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BNF

BNF. What is BNF?. BNF stands for “Backus-Naur Form,” after the people who invented it BNF is a metalanguage --a language used to describe another language BNF is a precise way of describing the syntax of a computer language BNF is really, really easy!. The syntax of BNF.

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BNF

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  1. BNF

  2. What is BNF? • BNF stands for “Backus-Naur Form,” after the people who invented it • BNF is a metalanguage--a language used to describe another language • BNF is a precise way of describing the syntax of a computer language • BNF is really, really easy!

  3. The syntax of BNF • Any word or words enclosed in angle brackets, < >, is a nonterminal -- it stands for some string (it’s like a string variable) • The symbol ::= means “is defined as” • The symbol | means “or” • Anything else is a terminal -- it stands for itself • That’s all!

  4. Examples • <vowel> ::= a | e | i | o | u • <consonant> ::= b | c | d | f | g | h | j | k | l | m | n | p | q | r | s | t | v | w | x | y | z • <letter> ::= <vowel> | <consonant> • <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 • <hex digit> ::= <digit> | a | b | c | d | e | f

  5. Recursion • Suppose that an “unsigned integer” consists of one or more digits (but there is no limit to the number of digits) • <unsigned integer> ::= <digit> | <unsigned integer> <digit> • BNF makes heavy use of recursion

  6. More examples • Suppose that (in some computer language) a variable consists of letters, digits, and underscores, but must begin with a letter • <variable> ::= <letter> | <variable> <letter> | <variable> <digit> | <variable> _

  7. Length limitations • Suppose that a variable is as before, but can only be six characters long • <variable> ::= <letter> | <letter> <v2> | <letter> <v2> <v2> | <letter> <v2> <v2> <v2> | <letter> <v2> <v2> <v2> <v2> | <letter> <v2> <v2> <v2> <v2> <v2> • <v2> ::= <letter> | <digit> | _ • BNF isn’t great for setting limits on lengths!

  8. Recursive structures • A while loop can contain any number of other statements, including other while loops • <while loop> ::= while ( <condition> ) { <statements> } • <statement> ::= <while loop> | ...other statements... • <statements> ::= <empty> | <statements> <statement> • <empty> ::=

  9. What BNF cannot do • BNF can only describe local syntax; it cannot refer to another part of the program • Example: BNF cannot say that variables must be declared before they are used • BNF cannot do numeric comparisons • Example: BNF cannot say that int values must be between -2147483648 and 2147483647

  10. Extended BNF • After 40 years, BNF is still the preferred way of describing syntax • There are two commonly used extensions: • [ ] to indicate the bracketed thing is optional • { } to indicate zero or more of the enclosed thing • Example: <integer> ::= [+ | -] <digit> { <digit> }

  11. Trivial Variations • Sometimes different fonts are used to distinguish terminals from nonterminals (instead of marking nonterminals with < > ) • Sometimes different symbols are used, such as = for ::= • Sometimes definitions end with a period • However you write it, it’s still BNF!

  12. The End

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