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

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

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

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

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

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

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

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

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

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

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 addresses. Draw the parse tree for Try to derive the string (this should not be possible). Recall: 11

PDA Push down automata FA + stack 12

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

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

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

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