1. ISBN 0-321-49362-1 Chapter 4 Lexical and Syntax Analysis

2. CS380 Test 1 #5 if ( expr1 ) stmts_1; else if (expr2) stmts_2; else stmts_3; Operational semantics: if (expr1 == fase ) goto L1 stmts_1; goto LOUT L1: if (expr2 == false) goto L2 stmts_2; goto LOUT L2: stmts_3; LOUT: Copyright © 2009 Addison-Wesley. All rights reserved.1-2

3. Ch4 Syntax Analysis Based on BNF Two part: –Lexical analyzer (scanner): low level part (names, numerical literals …) –Syntax analyzer (parser): high-level part (expr., stmts, prog. units), directly on BNF; portable Copyright © 2009 Addison-Wesley. All rights reserved.1-3

4. Lexical analysis, p.173 Lexical analyzer is a pattern matcher for character strings. Identify lexemes – extract string (lexemes) from input and produce tokens/lexemes Assignment stmt: result = oldsum – value / 100; lexemetokentoken code resultID0 =ASSIGN_OP1 … Copyright © 2009 Addison-Wesley. All rights reserved.1-4

5. Lexical analysis, p.173 Lexical analyzer is a function that is called by the parser when it needs the next token –Skip comments, blanks –Insert user-defined names to the symbol table used by the parser –Detect syntactic errors in lexemes/token and report to user. Copyright © 2009 Addison-Wesley. All rights reserved.1-5

6. Build a lexical analyzer, p.175 Design a state diagram to describe the tokens and write a program to implement it. P.178, Figure 4.1. Copyright © 2009 Addison-Wesley. All rights reserved.1-6

7. Lab assignment, p.176 - 181 C code gcc front.c./a.out > front.out p.177, file name: front.in (content of the file is in p.181) Output file is similar to the output in p.181 Copyright © 2009 Addison-Wesley. All rights reserved.1-7

8. The fun. getChar(), p.179 Read the next char from input and put it to nextChar (global varialbe) Determine its class (letter, digit, unknown)  charClass Copyright © 2009 Addison-Wesley. All rights reserved.1-8

9. Fun. addChar(), p.179 Puts the char from nextChar into place the lexeme is being accumulated – a string name lexeme (global c-string) Copyright © 2009 Addison-Wesley. All rights reserved.1-9

10. Fun. Lookup(), p.178 Determine the token values for operators, and (, ). Copyright © 2009 Addison-Wesley. All rights reserved.1-10

11. Lexical analyzer lex(), p.180 Letter  Identifier Digit  literal integer Unknown: operators (+, -, *, /), (, ) Copyright © 2009 Addison-Wesley. All rights reserved.1-11

12. Parsing, p.182 Syntax analysis Parser syntax analyzer Goals: –Find all syntax errors; produce diagnostic message; recover quickly –Produce parse tree, or at least a trace of parse tree for the program Copyright © 2009 Addison-Wesley. All rights reserved.1-12

13. Parsing, p.182 (ctd) Two categories –Top down: produce the tree from the root down to the leaves. Use the order of the left-most derivation –Bottom up: from the leaves up to the root. Use reverse order of the right most derivation Copyright © 2009 Addison-Wesley. All rights reserved.1-13

14. Top-down parser, p.183 Sentence form xAα x - terminals (a, b, c) A – non-terminals α – mixed Left most derivation- A  bB | cBb | a depends on the next token/lexeme of input Copyright © 2009 Addison-Wesley. All rights reserved.1-14

15. Algorithms of top-down parsing, p.184 Recursive descent parser: coded version directly from the rules of BNF LL parser: use parsing table to implement BNF (Left-to-right scan of the input & left most derivation) Copyright © 2009 Addison-Wesley. All rights reserved.1-15

16. Bottom up parser, p.184 From leaves to root Produce a reverse of a right most derivation  … B( B  Ac)  … Ac( A  a)  … ac β B A c a Copyright © 2009 Addison-Wesley. All rights reserved.1-16

17. Pair-wise dis-jointness test For non-left recursive grammar, p.193 If true, parser can choose the correct RHS on the next token of input If false, use left factoring process Assume A  α i | α j P.D.T. is First(α i ) ƞ First(α j ) = 0 (non-intersect) First(α i ) the first left terminal. Copyright © 2009 Addison-Wesley. All rights reserved.1-17

18. Pair-wise dis-jointness test (ctd) A  aB | bAb | c First (aB) = a First (bAb) = b first (c) = c They are not intersected  pass the P.D.T Copyright © 2009 Addison-Wesley. All rights reserved.1-18

19. P.190, Figure 4.2, Parse tree Code from p.186 – 189, recursive decent parsing P.189, trace the code Copyright © 2009 Addison-Wesley. All rights reserved.1-19

20. Copyright © 2009 Addison-Wesley. All rights reserved.1-20 Chapter 4 Topics Introduction Lexical Analysis The Parsing Problem Recursive-Descent Parsing Bottom-Up Parsing

21. Copyright © 2009 Addison-Wesley. All rights reserved.1-21 Introduction Language implementation systems must analyze source code, regardless of the specific implementation approach Nearly all syntax analysis is based on a formal description of the syntax of the source language (BNF)

22. Copyright © 2009 Addison-Wesley. All rights reserved.1-22 Syntax Analysis The syntax analysis portion of a language processor nearly always consists of two parts: –A low-level part called a lexical analyzer (mathematically, a finite automaton based on a regular grammar) –A high-level part called a syntax analyzer, or parser (mathematically, a push-down automaton based on a context-free grammar, or BNF)

23. Copyright © 2009 Addison-Wesley. All rights reserved.1-23 Advantages of Using BNF to Describe Syntax Provides a clear and concise syntax description The parser can be based directly on the BNF Parsers based on BNF are easy to maintain

24. Copyright © 2009 Addison-Wesley. All rights reserved.1-24 Reasons to Separate Lexical and Syntax Analysis Simplicity - less complex approaches can be used for lexical analysis; separating them simplifies the parser Efficiency - separation allows optimization of the lexical analyzer Portability - parts of the lexical analyzer may not be portable, but the parser always is portable

25. Copyright © 2009 Addison-Wesley. All rights reserved.1-25 Lexical Analysis A lexical analyzer is a pattern matcher for character strings A lexical analyzer is a “front-end” for the parser Identifies substrings of the source program that belong together - lexemes –Lexemes match a character pattern, which is associated with a lexical category called a token –sum is a lexeme; its token may be IDENT

26. Copyright © 2009 Addison-Wesley. All rights reserved.1-26 Lexical Analysis (continued) The lexical analyzer is usually a function that is called by the parser when it needs the next token Three approaches to building a lexical analyzer: –Write a formal description of the tokens and use a software tool that constructs table-driven lexical analyzers given such a description –Design a state diagram that describes the tokens and write a program that implements the state diagram –Design a state diagram that describes the tokens and hand-construct a table-driven implementation of the state diagram

27. Copyright © 2009 Addison-Wesley. All rights reserved.1-27 State Diagram Design –A naïve state diagram would have a transition from every state on every character in the source language - such a diagram would be very large!

28. Copyright © 2009 Addison-Wesley. All rights reserved.1-28 Lexical Analysis (cont.) In many cases, transitions can be combined to simplify the state diagram –When recognizing an identifier, all uppercase and lowercase letters are equivalent Use a character class that includes all letters –When recognizing an integer literal, all digits are equivalent - use a digit class

29. Copyright © 2009 Addison-Wesley. All rights reserved.1-29 Lexical Analysis (cont.) Reserved words and identifiers can be recognized together (rather than having a part of the diagram for each reserved word) –Use a table lookup to determine whether a possible identifier is in fact a reserved word

30. Copyright © 2009 Addison-Wesley. All rights reserved.1-30 Lexical Analysis (cont.) Convenient utility subprograms: –getChar - gets the next character of input, puts it in nextChar, determines its class and puts the class in charClass –addChar - puts the character from nextChar into the place the lexeme is being accumulated, lexeme –lookup - determines whether the string in lexeme is a reserved word (returns a code)

31. Copyright © 2009 Addison-Wesley. All rights reserved.1-31 State Diagram : to recognize names, parentheses, and arithmetic operators getChar()

32. Copyright © 2009 Addison-Wesley. All rights reserved.1-32 Lexical Analyzer Implementation:  SHOW front.c (pp. 176-181) - Following is the output of the lexical analyzer of front.c when used on (sum + 47) / total Next token is: 25 Next lexeme is ( Next token is: 11 Next lexeme is sum Next token is: 21 Next lexeme is + Next token is: 10 Next lexeme is 47 Next token is: 26 Next lexeme is ) Next token is: 24 Next lexeme is / Next token is: 11 Next lexeme is total Next token is: -1 Next lexeme is EOF

33. Copyright © 2009 Addison-Wesley. All rights reserved.1-33 The Parsing Problem Goals of the parser, given an input program: –Find all syntax errors; for each, produce an appropriate diagnostic message and recover quickly –Produce the parse tree, or at least a trace of the parse tree, for the program

34. Copyright © 2009 Addison-Wesley. All rights reserved.1-34 The Parsing Problem (cont.) Two categories of parsers –Top down - produce the parse tree, beginning at the root Order is that of a leftmost derivation Traces or builds the parse tree in preorder –Bottom up - produce the parse tree, beginning at the leaves Order is that of the reverse of a rightmost derivation Useful parsers look only one token ahead in the input

35. Copyright © 2009 Addison-Wesley. All rights reserved.1-35 The Parsing Problem (cont.) Top-down Parsers –Given a sentential form, xA , the parser must choose the correct A-rule to get the next sentential form in the leftmost derivation, using only the first token produced by A The most common top-down parsing algorithms: –Recursive descent - a coded implementation –LL parsers - table driven implementation

36. Copyright © 2009 Addison-Wesley. All rights reserved.1-36 The Parsing Problem (cont.) Bottom-up parsers –Given a right sentential form, , determine what substring of  is the right-hand side of the rule in the grammar that must be reduced to produce the previous sentential form in the right derivation –The most common bottom-up parsing algorithms are in the LR family

37. Copyright © 2009 Addison-Wesley. All rights reserved.1-37 The Parsing Problem (cont.) The Complexity of Parsing –Parsers that work for any unambiguous grammar are complex and inefficient ( O(n 3 ), where n is the length of the input ) –Compilers use parsers that only work for a subset of all unambiguous grammars, but do it in linear time ( O(n), where n is the length of the input )

38. Copyright © 2009 Addison-Wesley. All rights reserved.1-38 Recursive-Descent Parsing There is a subprogram for each nonterminal in the grammar, which can parse sentences that can be generated by that nonterminal EBNF is ideally suited for being the basis for a recursive-descent parser, because EBNF minimizes the number of nonterminals

39. Copyright © 2009 Addison-Wesley. All rights reserved.1-39 Recursive-Descent Parsing (cont.) A grammar for simple expressions:  {(+ | -) }  {(* | /) }  id | int_constant | ( )

40. Copyright © 2009 Addison-Wesley. All rights reserved.1-40 Recursive-Descent Parsing (cont.) Assume we have a lexical analyzer named lex, which puts the next token code in nextToken The coding process when there is only one RHS: –For each terminal symbol in the RHS, compare it with the next input token; if they match, continue, else there is an error –For each nonterminal symbol in the RHS, call its associated parsing subprogram

41. Copyright © 2009 Addison-Wesley. All rights reserved.1-41 Recursive-Descent Parsing (cont.) /* Function expr Parses strings in the language generated by the rule: → {(+ | -) } */ void expr() { printf ( “Enter \n”); /* Parse the first term */ term(); /* As long as the next token is + or -, call lex to get the next token and parse the next term */ while (nextToken == ADD_OP || nextToken == SUB_OP){ lex(); term(); } printf ( “Exit \n”); }

42. Copyright © 2009 Addison-Wesley. All rights reserved.1-42 Recursive-Descent Parsing (cont.) This particular routine does not detect errors Convention: Every parsing routine leaves the next token in nextToken

43. Copyright © 2009 Addison-Wesley. All rights reserved.1-43 Recursive-Descent Parsing (cont.) A nonterminal that has more than one RHS requires an initial process to determine which RHS it is to parse –The correct RHS is chosen on the basis of the next token of input (the lookahead) –The next token is compared with the first token that can be generated by each RHS until a match is found –If no match is found, it is a syntax error

44. Recursive-Descent Parsing (cont.) /* term Parses strings in the language generated by the rule: -> {(* | /) ) */ void term() { printf("Enter \n"); /* Parse the first factor */ factor(); /* As long as the next token is * or /, next token and parse the next factor */ while (nextToken == MULT_OP || nextToken == DIV_OP) { lex(); factor(); } printf("Exit \n"); } /* End of function term */ Copyright © 2009 Addison-Wesley. All rights reserved.1-44

45. Copyright © 2009 Addison-Wesley. All rights reserved.1-45 Recursive-Descent Parsing (cont.) /* Function factor Parses strings in the language generated by the rule: -> id | ( ) */ void factor() { /* Determine which RHS */ if (nextToken) == ID_CODE || nextToken == INT_CODE) /* For the RHS id, just call lex */ lex(); /* If the RHS is ( ) – call lex to pass over the left parenthesis, call expr, and check for the right parenthesis */ else if (nextToken == LP_CODE) { lex(); expr(); if (nextToken == RP_CODE) lex(); else error(); } /* End of else if (nextToken ==... */ else error(); /* Neither RHS matches */ }

46. Copyright © 2009 Addison-Wesley. All rights reserved.1-46 Recursive-Descent Parsing (cont.) - Trace of the lexical and syntax analyzers on (sum + 47) / total Next token is: 25 Next lexeme is (Next token is: 11 Next lexeme is total Enter Enter Enter Next token is: -1 Next lexeme is EOF Enter Exit Next token is: 11 Next lexeme is sumExit Enter Exit Enter Next token is: 21 Next lexeme is + Exit Next token is: 10 Next lexeme is 47 Enter Next token is: 26 Next lexeme is ) Exit Next token is: 24 Next lexeme is / Exit

47. Copyright © 2009 Addison-Wesley. All rights reserved.1-47 Recursive-Descent Parsing (cont.) The LL Grammar Class –The Left Recursion Problem If a grammar has left recursion, either direct or indirect, it cannot be the basis for a top-down parser –A grammar can be modified to remove left recursion For each nonterminal, A, 1.Group the A-rules as A → Aα 1 | … | Aα m | β 1 | β 2 | … | β n where none of the β‘s begins with A 2. Replace the original A-rules with A → β 1 A’ | β 2 A’ | … | β n A’ A’ → α 1 A’ | α 2 A’ | … | α m A’ | ε

48. Copyright © 2009 Addison-Wesley. All rights reserved.1-48 Recursive-Descent Parsing (cont.) The other characteristic of grammars that disallows top-down parsing is the lack of pairwise disjointness –The inability to determine the correct RHS on the basis of one token of lookahead –Def: FIRST(  ) = {a |  =>* a  } (If  =>* ,  is in FIRST(  ))

49. Copyright © 2009 Addison-Wesley. All rights reserved.1-49 Recursive-Descent Parsing (cont.) Pairwise Disjointness Test: –For each nonterminal, A, in the grammar that has more than one RHS, for each pair of rules, A   i and A   j, it must be true that FIRST(  i ) ⋂ FIRST(  j ) =  Examples: A  a | bB | cAb A  a | aB

50. Copyright © 2009 Addison-Wesley. All rights reserved.1-50 Recursive-Descent Parsing (cont.) Left factoring can resolve the problem Replace  identifier | identifier [ ] with  identifier   | [ ] or  identifier [[ ]] (the outer brackets are metasymbols of EBNF)

51. Copyright © 2009 Addison-Wesley. All rights reserved.1-51 Bottom-up Parsing The parsing problem is finding the correct RHS in a right-sentential form to reduce to get the previous right-sentential form in the derivation

52. Copyright © 2009 Addison-Wesley. All rights reserved.1-52 Bottom-up Parsing (cont.) Intuition about handles: –Def:  is the handle of the right sentential form  =  w if and only if S =>* rm  Aw => rm  w –Def:  is a phrase of the right sentential form  if and only if S =>*  =  1 A  2 =>+  1  2 –Def:  is a simple phrase of the right sentential form  if and only if S =>*  =  1 A  2 =>  1  2

53. Copyright © 2009 Addison-Wesley. All rights reserved.1-53 Bottom-up Parsing (cont.) Intuition about handles (continued): –The handle of a right sentential form is its leftmost simple phrase –Given a parse tree, it is now easy to find the handle –Parsing can be thought of as handle pruning

54. Copyright © 2009 Addison-Wesley. All rights reserved.1-54 Bottom-up Parsing (cont.) Shift-Reduce Algorithms –Reduce is the action of replacing the handle on the top of the parse stack with its corresponding LHS –Shift is the action of moving the next token to the top of the parse stack

55. Copyright © 2009 Addison-Wesley. All rights reserved.1-55 Bottom-up Parsing (cont.) Advantages of LR parsers: –They will work for nearly all grammars that describe programming languages. –They work on a larger class of grammars than other bottom-up algorithms, but are as efficient as any other bottom-up parser. –They can detect syntax errors as soon as it is possible. –The LR class of grammars is a superset of the class parsable by LL parsers.

56. Copyright © 2009 Addison-Wesley. All rights reserved.1-56 Bottom-up Parsing (cont.) LR parsers must be constructed with a tool Knuth’s insight: A bottom-up parser could use the entire history of the parse, up to the current point, to make parsing decisions –There were only a finite and relatively small number of different parse situations that could have occurred, so the history could be stored in a parser state, on the parse stack

57. Copyright © 2009 Addison-Wesley. All rights reserved.1-57 Bottom-up Parsing (cont.) An LR configuration stores the state of an LR parser (S 0 X 1 S 1 X 2 S 2 …X m S m, a i a i +1…a n $)

58. Copyright © 2009 Addison-Wesley. All rights reserved.1-58 Bottom-up Parsing (cont.) LR parsers are table driven, where the table has two components, an ACTION table and a GOTO table –The ACTION table specifies the action of the parser, given the parser state and the next token Rows are state names; columns are terminals –The GOTO table specifies which state to put on top of the parse stack after a reduction action is done Rows are state names; columns are nonterminals

59. Copyright © 2009 Addison-Wesley. All rights reserved.1-59 Structure of An LR Parser

60. Copyright © 2009 Addison-Wesley. All rights reserved.1-60 Bottom-up Parsing (cont.) Initial configuration: (S 0, a 1 …a n $) Parser actions: –If ACTION[S m, a i ] = Shift S, the next configuration is: (S 0 X 1 S 1 X 2 S 2 …X m S m a i S, a i+1 …a n $) –If ACTION[S m, a i ] = Reduce A   and S = GOTO[S m-r, A], where r = the length of , the next configuration is (S 0 X 1 S 1 X 2 S 2 …X m-r S m-r AS, a i a i+1 …a n $)

61. Copyright © 2009 Addison-Wesley. All rights reserved.1-61 Bottom-up Parsing (cont.) Parser actions (continued): –If ACTION[S m, a i ] = Accept, the parse is complete and no errors were found. –If ACTION[S m, a i ] = Error, the parser calls an error-handling routine.

62. Copyright © 2009 Addison-Wesley. All rights reserved.1-62 LR Parsing Table

63. Copyright © 2009 Addison-Wesley. All rights reserved.1-63 Bottom-up Parsing (cont.) A parser table can be generated from a given grammar with a tool, e.g., yacc

64. Copyright © 2009 Addison-Wesley. All rights reserved.1-64 Summary Syntax analysis is a common part of language implementation A lexical analyzer is a pattern matcher that isolates small-scale parts of a program –Detects syntax errors –Produces a parse tree A recursive-descent parser is an LL parser –EBNF Parsing problem for bottom-up parsers: find the substring of current sentential form The LR family of shift-reduce parsers is the most common bottom-up parsing approach