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Lexical analysis and parsing

Lexical analysis and parsing
Lexical Analysis www.ThesisScientist.comOutline  Role of lexical analyzer  Specification of tokens  Recognition of tokens  Lexical analyzer generator  Finite automata  Design of lexical analyzer generator www.ThesisScientist.comThe role of lexical analyzer token Source To semantic Lexical Parser program analysis Analyzer getNextToken Symbol table www.ThesisScientist.comWhy to separate Lexical analysis and parsing 1. Simplicity of design 2. Improving compiler efficiency 3. Enhancing compiler portability www.ThesisScientist.comTokens, Patterns and Lexemes  A token is a pair a token name and an optional token value  A pattern is a description of the form that the lexemes of a token may take  A lexeme is a sequence of characters in the source program that matches the pattern for a token www.ThesisScientist.comExample Token Informal description Sample lexemes if if Characters i, f else Characters e, l, s, e else =, = comparison or or = or = or == or = id Letter followed by letter and digits pi, score, D2 Any numeric constant 3.14159, 0, 6.02e23 number literal Anything but “ sorrounded by “ “core dumped” printf(“total = d\n”, score); www.ThesisScientist.comAttributes for tokens  E = M C 2  id, pointer to symbol table entry for E  assignop  id, pointer to symbol table entry for M  multop  id, pointer to symbol table entry for C  expop  number, integer value 2 www.ThesisScientist.comLexical errors  Some errors are out of power of lexical analyzer to recognize:  fi (a == f(x)) …  However it may be able to recognize errors like:  d = 2r  Such errors are recognized when no pattern for tokens matches a character sequence www.ThesisScientist.comError recovery  Panic mode: successive characters are ignored until we reach to a well formed token  Delete one character from the remaining input  Insert a missing character into the remaining input  Replace a character by another character  Transpose two adjacent characters www.ThesisScientist.comInput buffering  Sometimes lexical analyzer needs to look ahead some symbols to decide about the token to return  In C language: we need to look after , = or to decide what token to return  In Fortran: DO 5 I = 1.25  We need to introduce a two buffer scheme to handle large lookaheads safely E = M C 2 eof www.ThesisScientist.comSentinels eof E = M eof C 2 eof Switch (forward++) case eof: if (forward is at end of first buffer) reload second buffer; forward = beginning of second buffer; else if forward is at end of second buffer) reload first buffer;\ forward = beginning of first buffer; else / eof within a buffer marks the end of input / terminate lexical analysis; break; cases for the other characters; www.ThesisScientist.com Specification of tokens  In theory of compilation regular expressions are used to formalize the specification of tokens  Regular expressions are means for specifying regular languages  Example:  Letter(letter digit)  Each regular expression is a pattern specifying the form of strings www.ThesisScientist.comRegular expressions Ɛ is a regular expression, L(Ɛ) = Ɛ  If a is a symbol in ∑then a is a regular expression, L(a) = a  (r) (s) is a regular expression denoting the language L(r) ∪ L(s)  (r)(s) is a regular expression denoting the language L(r)L(s)  (r) is a regular expression denoting (L9r))  (r) is a regular expression denting L(r) www.ThesisScientist.comRegular definitions d1 r1 d2 r2 … dn rn  Example: letter A B … Z a b … Z digit 0 1 … 9 id letter (letter digit) www.ThesisScientist.comExtensions  One or more instances: (r)+  Zero of one instances: r  Character classes: abc  Example:  letter AZaz  digit 09  id letter(letterdigit) www.ThesisScientist.comRecognition of tokens  Starting point is the language grammar to understand the tokens: stmt if expr then stmt if expr then stmt else stmt Ɛ expr term relop term term term id number www.ThesisScientist.comRecognition of tokens (cont.)  The next step is to formalize the patterns: digit 09 Digits digit+ number digit(.digits) (E+ Digit) letter AZaz id letter (letterdigit) If if Then then Else else Relop = = =  We also need to handle whitespaces: ws (blank tab newline)+ www.ThesisScientist.comTransition diagrams  Transition diagram for relop www.ThesisScientist.comTransition diagrams (cont.)  Transition diagram for reserved words and identifiers www.ThesisScientist.comTransition diagrams (cont.)  Transition diagram for unsigned numbers www.ThesisScientist.comTransition diagrams (cont.)  Transition diagram for whitespace www.ThesisScientist.comArchitecture of a transition diagrambased lexical analyzer TOKEN getRelop() TOKEN retToken = new (RELOP) while (1) / repeat character processing until a return or failure occurs / 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: … … case 8: retract(); retToken.attribute = GT; return(retToken); www.ThesisScientist.comLexical Analyzer Generator Lex Lex Source program Lexical lex.yy.c lex.l Compiler C lex.yy.c a.out compiler Sequence Input stream a.out of tokens www.ThesisScientist.comStructure of Lex programs declarations translation rules Pattern Action auxiliary functions www.ThesisScientist.comExample Int installID() / funtion to install the / definitions of manifest constants lexeme, whose first character is LT, LE, EQ, NE, GT, GE, pointed to by yytext, and whose IF, THEN, ELSE, ID, NUMBER, RELOP / length is yyleng, into the symbol table and return a pointer thereto / / regular definitions delim \t\n Int installNum() / similar to ws delim+ installID, but puts numerical letter AZaz constants into a separate table / digit 09 id letter(letterdigit) number digit+(\.digit+)(E+digit+) ws / no action and no return / if return(IF); then return(THEN); else return(ELSE); id yylval = (int) installID(); return(ID); number yylval = (int) installNum(); return(NUMBER); … www.ThesisScientist.comFinite Automata  Regular expressions = specification  Finite automata = implementation  A finite automaton consists of  An input alphabet   A set of states S  A start state n  A set of accepting states F  S input  A set of transitions state  state www.ThesisScientist.comFinite Automata  Transition a s s 1 2  Is read In state s on input “a” go to state s 1 2  If end of input  If in accepting state = accept, othewise = reject  If no transition possible = reject www.ThesisScientist.comFinite Automata State Graphs  A state • The start state • An accepting state a • A transition www.ThesisScientist.comA Simple Example  A finite automaton that accepts only “1” 1  A finite automaton accepts a string if we can follow transitions labeled with the characters in the string from the start to some accepting state www.ThesisScientist.comAnother Simple Example  A finite automaton accepting any number of 1’s followed by a single 0  Alphabet: 0,1 1 0  Check that “1110” is accepted but “110…” is not www.ThesisScientist.comAnd Another Example  Alphabet 0,1  What language does this recognize 0 1 0 0 1 1 www.ThesisScientist.comAnd Another Example  Alphabet still 0, 1 1 1  The operation of the automaton is not completely defined by the input  On input “11” the automaton could be in either state www.ThesisScientist.comEpsilon Moves  Another kind of transition: moves  A B • Machine can move from state A to state B without reading input www.ThesisScientist.comDeterministic and Nondeterministic Automata  Deterministic Finite Automata (DFA)  One transition per input per state  No moves  Nondeterministic Finite Automata (NFA)  Can have multiple transitions for one input in a given state  Can have moves  Finite automata have finite memory  Need only to encode the current state www.ThesisScientist.comExecution of Finite Automata  A DFA can take only one path through the state graph  Completely determined by input  NFAs can choose  Whether to make moves  Which of multiple transitions for a single input to take www.ThesisScientist.comAcceptance of NFAs  An NFA can get into multiple states 1 0 1 1 0 1 • Input: • Rule: NFA accepts if it can get in a final state www.ThesisScientist.com 0NFA vs. DFA (1)  NFAs and DFAs recognize the same set of languages (regular languages)  DFAs are easier to implement  There are no choices to consider www.ThesisScientist.comNFA vs. DFA (2)  For a given language the NFA can be simpler than the DFA 1 0 0 NFA 1 0 0 0 DFA 1 1 • DFA can be exponentially larger than NFA www.ThesisScientist.com 0Regular Expressions to Finite Automata  Highlevel sketch NFA Regular DFA expressions Lexical Tabledriven Specification Implementation of DFA www.ThesisScientist.comRegular Expressions to NFA (1)  For each kind of rexp, define an NFA  Notation: NFA for rexp A A • For   • For input a a www.ThesisScientist.comRegular Expressions to NFA (2)  For AB  A B • For A B B     A www.ThesisScientist.comRegular Expressions to NFA (3)  For A  A   www.ThesisScientist.comExample of RegExp NFA conversion  Consider the regular expression (1 0)1  The NFA is  1   C E 1 B A G H I J  0   D F   www.ThesisScientist.comNext NFA Regular DFA expressions Lexical Tabledriven Specification Implementation of DFA www.ThesisScientist.comNFA to DFA. The Trick  Simulate the NFA  Each state of resulting DFA = a nonempty subset of states of the NFA  Start state = the set of NFA states reachable through moves from NFA start state a  Add a transition S  S’ to DFA iff  S’ is the set of NFA states reachable from the states in S after seeing the input a  considering moves as well www.ThesisScientist.comNFA DFA Example  1   C E 1 B A G H I J  0   D F   0 FGABCDHI 0 1 0 ABCDHI 1 1 EJGABCDHI www.ThesisScientist.comNFA to DFA. Remark  An NFA may be in many states at any time  How many different states  If there are N states, the NFA must be in some subset of those N states  How many nonempty subsets are there N  2 1 = finitely many, but exponentially many www.ThesisScientist.comImplementation  A DFA can be implemented by a 2D table T  One dimension is “states”  Other dimension is “input symbols” a  For every transition S S define Ti,a = k i k  DFA “execution”  If in state S and input a, read Ti,a = k and skip to state i S k  Very efficient www.ThesisScientist.comTable Implementation of a DFA 0 T 0 1 0 S 1 1 U 0 1 S T U T T U U T U www.ThesisScientist.comImplementation (Cont.)  NFA DFA conversion is at the heart of tools such as flex or jflex  But, DFAs can be huge  In practice, flexlike tools trade off speed for space in the choice of NFA and DFA representations www.ThesisScientist.comReadings  Chapter 3 of the book www.ThesisScientist.com
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