1 / 64

Lecture 4 Concepts of Programming Languages

Lecture 4 Concepts of Programming Languages. Arne Kutzner Hanyang University / Seoul Korea. Topics. Lexical Analysis The Parsing Problem Recursive-Descent Parsing Bottom-Up Parsing. Introduction.

jaquelinec
Download Presentation

Lecture 4 Concepts of Programming Languages

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 4Concepts of Programming Languages Arne Kutzner Hanyang University / Seoul Korea

  2. Topics • Lexical Analysis • The Parsing Problem • Recursive-Descent Parsing • Bottom-Up Parsing Concepts of Programming Languages

  3. 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 Concepts of Programming Languages

  4. Advantages of Using CFG/BNF to Describe Syntax • Provides a clear and concise syntax description • A parser can be constructed on foundation of CFG/BNF Concepts of Programming Languages

  5. 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) Concepts of Programming Languages

  6. Lexical Analysis • A lexical analyzer is a “front-end” for the parser • pattern matcher for character strings • 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 Concepts of Programming Languages

  7. Reasons to Separate Lexical and Syntax Analysis • Simplicity - less complex approaches can be used for lexical analysis (no need for the use of grammars for token extraction) • Efficiency - separation allows significant less complex parsers Concepts of Programming Languages

  8. We need first some theory…

  9. Regular Expressions • Given a finite alphabet Σ, the following constants are defined as regular expressions: • (empty set) Ø denoting the set Ø. • (empty string) ε denoting the set containing only the "empty" string, which has no characters at all. • (literal character) a in Σ denoting the set containing only the character a. Concepts of Programming Languages

  10. Regular Expressions (cont.) • Given regular expressions R and S, the following operations over them are defined to produce regular expressions: • (concatenation) RS denotes the set of strings that can be obtained by concatenating a string in R and a string in S. For example {"ab", "c"}{"d", "ef"} = {"abd", "abef", "cd", "cef"}. • (alternation) R | S denotes the set union of sets described by R and S. For example, if R describes {"ab", "c"} and S describes {"ab", "d", "ef"}, expression R | S describes {"ab", "c", "d", "ef"}. • Alternation is sometimes denoted by + Concepts of Programming Languages

  11. Regular Expressions (cont.) 3. (Kleene star) R* denotes the smallest superset of set described by Rthat contains ε and is closed under string concatenation. This is the set of all strings that can be made by concatenating any finite number (including zero) of strings from set described by R. For example, {"0","1"}* is the set of all finite binary strings (including the empty string), and {"ab", "c"}* = {ε, "ab", "c", "abab", "abc", "cab", "cc", "ababab", "abcab", ... }. Concepts of Programming Languages

  12. Regular Languages • The collection of regular languages over an alphabet Σ is defined recursively as follows: • The empty language Ø is a regular language. • For each a ∈ Σ (a belongs to Σ), the singleton language {a} is a regular language. • If A and B are regular languages, then A ∪ B (union), A • B (concatenation), and A* (Kleene star) are regular languages. • No other languages over Σ are regular. Concepts of Programming Languages

  13. Regular Expressions and Regular Languages • The family of languages defined by regular expressions are the regular languages. • Regular expressions can be used for lexeme/token description/specification. E.g.: description of a token Identifier as Letter (Digit | Letter)* • Regular expressions are generators like grammars • In fact, you can describe every regular expressions by means of a grammar Concepts of Programming Languages

  14. Examples of regular expressions • What are the words of the following expressions? • (0 | 1)(00 | 01 | 10 | 11)* • (0 | 1)(0 | 1)(0 | 1)(0 | 1)(0 | 1) • Are languages of the following 3 expressions • 0* 1 (0 | 1)* • (0 | 1)* 1 (0 | 1)* • (0 | 1)* 1 0* equal? Concepts of Programming Languages

  15. Recognizer for Regular Expressions • A deterministic finite automaton (DFA)M is a 5-tuple, (Q, Σ, δ, q0, F), consisting of • a finite set of states (Q) • a finite set of input symbols called the alphabet (Σ) • a transition function (δ : Q × Σ → Q) • a start state (q0 ∈ Q) • a set of accept states (F ⊆ Q) Concepts of Programming Languages

  16. Language accepted by a DFA • Let w = a1a2 ... an be a string over the alphabet Σ. The automaton M accepts the string w if a sequence of states, r0,r1, ..., rn, exists in Q with the following conditions: • r0 = q0 • ri+1 = δ(ri, ai+1), for i = 0, ..., n−1 • rn ∈ F. Concepts of Programming Languages

  17. DFA Example corresponding state diagram for M • M = (Q, Σ, δ, q0, F) where • Q = {S1, S2}, • Σ = {0, 1}, • q0 = S1, • F = {S1}, • δ is the following state transition table: Concepts of Programming Languages

  18. DFA Example (cont.) • The Language recognized by M is the regular language given by the regular expression 1*( 0 1* 0 1* )*, • The accepted language consists of all words that contains an even number of 0s. Concepts of Programming Languages

  19. Kleene’s Theorem • Part 1: If R is regular expression over the alphabet Σ, and L is the language in Σ* corresponding to R, then there is a (deterministic) finite automaton M recognizing L. • Part 2: If M = (Q, Σ, δ, q0, F) is a (deterministic) finite automaton recognizing the language L, then there is a regular expression over Σ corresponding to L. • So, DFAs recognize exactly the set of regular languages/expressions. Concepts of Programming Languages

  20. Limitations of regular languages • There is no regular expression for the language 1n 0n , n≥ 0 (n ones followed by n zeros) • But you can easily give a CFG for the above language:<A> -> 1 <A> 0 | ε • Other example: Dyck language; balanced strings of parentheses (e.g. [ [ ] [ [ ] ] ] [ ] ) • Grammar ? (-> Exercise) Concepts of Programming Languages

  21. Practical implementation of lexical analyzers • DFAs and regular expressions are the foundations of lexical analyzer construction • Possible approaches for implementing 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 Concepts of Programming Languages

  22. Lexical Analysis (cont.) • In many cases, symbols of transitions are “combined/grouped” in order 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 Concepts of Programming Languages

  23. Lexical Analysis (cont.) • Reserved words can be recognized in the context of identifier recognition • Use a table lookup to determine whether a possible identifier is in fact a reserved word Concepts of Programming Languages

  24. Lexical Analysis (cont.)Example Program … • The proposed lexical analyzer is a function that should be called by the parser when it request a fresh token/lexems • 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) Concepts of Programming Languages

  25. State diagram for recognizing identifiers and integer numbers Concepts of Programming Languages

  26. Lexical Analysis / Example Prg. int lex() { lexLen = 0; static int first = 1; /* If it is the first call to lex, initialize by calling getChar */ if (first) { getChar(); first = 0; } getNonBlank(); switch (charClass) { /* Parse identifiers and reserved words */ case LETTER: addChar(); getChar(); while (charClass == LETTER || charClass == DIGIT){ addChar(); getChar(); } return lookup(lexeme); break; … Concepts of Programming Languages

  27. Lexical Analysis / Example Prg. … /* Parse integer literals */ case DIGIT: addChar(); getChar(); while (charClass == DIGIT) { addChar(); getChar(); } return INT_LIT; break; } /* End of switch */ } /* End of function lex */ Concepts of Programming Languages

  28. Parsing Problem…

  29. The Parsing Problem • Goals of the parser, given an input program: • Produce a parse tree • Find all syntax errors; for each, produce an appropriate diagnostic message and recover quickly Concepts of Programming Languages

  30. 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 Concepts of Programming Languages

  31. 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 Concepts of Programming Languages

  32. The Parsing Problem (cont.) • Bottom-up parsers • Special form of push down automata • 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 Concepts of Programming Languages

  33. Recursive-Descent Parsing (cont.) • Example grammar in BNF(CFG): <expr>  <term> - <expr> | <term1> <term> a + <term> | b <term1> c | ( <expr> ) a + b – (a + b – c) Concepts of Programming Languages

  34. Recursive-Descent Parsing • Approach - Coded parser: • Subprogram for each nonterminal in the grammar, which can parse sentences that can be generated by that nonterminal • EBNF well suited for being the basis of a recursive-descent parser, because EBNF minimizes the number of nonterminals Concepts of Programming Languages

  35. Recursive-Descent Parsing (cont.) • A grammar for simple expressions: <expr>  <term> {(+ | -) <term>} <term>  <factor> {(* | /) <factor>} <factor>  id | ( <expr> ) Concepts of Programming Languages

  36. 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 Concepts of Programming Languages

  37. 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(); … Concepts of Programming Languages

  38. Recursive-Descent Parsing /* As long as the next token is + or -, call lex to get the next token, and parse the next term */   while (nextToken == PLUS_CODE || nextToken == MINUS_CODE){     lex();     term();   } } • This particular routine does not detect errors • Convention: Every parsing routine leaves the next token in nextToken Concepts of Programming Languages

  39. 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 look-ahead) • 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 Concepts of Programming Languages

  40. 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) /* For the RHS id, just call lex */      lex(); Concepts of Programming Languages

  41. Recursive-Descent Parsing (cont.) /* If the RHS is (<expr>) – call lex to pass over the left parenthesis, call expr, and check for the right parenthesis */    else if (nextToken == LEFT_PAREN_CODE) {      lex(); expr();     if (nextToken == RIGHT_PAREN_CODE) lex(); else error(); } /* End of else if (nextToken == ... */ else error(); /* Neither RHS matches */ } Concepts of Programming Languages

  42. Recursive-Descent Parsing (cont.) • The Left Recursion Problem:If a grammar comprises left recursion, either direct or indirect, it cannot be the basis of a top-down (recursive-decent) parser • A grammar can be modified, so that it becomes free of left recursion • LL Grammar Class = Class of grammars without left recursion Concepts of Programming Languages

  43. Elimination of left recursion • Direct 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 • Indirect recursion: • See separated PDF-document Concepts of Programming Languages

  44. 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()) Concepts of Programming Languages

  45. 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 Concepts of Programming Languages

  46. Recursive-Descent Parsing (cont.) • Left factoring can be used for removing pairwise disjointness. • Example:<variable>ident | ident'('<expression>')' left factor to:<variable>  ident <new><new>   | '('<expression>')' or in EBNF:<variable>  ident [ '('<expression>')' ] • Problem with first transformation: Introduction of  rule. (Troublemaker in the context of the elimination of left recursion) Concepts of Programming Languages

  47. 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 • Bottom-up parser represent an extended form of push down automata. Concepts of Programming Languages

  48. Definition PushDown Automaton A PDA is formally defined as a 7-tuple (Q, Σ, Γ, δ, q0, Z, F), where • Q is a finite set of states • Σ is a finite set which is called the input alphabet • Γ is a finite set which is called the stack alphabet • δ : Q × (Σ{ε}) × Γ → Q × Γ* , the transition function • q0 ∈ Q is the start state • Z ∈ Γ is the initial stack symbol • F ⊆ Q is the set of accepting states Concepts of Programming Languages

  49. PDA computation • Assume δ of M maps (p,a,A) to (q,α) and that M is • in state p∈Q, • with a ∈(Σ{ε}) on input • and A∈ Γ as topmost stack symbol, Then M performs the following actions: • may read a (move one position right on input) • change the state to q • pop A, replacing it by α • IMPORTANT:The (Σ{ε}) component of the transition relation is used to formalize that the PDA can either read a letter from the input, or proceed leaving the input untouched. Concepts of Programming Languages

  50. PDA computation graphically Concepts of Programming Languages

More Related