COP 3402 System Software

1. COP 3402 System Software Recitation Notes 21st September 2007

2. Limits Of Regular Expressions • Regular expressions are very useful for recognizing patterns • However, there are some patterns they cannot handle. • An Example is strings of the form anbn

3. Context Free Languages • Since regular expressions cannot handle some important patterns, we need a more powerful method of describing patterns. • Context Free Languages are one such mechanism • Proposed by Noam Chomsky in the 1950s.

4. BNF • BNF is a way to express Context free languages. • First used in ALGOL 58. • BNF stands for Backus-Naur Form • Named after two members of the ALGOL design team.

5. BNF Example for PL/0 • Next slide contains a BNF description that can verify the correctness of any PL/0 program. • Conventions: • Variables/Tokens are written between “<“ and ”>”. • The “→” symbol can be read as “is defined as”. • “ε “ is the empty string.

6. BNF Grammer for PL/0

7. Sample PL/0 Programme • const m = 7, n = 85; • var i,x,y,z,q,r; • procedure mult; • var a, b; • begin • a := x; b := y; z := 0; • while b > 0 do • begin • if odd x then z := z+a; • a := 2*a; • b := b/2; • end • end; • begin • x := m; • y := n; • call mult; • end.

8. Syntax Graphs Visual Way to represent BNF Grammars

9. Syntax Graphs Cont’d

10. Extended BNF • Conventions • Optional Constructions are enclosed in square braces ‘[‘ and ‘]’. • Constructs enclosed in curly braces ‘{‘ and ‘}’ are repeated zero or more times. • Example on next slide

11. EBNF Example for PL/0

12. Another Example • Try to write a BNF Grammar that validates strings of the type anbn. • Hint: anbn can be rewritten as aan-1bn-1b.

13. Solution • <string> → a<string>b | ε • Will ensure that • string always has the same number of a’s and b’s • The a’s always come before the b’s in the string. • As to keeping track of the ‘n’, we don’t care in this example because the number of a’s and b’s will always be matched.s