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BNF

BNF. Metalanguages. A metalanguage is a language used to talk about a language (usually a different one) We can use English as its own metalanguage (e.g. describing English grammar in English) We need a formal, precise means of describing the syntax of programming languages

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BNF

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  1. BNF

  2. Metalanguages • A metalanguage is a language used to talk about a language (usually a different one) • We can use English as its own metalanguage (e.g. describing English grammar in English) • We need a formal, precise means of describing the syntax of programming languages • For decades, BNF has met that need • One of the irritating things about Java is that it has no official BNF definition—hence, it’s sometimes hard to tell what is legal syntax • It is essential to distinguish between the metalanguage terms and the object language terms • For example, BNF uses the | symbol, as do many programming languages—so if we see a |, what is it?

  3. BNF • BNF stands for either Backus-Naur Form or Backus Normal Form • BNF is a metalanguage that is frequently used to describe the grammar of a programming language • BNF is formal and precise • BNF is essential in compiler construction • If you know about “context-free grammars (CFGs),” BNF is one way of defining CFGs • There are many dialects of BNF in use, but… • …the differences are almost always minor

  4. BNF metasymbols • Anything enclosed in < > is a nonterminal that needs to be further expanded, e.g. <variable> • That is, if you see <variable> in the description of a programming language, that means “a variable goes here” • Symbols not enclosed in< >are terminals; they represent themselves, e.g. if, while, ( • That is, if you see while in the description of a programming language, that means “the actual word ‘while’ goes here” • The symbol::=means is defined as • The symbol|means or; it separates alternatives, for example, <addop> ::= + | - • That is, if you see an <addop>, it means “either a ‘+’ or a ‘-’ goes here”

  5. BNF uses recursion • <integer> ::= <digit> | <integer> <digit>or<integer> ::= <digit> | <digit> <integer> • Many people find recursion confusing • “Extended BNF” (which we’ll talk about shortly) allows repetition as well as recursion • Repetition is often easier to implement (with a loop) than recursion, so Extended BNF has become popular

  6. BNF Examples I • <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 • This defines the metasymbol ‘<digit>’ • What it means is, “If the description of the syntax says ‘<digit>’, you need an actual digit in this location” • <if statement> ::= if ( <condition> ) <statement> | if ( <condition> ) <statement> else <statement> • The symbols if, (, ), and else are terminals—they stand for themselves • <if statement>, <condition>, and <statement> are metasymbols • If you see an <if statement>, you should replace it by eitherif (<condition>) <statement>or withif (<condition>) <statement> else <statement> • Next, you need to replace <condition> and <statement> with their definitions

  7. BNF Examples II • <unsigned integer> ::= <digit> | <unsigned integer> <digit> • <integer> ::= <unsigned integer> | + <unsigned integer> | - <unsigned integer>

  8. BNF Examples III • <identifier> ::= <letter> | <identifier> <letter> | <identifier> <digit> • <block> ::= { <statement list> } • <statement list> ::= <statement> | <statement list> <statement>

  9. BNF Examples IV • <statement> ::= <block> | <assignment statement> | <break statement> | <continue statement> | <do statement> | <for loop> | <goto statement> | <if statement> | . . .

  10. Extended BNF • Dialects differ, but the following are pretty standard: • [ ] enclose an optional part of the rule • Example:<if statement> ::= if ( <condition> ) <statement>[else <statement>] • { } mean the enclosed can be repeated any number of times (including zero) • Example:<parameter list> ::= ( ) | ( {<parameter> ,}<parameter> )

  11. Variations • The preceding notation is the original and most common notation • BNF was designed before we had boldface, color, more than one font, etc. • A typical modern variation might: • Use boldface to indicate multi-character terminals • Quote single-character terminals (because boldface isn’t so obvious in this case) • Example: • if_statement ::=if "(" condition ")" statement [ elsestatement ]

  12. Limitations of BNF • No easy way to impose length limitations, such as maximum length of variable names • No way to impose distributed requirements, such as, a variable must be declared before it is used • Describes only syntax, not semantics • Nothing clearly better has been devised

  13. The End

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