimitiveValue);

[3] Tag: OneOctetTag / MultiOctetTag / FATAL;[4] ^^OneOctetTag: !BITS BITS;[5] ^^MultiOctetTag: . (&BITS BITS add_Tag_)* BITSadd_Tag_;[6] Length : OneOctetLength / MultiOctetLength

/ FATAL;[7] ^^OneOctetLength: &BITS BITS;[8]^^MultiOctetLength: &BITS BITS ( .:byte addLength_){:n};[9]^^PrimitiveValue: .{:length} / FATAL;[10]^^CompositeDelimValue: (!(#0#0) TLV)*;[11]^^CompositeValue{

int len;PegBegEnd begEnd;bool save_() {len= length;return true;}bool at_end_(){return len=0;}

}: save_

(!at_end_ TLV:begEnd(decr_/FATAL))*;

Scientific Calculator (Build Tree + Evaluate Tree)


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This calculator supports the basic arithmetic operations + - * /, built in functions taking one

argument like 'sin','cos',.. and assignments to variables. The calculator expects line separatedexpressions and assignments. It works as two step interpreter which first builds a tree, then

evaluates the tree. The PEG grammar for this calculator can be translated to a peg parser by the

parser generator coming with the PEG Grammar Explorer. The evaluator must be written by

hand. It works by walking the tree and evaluating the results as it visits the nodes.

The grammar for the calculator is:

Collapse[1]^^Calc: ((^'print' / Assign / Sum)

([\r\n]/!./FATAL)[ \r\n\t\v]* )+(!./FATAL);

[2]^Assign:S ident S '=' S Sum;[3]^Sum: Prod (^[+-] S @Prod)*;[4]^Prod: Value (^[*/] S @Value)*;

[5] Value: (Number/'('S Sum @')'S/Call/ident) S;[6]^Call: ident S '(' @Sum @')' S;[7]^Number:[0-9]+ ('.' [0-9]+)?([eE][+-][0-9]+)?;[8]^ident: [A-Za-z_][A-Za-z_0-9]*;[9] S: [ \t\v]*;

PEG Parser Generator

A PEG Generator Implemented with PEG

The library classes PegCharParser and PegByteParser are designed for manual Parserconstruction of PEG parsers. But it is highly recommended in any case to first write the grammar

on paper before implementing it. I wrote a little parser generator (using PegCharParser) whichtranslates a 'paper' Peg grammar to a C# program. The current version of the PEG parser

generator just generates a C# parser. It uses optimizations for huge character sets and for big setsof literal alternatives. Future versions will generate source code for C/C++ and other languages

and furthermore support debugging, tracing and direct execution of the grammar without the

need to translate it to a host language. But even the current version of the PEG parser generatoris quite helpful.

All the samples presented in the chapterExpression Grammar Exampleswere generated with it.

The PEG Parser Generator is an example of a PEG parser which generates a syntax tree. It takesa PEG grammar as input, validates the generated syntax tree and then writes a set of C# code

files, which implement the parser described by the PEG grammar.

PEG Parser Generator Grammar
http://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammar%20Exampleshttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammar%20Exampleshttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammar%20Exampleshttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammar%20Examples


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The PEG Parser Generator coming with this article expects a set of grammar rules written as

described in the chapterParsing Expression Grammars Basics. These rules must be preceded bya header and terminated by a trailer as described in the following PEG Grammar:

Collapsepeg_module: peg_head peg_specification peg_tail;peg_head: S '';attribute: attribute_key S '=' S attribute_value S;attribute_key: ident;attribute_value: "attribute value in single or double quotes";peg_specification: toplevel_semantic_blocks peg_rules;toplevel_semantic_blocks:semantic_block*;semantic_block: named_semantic_block / anonymous_semantic_block;named_semantic_block: sem_block_name S anonymous_semantic_block;anonymous_semantic_block:'{' semantic_block_content '}' S;peg_rules: S peg_rule+;peg_rule: lhs_of_rule ':'S rhs_of_rule ';' S;lhs_of_rule: rule_id? tree_or_ast? create_spec?

rule_name_and_params(semantic_block/using_sem_block)?;

rule_id: (![A-Za-z_0-9^] .)* [0-9]+ (![A-Za-z_0-9^] .)*;tree_or_ast: '^^'/'^';create_spec: 'CREATE' S '' S;create_method: ident;ident: [A-Za-z_][A-Za-z_0-9]*;rhs_of_rule: "right hand side of rule as described in

%22#Parsing" expression="" grammars=""

basics"="">Parsing Expression Grammars Basics";semantic_block_content: "semantic block content as described in

"%22#Parsing" expression="" grammars=""

basics"="">Parsing Expression Grammars Basics";peg_tail: '';

The header of the grammar contains HTML/XML-style attributes which are used to determinethe name of the generated C# file and the input file properties. The following attributes are used

by the C# code generator:

Attribute Key Optionality Attribute Value

Name Mandatory Name for the generated C# grammar file and namespace

encoding_class OptionalEncoding of the input file. Must be one ofbinary, unicode,

utf8 or ascii. Default is ascii

encoding_detection Optional

Must only be present if the encoding_class is set to unicode.

In this case one of the values FirstCharIsAscii or BOM isexpected.

All further attributes are treated as comments. The attribute reference in the following sampleheader
http://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammars%20Basicshttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammars%20Basicshttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammars%20Basicshttp://www.codeproject.com/KB/recipes/%22%3C/spanhttp://www.codeproject.com/KB/recipes/%22%3C/spanhttp://www.codeproject.com/KB/recipes/%3Cspanhttp://www.codeproject.com/KB/recipes/%3Cspanhttp://www.codeproject.com/KB/recipes/%3Cspanhttp://www.codeproject.com/KB/recipes/%3Cspanhttp://www.codeproject.com/KB/recipes/%22%3C/spanhttp://www.codeproject.com/KB/recipes/%22%3C/spanhttp://www.codeproject.com/KB/recipes/grammar_support_1.aspx#Parsing%20Expression%20Grammars%20Basics


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Collapse

is treated as comment.

The PEG Parser Generator's Handling of Semantic Blocks

Semantic blocks are translated to local classes. The code inside semantic blocks must be C#

source text as expected in a class body, except that access keywords can be left out. The parser

generator prepends an internal access keyword when necessary. Top level semantic blocks arehandled differently than local semantic blocks.

A top level semantic block is created in the grammar's constructor, wheras a local semantic block

is created each time the associated rule method is called. There is no need to define a constructor

in a local semantic block, since the parser generator creates a constructor with one parameter, a

reference to the grammar class. The following sample shows a grammar excerpt with a top leveland a local semantic block and its translation to C# code.

CollapseTop{ // semantic top level block

double result;bool print_(){Console.WriteLine("{0}",result);return true;}

}...Number{ //local semantic block

string sNumber;bool store_(){double.TryParse(sNumber,out result);return true;}} : ([0-9]+ ('.' [0-9]+)?):sNumber store_ ;

These semantic blocks will be translated to the following C# source code

Collapseclass calc0_direct : PegCharParser{

class Top{ // semantic top level blockinternal double result;internal bool print_(){Console.WriteLine("{0}",result);return true;}

}

Top top;

#region Constructorspublic calc0_direct(): base(){ top= new Top();}public calc0_direct(string src,TextWriter FerrOut): base(src,FerrOut){top=

new Top();}#endregion Constructors...class _Number{ //local semantic block

internal string sNumber;


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internal bool store_(){double.TryParse(sNumber,outparent_.top.result);return true;}

internal _Number(calc0_direct grammarClass){parent_ = grammarClass; }calc0_direct parent_;

}public bool Number(){

var _sem= new _Number(this);...

}

Quite often, several grammar rules must use the same local semantic block. To avoid code

duplication, the parser generator supports the using SemanticBlockName clause. The semantic

block named SemanticBlockName should be defined before the first grammar rule at the sameplace where the top level semantic blocks are defined. But because such a block is referenced in

the using clause of a rule, it is treated as local semantic block.

Local semantic blocks also support destructors. A destructor is tranlsated to a IDispose interface

and the destructor code is placed into the corresponding Dispose() function. The grammar rulefunction which is generated by the parser generator will be enclosed in a using block. This

allows to execute cleanup code at the end of the rule even in the presence of exceptions. The

following sample is taken from the Python 2.5.2 sample parser.

CollapseLine_join_sem_{

bool prev_;Line_join_sem_ (){set_implicit_line_joining_(true,out prev_);}~Line_join_sem_(){set_implicit_line_joining_(prev_);}

}...

[8] parenth_form: '(' parenth_form_content @')' S;[9] parenth_form_contentusing Line_join_sem_: S expression_list?;

...[17]^^generator_expression: '(' generator_expression_content @')' S;[18]generator_expression_content

using Line_join_sem_: S expression genexpr_for;

The Line_join_sem semantic block turns Python's implicit line joining on and off (Python isline oriented except that line breaks are allowed inside constructs which are parenthized as in

(...) {...) [...]. The Line_join_sem semantic block and rule [8] of the above grammar

excerpt are translated to

Collapseclass Line_join_sem_ : IDisposable{

bool prev_;internal Line_join_sem_(python_2_5_2_i parent){

parent_= parent;parent_._top.set_implicit_line_joining_(true,out prev_);

}python_2_5_2_i parent_;


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public void Dispose(){parent_._top.set_implicit_line_joining_(prev_);}}public bool parenth_form_content() /*[9] parenth_form_content

using Line_join_sem_: Sexpression_list?;*/{

using(var _sem= new Line_join_sem_(this)){return And(()=> S() && Option(()=> expression_list() )

);}

Parsing Expression Grammars in Perspective

Parsing Expression Grammars narrow the semantic gap between formal grammar and

implementation of the grammar in a functional or imperative programming language. PEGs aretherefore particularly well suited for manually written parsers as well as for attempts to integrate

a grammar very closely into a programming language. As stated in [1], the elements which form

the PEG framework are not new, but are well known and commonly used techniques when

implementing parsers manually. What makes the PEG framework unique is the selection andcombination of the basic elements, namely

PEG Feature Advantage Disadvantage

Scannerless

parsing

Only one level of abstraction. No

scanner means no scanner worries.

Grammar sligthly cluttered up.

Recognition of overlapping tokensmight be inefficient (e.g. identifier

token overlaps with keywords ->

ident: !keyword [A-Z]+; )

Lack of

ambiguity

There is only one interpretation for a

grammar. The effect is, that PEGgrammars are "executable".

---

Error handling by

using FATALalternative

Total user control over error diagnostics Bloats the grammar.

Excessive

Backtrackingpossible

Backtracking adds to the powerfulnessof PEG. If the input string is in memory,

backtrackting just means resetting the

input position.

Potential memory hogg. Interferes

with semantic actions. Solution:

Issue a fatal error in casebacktracking cannot succeed

anymore.

Greedy repetition

Greedy repetition conforms to the

"maximum munch rule" used inscanning and therefore allows

scannerless parsing.

Some patterns are more difficult torecognize.

Ordered ChoiceThe author of the grammar determines

the selection strategy.

Potential error source for the

unexperienced. R: '


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PEG Feature Advantage Disadvantage

operators & and ! cost/gain ratio if backtracking is anywaysupported. Lookahead e.g. allows better

reuse of grammar rules and supports

more expressive error diagnostics.

parser slow.

A PEG grammar can incur a serious performance penalty, when backtracking occurs frequently.This is the reason that some PEG tools (so called packrat parsers) memoize already read input

and the associated rules. It can be proven, that appropriate memoization guarantees linear parse

time even when backtracking and unlimited lookahead occurs. Memoization (saving information

about already taken paths) on the other hand has its own overhead and impairs performance inthe average case. The far better approach to limit backtracking is rewriting the grammar in a

way, which reduces backtracking. How to do this will be shown in the next chapter.

The ideas underlying PEG grammars are not entirely new and many of them are regularly used to

manually construct parsers. Only in its support and encouragement for backtracking and

unlimited lookahead deviates PEG from most earlier parsing techniques. The simplestimplementation for unlimited lookahead and backtracking requires that the input file must be

read into internal memory before parsing starts. This is not a problem nowadays, but was not

acceptable earlier when memory was a scarce resource.

Parsing Expression Grammars Tuning

A set of grammar rules can recognize a given language. But the same language can be describedby many different grammars even within the same formalism (e.g. PEG grammars). Grammar

modifications can be used to meet the following goals:

Goal Before modification After modification

More informative

tree nodes [1]

Collapse[1]^^string:'"' ('\\' ["'bfnrt\\])/!'"'

.)* '"';

Collapse[1]^^string:'"'(escs/chars)* '"';[3] ^^escs: ('\\'["'bfnrt\\])*;[4] ^^chars: (!["\\] .)*;

Better placed

error indication [2]

Collapse'/*' (!'*/' . )*('*/' /FATAL);

Collapse'/*'( (!'*/' .)* '*/'/ FATAL

);

FasterGrammar

(reduce calling depth)

[3]

Collapse[10]string: '"' char* '"'

;[11]char: escape

/ !(["\\]/control)unicode/!'"' FATAL;

Collapse[10]string:'"'( '\\'["\\/bfnrt]/ [#0x20-#0x21#0x23-#0x5B#0x5D-#0xFFFF]/ !'"' FATAL


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[12]escape: '\\' ["\\/bfnrt];[17]control [#x0-#x1F];[18]unicode: [#x0-#xFFFFF];

character">

)*'"';

FasterGrammar,

Less Backtracking(left factoring)

Collapse[1] if_stat:

'if' S '('expr')' stat /'if' S '('expr')' stat

'else' S stat;

Collapse[1] if_stat:

'if' S '(' expr ')' stat('else' S

stat)?;

Remarks:

[1] More informative tree nodes can be obtained by syntactical grouping of grammar elements so

that postprocessing is easier. In the above example, access to the content of the string isimproved by grouping consecutive non-escape characters into one syntactical unit.

[2] The source reference place which is given by an error message is important. In the example

of a c comment which is not closed until the end of the input, the error message should be given

where the comment opens.

[3] Reducing calling depth means inlinig of function calls, since each rule corresponds to onefunction call in our PEG implementation. Such a transformation should only be carried out for

hot spots, otherwise the expressiveness of the grammar gets lost. Furthermore, some aggressive

inlining compilers may do this inlining for you. Reducing calling depth may be questionable, butleft factorization is certainly not. It not only improves performance but also eliminiates potential

disruptive backtracking. When embedding semantic actions into a PEG parser, backtracking

should in many cases not occur anymore, because undoing semantic actions may be tedious.

Comparison of PEG Parsing with other Parsing Techniques

Most parsing strategies currently in use are based on the notion of a context free grammar. (The

following explanations follow -for the next 50 lines- closely the material used in the Wikipediaon Context free grammars [3]) A context free grammar consists of a set of rules similar to the set

of rules for a PEG parser. But context free grammars are quite differently interpreted than PEGgrammars. The main difference is the fact, that context free grammars are nondeterministic,

meaning that

1. Alternatives in context free grammars can be chosen arbitrarily2. Nonterminals can be substituted in an arbitrary order (Substitution means replacing a

Nonterminal on the right hand side of a rule by the definition of the Nonterminal). Bystarting with the start rule and choosing alternatives and substituting nonterminals in all

possible orders we can generate all the strings which are described by the grammar (also

called the language described by the grammar).

With the context free grammarCollapse

S : 'a' S 'b' | 'ab';

e.g. we can generate the following language strings


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Collapseab, aabb, aaabbb,aaaabbbb,...

With PEG we cannot generate a language, we can only recognize an input string. The same

grammar interpreted as PEG grammar

CollapseS: 'a' S 'b' / 'ab';

would recognize any of the following input strings

Collapseabaabbaaabbbaaaabbbb

It turns out, that the nondeterministic nature of context free grammars, while being indispensablefor generating a language, can be a problem when recognizing an input string. If an input string

can be parsed in two different ways we have the problem of ambiguity, which must be avoidedby parsers. A further consequence of nondeterminism is that a context free input string

recognizer (a parser) must choose a strategy how to substitute nonterminals on the right hand

side of a rule. To recognize the input string

Collapse1+1+a

with the context free rule

CollapseS: S '+' S | '1' | 'a';

we either can e.g use the following substitutions:Collapse

S '+' S ->(S '+' S) '+' S ->(('1') '+' S) '+' S ->(('1') '+' ('1')) '+' S ->(('1') '+' ('1')) '+' ('a')

This is called a leftmost derivation. Or we can use the substitutions:

CollapseS '+' S ->

S '+' (S '+' S) ->

S '+' (S '+' ('a')) ->S '+' (('1') '+' ('a')) ->('1') '+' (('1') '+' ('a'));

This is called a rightmost derivation. A leftmost derivation parsing strategy is called LL, wherasa rightmost derivation parsing strategy is called LR (the first L in LL and LR stands for "parsethe input string from Left", but who will try it from right?). Most parsers in use are either LL or


32/51

LR parsers. Furthermore, grammars used for LL parsers and LR parsers must obey different

rules. A grammar for an LL parser must never use left recursive rules, whereas a grammar for anLR parser prefers immediate left recursive rules over right recursive ones. The C# grammar e.g.

is written for an LR parser. The rule for a list of local variables is therefore:

Collapselocal-variable-declarators:local-variable-declarator

| local-variable-declarators ',' local-variable-declarator;

If we want use this grammar with an LL parser, then we must rewrite this rule to:

Collapselocal-variable-declarators:

local-variable-declarator (',' local-variable-declarator)*;

Coming back to original context free rule

CollapseS: S '+' S | '1' | 'a';

and interpreting it as a PEG rule

CollapseS: S '+' S / '1' / 'a';

we do not have to do substitutions or/and choose a parsing strategy to recognize the input string

Collapse1+1+a

We only must follow the execution rules for a PEG which translates to the following steps:

1. Set the input position to the start of the input string2. Choose the first alternative of the start rule (here: S '+' S)3. Match the input against the first component of the sequence S '+' S4. Since the first component is the nonterminal S, call this nonterminal.

This obviously results in infinite recursion. The rule S: S '+' S / '1' / 'a'; is therefore not a

valid PEG rule. But almost any context free rule can be transformed into a PEG rule. The context

free rule S: S '+' S | '1' | 'a'; translates to the valid PEG rule

CollapseS: ('1'/'a')('+' S)*;

One of the following chapters shows how to translate a context free rule into a PEG rule.

The following table compares the prevailing parser types.


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ParserType

Sub Type Scanner Lookahead Generality Implementation Examples

Context

FreeLR-Parser yes - - table driven

Context

Free SLR-Parser yes 1 medium table driven

handcomputed

table

Context

Free

LALR(1)-

Parseryes 1 high table driven YACC,Bison

ContextFree

LL-Parser yes - -code or tabledriven

Context

FreeLL(1)-Parser yes 1 low

code or table

drivenPredictive parsing

Context

FreeLL(k)-Parser yes k high

code or table

drivenANTLR,Coco-R

Context

Free LL(*)-Parser yes unlimited high+

code or table

driven boost::spirit

PEG-

ParserPEG-Parser no unlimited very high code preferred Rats,Packrat,Pappy

The reason, that the above table qualifies the generality and powerfulness of PEG as very high isdue to the PEG operators & (peek) and ! (not). It is not difficult to implement these operations,

but heavy use of them can impair the parser performance and earlier generations of parser writers

carefully avoided such features because of the implied costs.

When it comes to runtime performance, the differences between the above parser strategies are

not so clear. LALR(1) Parser can be very fast. The same is true for LL(1) parsers (predictiveparsers). When using LL(*) and PEG-Parsers, runtime performance depends on the amount oflookahead actually used by the grammar. Special versions of PEG-Parsers (Packrat parsers) can

guarantee linear runtime behaviour (meaning that doubling the length of the input string just

doubles the parsing time).

An important difference between LR-Parsers and LL- or PEG-Parsers is the fact that LR-Parser

are always table driven. A manually written Parser is therefore in most cases either an LL-Parseror a PEG-Parser. Table driven parsing puts parsing into a black box which only allows limited

user interaction. This is not a problem for a one time, clearly defined parsing task, but is not ideal

if one frequently corrects/improves and extends the grammar because changing the grammar

means in case of a table driven parser a complete table and code regeneration.

Translating LR grammars to PEG Grammars

Most specifications for popular programming languages come with a grammar suited for an LR

parser. LL and PEG parsers can not directly use such grammars because of left recursive rules.

Left recursive rules are forbidden in LL and PEG parsers because they result in idefiniterecursion. Another problem with LR grammars is that they often use alternatives with the same


34/51

beginning. This is legal in PEG but results in unwanted backtracking. The following table shows

the necessary grammar transformations when going from an LR grammar to a PEG grammar.

Transformation Category LR rule~PEG rule (result oftransformation)

Immediate Left Recursion =>Factor out non recursive

alternatives

Collapse// s1, s2 are termswhich are not//left recursive// and not emptyA: A t1 | A t2 | s1 |s2;

CollapseA: (s1 | s2) (t1 | t2)*

Indirect Left Recursion =>Transfrom to Immediate Left

Recursion=>

Factor out non recursivealternatives

CollapseA: B t1 | s1 ;B: A t2 | s3 ;

Collapse// we substitute B by itsright hand sideA: (A t2 | s3) t1 | s1;//Eliminate immediate leftrecursion

A: (s3 t1 | s1) (t2 t1)*...;

Alternatives with same

beginning =>

Merge alternatives using LeftFactorization

CollapseA: s1 t1 | s1 t2;

CollapseA: s1 (t1 | t2);

The following sample shows the transformation of part of the "C" grammar from the LRgrammar as presented in Kernighan and Ritchies book on "C" to a PEG grammar (the symbol S

is used to denote scanning of white space).

LR grammar: "C" snippet declarator stuff... PEG grammar: "C" declarator stuff...

Collapsedeclarator: pointer?direct_declarator;

Collapsedeclarator: pointer?direct_declarator;

Collapse

Collapsedirect_declarator:

identifier| '(' declarator ')'| direct_declarator '['constant_expression? ']'

| direct_declarator '('parameter_type_list ')'| direct_declarator '('identifier_list? ')';

Collapsedirect_declarator:(identifier / '(' S declarator')' S)( '[' S constant_expression?']' S

/ '(' S parameter_type_list

')' S/ '(' S identifier_list? ')'

S)*;

Collapsepointer:

'*' type_qualifier_list?| '*' type_qualifier_list?pointer;;

Collapsepointer:

'*' S type_qualifier_list?pointer?


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LR grammar: "C" snippet declarator stuff... PEG grammar: "C" declarator stuff...

Collapseparameter_type_list:

parameter_list| parameter_list ',' '...';

Collapseparameter_type_list:

parameter_list (',' S'...')?;

Collapse

Collapsetype_qualifier_list:type_qualifier

| type_qualifier_listtype_qualifier;

Collapsetype_qualifier_list:

type_qualifier+;Collapse

Collapseparameter_declaration:

declaration_specifiers declarator| declaration_specifiersabstract_declrator?;

Collapseparameter_declaration:

declaration_specifiers(declarator /

abstract_declarator?);

Collapse

Collapseidentifier_list:

identifier

| identifier_list ',' identifier;

Collapseidentifier_list:

identifier S

(',' S identifier)*;

Collapse

Future Developments

The planned series of articles consists of the following parts

SubjectPlanned

Release dateDescription

Parser and ParserGenerator

october 2008C# classes to support work with Parsing expressiongrammars

PEG-

Debugger/Interpreterjanuary 2009

Direct interpretation and debugging of PEG grammars

without need to generate C# module

Sample Applications june 2009 More grammar samples with postprocessing

History

2008 October: initial version 2008 October:..minor update

o improved semantic block support (using clause,IDispose Interface)o added new sample parser Python 2.5.2

References

[1]Parsing Expression Grammars,Bryan Ford, MIT, January 2004 [^]

[2]Parsing expression grammar, Wikipedia.en [^][3]Context-free grammar, Wikipedia.en [^]

[4]ITU-T X.690: Specification of BER, CER and DER, INTERNATIONAL
http://www.brynosaurus.com/pub/lang/peg-slides/img0.htmlhttp://www.brynosaurus.com/pub/lang/peg-slides/img0.htmlhttp://www.brynosaurus.com/pub/lang/peg-slides/img0.htmlhttp://www.brynosaurus.com/pub/lang/peg-slides/img0.htmlhttp://www.brynosaurus.com/pub/lang/peg-slides/img0.htmlhttp://en.wikipedia.org/wiki/Parsing_expression_grammarhttp://en.wikipedia.org/wiki/Parsing_expression_grammarhttp://en.wikipedia.org/wiki/Parsing_expression_grammarhttp://en.wikipedia.org/wiki/Parsing_expression_grammarhttp://en.wikipedia.org/wiki/Parsing_expression_grammarhttp://en.wikipedia.org/wiki/Context-free_grammarhttp://en.wikipedia.org/wiki/Context-free_grammarhttp://en.wikipedia.org/wiki/Context-free_grammarhttp://en.wikipedia.org/wiki/Context-free_grammarhttp://en.wikipedia.org/wiki/Context-free_grammarhttp://www.itu.int/ITU-T/studygroups/com17/languages/X.690-0207.pdfhttp://www.itu.int/ITU-T/studygroups/com17/languages/X.690-0207.pdfhttp://www.itu.int/ITU-T/studygroups/com17/languages/X.690-0207.pdfhttp://en.wikipedia.org/wiki/Context-free_grammarhttp://en.wikipedia.org/wiki/Context-free_grammarhttp://en.wikipedia.org/wiki/Parsing_expression_grammarhttp://en.wikipedia.org/wiki/Parsing_expression_grammarhttp://www.brynosaurus.com/pub/lang/peg-slides/img0.htmlhttp://www.brynosaurus.com/pub/lang/peg-slides/img0.html


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TELECOMMUNICATION UNION [^]

[5]RFC 4627:The application/json Media Type for JavaScript Object Notation (JSON) [^][6]Introducing JSON [^]

License

This article, along with any associated source code and files, is licensed under The Code Project

Open License (CPOL)

About the Author

Martin.Holzherr

Switzerland

Member

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Great work! Pedro J. Molina 17:15 8 Feb '11

Congratulations Martin!

I enjoyed a lot reading your educational article. Amazing work!

Are you continuing with the roadmap on PEGs and creating the debugger and the interpreter?

I am looking forward to see more...

Pedro J. Molina, PhD

http://pjmolina.com/metalevel

ReplyEmailView ThreadLinkBookmark Rate this message: 12345

Boost.Spirit OvermindDL1 7:53 18 Aug '09

Actually Boost.Spirit (now known as Classic Spirit) is a PEG parser (regardless of what the

docs say) and it does have the & and ! operators in exactly the format you specified. Theydid not call it a PEG parser because the creator of the library did not know that PEG parsers

existed. Boost.Spirit2.1 is worlds faster then Classic Spirit, is even more capable and

powerful, and the docs actually call it what it is now, a PEG parser (which it has been all

along).

I have to say that your code looks a *lot* like Boost.Spirit2.1, just a lot longer due to the lack

of overloading the operators, although Boost.Spirit2.1 handles semantic actions a lot betterand more powerful. You should probably look at Boost.Spirit2.1 and you could take some

ideas from it (if C# is capable of such power). Since C# templates do not have the full power

of C++ templates it may be more verbose, but you should still be able to emulate much of the

power, which would be useful for the C# programmers since they lack the power of the Boostversions otherwise.

ReplyEmailView ThreadLinkBookmarkRate this message: 1234

5

Great Stuff ! LarsAC

7:14 27 Jul '09Dear Martin,

this is really a great article and even comes along with excellent code.

The code gave me a good jump start into PEGs and has permitted me to successfully tackle

the context-dependent grammar of the legacy software I'm working on.
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PEG GrammarExplorer