Lexical Analysis - 1. A. Overview A.a) Role of Lexical Analyzer
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1 CMPSC 470 Lecture 02 Topics: Regular Expression Transition Diagram Lexical Analyzer Implementation A. Overview A.a) Role of Lexical Analyzer Lexical Analysis - 1 Lexical analyzer does: read input character of source program group them into lexemes (lexically meaningful units) produce a sequence of tokens for each lexeme How does lexical analyzer interact with parser?
2 A.b) What is token, pattern, and lexeme? Token: Lexeme: Pattern: Example 1) Tokens, and lexeme, and pattern of pos = init + 11 Token Sample lexeme Informal description if else assign comparison number id literal or string
3 B. Regular Expression Regular expressions are very effective in specifying types of patterns of tokens. B.a) Terms and Operations Terms Alphabet: String: Language: Operations on String Concatenation: Exponentiation:
4 Operations on Language Given two languages LL and MM, Union of LL and MM is a language such that: LL MM = {ss ss LL oooo ss MM}. Concatenation of LL and MM is a language such that: LLLL = {ssss ss LL aaaaaa tt MM}. LL 00 = {εε} LL ii = LLLL ii 11 = LL ii 11 LL Kleene closure of LL is LL = LL ii ii=00 Positive closure of LL is LL + = LL ii ii=11
5 B.b) Regular Expression Regular expression is a sequence of characters that define a pattern. Example) Let letter_ {aa,, zz, AA,, ZZ}, and digit {0,1,,9}. Then, the language of C programming language identifiers is defined, using a pattern rr, such that rr = rr is regular expression, and LL(rr) is the language defined/determined by rr. Definition of Regular Expression: Regular expressions are built recursively out of smaller regular expressions. BASIS: INDUCTION: Let rr and ss are regular expression, whose languages are LL(rr) and LL(ss), respectively. 3.
6 Applying Order: Example) Let symbols Σ = {aa, bb} aa bb denotes language { } (aa bb)(aa bb) denotes language { } aa denotes language { } aa aa bb denotes language { }
7 Regular Set: A language defined by regular expression is a regular set. Algebraic Laws for Regular Expression: Let ss, tt, rr are regular expressions
8 B.c) Extension of Regular Expression Let rr be a regular expression, and aa 1, aa 2,, aa nn are alphabets. Positive Closure rr + : Zero or one instance rr?: Character classes: Extension of regular definitions for the language of C identifiers, and the unsigned numbers:
9 B.d) Regular Definitions: Regular definitions is a sequence of definition of the form: dd 1 rr 1 dd 2 rr 2 dd nn rr nn where Example) Regular definitions for the language of C identifiers: Regular definitions for unsigned numbers (int or float)
10 C. Recognize Lexeme from Input Stream Let we have a program xyz := 10 if xyz <= 10 then xyz := xyz + 1.0E2 end The pattern of tokens can be described using regular definition and regular expression, as follows:
11 Lexical analyzer (lexer) will receive the input as character stream, as follows. How lexical analyzer will scan input to find a lexeme with given patterns? x y z : = 1 0 \n i f x y z < = 1 0 Note: Actual implementation is more complex. The implementation uses technique called doublebuffering to reduce the overhead of processing input stream.
12 D. Transition Diagram As an intermediate step to recognize lexeme, we convert regular expression pattern to transition diagram (stylized flow chart). D.a) Transition diagram The regular definition for op token op < > <= >= = <> has the following form of transition diagram Followings are the properties of the transition diagram: It has collection of nodes (or circle) and edges. Edges are labeled by a symbol or set of symbols. Double circle are * indicates start indicates
13 How does this transition diagram recognizes = and < from the following input stream? if xyz=10 or abc<20 then Assume that last token returned by lexer was xyz, and forward points z. Assume that last token returned by lexer was abc, and forward points c.
14 D.b) Architecture of a Transition-Diagram-Based Lexical Analyzer TOKEN getrelop() { // TOKEN has two components TOKEN rettoken = new(relop); // First component set here while (true) { switch(state) { case 0: c = nextchar(); if (c == '<') state = 1; else if (c == '=') state = 5; else if (c == '>') state = 6; else fail(); // lexeme is not a relop break; case 1: c = nextchar(); if (c == '=') { rettoken.attribute = LE; // second component return rettoken; }... case 8: retract(); // an accepting state with star rettoken.attribute = GT; // second component return rettoken; } } }
15 D.c) Recognition of reserved words and identifiers Reserved words and identifiers has similar forms: if if then then end end id [A-Za-z][A-Za-z0-9]* How to distinguish the reserved words from identifiers?
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