Lesson 2

1. Lesson 2 CDT301 – CompilerTheory, Spring 2011 Teacher: Linus Källberg

2. Outline • Context-freelanguages • Context-free grammars • Parsetrees • Pushdown automata

3. Grammars S → a B B → ε B → b B • Regex: ab* • Derivation of “abb”: S ⇒ a B ⇒ a b B ⇒ a b b B ⇒ a b b

4. Parsetrees S ⇒ a B⇒ a b B⇒ a b bB⇒ a b b S a B b B b B ε

5. Parsetrees S → a B B → ε B → b B String: “abb” S

6. Parsetrees S → a B B → ε B → b B String: “abb” S a B

7. Parsetrees S → a B B → ε B → b B String: “abb” S a B b B

8. Parsetrees S → a B B → ε B → b B String: “abb” S a B b B b B

9. Parsetrees S → a B B → ε B → b B String: “abb” S a B b B b B ε

10. Parsetrees S → a B B → ε B → b B String: “abb” S B B B a b b ε

11. Exercise (1) • Write grammars that produce • strings over { a, b } that start and end with the same letter. Draw the parse tree for “abaaa”. • palindromes over { a, b }. Draw the parse tree for “ababa”. • valid e-mail addresses. Draw the parse tree for “ab@c.d”. Try to derive the string “a@b@c” (this should not be possible). • Recall: S+(.S+)*@S+(.S+)*

12. PDA • Push down automata • FA + stack

13. PDA example • Language: { (), (()), ((())), … }

14. Exercise (2) • Write grammars for • general parenthesis expressions:{ ε, (), ()(), (()), ()(()), ((()))()(), … }. • simple infix addition between single-digit numbers, with support for prioritizing with parentheses:{ 7, 1 + 2, 1 + (9 + 1), ((6) + 0), … }. • Create PDAs for the above languages. • Create a PDA that accepts palindromes.

15. Conclusion • Context-free languages • Context-free grammars • Parse trees • Push down automata

16. Next time • Specifying language syntax using CFGs • Introduction to parsing • Ambiguous grammars