Rats!, a parser generator supporting extensible syntax.

Grammars for Rats! build on the Parsing Expression Grammar (PEG) formalism described in Brian Ford's Parsing Expression Grammars paper. However, since Rats! produces working parsers, the syntax of Rats! grammars is somewhat different from and more expressive than the PEG syntax described in the paper. Additionally, to make grammars more easily reusable and extensible, Rats organizes grammar fragments into modules. A good starting point for learning how to use Rats!, in addition to this introduction, are Rats!' own grammar in package xtc.parser and the C and Java grammars in package xtc.lang.

The rest of this document covers the following topics:


Here is the syntax of Rats!' grammar modules, expressed in PEG syntax:
Module        <- Spacing Intro Production* EOF

Intro         <- ModuleDecl Dependency* Header? Body? Footer? Option?
ModuleDecl    <- "module" FSpacing ModuleRef SEMICOLON
Dependency    <- Modification / Instantiation / Import
Modification  <- "modify" FSpacing ModuleRef ModuleTarget? SEMICOLON
Instantiation <- "instantiate" FSpacing ModuleRef ModuleTarget? SEMICOLON
Import        <- "import" FSpacing ModuleRef ModuleTarget? SEMICOLON
ModuleRef     <- QName ModuleParams?
ModuleParams  <- OPEN ( QName (COMMA QName)* )? CLOSE
ModuleTarget  <- "as" FSpacing QName
Header        <- "header" Spacing Action
Body          <- "body" Spacing Action
Footer        <- "footer" Spacing Action
Option        <- "option" FSpacing Attribute (COMMA Attribute)* SEMICOLON

Production    <- Full / Addition / Removal / Override
Full          <- PAttributes QName Identifier EQUAL Choice SEMICOLON
Addition      <- QName Identifier PLUSEQUAL
                 ( SName ELLIPSIS SLASH Choice SEMICOLON
                 / Choice SLASH SName ELLIPSIS SEMICOLON )
Removal       <- QName Identifier MINUSEQUAL
                 SName ( COMMA SName )* SEMICOLON
Override      <- QName Identifier COLONEQUAL Choice SEMICOLON
                 / QName Identifier COLONEQUAL ELLIPSIS SLASH Choice SEMICOLON
                 / QName Identifier COLONEQUAL Choice SLASH ELLIPSIS SEMICOLON
                 / PAttributes QName Identifier COLONEQUAL ELLIPSIS SEMICOLON
PAttributes   <- &(QName Identifier EQUAL) / Attribute PAttributes
Choice        <- Sequence (SLASH Sequence)*
Sequence      <- !(SName ELLIPSIS / ELLIPSIS) SName? Voided*
Voided        <- ("void" Spacing COLON)? Prefix
Prefix        <- (AND / NOT / CARET / Identifier COLON
                 / StringLit Spacing COLON)? Suffix
Suffix        <- Primary (QUESTION / STAR / PLUS)?
Primary       <- NullLit / QName / Literal / NodeMarker / Action 
                 / OPEN Choice CLOSE

NullLit       <- "null" Spacing

NodeMarker    <- '@' Id Spacing

Action        <- '{' ActionBody* '}' Spacing
ActionBody    <- Action / CharLit / StringLit / MLComment / SLComment / !'}' .

Attribute     <- Identifier (OPEN AttValue CLOSE)?
AttValue      <- Integer / QName / StringLit Spacing

QName         <- Id ('.' Id)* Spacing
SName         <- LESS Id GREATER
Identifier    <- Id Spacing
Id            <- [a-zA-Z] [a-zA-Z0-9]*

Literal       <- ('_' / CharLit / StringLit / Class) Spacing
CharLit       <- ['] (Escape / !['\\] .)  [']
StringLit     <- ["] (Escape / !["\\] .)* ["]
Class         <- '[' (Char '-' Char / Char)* ']'
Char          <- Escape / ![-\]\\] .
Escape        <- '\\' [btnfr"'\[\\\]-] / '\\' 'u' HexQuad / OctalEscape
OctalEscape   <- '\\' ([0-3] OctDigit OctDigit / OctDigit OctDigit / OctDigit)

Integer       <- (HexNumber / OctNumber / Number) Spacing
HexNumber     <- '0' [xX] HexDigit+
HexQuad       <- HexDigit HexDigit HexDigit HexDigit
HexDigit      <- [0-9a-fA-F]
Number        <- '0' / NZDigit Digit*
NZDigit       <- [1-9]
Digit         <- [0-9]
OctNumber     <- '0' OctDigit+
OctDigit      <- [0-7]

ELLIPSIS      <- "..." Spacing
PLUSEQUAL     <- "+=" Spacing
MINUSEQUAL    <- "-=" Spacing
COLONEQUAL    <- ":=" Spacing
COMMA         <- ',' Spacing
EQUAL         <- '=' Spacing
SLASH         <- '/' ![/*] Spacing
AND           <- '&' Spacing
NOT           <- '!' Spacing
CARET         <- '^' Spacing
COLON         <- ':' Spacing
QUESTION      <- '?' Spacing
STAR          <- '*' Spacing
PLUS          <- '+' Spacing
OPEN          <- '(' Spacing
CLOSE         <- ')' Spacing
SEMICOLON     <- ';' Spacing
LESS          <- '<'
GREATER       <- '>' Spacing

Spacing       <- (Space / SLComment / MLComment)*
FSpacing      <- (Space / SLComment / MLComment)+
Space         <- ' ' / '\t' / '\f' / EOL
SLComment     <- "//" (![\n\r] .)* EOL
MLComment     <- "/*" ('*' !'/' / !'*' .)* "*/"
EOL           <- '\r' '\n' / '\r' / '\n'
EOF           <- !.
Note that QName stands for "qualified name," SName stands for "sequence name," PAttributes for "production attributes," AttValue for "attribute value," NZDigit for "non-zero digit," FSpacing for "forced spacing," SLComment for "single-line comment," and MLComment for "multi-line comment."

Overview of Expressions and Operators

The biggest difference between parsing expression grammars and the more familiar context-free grammars (CFGs) is the use of ordered choices instead of symmetric choices. Hence, the different options in a PEG choice (and also a Rats! choice) are separated by a slash / instead of a vertical bar |. Furthermore, to emphasize that PEGs define how to parse a language instead of how to generate a language, PEGs use a left arrow <- instead of the right arrow -> used in CFGs. Note that Rats! uses an equal sign instead.

Otherwise, PEGs have many of the same expressions and operators as other syntax and grammar formalisms. For example, the any character constant . (_ for Rats!) matches any character in the input, and a character class, as defined by the [] operator, matches any of the characters in the class. The option operator ? makes an expression optional, and the star * and plus + operators indicate zero-or-more and one-or-more repetitions, respectively. Somewhat less common are the and & and not ! operators, which denote syntactic predicates. Expressions in a syntactic predicate must match (for the and & operator) or not match (for the not ! operator) the input, though the corresponding text in the input is not consumed.

Rats! grammars differ from PEGs in that they have additional expressions and operators necessary for generating actual parsers. Most importantly, Rats! grammars include actions that generate semantic values. Actions are surrounded by curly brackets {}, just like blocks of code in C, C++, or Java. To access such semantic values, Rats! grammars can also include bindings. Bindings first specify the variable name, followed by a colon :, and then the expression to be bound. Additionally, Rats! grammars support semantic predicates, which are denoted by the and & operator directly followed by an action (which must be an expression evaluating to a boolean value). Furthermore, Rats! grammars support text matching expressions, which first specify the text to be matched as a string literal, followed by a colon :, and then the expression to be matched. A text matching expression


is equivalent to the expression

      fresh-variable:expr &{ "text".equals(fresh-variable) }

but implemented more efficiently. Rats! grammars also support a voiding operator, which is specified as "void:" followed by an expression, node markers, which are specified as an at sign '@' immediately followed by an identifier, and parser actions, which are actions prefixed by a caret '^'. Voided expressions and node markers help with the automatic generation of abstract syntax trees and are explained here. Parser actions provide a low-level interface for extending parsers generated by Rats! and are explained here.

Other differences between PEGs and Rats! grammars include that, as already mentioned Rats! uses an underscore '_' as the any character constant, while PEGs use a dot '.'. Furthermore, Rats!, just like C/C++/Java, requires that single-quoted literals specify exactly one character, while double-quoted literals may specify an arbitrary number of characters. Escape sequences include basic C/C++/Java escapes such as '\n' and '\\', Java Unicode escapes such as '\u00ff', and '\[', '\-', and '\]' for character class specifications. Rats! grammars also use standard C/C++/Java comments. Note that, while Rats! supports Unicode, it only supports 16 bit characters in the basic multilingual plane (i.e., with code points between U+0000 and U+FFFF). Expressions recognizing supplementary characters (i.e., with code points between U+10000 and U+10FFFF) need to use Java's encoding as a pair of char values in the surrogates range.

Grammar Modules

A Rats! grammar consists of one top-level module, which is the module specified on the command line when invoking Rats!, and zero or more dependent modules. Each module starts with several declarations, whose syntax follows from Intro in the Rats! syntax specification above:

A grammar's top-level module (i.e., the module specified on the command line when invoking Rats!) is treated somewhat differently from its dependent modules:

Similar to the Java compiler automatically loading dependent Java classes, Rats! automatically loads dependent modules from the file system. For example, when looking for the dependent module xtc.util.Spacing, Rats! searches for the file xtc/util/Spacing.rats on Unix-like systems. One or more root directories for this search can be specified through the -in command line option.

A grammar's modules can be visualized by using Rats!' -html command line option combined with either the -instantiated, -applied, or -processed command line option to specify the stage of Rats!' processing. In all three cases, Rats! creates a hyperlinked version of the grammar at that processing stage. Make sure that the grammar.css stylesheet is in the same directory as the generated HTML file(s). The output directory can be controlled with the -out command line option.

Productions and Semantic Values

After the module declarations follow the productions, with each production defining how to parse a nonterminal. Regular modules may only contain full productions, whose syntax follows from Full in the Rats! syntax specification above. Module modifications may also contain alternative additions, alternative removals, and production overrides, which are discussed below.

Each full production first lists zero or more attributes, then declares the type of the semantic value it returns, and then specifies the name of the nonterminal it defines (which must be unqualified). The definition follows after the equals sign = and is terminated by a semicolon ;. Each full production can either be public, protected, or private, as indicated by the corresponding attribute of the same name. A public production is a top-level production for the grammar if it appears in the top-level module. Otherwise, it is treated as a protected production, which is the default, can be omitted, and makes the production referenceable from other modules. Finally, a private production can only be referenced from within the same module. Note that the use of the transient attribute is explained here. All per-production attributes supported by Rats! are discussed here. Further note that types cannot be primitive types, such as int; though, as discussed here, void is allowed.

A production's semantic value is usually defined in an action by setting the yyValue variable (so named in deference to the Yacc parser generator) to the desired value. The action code can use characters or strings matched by a literal as well as semantic values returned by nested nonterminals through bindings. As specified above, each binding first declares the variable, followed by a colon, and then the bound expression.

For example, this is the production for the FullProduction nonterminal from Rats!' own grammar:

FullProduction FullProduction =
   type:Name nt:UnqualifiedNonTerminal "=":Symbol choice:Choice ";":Symbol
      { yyValue = new FullProduction(atts.list(), type, nt, choice); }

The production first declares the type of the semantic value it returns to be FullProduction (which only coincidentally has the same name as the production). In the definition, the semantic value of recognizing the production's attributes is bound to the variable atts, the semantic value returned by the Name production is bound to the variable type, the semantic value returned by the UnqualifiedNonTerminal production is bound to the variable nt, and the semantic value returned by the Choice production is bound to the variable choice. The action code then uses these variables to create a new FullProduction object and assigns that object to yyValue, thus making the newly created object the production's semantic value.

In the generated parser, Rats! declares the types of variables as following:

Passing the Semantic Value Through

Sometimes, the semantic value of a production is the same as the semantic value of one of the expressions appearing in that production. To avoid first binding that expression to some variable and then assigning that variable to yyValue , it is possible to directly bind yyValue.

For example, the production for the Header nonterminal from Rats!' own grammar makes use of this feature:

Action Header = "header":Word yyValue:Action ;
An equivalent, but more verbose definition might look like this:
Action Header = "header":Word a:Action { yyValue = a; } ;

Options, Repetitions, and Nested Choices

In general, Rats! lifts options, repetitions, and nested choices into their own, newly generated productions. It also desugars options and repetitions into equivalent productions without the option or repetition operators. Note that nested choices are not lifted if they are the last element in a sequence. Further note that repetitions are not desugared if they appear in a transient production. Finally, options are not desugared if they are not bound or if Rats can automatically deduce the value of the bound optional expression.

This lifting and desugaring raises several questions:

We now answer these questions in turn.

To determine the semantic value of an expression before applying the option or repetition operator and that of a nested choice, Rats! generally requires that each expression has its own, embedded action that defines the corresponding value. As a result, the definition of a production may contain several actions that all assign values to yyValue, even in nested expressions.

However, for some expressions, Rats! is able to automatically deduce their semantic values. Notably, if a nonterminal is optional or repeated, the semantic value of the expression before applying the option or repetition operator simply is the semantic value of the nonterminal's production. Similarly, if a nonterminal is the only expression appearing in an option, the semantic value for that option simply is the semantic value of the nonterminal's production. In these cases, no embedded actions are necessary.

For options, the semantic value after applying the option operator is the semantic value of the expression, if that expression can be matched in the input. Otherwise, the overall semantic value is simply null. For repetitions, the semantic value after applying the repetition operator is a {@link xtc.util.Pair}. Pairs are used to implement singly-linked lists and contain the semantic values of the repeated expressions. In the case of zero matches, the pair is the special {@link xtc.util.Pair#EMPTY empty pair}, which is also accessible through the type-safe {@link xtc.util.Pair#empty()} method. Rats! uses pairs as they allow for efficient addition of an element to the front of a sequence of pairs. Note that pairs can easily be converted into a Java Collections Framework list by calling {@link xtc.util.Pair#list()} (as illustrated in the production for Rats! productions shown above).

The type of a newly generated production representing a desugared option generally is Object. However, if Rats! can automatically determine the semantic value of an optional expression, it uses the more specific type (which, in the case of desugared optional nonterminals, is the type of the corresponding production). The type of a newly generated production representing a desugared repetition always is xtc.util.Pair. Finally, the type of a newly generated production representing a lifted choice always is Object.

To illustrate the general case of repetitions and nested choices, consider the following snippet from Rats!' own grammar, which is taken from the Terminal production and parses character class specifications:

   / '['
      l:( c1:ClassChar '-' c2:ClassChar
            yyValue = new CharRange(Utilities.unescape(c1).charAt(0),
        / c1:ClassChar
            yyValue = new CharRange(Utilities.unescape(c1).charAt(0));
     ']' Spacing
      { yyValue = new CharClass(l.list()); }
The nested choice has its own actions, which create character ranges as their semantic values. The parser collects these character ranges into a sequence of pairs, which is then bound to the l variable. The outer action uses this sequence of pairs to create a new character class as the overall semantic value (converting the sequence of pairs into a Java Collections Framework list along the way).

To illustrate the automatic deduction of a semantic value, consider the production for sequences from Rats!' own grammar:

Sequence Sequence =
   !Ellipsis n:SequenceName? l:Voided*
      { yyValue = new Sequence(n, l.list()); }
A sequence essentially consists of zero or more repetitions of the Voided nonterminal; no embedded action is necessary for the repetition. Rats! automatically collects the individual semantic values into a sequence of pairs. The optional sequence name preceding the repeated Voided nonterminal simply is an identifier between less-than < and greater-than > signs and is used when modifying productions. It can also be used for documentation, as Rats! tries to preserve it throughout its internal processing, so that it will be included in the generated parser (within a comment). The corresponding optional expression does not need an embedded action either. The syntactic predicate !Ellipsis excludes sequence names followed by an ellipsis ... or an ellipsis by itself from sequences, as they are used to modify productions.

Void and Text-Only Productions

Adding actions to create a production's semantic value can seem tedious and may make grammars unnecessarily verbose. To reduce the need for explicit actions, Rats! supports special types of productions, which need no semantic actions at all. We now discuss void and text-only productions, which are especially useful for recognizing lexical syntax (such as identifiers, punctuation, numbers, and so on).

A void production is a production that declares the type of its semantic value to be void. Such a production does not require any actions, but it may not be bound to an identifier either. A void production is typically used for ignored spacing or punctuation elements. Void productions also improve the accuracy of Rats!' deduction of a compound expression's semantic value. If the compound expression only contains a single non-void nonterminal, that nonterminal's semantic value is used as the semantic value of the entire expression.

Here is an example void production from Rats!' own grammar:

transient void Spacing =
  (Space / LineTerminator / TraditionalComment/ EndOfLineComment)*
This production matches space characters, line terminators, and comments. Note that the transient keyword is explained here.

The fact the Spacing is declared as void is then used in the production for Symbol:

String Symbol = SymbolCharacters Spacing ;
No action is necessary because only the SymbolCharacters nonterminal produces a semantic value. Rats! automatically detects this case and passes the value of SymbolCharacters through.

In general, Rats! tries to deduce a compound expression's value, even if it is nested within another expression, ignoring nonterminals referencing a void production or explicitly voided expressions. Furthermore, for repetitions, options, and nested choices that do not appear as the last expression in a sequence, it treats the entire repetition, option, or nested choice as void, if all component expressions are nonterminals referencing void productions, explicitly voided expressions, or predicates. For example, if nt references a void production, then the expression "nt*" is equivalent to "void:(nt*)" (note that the parentheses are not strictly necessary).

A text-only production is a production that declares the type of its semantic value to be a String, does not contain any bindings to yyValue nor actions that reference yyValue and references only other text-only productions (if any). The semantic value of a text-only production is the text matched in the input, represented as a String. Note that the above Symbol production is not text-only because it references a void production. Also note that bindings (besides to yyValue) and semantic predicates may appear in text-only productions.

To illustrate text-only productions, consider the following productions from Rats!' own grammar:

String StringLiteral            = ["] ( EscapeSequence / !["\\] _ )* ["] ;

transient String EscapeSequence = 
   '\\' ( [btnfr\"\'\-\[\\\]] / 'u' HexNumber ) ;
transient String HexNumber      = HexDigit HexDigit HexDigit HexDigit ;
transient String HexDigit       = [0-9a-fA-F] ;
The StringLiteral production only references terminals and other productions that are also text-only. As a result, its semantic value is the text matched in the input, exactly what we expect from a production that matches string literals. Note that the transient keyword is explained here.

A note on bindings within text-only productions: When binding to a character terminal (the any character constant, a character class, or a character literal), the bound variable is a char (just as for all other productions). However, for all other expressions (including options, repetitions, and nested choices), the value of the bound variable always is a string representing the text matched by that expression in the input. For options that cannot be matched in the input, the value is the empty string (and not null).

Generic Productions

Void and text-only productions typically help with recognizing lexical syntax; though, they are of limited use for productions that recognize hierarchical syntax, such as the productions for FullProduction, Header, or Sequence shown above. Generic productions help simplify productions for hierarchical syntax. Just as for void and text-only productions, no explicit semantic actions are required.

A generic production is a production that declares generic as its type and returns a semantic value that is a {@link xtc.tree.GNode generic node}. Rats! automatically creates the production's semantic value: its name is the name of the production, and its children are the semantic values of the component expressions in the recognized sequence, with the exception of any voided expressions (using the void: operator), void nonterminals, and character terminals, which are ignored.

For example, we could rewrite the production for FullProduction as a generic production:

generic FullProduction =
   Name UnqualifiedNonTerminal void:"=":Symbol Choice void:";":Symbol ;
The rewritten production has a generic node as its semantic value; the grammar author thus does not need to define a FullProduction class to represent the semantic value. Furthermore, the rewritten production is equivalent to the following production with an explicit semantic action:
Node FullProduction =
   v2:Name v3:UnqualifiedNonTerminal "=":Symbol v4:Choice ";":Symbol
     { yyValue = GNode.create("Production", v1, v2, v3, v4); }
The two symbol references are not bound because they are explicitly voided.

Options, repetitions, and nested choices in generic productions are treated just like the corresponding expressions in regular productions. In other words, they may be desugared and lifted into their own productions. As a result, they require explicit actions to create their semantic values, unless, of course, Rats! can automatically determine the corresponding values.

The creation of generic syntax tree nodes can be customized through the factory attribute, which specifies a class different from GNode. For example, factory(MyTreeFactory) causes Rats! to emit invocations to MyTreeFactory.create methods instead of GNode.create.

List-Valued Productions

If a grammar has the flatten attribute, pairs resulting from a repeated expression are treated somewhat differently in generic productions: the values on the list are added to the production's generic node as individual children. For example, consider this production for recognizing parameter lists in C:

generic ParameterList =
   ParameterDeclaration (void:",":Symbol ParameterDeclaration)* ;
Because the semantic values of the embedded repetition are added as invidividual children to the production's generic node, that node's children are all parameter declarations, which is exactly the desired behavior.

Alternatively, Rats! can automatically deduce the semantic value of productions with a Pair type. The production's value is a list of all of a sequence's component expressions. For example, consider this rewritten production for recognizing parameter lists:

Pair<Node> ParameterList =
   ParameterDeclaration (void:",":Symbol ParameterDeclaration)* ;
Beacuse the declared type is Pair<Node>, Rats! automatically deduces the semantic value of the production. It is a list containing the value of the first parameter declaration followed by the value of the repetition. The production is equivalent to the following production using an explicit semantic action:
Pair<Node> ParameterList =
   head:ParamterDeclaration tail:(void:",":Symbol ParameterDeclaration)*
   { yyValue = new Pair<Node>(head, tail); } ;
As illustrated by this version, Rats! recognizes when the last component expression in a list-valued production already has a list value and turns that value into the overall list's tail. If the last component expression does not have a list value, the overall list's tail is the empty list.

Whether to (1) use the flatten attribute so that list elements are added as individual children to generic nodes or (2) use list-valued productions to create lists and preserve them as generic nodes' children is a trade-off. With the flatten attribute, ASTs are more uniform, typically consisting of only generic nodes and strings. In contrast, without the flatten attribute, generic nodes may also contain lists of, say, nodes or strings. However, flattening lists may result in the loss of information. For example, consider this production for Java compilation units:

public generic CompilationUnit =
  PackageDeclaration? ImportDeclaration* Declaration*
  EndOfFile ;
When lists are flattened, there is no way to distinguish import declarations from regular declarations without looking at the actual children. In contrast, when lists are not flattened, the generic node for compilation units has exactly three children, corresponding to package, import, and regular declarations respectively. Additionally, the preservation of lists in generic nodes enables more exact typing of ASTs through Rats!' -ast option. Consequently, the recommended practice is not to use the flatten attribute.

Left-Recursive Productions

To simplify the specification of productions that recognize expressions at different precedence levels, void, text-only, and generic productions may contain direct left-recursions; though arbitrary left-recursions are illegal in Rats! grammars just as for PEGs. Directly left-recursive productions are automatically transformed into equivalent right-iterative productions, while preserving the left-recursive structure of the original production's semantic value. As an example, consider the following generic production for recognizing logical and expressions in C:

generic LogicalAndExpression =
     LogicalAndExpression void:"&&":Symbol BitwiseOrExpression
   / BitwiseOrExpression
This directly left-recursive production is equivalent to the following two productions, which leverage so-called actions (i.e., promises) to create the semantic values:
Node LogicalAndExpression =
   seed:BitwiseOrExpression actions:LogicalAndExpressionTail*
      { yyValue = apply(actions, seed); }

constant Action<Node> LogicalAndExpressionTail =
   "&&":Symbol right:BitwiseOrExpression
         yyValue = new Action<Node>() {
            public Node run(Node left) {
               Node result = GNode.create("LogicalAndExpression", left, right);
               return result;
The LogicalAndExpressionTail* expression creates a list of {@link xtc.util.Action actions}, with each action on the list creating a generic node that is annotated with the source location corresponding to the start of the production. (The constant attribute ensures that the Java binding for right is declared final; this is necessary because right is referenced in an anonymous inner class.) The LogicalAndExpression production uses {@link xtc.parser.ParserBase#apply(Pair,Object)} to apply each action in the list onto the result of the previous action, starting with the seed value for the first action. If the list is empty, the seed value is simply passed through, which is the desired behavior. By using actions and thus delaying the creation of generic nodes, the rewritten productions ensure that the resulting abstract syntax tree preserves left-associativity. Note that actions can also be used outside of generic productions to create left-associative abstract syntax trees.

In the previous example, the use of a list of actions results in the correct treatment of the base case: no new generic node is created, rather the semantic value of the bitwise or expression is simply passed through. When specifying productions that do not use actions, grammar writers can achieve similar results by explicitly binding yyValue. For alternatives in a generic production that assign yyValue either through a binding or a semantic action, Rats! does not create a new generic node but rather uses the explicitly specified semantic value.

Node Markers in Generic Productions

Also in the previous example, there is only one recursive alternative; consequently, the production's name, i.e., "LogicalAndExpression", provides a meaningful name for the newly created generic node. However, languages such as C contain more than one left-recursive operator at the same precedence level. Using the features described so far, grammar developers can either write one directly left-recursive generic production for all operators, thus using the same name for all operators' generic nodes, or they can write several right-iterative productions that create the generic nodes through explicit semantic actions. Neither option is particularly attractive and node markers provide a more elegant solution. They are written as an at sign '@' immediately followed by an identifier and specify a generic node's name for nodes generated by the sequence they appear in.

As an example, consider the following generic production for recognizing postfix expressions in C:

generic PostfixExpression =
    <Subscript>         PostfixExpression void:"[":Symbol Expression
  / <DirectSelection>   PostfixExpression void:".":Symbol Identifier
  / <IndirectSelection> PostfixExpression void:"->":Symbol Identifier
  / <FunctionCall>      PostfixExpression void:"(":Symbol ExpressionList?
  / <Increment>         PostfixExpression void:"++":Symbol
  / <Decrement>         PostfixExpression void:"--":Symbol
  / <Compound>          CompoundLiteral
  / <Primary>           PrimaryExpression
In a single directly left-recursive production, the example specifies all of C's postfix expressions. Yet, each recursive alternative contains a distinct node marker, thus resulting in a differently named generic node. Internally (and as described above), Rats! converts the directly left-recursive production into the corresponding right-iterative version, which uses actions to create left-recursive AST nodes. Note that the last two alternatives do not require node markers (nor bindings to yyValue) because they provide the base cases for the recursion.

Modules, Name Spaces, and Parameters

The intent behind Rats!' module system is to facilitate the re-use and extensibility of grammar specifications. Even without parameters and modifications, basic modules help, as they allow a grammar writer to break up a grammar into several units. All modules exist in the same global name space. Without parameters and modifications, this name space consists simply of the module names as specified by the corresponding module declarations. With parameters and modifications, this name space consists of the module names of all instantiated modules (with instantiation being the process of providing arguments to parameterized modules).

In contrast to module names, nonterminals are only meaningful in relation to a specific module. Without any import or modify declarations, a module can only reference the nonterminals defined in that module. In the presence of import or modify declarations, a module can also reference the public and protected nonterminals defined by imported modules and all nonterminals defined by modified modules.

Nonterminals may be ambiguous, e.g., the same nonterminal may be defined within a module and an imported module or in several imported modules. Rats! gives precedence to nonterminals defined in the same module as the nonterminal reference. For example, if module Foo defines nonterminal Name and imports module Bar, which also defines nonterminal Name, then a reference to Name appearing in one of Foo's productions is interpreted to mean Foo's Name. Bar's Name can still be referenced by using the qualified notation Bar.Name. Furthermore, if module Foo does not define Name but imports Bar and Baz, which both define Name, any reference to Name in Foo must be qualified, writing Bar.Name and Baz.Name respectively. Note that, while qualified nonterminals are globally unique and thus always unambiguous, a nonterminal, whether qualified or not, can only be used if the corresponding production's module is the same module, imported by the referencing module, or modified by the referencing module.

Parameterized modules improve re-use when compared to basic modules, as the same parameterized module can be used with different actual dependencies. For example, module xtc.util.Symbol takes one parameter for a module defining spacing:

module xtc.util.Symbol(Spacing);

import Spacing;

String Symbol = SymbolCharacters Spacing ;

transient String SymbolCharacters = ..elided.. ;
As a result, this module can be instantiated with different forms of spacing, without changing xtc.util.Symbol. At the same time, an instantiation must provide a module that specifies a void nonterminal Spacing for the resulting module to be meaningful.

A parameterized module is instantiated by specifying the corresponding arguments in the corresponding import declaration:

import xtc.util.Symbol(xtc.util.Spacing);
This import declaration without a target name is equivalent to the following declaration with a target name:
import xtc.util.Symbol(xtc.util.Spacing) as xtc.util.Symbol;
In either case, all occurrences of the parameter module name Spacing are replaced by the specified argument module name xtc.util.Spacing. Furthermore, all occurrences of the module name itself are replaced by the specified target name (which, in this example, is the same as the module name). Finally, the instantiated module becomes the sole module of that name in the global module name space. No other instantiation with the same target name is possible, unless it instantiates exactly the same module with the same arguments.

Note that the nonterminal Spacing in the production for Symbol is not renamed during instantiation, as it denotes a nonterminal and not a module. However, if the nonterminal was written as Spacing.Spacing, it would be renamed to xtc.util.Spacing.Spacing. Further note that xtc.util.Symbol could be instantiated with a different argument within the same grammar, as long as that instantiation's target name is different. Finally, note that once instantiated, other modules can reference the instantiated module through its target name. For example, after module xtc.util.Symbol has been instantiated through either of the above import declarations, it can also be imported as following:

import xtc.util.Symbol;
This import declaration, when appearing in a dependent module, references the same instantiated module.

While module parameters and arguments can only be module names and never more complex expressions, sometimes more complex arguments are desirable. For example, a grammar writer may want to instantiate xtc.util.Symbol with a more complex module my.Spacing, which requires its own argument my.Argument. In this case, the grammar writer can use an instantiate declaration, which instantiates a module but does not make its nonterminals accessible from within the instantiating module. In the example, the grammar writer would use the following declarations:

instantiate my.Spacing(my.Argument) as Spacing;
import xtc.util.Symbol(Spacing);

Module dependencies are resolved through a breadth-first search starting with the top-level module. In other words, a dependent module's dependencies are only processed after all the dependencies of the depending module have been resolved. As a result, the order of import, instantiate, and modify declarations in a module does not matter and mutually dependent modules can be instantiated within the same module. For example, xtc.lang.CSpacing has a parameter for a constant module and xtc.lang.CConstant has a parameter for a spacing module, with each module importing the parameterized module. To instantiate these two mutually dependent modules, module xtc.lang.C simply declares (with some intermediate declarations omitted and ignoring the additional xtc.lang.CState argument):

instantiate xtc.lang.CConstant(xtc.lang.CSpacing);
instantiate xtc.lang.CSpacing(xtc.lang.CState, xtc.lang.CConstant);
Because it uses breadth-first search, Rats! processes these two instantiate declarations before processing the corresponding import declarations in xtc.lang.CConstant and xtc.lang.CSpacing. By the time Rats reaches the import declarations in the dependent modules, the modules have been instantiated and no arguments are necessary.

Module Modifications

To further facilitate re-use and extensibility, Rats! supports module modifications, which concisely express extensions to a grammar and, in addition to full productions, can also contain alternative additions, which add new alternatives to a production's top-level choice, alternative removals, which remove alternatives from a production's top-level choice, and production overrides, which can override an entire production, specific alternatives, or a production's attributes. All three types of partial production, whose syntax is specified above and illustrated below, depend on the different alternatives in a production's top-level choice having sequence names. Consequently, it is good practice to always name your sequences!

A module modification must contain a single modify declaration, which specifies the module to be modified. For example, the following declaration specifies that module xtc.lang.JavaSymbol modifies module Symbol:

module xtc.lang.JavaSymbol(Symbol);

modify Symbol;
The example uses a module parameter to ensure that module xtc.lang.JavaSymbol can be applied to different versions of Symbol. The resulting module contains all full productions appearing in both the modifying and modified modules (in the example, xtc.lang.JavaSymbol and Symbol, respectively). Furthermore, all productions in the resulting module are modified as specified by the alternative additions, alternative removals, and production overrides in the modifying module. Modifications are applied in the same order as they appear in the modifying module (in the example, xtc.lang.JavaSymbol). The resulting productions are the only versions; i.e., all nonterminals, whether they originally appear in the modifying module or the modified module reference the modified productions.

The resulting module's options are the options of the modifying module, with exception of any stateful, setOfString, and flag options, which are preserved if they appear in the modified module's options. Furthermore, the modifying module's header, body, and footer actions are combined with the modified module's actions (if they exist).

An alternative addition adds an expression before or after an existing sequence. For example, the following addition adds sequence s after sequence <Bar> in production Foo:

Type Foo += <Bar> ... / <NewSequence> s ;
Similarly, the following addition adds the new sequence before sequence <Bar>:
Type Foo += <NewSequence> s / <Bar> ... ;
Note that the new expression may actually consist of several sequences and not only one as suggested by the examples. Further note that the type and nonterminal must both be specified and match an existing full production.

An alternative removal removes one or more sequences from a production. For example, the following removal eliminates sequences <Bar> and <Baz> from production Foo:

Type Foo -= <Bar>, <Baz> ;
As before, the type and nonterminal must both be specified and match an existing full production.

A production override can replace all alternatives, only specific alternatives, or a production's attributes. For example, the following override replaces all alternatives of production Foo with expression e:

Type Foo := e ;
In contrast, this override only replaces alternatives <Bar> and <Baz<:
Type Foo := ... / <Bar> s1 / <Baz> s2 ;
Finally, this override replaces Foo's attributes with the public attribute:
public Type Foo := ... ;
Note that the list of attributes may be empty, thus removing all attributes from the full production.

Memoization and Transient Productions

Packrat parsers process their input in time linear to the size of the input, even if they need to backtrack. The reason they can do this is that they store, or memoize, the result of trying each nonterminal at every input position – hence the name "packrat" parser.

The benefits of memoization are best illustrated with a production from Rats!' own grammar:

Element Suffix =
   ( p:Primary "?":Symbol { yyValue = new Option(p);            }
   / p:Primary "*":Symbol { yyValue = new Repetition(false, p); }
   / p:Primary "+":Symbol { yyValue = new Repetition(true,  p); }
   / Primary
The Suffix production matches possible suffix expressions in the input, with each of the four alternatives in the choice first trying to parse a primary expression. Assume that the current input contains a primary expression without a suffix (i.e., the fourth alternative is the alternative that will succeed). If the parser did not memoize its results, the primary expression would be parsed four times, once for each alternative, resulting in suboptimal performance. However, because parsers generated by Rats! memoize their results, the primary expression is parsed exactly once. Each subsequent alternative simply looks up the result of the first parse.

Note that it is possible to rewrite the production for Suffix to not require backtracking. An alternative expression, without semantic actions, might look like this:

   Primary ( Question / Star / Plus / /* Empty */ )
Further note that other top-down parsers, such as JavaCC and ANTLR, may not require backtracking, even with a comparable production to the one used in Rats!' own grammar as they support (limited) lookahead. However, the original form clearly and concisely expresses the intent behind this production and, because parsers generated by Rats! memoize their results, does not require any fiddling with lookahead (as would be necessary for other top-down parsers).

In theory, packrat parsers create a two-dimensional array, with characters in the input stream along the x-axis and nonterminals along the y-axis. In practice, not all values in this array are calculated (many of them represent mismatched nonterminals anyway) and the array is sparse. To avoid allocating memory for the entire array, parsers generated by Rats! break each column into several chunks. Memory for the different chunks is allocated independently and on demand (i.e., if a parsing result needs to be stored). Furthermore, for productions that are only referenced once in the entire grammar the corresponding row is never allocated.

Grammar writers have further control over memory allocation by declaring productions to be transient: if a production is transient, the corresponding row is not allocated either. The transient keyword can thus reduce a parser's memory footprint and also improve its performance. However, it is also dangerous because, if overused, the resulting parser may need to reparse the same input for the same nonterminal several times and thus perform in time superlinear to the size of the input.

So, which productions should be declared transient? In other parsers, the parser processes tokens generated by a separate lexer instead of accessing the character stream directly. Packrat parser grammars thus need to include productions that build up tokens. Examples include the Escape, HexNumber, and HexDigit productions in Rats!' own grammar (shown above). Such productions can be declared transient, as the parser typically does not backtrack at the level of individual characters. Furthermore, productions that cover ignored input characters, notably all productions that cover white space and comments, can be declared transient as well. However, when in doubt, it is best to not declare a production as transient, or to perform performance studies on several inputs to see how such declarations impact the parser's memory footprint and performance.

Grammar and Production Attributes

Rats! supports a number of options, which are either specified as a grammar-wide option in the top-level module's introduction or as per-production attributes:

A note on licensing: Parsers generated with the main, printer, and dump attributes link with code licensed under the GNU GPL version 2. As a result, parsers generated with these attributes may not be used in software that is not compatible with the GPL version 2. To generate parsers that are not restricted by the GPL, use the -lgpl option when running Rats!.

Parser Actions

Some languages cannot be expressed by PEGs or Rats! grammars. For example, the on-the-wire format for SPKI/SDSI represents byte strings as one or more digits, followed by a colon, followed by the number of characters specified by the sequence of digits (when interpreted as a decimal integer); but parsing a specific number of characters cannot be expressed by PEGs. Parser actions allow grammar writers to still use Rats! for such languages by providing a low-level extensibility mechanism.

Parser actions work as follows. Before executing the code in a parser action, the variable yyBase is assigned the index of the current parser position. The parser action can then use this index together with the parser's methods to further consume the input, parsing the expression not expressible by PEGs. When finished, it assigns the corresponding result to yyResult, which must either be a {@link xtc.parser.SemanticValue} object indicating a successful parse or a {@link xtc.parser.ParseError} object indicating a parse error. In the case of a semantic value object, that object's semantic value becomes the semantic value of the production, unless another action after the parser action changes it.

The following grammar illustrates the use of a parser action for parsing byte strings as used by SPKI/SDSI. Note that the yyStart reference in the parser action is the parser position at the beginning of the production and is used for indicating the position of an error.

module ByteString;

body {
  Result parseChars(String number, int start, int base) throws IOException {
    int n;

    try {
      n = Integer.parseInt(number);
    } catch (NumberFormatException x) {
      return new ParseError("Malformed length", start);
    StringBuilder buf = new StringBuilder(n);
    for (int i=0; i<n; i++) {
      int c = character(base + i);

      if (c != -1) {
      } else {
        return new ParseError("Unexpected end of bytestring", base + i);

    return new SemanticValue(buf.toString(), base + n);

option main(ByteString);

public String ByteString =
  n:Integer ':' ^{ yyResult = parseChars(n, yyStart, yyBase); } ;

String Integer = [0-9]+ ;