Introduction to Bottom-Up Parsing
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1 Introduction to Bottom-Up Parsing Lecture 11 CS 536 Spring
2 Outline he strategy: shift-reduce parsing Ambiguity and precedence declarations Next lecture: bottom-up parsing algorithms CS 536 Spring
3 Predictive Parsing Summary First and Follow sets are used to construct predictive tables For non-terminal A and input t, use a production A α where t First(α) For non-terminal A and input t, if ε First(A) and t Follow(α), then use a production A α where ε First(α) We ll see First and Follow sets again... CS 536 Spring
4 Bottom-Up Parsing Bottom-up parsing is more general than topdown parsing And just as efficient Builds on ideas in top-down parsing Bottom-up is the preferred method in practice Concepts today, algorithms next time CS 536 Spring
5 An Introductory Example Bottom-up parsers don t need left-factored grammars Hence we can revert to the natural grammar for our example: E + E * (E) Consider the string: * + CS 536 Spring
6 he Idea Bottom-up parsing reduces a string to the start symbol by inverting productions: * + * E E * E E + E CS 536 Spring
7 ES YOURSELF #1 Question: find the rightmost derivation of the string * + CS 536 Spring
8 Observation Read the productions found by bottom-up parse in reverse (i.e., from bottom to top) his is a rightmost derivation! * + * E E * E E + E CS 536 Spring
9 Important Fact #1 Important Fact #1 about bottom-up parsing: A bottom-up parser traces a rightmost derivation in reverse CS 536 Spring
10 A Bottom-up Parse * + E * + + E + + E E * + CS 536 Spring
11 A Bottom-up Parse in Detail (1) * + * + CS 536 Spring
12 A Bottom-up Parse in Detail (2) * + * + * + CS 536 Spring
13 A Bottom-up Parse in Detail (3) * + * + + * + CS 536 Spring
14 A Bottom-up Parse in Detail (4) * + * * + CS 536 Spring
15 A Bottom-up Parse in Detail (5) * + * + + E + + E * + CS 536 Spring
16 A Bottom-up Parse in Detail (6) * + E * + + E + + E E * + CS 536 Spring
17 A rivial Bottom-Up Parsing Algorithm Let I = input string repeat pick a non-empty substring β of I where X β is a production if no such β, backtrack replace one β by X in I until I = S (the start symbol) or all possibilities are exhausted CS 536 Spring
18 Questions Does this algorithm terminate? How fast is the algorithm? Does the algorithm handle all cases? How do we choose the substring to reduce at each step? CS 536 Spring
19 How to build the house of cards? CS 536 Spring
20 Where Do Reductions Happen Important Fact #1 has an eresting consequence: Let αβω be a step of a bottom-up parse Assume the next reduction is by X β hen ω is a string of terminals Why? Because αxω αβω is a step in a rightmost derivation CS 536 Spring
21 Notation Idea: Split string o two substrings Right substring is as yet unexamined by parsing (a string of terminals) Left substring has terminals and non-terminals he dividing po is marked by a he is not part of the string Initially, all input is unexamined x 1 x 2... x n CS 536 Spring
22 Shift-Reduce Parsing Bottom-up parsing uses only two kinds of actions: Shift Reduce CS 536 Spring
23 Shift Shift: Move one place to the right Shifts a terminal to the left string ABC xyz ABCx yz CS 536 Spring
24 Reduce Apply an inverse production at the right end of the left string If A xy is a production, then Cbxy ijk CbA ijk CS 536 Spring
25 he Example with Reductions Only * + * + reduce reduce * + reduce + reduce E + E reduce E + E E CS 536 Spring
26 he Example with Shift-Reduce Parsing * + shift * + shift * + shift * + reduce * + reduce * + shift + shift + reduce + reduce E + E reduce E + E E CS 536 Spring
27 A Shift-Reduce Parse in Detail (1) * + * + CS 536 Spring
28 A Shift-Reduce Parse in Detail (2) * + * + * + CS 536 Spring
29 A Shift-Reduce Parse in Detail (3) * + * + * + * + CS 536 Spring
30 A Shift-Reduce Parse in Detail (4) * + * + * + * + * + CS 536 Spring
31 A Shift-Reduce Parse in Detail (5) * + * + * + * + * + * + CS 536 Spring
32 A Shift-Reduce Parse in Detail (6) * + * + * + * + * + + * + CS 536 Spring
33 A Shift-Reduce Parse in Detail (7) * + * + * + * + * * + CS 536 Spring
34 A Shift-Reduce Parse in Detail (8) * + * + * + * + * * + CS 536 Spring
35 A Shift-Reduce Parse in Detail (9) * + * + * + * + * * + CS 536 Spring
36 A Shift-Reduce Parse in Detail (10) * + * + * + * + * + E E * + CS 536 Spring
37 A Shift-Reduce Parse in Detail (11) * + * + * + * + * E E E E * + CS 536 Spring
38 he Stack Left string can be implemented by a stack op of the stack is the Shift pushes a terminal on the stack Reduce pops 0 or more symbols off of the stack (production rhs) and pushes a nonterminal on the stack (production lhs) CS 536 Spring
39 Key Issue (will be resolved by algorithms) How do we decide when to shift or reduce? Consider step * + We could reduce by giving * + A fatal mistake: No way to reduce to the start symbol E CS 536 Spring
40 Conflicts Generic shift-reduce strategy: If there is a handle on top of the stack, reduce Otherwise, shift But what if there is a choice? If it is legal to shift or reduce, there is a shift-reduce conflict If it is legal to reduce by two different productions, there is a reduce-reduce conflict CS 536 Spring
41 Source of Conflicts Ambiguous grammars always cause conflicts But beware, so do many non-ambiguous grammars CS 536 Spring
42 Conflict Example Consider our favorite ambiguous grammar: E E + E E * E (E) CS 536 Spring
43 One Shift-Reduce Parse * +... E * E + E + E + E + E + E E shift... reduce E E * E shift shift reduce E reduce E E + E CS 536 Spring
44 Another Shift-Reduce Parse * +... E * E + E * E + E * E + E * E + E E * E E shift... shift shift reduce E reduce E E + E reduce E E * E CS 536 Spring
45 Example Notes In the second step E * E + we can either shift or reduce by E E * E Choice determines associativity of + and * As noted previously, grammar can be rewritten to enforce precedence Precedence declarations are an alternative CS 536 Spring
46 Precedence Declarations Revisited Precedence declarations cause shift-reduce parsers to resolve conflicts in certain ways Declaring * has greater precedence than + causes parser to reduce at E * E + More precisely, precedence declaration is used to resolve conflict between reducing a * and shifting a + CS 536 Spring
47 Precedence Declarations Revisited (Cont.) he term precedence declaration is misleading hese declarations do not define precedence; they define conflict resolutions Not quite the same thing! CS 536 Spring
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