1. LL(1) Parsing LL(1) is a Top Down parsing scheme. Applies productions from goal symbol to derive grammar sentence. First L – Scanner moves from left to right. Second L – Parser expands leftmost non-terminal first. (1) – Scanner supplies parser with one terminal/token to figure out which production to apply next.

2. Top-Down Parse E 1 / | \ E 2 + T 5 | / | \ T 3 T 6 * F 8 | | | F 4 F 7 id | | id id

3. Parse Stack for $ id + id * id $ ETFidTF +++++**** ETTTTTTFFFFF $$$$$$$$$$$$$$

4. Def: Unambiguous Grammar Context Free. Every sentence in grammar has at most one leftmost derivation.

5. LR(1) Grammar LR(1) is a bottom-up parsing scheme. Reduces from grammar sentence to goal symbol using reductions. L – Scanner moves from left to right. R – Rightmost derivation in reverse. (1) – Scanner supplies parser with one terminal/token to figure out which reduction to apply next.

6. Bottom-Up Parse E 8 -------------------- | | T 7 E 3 | | | | --------------- T 2 | T 5 | | | | | | | F 1 | F 4 | F 6 | | | | | id + id * id

7. Rightmost Derivation in Reverse id + id * id  F 1 + id * id  T 2 + id * id  E 3 + id * id  E + F 4 * id  E + T 5 * id  E + T * F 6  E + T 7  E 8 Notice that proceeding backwards, the rightmost non-terminal symbol (highest number) is expanded.

8. Grammar Design Design an unambiguous context-free grammar G 1 where +, -, *, and / are left associative ^ (exponentiation) is right associative Precedence from lowest to highest is: 1)Binary +, - 2)Binary *, / 3)Binary ^ 4)Unary -

9. Grammar G 1 E  E + T | E – T | T T  T * F | T / F | F F  P ^ F | P P  -P | Q {or P  -Q | Q} Q  ( E ) | id

10. Semantic Actions Grammar G 5 E  E + T [a] | T T  T * F [m] | F F  ( E ) | id [p] [a] = add – add top two elements of semantic stack and emit add instruction. [m] =multiply – multiply top two elements of semantic stack and emit multiply instruction. [p] = load current token in register R i and push current token on semantic stack

11. Input String for G 2 $ id 0 + id 1 * id 2 $

12. Parse Stack for Grammar G 2 id 1 id 0 TF[p] ETF **id 2 ++FF[p] TT[m] E[a] $$$

13. Semantic Stack for G 2 id 2 id 1 R2R2 id 0 R2R2

14. Instructions Emitted by G 2 load R 0 id 0 load R 1 id 1 load R 2 id 2 mul R 1 R 2 add R 0 R 2