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Sohail Aslam Compiler Construction Notes Set:3-
Le Leccttuurree 2 222
Example: here is the bottom-up parser’s action when it parses the expression grammar sentence x – 2 × y
(tokenized as id – num (^) * id)
word Stack Handle Action
1 id ► - none - shift
2 – id ► (^) 〈Factor → id, 1 〉 reduce
3 – Factor ► (^) 〈Term → Factor, 1 〉 reduce
4 – Term ► (^) 〈Expr → Term, 1 〉 reduce
5 – Expr ► - none - shift
6 num Expr – ► - none - shift
(^7) × Expr – num ► (^) 〈Factor → num, 3 〉 reduce
(^8) × Expr – Factor ► (^) 〈Term → Factor, 3 〉 shift
(^9) × Expr – Term ► - none - shift
10 id (^) Expr – Term × ► - none - shift
11 $ (^) Expr – Term × id► 〈Factor → id, 5 〉 reduce
12 $ (^) Expr–Term × Factor► 〈Term→Term×Factor, 5 〉 reduce
13 $ Expr – Term ► (^) 〈Expr → Expr – Term, 3 〉 reduce
14 $ Expr ► (^) 〈Goal → Expr, 1 〉 reduce
15 $ Goal - none - accept
Handles
The handle-finding mechanism is the key to efficient bottom-up parsing. As it process an input string, the parser must find and track all potential handles. For example, every legal input eventually reduces the entire frontier to grammar’s goal symbol. Thus, 〈Goal → Expr,1〉 is a potential handle at the start of every parse. As the parser builds a derivation, it discovers other handles. At each step, the set of potential handles represent different suffixes that lead to a reduction. Each potential handle represent a string of grammar symbols that, if seen, would complete the right-hand side of some production.
Sohail Aslam Compiler Construction Notes Set:3-
For the bottom-up parse of the expression grammar string, we can represent the potential handles that the shift-reduce parser should track. Using the placeholder • to represent top of the stack, there are nine handles:
Handles (^1) 〈Factor → id •〉 (^2) 〈Term → Factor•〉 (^3) 〈Expr → Term •〉 (^4) 〈Factor → num•〉 (^5) 〈Term → Factor•〉 (^6) 〈Factor → id •〉 (^7) 〈Term → Term × Factor •〉 (^8) 〈Expr → Expr – Term •〉 (^9) 〈Goal → Expr •〉
This notation shows that the second and fifth handles are identical, as are first and sixth. It also create a way to represent the potential of discovering a handle in future. Consider the parser’s state in step 6: The parser has recognized Expr –. Using the stack-relative notation, we can represent the parser’s state as Expr → Expr – • Term. The parser has already recognized an Expr and a –. If the parser reaches a state where it shifts a Term on top of Expr and –, it will complete the handle Expr → Expr – Term •. How many potential handles must the parser recognize? The right-hand side of each production can have a placeholder at its start, at its end and between any two consecutive symbols.
Expr → • Expr –Term Expr → Expr • – Term Expr → Expr – • Term Expr → Expr – Term •
If the right-hand side of a production has k symbols, it has k +1 placeholder positions.
