# 컴파일러입문 제 6 장 구문분석

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1 컴파일러입문 제 6 장 구문분석

2 목차 6.1 구문분석방법 6.2 구문분석기의출력 6.3 Top-down 방법 6.4 Bottom-up 방법 Syntax Analysis Page 2

3 구문분석방법 Text p.220 How to check whether an input string is a sentence of a grammar and how to construct a parse tree for the string. Parsing :? ω L(G) A Parser for grammar G is a program that takes as input a string ω and produces as output either a parse tree(or derivation tree) for ω, if ω is a sentence of G, or an error message indicating that ω is not sentence of G. A sequence of tokens Parser Correct sentence : Parse tree Incorrect sentence : Error message Syntax Analysis Page 3

4 Two basic types of parsers for context-free grammars 1 Top down - starting with the root and working down to the leaves. recursive descent parser, predictive parser. 2 Bottom up - beginning at the leaves and working up the root. precedence parser, shift-reduce parser. ex) A XYZ reduce A expand bottom-up X Y Z top-down start symbol 로 sentence 로 Syntax Analysis Page 4

5 구문분석기의출력 Text p.225 The output of a parser: 1 Parse - left parse, right parse 2 Parse tree 3 Abstract syntax tree ex) G : 1. E E + T string : a + a * a 2. E T 3. T T * F 4. T F 5. F (E) 6. F a Syntax Analysis Page 5

6 left parse : a sequence of production rule numbers applied in leftmost derivation. E E + T T + T F + T a + T a + T * F a + F * F a + a * F 6 6 a + a * a right parse : reverse order of production rule numbers applied in rightmost derivation. E E + T E + T * F E + T * a E + F * a E + a * a T + a * a F + a * a 4 6 a + a * a Syntax Analysis Page 6

7 parse tree : derivation tree E string : a + a * a E + T T T * F F F a a a Syntax Analysis Page 7

8 Abstract Syntax Tree(AST) ::= a transformed parse tree that is a more efficient representation of the source program. Text p.229 leaf node - operand(identifier or constant) internal node - operator(meaningful production rule name) ex) G: 1. E E + T add 2. E T 3. T T * F mul 4. T F 5. F (E) 6. F a string : a + a * a a add a mul a Syntax Analysis Page 8

9 의미있는 terminal terminal node 의미있는 production rule nonterminal node naming : compiler designer 가지정. ex) if (a > b) a = b + 1; else a = b 2; Text p.231 IF_ST GT ASSIGN_OP ASSIGN_OP a b a ADD a SUB b 1 b 2 Syntax Analysis Page 9

10 Representation of a parse tree Implicit representation - the sequence of production rule numbers used in derivation Explicit representation - a linked list structure LLINK INFO RLINK LLINK INFO RLINK INFO * left son/right brother Syntax Analysis Page 10

11 Top-Down 방법 Text p.231 ::= Beginning with the start symbol of the grammar, it attempts to produce a string of terminal symbol that is identical to a given source string. This matching process proceeds by successively applying the productions of the grammar to produce substrings from nonterminals. ::= In the terminology of trees, this is moving from the root of the tree to a set of leaves in the parse tree for a program. Top-Down parsing methods (1) Parsing with backup or backtracking. (2) Parsing with limited or partial backup. (3) Parsing with nobacktracking. backtracking : making repeated scans of the input. Syntax Analysis Page 11

12 General Top-Down Parsing method called a brute-force method with backtracking ( Top-Down parsing with full backup ) 1. Given a particular nonterminal that is to be expanded, the first production for this nonterminal is applied. 2. Compare the newly expanded string with the input string. In the matching process, terminal symbol is compared with an input symbol is selected for expansion and its first production is applied. 3. If the generated string does not match the input string, an incorrect expansion occurs. In the case of such an incorrect expansion this process is backed up by undoing the most recently applied production. And the next production of this nonterminal is used as next expansion. 4. This process continues either until the generated string becomes an input string or until there are no further productions to be tried. In the latter case, the given string cannot be generated from the grammar. ex) text p. 233 [ 예 8] Syntax Analysis Page 12

13 Several problems with top-down parsing method left recursion A nonterminal A is left recursive if A Aα for some α. A grammar G is left recursive if it has a left-recursive nonterminal. A left-recursive grammar can cause a top down parser to go into an infinite loop. eliminate the left recursion. Backtracking the repeated scanning of input string. the speed of parsing is much slower. (very time consuming) the conditions for nobacktracking : FIRST, FOLLOW 을 이용하여 formal 하게정의. Syntax Analysis Page 13

14 Elimination of left recursion direct left-recursion : A Aα P indirect left-recursion : A Aα general form : + A Aα β A = Aα + β = βα* introducing new nonterminal A which generates α*. ==> A βa' A' αa' ε Syntax Analysis Page 14

15 ex) E E + T T T T F F F (E) a * E E(+T) * T(+T) * E' E' +TE' ε E TE' E' +TE' ε general method : A Aα 1 Aα 2... Aα m β 1 β 2... β n ==> A β 1 A' β 2 A'... β n A' A' α 1 A' α 2 A'... α m A' ε Syntax Analysis Page 15

16 Left-factoring if A αβ αγ are two A-productions and the input begins with a non-empty string derived from α, we do not know whether to expand A to αβ or to αγ. ==> left-factoring : the process of factoring out the common prefixes of alternates. method : A αβ αγ ==> A α(β γ) ==> A αa', A' β γ ex) S icts ictses a C b Syntax Analysis Page 16

17 S icts ictses a icts(ε es) a S ictss' a S' ε es C b No-backtracking ::= deterministic selection of the production rule to be applied. Syntax Analysis Page 17

18 Bottom-up 방법 Text p.247 ::= Reducing a given string to the start symbol of the grammar. ::= It attempts to construct a parse tree for an input string beginning at the leaves (the bottom) and working up towards the root(the top). ex) G: S aacbe A Ab b B d string : abbcde S A A B a b b c d e Syntax Analysis Page 18

19 Reduce [Def 3.1] reduce : the replacement of the right side of a production with the left side. S * αβω, A β P rm S * αaω αβω rm * rm [Def 3.2] handle : If S αaω αβω, then β is a handle of αβω. rm [Def 3.3] handle pruning : S r 0 r 1... r n-1 r n rm rm rm rm rm ω r n-1 r n-2... S = = = = = ω reduce sequence ex) G : S bae A a;a a ω : b a ; a e Syntax Analysis Page 19

20 Right Sentential form ba ; ae ba ; Ae bae S Reducing Production A a 3 A a;a 2 S bae 1 reduce sequence : S b A e b a ; A e b a ; a e right parse : (rightmost derivation in reverse) note Bottom-Up parsing 의 main aspect 는 right sentential form 에서 handle 을찾아적용할 production rule 을 deterministic 하게선택하는것이다. Syntax Analysis Page 20

21 Shift-Reduce Parsing ::= a bottom-up style of parsing. Two problems for automatic parsing 1. How to find a handle in a right sentential form. 2. What production to choose in case there is more than one production with the same right hand side. ====> grammar의종류에따라방법이결정되지만 handle를유지하기위하여 stack을사용한다. Syntax Analysis Page 21

22 Four actions of a shift-reduce parser Stack top 과 current input symbol 에따라파싱테이블을참조해서 action 을결정. 1. shift : the next input symbol is shifted to the top of the stack. 2. reduce : the handle is reduced to the left side of production. 3. accept : the parser announces successful completion of parsing. 4. error : the parser discovers that a syntax error has occurred and calls an error recovery routine. Syntax Analysis Page 22

23 ex) G: E E + T T T T F F F (E) a string : a + a a STACK INPUT ACTION (1) \$ a + a a \$ shift a (2) \$a + a a \$ reduce F a (3) \$F + a a \$ reduce T F (4) \$T + a a \$ reduce E T (5) \$E + a a \$ shift + (6) \$E + a a \$ shift a (7) \$E + a a \$ reduce F a (8) \$E + F a \$ reduce T F (9) \$E + T a \$ shift (10) \$E + T a \$ shift a (11) \$E + T a \$ reduce F a (12) \$E + T F \$ reduce T T * F (13) \$E + T \$ reduce E E + T (14) \$E \$ accept Syntax Analysis Page 23

24 << Thinking points >> 1. the handle will always eventually appear on top of the stack, never inside. rightmost derivation in reverse. stack에있는 contents와 input에남아있는 string이합해져서 right sentential form을이룬다. 따라서항상 stack의 top부분이 reduce된다. 2. How to make a parsing table for a given grammar. 문법의종류에따라 Parsing table 을만드는방법이다르다. SLR(Simple LR) LALR(LookAhead LR) CLR(Canonical LR) Syntax Analysis Page 24

25 Constructing a Parse tree 1. shift : create a terminal node labeled the shifted symbol. 2. reduce : A X 1 X 2...X n. (1) A new node labeled A is created. (2) The X 1 X 2...X n are made direct descendants of the new node. (3) If A ε, then the parser merely creates a node labeled A with no descendants. ex) G : 1. LIST LIST, ELEMENT 2. LIST ELEMENT 3. ELEMENT a string : a, a Syntax Analysis Page 25

26 Step \$ STACK INPUT ACTION PARSETREE (1) \$ a,a\$ shift a Build Node (2) \$a,a\$ reduce 3 Build Tree (3) \$ELEMENT,a\$ reduce 2 Build Tree (4) \$LIST,a\$ shift, Build Node (5) \$LIST, a\$ shift a Build Node (6) \$LIST, a \$ reduce 3 Build Tree (7) \$LIST, ELEMENT \$ reduce 1 Build Tree (8) \$LIST \$ accept return that tree LIST LIST ELEMENT ELEMENT a, a Syntax Analysis Page 26

27 Constructing an AST 1. build node : 의미있는 terminal 을 shift. 2. build tree : 의미있는생성규칙으로 reduce. ex) G: 1. LIST LIST, ELEMENT 2. LIST ELEMENT 3. ELEMENT a string: a,a 의미있는 terminal : a 의미있는생성규칙 : 0번 ===> 0. ACCEPT LIST list 1. LIST LIST, ELEMENT 2. LIST ELEMENT 3. ELEMENT a Syntax Analysis Page 27

28 STACK INPUT ACTION AST (1) \$ a,a\$ shift a Build Node (2) \$a,a\$ reduce 3 (3) \$ELEMENT,a\$ reduce 2 (4) \$LIST,a\$ shift, (5) \$LIST,,a\$ shift a Build Node (6) \$LIST, a \$ reduce 3 (7) \$LIST, ELEMENT \$ reduce 1 (8) \$LIST \$ reduce 0 Build Tree (9) \$ACCEPT \$ Accept return that tree list a a Syntax Analysis Page 28

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