编译原理 Chapter 5

zhangjing@
17
We can see that there are several phrases from Fig.5.3 T (For nonterminal E) T*F (For nonterminal T) T+T*F (For nonterminal E) i (For nontermina F) T + T * F + i (For nonterminal E)
zhangjing@
15
E E / E + E E E
E E + E E E / E
Fig. 5.2 Two syntax tree of string E+E/E 图5.2句型E+E/E的两棵语法树
zhangjing@
16
5.1.4 Leftmost Phrase
zhangjing@
5
1. a b , means there are rules U∷=…ab… or U∷=…aVb… 2. a < b, means there are rules U∷=…aR…,R+b…or R+Vb . 3. a > b, means there are rules U∷=…Rb…,R+…a or R+…aV
Chapter 5 Bottom-Up Parsing
Zhang Jing, Wang HaiLing College of Computer Science & Technology Harbin Engineering University
Shift-reduce parsing attempts to construct a parse tree for an input string beginning at the leaves which can be considered as bottom and working up towards the root, know as top. We can think of this process as one of reducing which reduce a string to the start symbol. At each reduction step, a particular substring matches the right side of production and is replaced by the symbol on the left of the production. An easy-to-implement form of shift-reduce parsing is operator-precedence parsing. A much more general method of shift-reduce parsing is LR(0) and SLR(1) parsing. The position of bottom-up syntax analyzer in compiler is shown by Fig.5.1.
Note: The precedence relations between a and b are different with arithmetic relations "less than", "equal to " and "greater than", that is, . a < b does not equal to b >a ,a b does not equal to b a
E∷=E+E | E*E | E/E | i
operator grammar
zhangjing@
14
Operator grammar also can be called OG. There are three types disjoint precedence relation between pair of terminals, the three types disjoint precedence are , and , But if a pair of terminals only has one certain type precedence relation, this kind of OG is operator precedence grammar, namely, OPG. For example, grammar E∷=E+E|E*E|E/E|i is not operator-precedence grammar. Because from Fig5.2, we know there are two grammar tree for(+,/), in addition there are two precedence relations between them, namely, . + > / and + < /
The syntax tree for sentence #T+T*F+i# in grammar G[E] of example 5.1 is shown by Fig.5.3.
E E E T + T T * + T F F i
Fig.5.3 syntax tree of #T+T*F+i# 图5.3 句型语法树
zhangjing@ 4
5.1.1 Relation between pairs of operator precedence
There are three relations between pairs of operator precedence, "a" and "b" belongs to VT , U, V and R belong to VN , then their operator precedence are
zhangjing@ 6
Example 5.1
grammar G〔E〕: E∷=E+T|T T∷=T*F|F F∷=(E)|i From rule F∷=(E),we can obtain the precedence relation between "(" and ")" ( ) From rule E∷=E+T,we know after "+" there is TT*…, so the precedence relation between "+" and "*": < + * From rule F∷=(E),and E+…+T,we can obtain the . > precedence relation between "+" and " ) " : + )
zhangjing@
7
5.1.2 Constructing Operatorprecedence Relation
This section, we will give a general method of constructing operator precedence, firstly, we will define two new sets: FIRSTTERM(U) and LASTTERM(U). b∈FIRSTTERM(U) when there is rule: U∷=+b… or U∷=+Vb… b∈LASTTERM(U) when there is rule: U∷=+…b or U∷=+…bV while b∈VT , V∈VN.
zhangjing@
2
zhangjing@
3
5.1 Operator-precedence Parsing
If a grammar has the property that has two adjacent nonterminals, we can easily construct efficient shift-reduce parsers by hand, the easy-toimplement parsing technique called operatorprecedence parsing. The technique is described as a manipulation on tokens without any reference to any grammar. Once we finish building an operator-precedence parser from a grammar, we may efficiently ignore the grammar, using the nonterminals on the stack only as placeholders for attributes associated with the nonterminals.
zhangjing@ 8
The algorithm of constructing operator precedence is Step1 constructing set of FIRSTTERM and set of LASTTERM for each nonterminal. a, b∈VT and U, R∈VN. Step2 If there is grammar G like U∷=…ab… or U∷=…aVb… a b If there is grammar G like U∷=…aR…, and, b∈FIRSTTERM(R) a < b If there is grammar G like U∷=…Rb…, and, . a∈LASTTERM(R) a > b