100_Bottom_Up_Parsing - CS143 Handout 10 Summer 2011 June...

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CS143 Handout 10 Summer 2011 June 29 th , 2011 Bottom-Up Parsing Handout written by Maggie Johnson and revised by Julie Zelenski. Bottom-up parsing As the name suggests, bottom-up parsing works in the opposite direction from top- down. A top-down parser begins with the start symbol at the top of the parse tree and works downward, driving productions in forward order until it gets to the terminal leaves. A bottom-up parse starts with the string of terminals itself and builds from the leaves upward, working backwards to the start symbol by applying the productions in reverse. Along the way, a bottom-up parser searches for substrings of the working string that match the right side of some production. When it finds such a substring, it reduces it, i.e., substitutes the left side nonterminal for the matching right side. The goal is to reduce all the way up to the start symbol and report a successful parse. In general, bottom-up parsing algorithms are more powerful than top-down methods, but not surprisingly, the constructions required are also more complex. It is difficult to write a bottom-up parser by hand for anything but trivial grammars, but fortunately, there are excellent parser generator tools like bison that build a parser from an input specification, not unlike the way flex builds a scanner to your spec. Shift-reduce parsing is the most commonly used and the most powerful of the bottom-up techniques. It takes as input a stream of tokens and develops the list of productions used to build the parse tree, but the productions are discovered in reverse order of a top- down parser. Like a table-driven predictive parser, a bottom-up parser makes use of a stack to keep track of the position in the parse and a parsing table to determine what to do next. To illustrate stack-based shift-reduce parsing, consider this simplified expression grammar: S –> E E –> T | E + T T –> id | (E) The shift-reduce strategy divides the string that we are trying parse into two parts: an undigested part and a semi-digested part. The undigested part contains the tokens that are still to come in the input, and the semi-digested part is put on a stack. If parsing the string v , it starts out completely undigested, so the input is initialized to v , and the stack is initialized to empty. A shift-reduce parser proceeds by taking one of three actions at each step:
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2 Reduce : If we can find a rule A –> w , and if the contents of the stack are qw for some q ( q may be empty), then we can reduce the stack to qA . We are applying the production for the nonterminal A backwards. For example, using the grammar above, if the stack contained (id we can use the rule T –> id to reduce the stack to (T . There is also one special case: reducing the entire contents of the stack to the
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100_Bottom_Up_Parsing - CS143 Handout 10 Summer 2011 June...

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