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Week 6 TopDown vs. BottomUp Parsing, Left Recursion, Predictive Parsing, Left Factoring 1. Layman’s Explanation Top‑Down Predictive Parsing Imagine starting at the top of a tree the start symbol and growing branches downward to match the input tokens. Bottom‑Up Shift‑Reduce Parsing Think of gathering leaves input tokens and gradually combining them into branches until you reach the root. Left Recursion A rule like A → A α β can loop forever if you try to expand A. We remove it so predictive parsers don’t go into infinite loops. Left Factoring If two rules share a common prefix, pull it out so the parser can decide which path to take based on the next token. 2. Solved Example Grammar E → E T T T → T F F F → E id Remove Left Recursion For E introduce E E → T E E → T E ε For T introduce T T → F T T → F T ε F has no left recursion. Left Factoring Not needed here no common prefixes beyond what’s handled. Week 7 Recursive‑Descent Table‑Driven Parsing, FIRST FOLLOW Sets 1. Layman’s Explanation Recursive‑Descent Hand‑write one function per nonterminal, calling each other down the parse tree. Table‑Driven Use a precomputed table to decide which production to apply based on the current nonterminal and lookahead. FIRSTA All tokens that can appear at the start of strings derived from A. FOLLOWA All tokens that can appear immediately after A in any sentential form. 2. Solved Example Dry‑Run Table Grammar S → E E → T E E → T E ε T → F T T → F T ε F → E id Compute FIRST and FOLLOW for E, E, T, T, F. Standard algorithm. Parse Table Entry For E on choose E → T E on or choose E → ε. Dry‑Run on input id id id Stack Input Action S id id id Expand S → E E id ... Expand E → T E T E id ... Expand T → F T F T E id ... Match F → id T E id id T → ε E id id E → T E T E id id Match T E id id ... continue similarly Week 8 LL1 Grammars, Parse Table Construction, LR Parsing Handles 1. Layman’s Explanation LL1 A grammar where a single lookahead token always decides the correct production—predictive parsing without backtracking. Parse Table A matrix indexed by nonterminals and lookahead tokens telling the parser which rule to apply. Handle The substring that matches the right side of a production and whose reduction is a valid step toward the start symbol. 2. Solved Example Dry‑Run Check LL1 for the grammar in Week 7—ensure FIRST sets of alternatives are disjoint, and if ε in FIRST, FIRST FOLLOW disjoint. Construct Table For E , entry is E → T E. For E , entry is E → ε. LR0 Handle‑Pruning On input id id, identify handles id, then id id