Chapter 6. Syntax Definition in SDF

Table of Contents

6.1. SDF: The Basics
6.1.1. Modules
6.1.2. Start Symbols
6.1.3. Sorts
6.1.4. Syntax
6.1.5. Disambiguation
6.2. Syntax
6.2.1. Lexical and Context-free Syntax
6.2.2. Productions, Sorts, and Symbols
6.2.3. Symbols and Regular Expressions
6.2.4. Character Classes
6.3. Examples: Defining Lexical Syntax
6.3.1. Simple Whitespace
6.3.2. Identifiers
6.3.3. Keywords
6.3.4. Integer Literals
6.3.5. Floating-Point Literals
6.4. Examples: Defining Context-Free Syntax
6.4.1. Expressions
6.4.2. Constructor Attributes and Abstract Syntax Trees
6.4.3. Ambiguities in Expressions
6.4.4. Associativity and Priorities
6.4.5. Array Creation and Access Ambiguity
6.4.6. Statements
6.4.7. Whitespace and Comments
6.5. Unit Testing of Syntax Definitions
6.5.1. Usage example
6.5.2. Parse Testsuite Syntax
6.5.3. Debugging Support
6.5.4. Invocation in Automake

First, basic structure of SDF. Second, how syntax is defined SDF. Third, examples of lexical and context-free syntax. Fourth, more detailed coverage of disambigation.

6.1. SDF: The Basics

In this section, we give an overview of the basic constructs of SDF. After this section, you will now the basic idea of SDF. The next sections will discuss these constructs more detail.

6.1.1. Modules

Before defining some actual syntax, we have to explain the basic structure of a module. For this, let's take a closer look at the language constructs that are used in the modules we showed earlier in Figure 5.4.

Example 6.1. Basic constructs of SDF

module Expression 1
  Lexical Operators 2

exports  3
  context-free start-symbol Exp 4
  context-free syntax 5
    Id          -> Exp {cons("Var")} 6
    IntConst    -> Exp {cons("Int")} 
    "(" Exp ")" -> Exp {bracket}

module Operators
  sorts Exp  7
  context-free syntax
    Exp "*" Exp -> Exp {left, cons("Times")} 8
    Exp "/" Exp -> Exp {left, cons("Div")}
    Exp "%" Exp -> Exp {left, cons("Mod")}
    Exp "+" Exp -> Exp {left, cons("Plus")} 
    Exp "-" Exp -> Exp {left, cons("Minus")}

  context-free priorities 9
      Exp "*" Exp -> Exp
      Exp "/" Exp -> Exp
      Exp "%" Exp -> Exp
  > {left:
      Exp "+" Exp -> Exp
      Exp "-" Exp -> Exp

module Lexical
  sorts Id IntConst 10
  lexical syntax 11
    [a-zA-Z]+ -> Id       
    [0-9]+    -> IntConst 
    [\ \t\n]  -> LAYOUT

  lexical restrictions 12
    Id -/- [a-zA-Z]

Example 6.1 shows these modules, highlighting some of the constructs that are important to know before we dive into the details of defining syntax.


Modules have a name, which can be a plain identifier, such as Expression in this example. The module must be in a file with same name and the .sdf extension. The module name can also be a path, for example java/expressions/Assignment. In this case, the module has to be in a file with name Assignment.sdf, which must be in a directory java/expressions.


A module can optionally import a number of other modules. Multiple modules can be imported with a single import, as we have done in this example, or multiple imports can be used. This is not very common: usually, modules have just a single imports declaration.

Modules are always imported by their full name. So, if the name of a module is a path, such as java/expressions/Assignment, then the module must be imported with that full name, even if it is in the directory java/expressions. If the name of the modules are long, which is typically the case if you use full paths to organize a large syntax definition in different directories, then the names are usually mentioned on separate lines, but still in a single import.


Modules contain a number of sections, of which we now only consider the exports section. An exports section defines a number of syntactic aspects, called a grammar, that will be available to modules that import this module. This includes syntax, but also declarations of sorts, start symbols, priorities, restrictions, etc.

A module can also just import other modules and not actually define any syntactical aspects itself. This is typically the case in main modules of large syntax definitions, which only import modules for names, expressions, statements, etc.

6.1.2. Start Symbols


Every syntax definition needs to define one or more start symbols, otherwise not a single input will accepted. Start symbols are the language constructs that are allowed at the top-level of a source file. For our simple expression language, the start symbol is Exp. For a java syntax definition, the start symbol could be CompilationUnit, which consists of a package, import, and type declarations.

6.1.3. Sorts

7 10

Every syntax definition introduces names for the syntactical sorts of a language, such as Exp and Id. These names can be declared in a sorts declaration. Declaring sorts is optional, but the SDF parser generator will give a warning if a sort that is used somewhere in the syntax definition is not declared. It is a good habit to declare all the sorts, since this makes it easier to find possible miss-spellings of these names.

Note that in SDF syntax definitions we do not directly use the terminology of terminal and non-terminal, since actually only single characters are terminals in SDF, and almost everything else is a non-terminal. Lexical and context-free sorts are both declared as sorts.

6.1.4. Syntax

5 11

The actual syntax is defined in lexical and context-free syntax. The lexical syntax defines the syntax of language constructs like literals, comments, whitespace, and identifiers, or what is usally referred to as terminals. The context-free syntax defines the syntax of constructs like operators, statements, or what is usually referred to as non-terminals.

In other parser generators the lexical syntax is often specified in a separate scanner specification, but in SDF these lexical aspects are integrated in the definition of the context-free syntax. We will come back to that later when we discuss the definition of lexical syntax.

6 8

Productions can have attributes can have attributes, specified between curly braces after the production. Some of these attributes, such as left have a special meaning for SDF itself. Other attributes can specify information about a production that target a different tool, such as bracket and cons, which target the tool that implodes parse trees to abstract syntax trees.

6.1.5. Disambiguation

9 12

SDF support constructs to define in a declarative way that certain kinds of derivations are not allowed, also known as disambiguation filters. In our example, there two examples of this: we define priorities of the arithmetic expressions, and there is a lexical restriction that specifies that an identifier can never be followed by a character that is allowed in an identifier. We will explain these mechanisms later.

6.2. Syntax

6.2.1. Lexical and Context-free Syntax

Usually, parsing is performed in two phases. First, a lexical analysis phase splits the input in tokens, based on a grammar for the lexical syntax of the language. This lexical grammar is usually specified by a set of regular expressions that specifiy the tokens of the language. Second, a parser based on a grammar for the context-free syntax of the language performs the syntactic analysis. This approach has several disadvantages for certain applications, which won't discuss in detail for now. One of the most important disadvantages is that the combination of the two grammars is not a complete, declarative definition of the syntax of the language.

SDF integrates the definition of lexical and context-free syntax in a single formalism, thus supporting the complete description of the syntax of a language in a single specification. All syntax, both lexical and context-free, is defined by productions, respectively in lexical syntax and context-free syntax sections. Parsing of languages defined in SDF is implemented by scannerless generalized-LR parsing, which operates on individual characters instead of tokens.

Expressive Power.  Since lexical and context-free syntax are both defined by productions, there is actually no difference in the expressive power of the lexical and context-free grammar. Hence, lexical syntax can be a context-free language, instead of being restricted to a regular grammar, which is the case when using conventional lexical analysis tools based on regular expression. For example, this means that you can define the syntax of nested comments in SDF, which we will illustrate later. In practice, more important is that it is easier to define lexical syntax using productions than using regular expressions.

Layout.  Then, why are there two different sections for defining syntax? The difference between these two kinds of syntax sections is that in lexical syntax no layout (typically whitespace and comments) is allowed between symbols. In contrast, in context-free syntax sections layout is allowed between the symbols of a production. We will explain later how layout is defined. The allowance of layout is the only difference between the two kinds of syntax sections.

6.2.2. Productions, Sorts, and Symbols

In the Section 5.1 we recapped context-free grammars and productions, which have the form A0 -> A1 ... An, where A0 is non-terminal and A1 ... An is a string of terminals and non-terminals. Also, we mentioned earlier that the distinction between terminals and non-terminals is less useful in SDF, since only single characters are terminals if the lexical and context-free syntax are defined in a single formalism. For this reason, every element of a production, i.e. A0 ... An is called a symbol. So, productions take a list of symbols and produce another symbol.

6.2.3. Symbols and Regular Expressions

There are two primary symbols:


Sorts are names for language specific constructs, such as Exp, Id, and IntConst. These names are declared using the previously introduced sorts declaration and defined by productions.

Character Classes

A character class is set of characters. Character classes are specified by single characters, character ranges, and can be combined using set operators, such as complement, difference, union, intersection. Examples: [abc], [a-z], [a-zA-Z0-9], ~[\n]. We will discuss character classes in more detail in Section 6.2.4.

Of course, defining an entire language using productions that can contain only sorts and character classes would be a lot of work. For example, programming languages usually contain all kinds of list constructs. Specification of lists with plain context-free grammars requires several productions for each list construct. SDF provides a bunch of regular expression operators abbreviating these common patterns. In the following list, A represents a symbol and c a character.

"c0 ... cn"

Literals are strings that must literally occur in the input, such as keywords (if, while, class), literals (null, true) and operators (+, *). Literals can be written naturally as, for example, "while". Escaping of special characters will be discussed in ???.


Zero or more symbols A. Examples: Stm*, [a-zA-Z]*


One or more symbols A. Examples: TypeDec+, [a-zA-Z]+

{A0 A1}*

Zero or more symbols A0 separated by A1. Examples: {Exp ","}*, {FormalParam ","}*

{A0 A1}+

One or more symbols A0 separated by A1. Examples: {Id "."}+, {InterfaceType ","}+


Optional symbol A. Examples: Expr?, [fFdD]?

A0 | A1

Alternative of symbol A0 or A1. Example: {Expr ","}* | LocalVarDec

(A0 ... An)

Sequence of symbols A0 ... An.

6.2.4. Character Classes

In order to define the syntax at the level of characters, SDF provides character classes, which represent a set of characters from which one character can be recognized during parsing. The content of a character classes is a specification of single characters or character ranges (c0-c1). Letters and digits can be written as themselves, all other characters should be escaped using a slash, e.g. \_. Characters can also be indicated by their decimal ASCII code, e.g. \13 for linefeed. Some often used non-printable characters have more mnemonic names, e.g., \n for newline, \ for space and \t for tab.

Character classes can be combined using set operations. The most common one is the unary complement operator ~, e.g ~[\n]. Binary operators are the set difference /, union \/ and intersection /\.

Example 6.2. Examples of Character Classes


Character class for digits: 0, 1, 2, 3, 4, 5, 6, 8, 9.


Characters typically used in hexi-decimal literals.


Characters used as a floating point type suffix, typically in C-like languages.

[\ \t\12\r\n]

Typical character class for defining whitespace. Note that SDF does not yet support \f as an escape for form feed (ASCII code 12).


Character class for the set of characters that are usually allowed as escape sequences in C-like programming languages.


The set of characters that is typically allowed in string literals.

6.3. Examples: Defining Lexical Syntax

Until now, we have mostly discussed the design of SDF. Now, it's about time to see how all these fancy ideas for syntax definition work out in practice. In this and the next section, we will present a series of examples that explain how typical language constructs are defined in SDF. This first section covers examples of lexical syntax constructs. The next section will be about context-free syntax.

6.3.1. Simple Whitespace

Before we can start with the examples of lexical constructs like identifiers and literals, you need to know the basics of defining whitespace. In SDF, layout is a special sort, called LAYOUT. To define layout, you have to define productions that produce this LAYOUT sort. Thus, to allow whitespace we can define a production that takes all whitespace characters and produces layout. Layout is lexical syntax, so we define this in a lexical syntax section.

lexical syntax
  [\ \t\r\n] -> LAYOUT

We can now also reveal how context-free syntax exactly works. In context-free syntax, layout is allowed between symbols in the left-hand side of the productions, by automatically inserting optional layout (e.g. LAYOUT?) between them.

In the following examples, we will assume that whitespace is always defined in this way. So, we will not repeat this production in the examples. We will come back to the details of whitespace and comments later.

6.3.2. Identifiers

Almost every language has identifiers, so we will start with that. Defining identifiers themselves is easy, but there is some more definition of syntax required, as we will see next. First, the actual definition of identifiers. As in most languages, we want to disallow digits as the first character of an identifier, so we take a little bit more restrictive character class for that first character.

lexical syntax
  [A-Za-z][A-Za-z0-9]* -> Id Reserving Keywords

If a language would only consists of identifiers, then this production does the job. Unfortunately, life is not that easy. In practice, identifiers interact with other language constructs. The best known interaction is that most languages do not allow keywords (such as if, while, class) and special literals (such as null, true). In SDF, keywords and special literals are not automatically preferred over identifiers. For example, consider the following, very simple expression language (for the context-free syntax we appeal to your intuition for now).

lexical syntax
  [A-Za-z][A-Za-z0-9]* -> Id
  "true"  -> Bool
  "false" -> Bool

context-free start-symbols Exp
context-free syntax
  Id   -> Exp {cons("Id")}
  Bool -> Exp {cons("Bool")}

The input true can now be parsed as an identifier as well as a boolean literal. Since the generalized-LR parser actually supports ambiguities, we can even try this out:

$ echo "true" | sglri -p Test.tbl
amb([Bool("true"), Id("true")])

The amb term is a representation of the ambiguity. The argument of the ambiguity is a list of alternatives. In this case, the first is the boolean literal and the second is the identifier true. So, we have to define explicitly that we do not want to allow these boolean literals as identifiers. For this purpose, we can use SDF reject productions. The intuition of reject productions is that all derivations of a symbol for which there is a reject production are forbidden. In this example, we need to create productions for the boolean literals to identifiers.

lexical syntax
  "true"  -> Id {reject}
  "false" -> Id {reject}

For true, there will now be two derivations for an Id: one using the reject production and one using the real production for identifiers. Because of that reject production, all derivations will be rejected, so true is not an identifier anymore. Indeed, if we add these productions to our syntax definition, then the true literal is no longer ambiguous:

$ echo "true" | sglri -p Test.tbl

We can make the definition of these reject productions a bit more concise by just reusing the Bool sort. In the same way, we can define keywords using separate production rules and have a single reject production from keywords to identifiers.

lexical syntax
  Bool    -> Id {reject}
  Keyword -> Id {reject}

  "class" -> Keyword
  "if"    -> Keyword
  "while" -> Keyword Longest Match

Scanners usually apply a longest match policy for scanning tokens. Thus, if the next character can be included in the current token, then this will always be done, regardless of the consequences after this token. In most languages, this is indeed the required behaviour, but in some languages longest match scanning actually doesn't work. Similar to not automatically reserving keywords, SDF doesn't choose the longest match by default. Instead, you need to specify explicitly that you want to recognize the longest match.

For example, suppose that we introduce two language constructs based on the previously defined Id. The following productions define two statements: a simple goto and a construct for variable declarations, where the first Id is the type and the second the variable name.

context-free syntax
  Id    -> Stm {cons("Goto")}
  Id Id -> Stm {cons("VarDec")}

For the input foo, which is of course intended to be a goto, the parser will now happily split up the identifier foo, which results in variable declarations. Hence, this input is ambiguous.

$ echo "foo" | sglri -p Test.tbl
amb([Goto("foo"), VarDec("f","oo"), VarDec("fo","o")])

To specify that we want the longest match of an identifier, we define a follow restriction. Such a follow restriction indicates that a string of a certain symbol cannot be followed by a character from the given character class. In this way, follow restrictions can be used to encode longest match disambiguation. In this case, we need to specify that an Id cannot be followed by one of the identifier characters:

lexical restrictions
  Id -/- [A-Za-z0-9]

Indeed, the input foo is no longer ambiguous and is parsed as a goto:

$ echo "foo" | sglri -p Test.tbl

6.3.3. Keywords

In Section 6.3.2 we explained how to reject keywords as identifiers, so we will not repeat that here. Also, we discussed how to avoid that identifiers get split. A similar split issue arises with keywords. Usually, we want to forbid a letter immediately after a keyword, but the scannerless parser will happily start a new identifier token immediately after the keyword. To illustrate this, we need to introduce a keyword, so let's make our previous goto statement a bit more clear:

context-free syntax
  "goto" Id -> Stm {cons("Goto")}

To illustrate the problem, let's take the input gotox. Of course, we don't want to allow this string to be a goto, but without a follow restriction, it will actually be parsed by starting an identifier after the goto:

$ echo "gotox" | sglri -p Test.tbl

The solution is to specify a follow restriction on the "goto" literal symbol.

lexical restrictions
  "goto" -/- [A-Za-z0-9]

It is not possible to define the follow restrictions on the Keyword sort that we introduced earlier in the reject example. The follow restriction must be defined on the symbol that literally occurs in the production, which is not the case with the Keyword symbol. However, you can specify all the symbols in a single follow restriction, seperated by spaces:

lexical restrictions
  "goto" "if" -/- [A-Za-z0-9]

6.3.4. Integer Literals

Compared to identifiers, integer literals are usually very easy to define, since they do not really interact with other language constructs. Just to be sure, we still define a lexical restriction. The need for this restriction depends on the language in which the integer literal is used.

lexical syntax
  [0-9]+ -> IntConst

lexical restrictions
  IntConst -/- [0-9]

In mainstream languages, there are often several notations for integer literal, for example decimal, hexadecimal, or octal. The alternatives are then usually prefixed with one or more character that indicates the kind of integer literal. In Java, hexadecimal numerals start with 0x and octal with a 0 (zero). For this, we have to make the definition of decimal numerals a bit more precise, since 01234 is now an octal numeral.

lexical syntax
  "0"         -> DecimalNumeral
  [1-9][0-9]* -> DecimalNumeral

  [0][xX] [0-9a-fA-F]+ -> HexaDecimalNumeral
  [0]     [0-7]+       -> OctalNumeral

6.3.5. Floating-Point Literals

Until now, the productions for lexical syntax have not been very complex. In some cases, the definition of lexical syntax might even seem to be more complex in SDF, since you explicitly have to define behaviour that is implicit in existing lexical anlalysis tools. Fortunately, the expressiveness of lexical syntax in SDF also has important advantages, even if it is applied to language that are designed to be processed with a separate scanner. As a first example, let's take a look at the definition of floating-point literals.

Floating-point literals consists of three elements: digits, which may include a dot, an exponent, and a float suffix (e.g. f, d etc). There are three optional elements in float literals: the dot, the exponent, and the float suffix. But, if you leave them all out, then the floating-point literal no longer distinguishes itself from an integer literal. So, one of the floating-point specific elements is required. For example, valid floating-point literals are: 1.0, 1., .1, 1f, and 1e5, but invalid are: 1, and .e5. These rules are encoded in the usual definition of floating-point literals by duplicating the production rule and making different elements optional and required in each production. For example:

lexical syntax
  [0-9]+ "." [0-9]* ExponentPart? [fFdD]? -> FloatLiteral
  [0-9]* "." [0-9]+ ExponentPart? [fFdD]? -> FloatLiteral
  [0-9]+            ExponentPart  [fFdD]? -> FloatLiteral
  [0-9]+            ExponentPart? [fFdD]  -> FloatLiteral

  [eE] SignedInteger -> ExponentPart
  [\+\-]? [0-9]+ -> SignedInteger

However, in SDF we can use reject production to reject these special cases. So, the definition of floating-point literals itself can be more naturally defined in a single production 1. The reject production 2 defines that there should at least be one element of a floating-point literal: it rejects plain integer literals. The reject production 3 defines that the digits part of the floating-point literals is not allowed to be a single dot.

lexical syntax
  FloatDigits ExponentPart? [fFdD]? -> FloatLiteral 1
  [0-9]* "." [0-9]* -> FloatDigits
  [0-9]+            -> FloatDigits

  [0-9]+ -> FloatLiteral {reject} 2
  "."    -> FloatDigits  {reject} 3


Similar to defining whitespace, comments can be allowed everywhere by defining additional LAYOUT productions. In this section, we give examples of how to define several kinds of common comments. End-of-line Comment

Most languages support end-of-line comments, which start with special characters, such as //, #, or %. After that, all characters on that line are part of the comment. Defining end-of-line comments is quite easy: after the initial characters, every character except for the line-terminating characters is allowed until a line terminator.

lexical syntax
  "//" ~[\n]* [\n] -> LAYOUT Traditional Block Comment

Block comments (i.e. /* ... */) are a bit more tricky to define, since the content of a block comment may include an asterisk (*). Let's first take a look at a definition of block comments that does not allow an asterisk in its content:

  "/*" ~[\*]* "*/" -> LAYOUT

If we allow an asterisk and a slash, the sequence */ will be allowed as well. So, the parser will accept the string /* */ */ as a comment, which is not valid in C-like languages. In general, allowing this in a language would be very inefficient, since the parser can never decide where to stop a block comment. So, we need to disallow just the specific sequence of characters */ inside a comment. We can specify this using a follow restriction: an asterisk in a block comments is allowed, but it cannot be followed by a slash (/).

But, on what symbol do we specify this follow restriction? As explained earlier, we need to specify this follow restriction on a symbol that literally occurs in the production. So, we could try to allow a "*", and introduce a follow restriction on that:

lexical syntax
  "/*" (~[\*] | "*")* "*/" -> LAYOUT

lexical restrictions
  "*" -/- [\/]

But, the symbol "*" also occurs in other productions, for example in multiplication expressions and we do not explicitly say here that we intend to refer to the "*" in the block comment production. To distinguish the block comment asterisk from the multiplication operator, we introduce a new sort, creatively named Asterisk, for which we can specify a follow restriction that only applies to the asterisk in a block comment.

lexical syntax
  "/*" (~[\*] | Asterisk)* "*/" -> LAYOUT
  [\*] -> Asterisk

lexical restrictions
  Asterisk -/- [\/] Balanced Block Comments

To illustrate that lexical syntax in SDF can actually be context-free, we now show an example of how to implement balanced, nested block comments, i.e. a block comment that supports block comments in its content: /* /* */ */. Defining the syntax for nested block comments is quite easy, since we can just define a production that allows a block comment inside itself 1. For performance and predictability, it is important to require that the comments are balanced correctly. So, in addition to disallowing */ inside in block comments, we now also have to disallow /*. For this, we introduce a Slash sort, for which we define a follow restriction 2, similar to the Asterisk sort that we discussed in the previous section.

lexical syntax
  BlockComment -> LAYOUT

  "/*" CommentPart* "*/" -> BlockComment
  ~[\/\*]      -> CommentPart
  Asterisk     -> CommentPart
  Slash        -> CommentPart
  BlockComment -> CommentPart 1
  [\/] -> Slash
  [\*] -> Asterisk

lexical restrictions
  Asterisk -/- [\/]
  Slash    -/- [\*]  2

6.4. Examples: Defining Context-Free Syntax

Context-free syntax in SDF is syntax where layout is allowed between the symbols of the productions. Context-free syntax can be defined in a natural way, thanks to the use of generalized-LR parsing, declarative disambiguation mechanism, and an extensive set of regular expression operators. To illustrate the definition of context-free syntax, we give examples of defining expressions and statements. Most of the time will be spend on explaining the disambiguation mechanisms.

6.4.1. Expressions

In the following sections, we will explain the details of a slightly extended version of the SDF modules in Example 6.1, shown in Example 6.3.

Example 6.3. Syntax of Small Expression Language in SDF

module Expression

  context-free start-symbols Exp
  context-free syntax
    Id          -> Var 1
    Var         -> Exp {cons("Var") 2}
    IntConst    -> Exp {cons("Int") 3}}
    "(" Exp ")" -> Exp {bracket 4}

    "-" Exp     -> Exp {cons("UnaryMinus")}
    Exp "*" Exp -> Exp {cons("Times"), left 5}
    Exp "/" Exp -> Exp {cons("Div"), left}
    Exp "%" Exp -> Exp {cons("Mod"), left}
    Exp "+" Exp -> Exp {cons("Plus") 6, left}
    Exp "-" Exp -> Exp {cons("Minus"), left}
    Exp "=" Exp -> Exp {cons("Eq"), non-assoc 7}
    Exp ">" Exp -> Exp {cons("Gt"), non-assoc}

  context-free priorities 8
       "-" Exp -> Exp 9
    > {left: 10
        Exp "*" Exp -> Exp
        Exp "/" Exp -> Exp
        Exp "%" Exp -> Exp
    > {left: 
        Exp "+" Exp -> Exp
        Exp "-" Exp -> Exp
    > {non-assoc: 11
        Exp "=" Exp -> Exp
        Exp ">" Exp -> Exp

6.4.2. Constructor Attributes and Abstract Syntax Trees

First, it is about time to explain the constructor attribute, cons, which was already briefly mentioned in Section 5.1.2. In the example expression language, most productions have a constructor attribute, for example 2, 3 and 6, but some have not, for example 1 and 4.

The cons attribute does not have any actual meaning in the definition of the syntax, i.e the presence or absence of a constructor does not affect the syntax that is defined in any way. The constructor only serves to specify the name of the abstract syntax tree node that is to be constructed if that production is applied. In this way, the cons attribute 3 of the production for integer literals, defines that an Int node should be produced for that production:

$ echo "1" | sglri -p Test.tbl

Note that this Int constructor takes a single argument, a string, which is the name of the variable. This argument of Int is a string because the production for IntConst is defined in lexical syntax and all derivations from lexical syntax productions are represented as strings, i.e. without structure. As another example, the production for addition has a Plus constructor attribute 3. This production has three symbols on the left-hand side, but the constructor takes only two arguments, since literals are not included in the abstract syntax tree.

$ echo "1+2" | sglri -p Test.tbl

However, there are also productions that have no cons attribute, i.e. 1 and 4. The production 1 from Id to Var is called an injection, since it does not involve any additional syntax. Injections don't need to have a constructor attribute. If it is left out, then the application of the production will not produce a node in the abstract syntax tree. Example:

$ echo "x" | sglri -p Test.tbl

Nevertheless, the production 4 does involve additional syntax, but does not have a constructor. In this case, the bracket attribute should be used to indicate that this is a symbol between brackets, which should be literals. The bracket attribute does not affect the syntax of the language, similar to the constructor attribute. Hence, the parenthesis in the following example do not introduce a node, and the Plus is a direct subterm of Times.

$ echo "(1 + 2) * 3" | sglri -p Test.tbl

Conventions.  In Stratego/XT, constructors are by covention CamelCase. Constructors may be overloaded, i.e. the same name can be used for several productions, but be careful with this feature: it might be more difficult to distinguish the several cases for some tools. Usually, constructors are not overloaded for productions with same number of arguments (arity).

6.4.3. Ambiguities in Expressions

Example 6.4. Ambiguous Syntax Definition for Expressions

  Exp "+" Exp -> Exp {cons("Plus")}
  Exp "-" Exp -> Exp {cons("Minus")}
  Exp "*" Exp -> Exp {cons("Mul")} 
  Exp "/" Exp -> Exp {cons("Div")}

Syntax definitions that use only a single non-terminal for expressions are highly ambiguous. Example 6.4 shows the basic arithmetic operators defined in this way. For every combination of operators, there are now multiple possible derivations. For example, the string a+b*c has two possible derivations, which we can actually see because of the use of a generalized-LR parser:

$ echo "a + b * c" | sglri -p Test3.tbl  | pp-aterm
  [ Times(Plus(Var("a"), Var("b")), Var("c"))
  , Plus(Var("a"), Times(Var("b"), Var("c")))

These ambiguities can be solved by using the associativities and priorities of the various operators to disallow undesirable derivations. For example, from the derivations of a + b * c we usually want to disallow the second one, where the multiplications binds weaker than the addition operator. In plain context-free grammars the associativity and priority rules of a language can be encoded in the syntax definition by introducing separate non-terminals for all the priority levels and let every argument of productions refer to such a specific priority level. Example 6.5 shows how the usual priorities and associativity of the operators of the example can be encoded in this way. For example, this definition will never allow an AddExp as an argument of a MulExp, which implies that * binds stronger than +. Also, AddExp can only occur at the left-hand side of an AddExp, which makes the operator left associative.

This way of dealing with associativity and priorities has several disadvantages. First, the disambiguation is not natural, since it is difficult to derive the more high-level rules of priorities and associativity from this definition. Second, it is difficult to define expressions in a modular way, since the levels need to be known and new operators might affect the carefully crafted productions for the existing ones. Third, due to all the priority levels and the productions that connect these levels, the parse trees are more complex and parsing is less efficient. For these reasons SDF features a more declarative way of defining associativity and priorities, which we discuss in the next section.

Example 6.5. Non-Ambiguous Syntax Definition for Expressions

  AddExp -> Exp

  MulExp -> AddExp
  AddExp "+" MulExp -> AddExp {cons("Plus")}
  AddExp "-" MulExp -> AddExp {cons("Minus")}

  PrimExp -> MulExp
  MulExp "*" PrimExp -> MulExp {cons("Mul")} 
  MulExp "/" PrimExp -> MulExp {cons("Div")}

  IntConst -> PrimExp {cons("Int")}
  Id       -> PrimExp {cons("Var")}

6.4.4. Associativity and Priorities

Work in Progress

This chapter is work in progress. Not all parts have been finished yet. The latest revision of this manual may contain more material. Refer to the online version.

In order to support natural syntax definitions, SDF provides several declarative disambiguation mechanisms. Associativity declarations (left, right, non-assoc), disambiguate combinations of a binary operator with itself and with other operators. Thus, the left associativity of + entails that a+b+c is parsed as (a+b)+c. Priority declarations (>) declare the relative priority of productions. A production with lower priority cannot be a direct subtree of a production with higher priority. Thus a+b*c is parsed as a+(b*c) since the other parse (a+b)*c has a conflict between the * and + productions.

> Exp "&"  Exp -> Exp
> Exp "^"  Exp -> Exp
> Exp "|"  Exp -> Exp
> Exp "&&" Exp -> Exp
> Exp "||" Exp -> Exp
> ... Group Associativity Priorities and Hedged Symbols

Solution: introduce an auxiliary non-terminal

6.4.5. Array Creation and Access Ambiguity

This is usually handled with introducing a new non-terminal.

context-free syntax
  "new" ArrayBaseType DimExp+ Dim*  -> ArrayCreationExp {cons("NewArray")}

  Exp "[" Exp "]" -> Exp {cons("ArrayAccess")}
  ArrayCreationExp "[" Exp "]" -> Exp {reject}

6.4.6. Statements

Figure 6.1 illustrates the use of these operators in the extension of the expression language with statements and function declarations. Lists are used in numerous places, such as for the sequential composition of statements (Seq), the declarations in a let binding, and the formal and actual arguments of a function (FunDec and Call). An example function definition in this language is:

Figure 6.1.  Syntax definition with regular expressions.

module Statements
imports Expressions 
  sorts Dec FunDec
  context-free syntax
    Var ":=" Exp            	     -> Exp {cons("Assign")}
    "(" {Exp ";"}* ")" 		     -> Exp {cons("Seq")}
    "if" Exp "then" Exp "else" Exp   -> Exp {cons("If")}
    "while" Exp "do" Exp      	     -> Exp {cons("While")}
    "let" Dec* "in" {Exp ";"}* "end" -> Exp {cons("Let")}
    "var" Id ":=" Exp                -> Dec {cons("VarDec")}
    FunDec+ 			     -> Dec {cons("FunDecs")}
    "function" Id "(" {Id ","}* ")"  
      "=" Exp 	    	             -> FunDec {cons("FunDec")}
    Var "(" {Exp ","}* ")" 	     -> Exp {cons("Call")}
  context-free priorities
     Exp "=" Exp 		     -> Exp
     Exp ">" Exp 		     -> Exp}
  >  Var ":=" Exp                    -> Exp
  > {right:
     "if" Exp "then" Exp "else" Exp  -> Exp
     "while" Exp "do" Exp      	     -> Exp}
  >  {Exp ";"}+ ";" {Exp ";"}+       -> {Exp ";"}+

context-free start-symbols Exp

function fact(n, x) =
  if n > 0 then fact(n - 1, n * x) else x Dangling Else

6.4.7. Whitespace and Comments

context-free restrictions
  LAYOUT? -/- [\ \t\12\n\r]

Why follow restrictions on whitespace is necessary

context-free restrictions
  LAYOUT?  -/- [\/].[\*]
  LAYOUT?  -/- [\/].[\/]

6.5. Unit Testing of Syntax Definitions

Parse-unit is a tool, part of Stratego/XT, for testing SDF syntax definitions. The spirit of unit testing is implemented in parse-unit by allowing you to check that small code fragments are parsed correctly with your syntax definition.

In a parse testsuite you can define tests with an input and an expected result. You can specify that a test should succeed (succeeds, for lazy people), fail (fails) or that the abstract syntax tree should have a specific format. The input can be an inline string or the contents of a file for larger tests.

6.5.1. Usage example Syntax Definition

Assuming the following grammar for a simple arithmetic expressions:

module Exp
  context-free start-symbols Exp
  sorts Id IntConst Exp
  lexical syntax
    [\ \t\n]  -> LAYOUT
    [a-zA-Z]+ -> Id
    [0-9]+    -> IntConst
  context-free syntax
    Id        -> Exp {cons("Var")}
    IntConst  -> Exp {cons("Int")}
    Exp "*"  Exp -> Exp  {left, cons("Mul")}
    Exp "/"  Exp -> Exp  {left, cons("Div")}
    Exp "%"  Exp -> Exp  {left, cons("Mod")}
    Exp "+"  Exp -> Exp  {left, cons("Plus")}
    Exp "-"  Exp -> Exp  {left, cons("Minus")}
  context-free priorities
      Exp "*"  Exp -> Exp
      Exp "/"  Exp -> Exp
      Exp "%"  Exp -> Exp
  > {left:
      Exp "+"  Exp -> Exp
      Exp "-"  Exp -> Exp
    } Parse Testsuite

You could define the following parse testsuite in a file expression.testsuite :

testsuite Expressions
topsort Exp

test simple int literal
  "5" -> Int("5")

test simple addition
  "2 + 3" -> Plus(Int("2"), Int("3"))

test addition is left associative
  "1 + 2 + 3" -> Plus(Plus(Int("1"), Int("2")), Int("3"))

  "1 + 2 + 3" succeeds

test multiplication has higher priority than addition
  "1 + 2 * 3" -> Plus(Int("1"), Mul(Int("2"), Int("3")))

  "x" -> Var("x")

  "x1" -> Var("x1")

  "x1" fails

  "1 * 2 * 3" -> Mul(Int("1"), Mul(Int("2"), Int("3"))) Running the Parse Testsuite

Running this parse testsuite with:

  $ parse-unit -i expression.testsuite -p Exp.tbl

will output:

executing testsuite Expressions with 9 tests
* OK   : test 1 (simple int literal)
* OK   : test 2 (simple addition)
* OK   : test 3 (addition is left associative)
* OK   : test 4 (1 + 2 + 3)
* OK   : test 5 (multiplication has higher priority than addition)
* OK   : test 6 (x)
sglr: error in g_0.tmp, line 1, col 2: character `1' (\x31) unexpected
* ERROR: test 7 (x1)
  - parsing failed
  - expected:  Var("x1")
sglr: error in h_0.tmp, line 1, col 2: character `1' (\x31) unexpected
* OK   : test 8 (x1)
* ERROR: test 9 (1 * 2 * 3)
  - succeeded: Mul(Mul(Int("1"),Int("2")),Int("3"))
  - expected:  Mul(Int("1"),Mul(Int("2"),Int("3")))
results testsuite Expressions
successes : 7
failures  : 2

6.5.2. Parse Testsuite Syntax

You cannot escape special characters because there is no need to escape them. The idea of the testsuite syntax is that test input typically contains a lot of special characters, which therefore they should no be special and should not need escaping.

Anyhow, you still need some mechanism make it clear where the test input stops. Therefore the testsuite syntax supports several quotation symbols. Currently you can choose from: ", "", """, and [, [[, [[[. Typically, if you need a double quote in your test input, then you use the [.

6.5.3. Debugging Support

Parse-unit has an option to parse a single test and write the result to the output. In this mode ambiguities are accepted, which is useful for debugging. The option for the 'single test mode' is --single nr where nr is the number in the testsuite (printed when the testsuite is executed). The --asfix2 flag can be used to produce an asfix2 parse tree instead of an abstract syntax tree.

6.5.4. Invocation in Automake

The following make rule can be used to invoke parse-unit from your build system.

%.runtestsuite : %.testsuite
      $(SDF_TOOLS)/bin/parse-unit -i $< -p $(PARSE_UNIT_PTABLE) --verbose 1 -o /dev/null

A typical fo testing your syntax definitions looks like:

EXTRA_DIST = $(wildcard *.testsuite)

  expressions.testsuite \

PARSE_UNIT_PTABLE = $(top_srcdir)/syn/Foo.tbl

installcheck-local: $(TESTSUITES:.testsuite=.runtestsuite)