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

2. 2 Outline Context-free languages –Context-free grammars –Parse trees –Push down 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 3

4. Parse trees S ⇒ a B ⇒ a b B ⇒ a b b B ⇒ a b b 4 S B B B ε a b b

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

6. Parse trees S → a B B → ε B → b B String: “abb” 6 S Ba

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

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

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

10. Parse trees S → a B B → ε B → b B String: “abb” 10 S B B B εabb

11. Exercise (1) Write grammars that produce a)strings over { a, b } that start and end with the same letter. Draw the parse tree for “abaaa”. b)palindromes over { a, b }. Draw the parse tree for “ababa”. c)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+)* 11

12. PDA Push down automata FA + stack 12

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

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

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

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