COMPUTING SCIENCE 370 -- Programming Languages

BNF and EBNF

Syntactic Structures

Lexics

rules by which characters are combined to form tokens (words, symbols)

Examples:

• Fortran -- an identifier is a token, where the rule is "a letter followed by no more than five letters and digits"
• Pascal -- assignment operator := is a token
• C -- the scanner decides that the expression
  

  i=j+++k;

  calls for variable j to be postincremented (not for k to be preincremented) by the maximal munch rule [no doubt named to be consistant with "bits", "bytes", and "nybbles"]:

  If the input stream has been parsed into tokens up to a given character, the next token is taken to include the longest string of characters which could possibly constitute a token.
  

  Kernighan and Ritchie, The C Programming Language, App. A, § 2

Syntax

rules by which tokens are combined to form language structures (expressions, statements, etc.)

Examples:

• Fortran -- syntax of assignment is

  <variable> = <expression>

• Pascal -- syntax of conditional is

  if <boolean expression> then <statement>

Semantics

the meaning attached to syntactic structures

Examples:

• The meaning of the if-then-else statement is the same in Pascal and Modula-2, but the syntax differs.
  Pascal:

  if <boolean expression> then <statement> else <statement>

  Modula-2:

  IF <boolean expression> THEN <statement sequence> ELSE <statement sequence> END

• The syntax for the Boolean operators AND and OR is the same in Pascal and Modula-2, but the semantics are different: Modula-2 uses "lazy" (short-circuit, McCarthy) evaluation.

Formal Methods of Syntax Specification

1. Backus-Naur Form (BNF), a metalanguage, gives a formula for constructing legal strings (but looks like examples of strings)

   Examples:

   <simpleExpr> ::= <term> | <sign><term> | <simpleExpr> <addOp> <term>
   
   <addOp> ::= + | - | or
   
   <unsigned integer> ::= <digit> | <unsigned integer><digit>
   

   where:

   • '::=' means "is defined as"
   • '|' means "or"
   • Terms enclosed in angle brackets, such as <term>, are nonterminal symbols.
   • All other symbols (shown in boldface above [although it's not obvious for some characters, such as '-', in some browsers]) are terminal symbols.
   • The concatenation of strings is represented by the juxtaposition of their descriptions. (The fact that there is no space between <sign> and <term> in the first example above is intended to be significant. However, it is not always clear in the examples in the textbook whether there are spaces between some pairs of elements or not.)

   Note that the last example above is a recursive definition. This is the standard way of specifying sequences of elements in BNF, and for describing nested syntax, as in:

   <statement> ::= <unconditional statement>
   
                | if <expression> then <unconditional statement>
   
                | if <expression> then <unconditional statement> else <statement>
   

   BNF was first used in the Algol-60 Report. (Backus had used a previous version to describe Algol-58.)

   Extended BNF improves the readability and conciseness of BNF through extensions:

   • Kleene cross -- a sequence of one or more elements of the class marked.

     <unsigned integer> ::= <digit>+

   • Kleene star -- a sequence of zero or more elements of the class marked.

     <identifier> ::= <letter><alphanumeric>*

   • Braces can be used for grouping elements, allowing us to avoid having to define intermediate classes such as <alphanumeric>.

     <identifier> ::= <letter>{<letter>|<digit>}*

     Note: Many authors use braces to mean zero or more repetitions of the enclosed elements (i.e., a Kleene star is assumed).

   • Square brackets may be used to indicate optional elements (i.e., zero or one occurrence of the enclosed elements).

     <integer> ::= [ + | - ]<unsigned integer>

     Do not use a Kleene cross or star with square brackets.

   • Stacking alternatives results in an even more pictorial representation of the syntax.

     <identifier> ::= <letter>

     {

     <letter> <digit>

     }

     *

     <integer> ::=

     [

     + -

     ]

     <unsigned integer>

2. Syntax diagrams show legal strings in diagram form

   

   Syntax diagrams were first used in the Pascal User Manual and Report by Jensen and Wirth.

Exercises

1. Give the equivalent of the syntax diagram above in EBNF.
    

2. Consider the following BNF grammar rules:

   <pop> ::= [<bop>, <pop>] | <bop>

<bop> ::= <boop> | (<pop>)

<boop> ::= a | b | c

   Note that, since this is BNF, not EBNF, square brackets are terminal symbols.

   For each of the strings listed below, indicate all the syntactic categories of which it is a member, if any.

   1. c
   2. (a)
   3. [b]
   4. ([a,b])
   5. [(a),b]
   6. [(a),[b,a]]

Some Links

Definition of Oberon 2 in EBNF

Some Pascal syntax diagrams