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  1. Chapter 4 Lexical and Syntax Analysis

  2. Chapter 4 Topics 4.1 Introduction 4.2 Lexical Analysis 4.3 The Parsing Problem 4.4 Recursive-Descent Parsing 4.5 Bottom-Up Parsing

  3. 4.1 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)

  4. 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)

  5. Advantages of Using BNF to Describe Syntax • BNF provides a clear and concise syntax description, both for human and for software system that uses them. • BNF description can be used as the direct basis for the syntax analyzer. • Implementations based on BNF are relatively easy to maintain because of their modularity.

  6. 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

  7. 4.2 Lexical Analysis • A lexical analyzer is a pattern matcher for character strings. • A lexical analyzer is a “front-end” for the parser. It is a part of syntax analyzer, and performs syntax analysis at the lowest level of program structure. An input program appears to a compiler as a single string of character. It collects characters into logical groupings and assigned internal codes to the groupings. • Logical groupings are named lexemes. Internal codes for categories of these groupings are named tokens.

  8. Example: result = oldsum – value / 100; Token Lexeme IDENT Result ASSIGN_OP = IDENT oldsum SUB_OP – IDENT value DIV_OP / INT_LIT 100 SEMICOLON ;

  9. 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

  10. Lexical Analysis (cont’d): 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!

  11. 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 52 letters • When recognizing an integer literal, all digits are equivalent - use a digit class for 10 integral literal.

  12. 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

  13. 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)

  14. State Diagram for Recognizing Arithmetic Expressions

  15. Lexical Analyzer Implementation:  SHOW front.c (pp. 176-181) - Following is the output of the lexical analyzer of front.cwhen 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

  16. 4.3 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

  17. 4.3.1 Introducing to Parsing • 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

  18. A set of notational conventions for grammar symbols • Terminals : lowercase letters at the beginning of the alphabet (a, b, …) • Nonterminals: uppercase letters at the beginning of the alphabet (A, B, …) • Terminals or nonterminals: uppercase letters at the end of the alphabet (W, X, Y, Z) • Strings of terminals: lowercase letters at the end of the alphabet (w, x, y, z) • Mixed strings (terminals and/or nonterminals):lowercase Greek letters (α, β, δ, γ)

  19. 4.3.2 Top-Down Parsers • Top-down Parsers • Top-down parsing is a type of parsing strategy wherein one first looks at the highest level of the parse tree and works down the parse tree by using the rewriting rules of a formal grammar. For example, if the current sentential form is: xAα and the A-rules are AbB, AcBb, and Aa, a top-down parser must choose among three rules to get the next sentential form, which could be xbBα, xcBbα, or xaα

  20. Top-Down Parsers (cont’d) • The most common top-down parsing algorithms: • Recursive descent parser - a coded implementation based directly on BNF description of syntax language. • Most common alternative to recursive descent parser is to use parsing table to implement BNF rules. Both are LL parsers (left-to-right leftmost derivation)

  21. 4.3.3 Bottom-Up Parsers • Bottom-up parsers • A bottom-up parser constructs a parse tree by beginning at the leaves and processing toward the root. In term of derivation, it can described as follows: 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 (left-to-right scan, rightmost derivation) family (such as LALR, canonical LR parser (LR(1) parser) , LR(0) parser)

  22. 4.3.4 The Complexity of Parsing • The Complexity of Parsing • Parsers that work for any unambiguous grammar are complex and inefficient ( O(n3), where n is the length of the input ) • All algorithms used for the syntax analyzers of commercial compilers have complexity O(n).

  23. 4.4 Recursive-Descent Parsing4.4.1 Recursive-Descent Parsing Process • A recursive-descent parsing is so named because it consists of collection of subprograms, many of which are recursive, and it produce a parse tree in top-down order. • EBNF is ideally suited for being the basis for a recursive-descent parser, because EBNF minimizes the number of nonterminals

  24. Recursive-Descent Parsing (cont.) • A grammar for simple arithmetic expressions: <expr>  <term> {(+ | -) <term>} <term>  <factor> {(* | /) <factor>} <factor>  id | int_constant | ( <expr> ) Note: Inf EBNF, additional metacharacters • { } for a series of zero or more • ( ) for a list, must pick one • [ ] for an optional list; pick none or one

  25. Recursive-Descent Parsing (cont.) • Assume we have a lexical analyzer named lex, which puts the next token code in nextToken • The coding process: • For each terminal symbol in the RHS, compare it with the nextToken. If they match, continue, else there is a syntax error • For each nonterminal symbol in the RHS, call its associated parsing subprogram

  26. Recursive-Descent Parsing (cont.) /* Function expr Parses strings in the language generated by the rule: <expr> → <term> {(+ | -) <term>} */ void expr() { /* 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();   } }

  27. Recursive-Descent Parsing (cont.) • This particular routine does not detect errors • Convention: Every parsing routine leaves the next token in nextToken

  28. 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

  29. Recursive-Descent Parsing (cont.) /* term Parses strings in the language generated by the rule: <term> -> <factor> {(* | /) <factor>) */ void term() { printf("Enter <term>\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 <term>\n"); } /* End of function term */

  30. Recursive-Descent Parsing (cont.) /* Function factor Parses strings in the language generated by the rule: <factor> -> id | (<expr>) */ void factor() { /* Determine which RHS */    if (nextToken) == ID_CODE || nextToken == INT_CODE) /* For the RHS id, just call lex */      lex(); /* If the RHS is (<expr>) – 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 */ }

  31. 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 <expr> Enter <factor> Enter <term> Next token is: -1 Next lexeme is EOF Enter <factor> Exit <factor> Next token is: 11 Next lexeme is sum Exit <term> Enter <expr> Exit <expr> Enter <term> Enter <factor> Next token is: 21 Next lexeme is + Exit <factor> Exit <term> Next token is: 10 Next lexeme is 47 Enter <term> Enter <factor> Next token is: 26 Next lexeme is ) Exit <factor> Exit <term> Exit <expr> Next token is: 24 Next lexeme is / Exit <factor>

  32. <expr> <term> <factor> <factor> / <id> ( <expr> ) total <term> + <term> <factor> <factor> int_constant <id> sum 47 <expr> <term>{(+|-)<term>} <term>  <factor>{(*|/)<factor>} <factor>  <id> | int_constant | (<expr>)

  33. 4.4.2 The LL Grammar Class The Left Recursion Problem • If a grammar has left recursion, either direct or indirect, it causes a catastrophic problem for LL parsers. e.g., A  A + B • A grammar can be modified to remove left recursion For each nonterminal, A, • Group the A-rules as A → Aα1 | … | Aαm | β1 | β2 | … | βn where none of the β’s begins with A 2. Replace the original A-rules with A →β1A’ | β2A’ | … | βnA’ A’ →α1A’ | α2A’ | … | αmA’ | ε (Note : ε specifies the empty string)

  34. E-rules α1=+T, β=T, (m=1,n=1) E-rules α1=*F, β=F, (m=1,n=1) • Example Grammar with Left Recursion E  E + T | T T  T*F | F Grammar 1 F  (E) | id • Complete Replacement Grammar E  T E’ E’  + T E’|ε T  F T’ Grammar 2 T’ *F T’| ε F  (E) | id Grammar 2 generates the same language as Grammar 1, but it is not left recursive.

  35. Indirect Left Recursion Problem e.g., A  B a A B  A b To remove indirect left recursion => Paper (Aho et al., 2006)

  36. Left Recursion Problem (cont’d) Two issues: • Left recursion disallow top-down parsing; • Whether the parser can always choose the correct RHS on the basis of the next token of input, using only the first token generated by the leftmost nonterminal in the current sentential form. Solution: To conduct a Pairwise Disjointness Test • Pairwise Disjointness Test: a test of non-left recursive grammar.

  37. Pairwise disjointness test • Define: FIRST(α) = { a | α =>* a β} (If α =>* ε, ε is in FIRST(α)) • For each nonterminal, A, that has more than one RHS, for each pair of rules, A αi and A αj, if FIRST(αi) FIRST(αj) = φ,this pair passes the test; otherwise it fails the test.

  38. Pairwise disjointness test Example: Perform the pairwise disjointness test for the following rules: A  aB | bAb | Bb B  cB | d Sol: FIRST(aB)={a}, FIRST(bAb)={b}, FIRST(Bb)={c,d} FIRST(aB) FIRST(bAb)= φ FIRST(aB) FIRST(Bb)= φ FIRST(bAb) FIRST(Bb)= φ