1 Bottom-up parsing Goal of parser : build a derivation –top-down parser : build a derivation by working from the start symbol towards the input. builds parse tree from root to leaves builds leftmost derivation –bottom-up parser : build a derivation by working from the input back toward the start symbol builds parse tree from leaves to root builds reverse rightmost derivation

2 Bottom-up parsing The parser looks for a substring of the parse tree's frontier –that matches the rhs of a production and –whose reduction to the non-terminal on the lhs represents on step along the reverse of a rightmost derivation Such a substring is called a handle. Important: not all substrings that match a rhs are handles.

3 Bottom-up parsing techniques Shift-reduce parsing –Shift input symbols until a handle is found. Then, reduce the substring to the non-terminal on the lhs. Operator-precedence parsing –Based on shift-reduce parsing. –Identifies handles based on precedence rules.

4 Example: Shift-reduce parsing 1. S  E 2. E  E + E 3. E  E * E 4. E  num 5. E  id Input to parse: id 1 + num * id 2 Accept$ S Reduce (rule 1)$ E Reduce (rule 2)$ E + E Reduce (rule 3)$ E + E * E Reduce (rule 5)$ E + E * id 2 Shift$ E + E * Shift$ E + E Reduce (rule 4)$ E + num Shift$ E + Shift$ E Reduce (rule 5)$ id 1 Shift$ ACTIONSTACK Grammar: Handles: underlined

5 Shift-Reduce parsing A shift-reduce parser has 4 actions: –Shift -- next input symbol is shifted onto the stack –Reduce -- handle is at top of stack pop handle push appropriate lhs –Accept -- stop parsing & report success –Error -- call error reporting/recovery routine

6 Shift-Reduce parsing How can we know when we have found a handle? –Analyze the grammar beforehand. –Build tables –Look ahead in the input LR(1) parsers recognize precisely those languages in which one symbol of look- ahead is enough to determine whether to reduce or shift. –L : for left-to-right parse of the input –R : for reverse rightmost derivation –1: for one symbol of lookahead

7 How does it work? Read input, one token at a time Use stack to keep track of current state –The state at the top of the stack summarizes the information below. –The stack contains information about what has been parsed so far. Use parsing table to determine action based on current state and look-ahead symbol. How do we build a parsing table?

8 LR parsing techniques SLR (not in the book) –Simple LR parsing –Easy to implement, not strong enough –Uses LR(0) items Canonical LR –Larger parser but powerful –Uses LR(1) items LALR (not in the book) –Condensed version of canonical LR –May introduce conflicts –Uses LR(1) items

9 Class examples id  F F  T T * F  T T  E E + T  E E  E' L  R id  L * R  L R  S L = R  S S  S'