Lexical Analyzer (Checker)

lec01-lexicalanalyzer April 23, 2017 Lexical Analyzer Lexical Analyzer reads the source program character by character to produce tokens. Normally a lexical analyzer doesn’t return a list of tokens at one shot, it returns a token when the parser asks a token from it.

Tokens, Lexemes, and Patterns Tokens include keywords, operators, identifiers, constants, literal strings, punctuation symbols e.g: identifier, number, addop, assgop A lexeme is a sequence of characters in the source program representing a token e.g: newval, oldval A pattern is a rule describing a set of lexemes that can represent a particular token e.g: Identifier represents a set of strings which start with a letter continues with letters and digits Regular expressions are widely used to specify patterns.

Attributes Since a token can represent more than one lexeme, attributes provide additional information about tokens For simplicity, a token may have a single attribute. For an identifier, attribute is a pointer to the symbol table Examples of some attributes: <id,attr> where attr is pointer to the symbol table <assgop,_> no attribute is needed (only one assignment operator) <num,val> where val is the actual value of the number. Token and its attribute uniquely identifies a lexeme.

Strings and Languages Alphabet – any finite set of symbols (e.g. ASCII, binary alphabet, or a set of tokens) String – A finite sequence of symbols drawn from an alphabet Language – A set of strings over a fixed alphabet

Operations on Languages Union: Concatenation: Kleene closure: Zero or more concatenations Positive closure: One or more concatenations

Regular Expressions Can give “names” to regular expressions Convention: names in boldface (to distinguish them from symbols) letter  A|B|…|Z|a|b|…|z digit  0|1|…|9 id  letter (letter | digit)*

Notational Shorthands One or more instances: r+ denotes rr* Zero or one Instance: r? denotes r|ε Character classes: [a-z] denotes [a|b|…|z] digit  [0-9] digits  digit+ optional_fraction  (. digits )? num  digits optional_fraction

Limitations Can not describe balanced or nested constructs Example, all valid strings of balanced parentheses This can be done with Context Free Grammar ( CFG)

Grammar Fragment (Pascal) stmt  if expr then stmt | if expr then stmt else stmt | ε expr  term relop term | term term  id | num

Related Regular Expression Definitions if  if then  then else  else relop  < | <= | = | <> | > | >= id  letter ( letter | digit )* num  digit+ (. digit+ )? ws  delim+ delim  blank | tab | newline

Tokens and Attributes Regular Expression Token Attribute Value ws - if then else id pointer to entry num < relop LT <= LE = EQ <> NE > GT => GE

Transition Diagrams A stylized flowchart Transition diagrams consist of states connected by edges Edges leaving a state s are labeled with input characters that may occur after reaching state s Assumed to be deterministic There is one start state and at least one accepting (final) state

Transition Diagram for “relop”

Identifiers and Keywords Share a transition diagram After reaching accepting state, code determines if lexeme is keyword or identifier

Numbers

Finding the Next Token token nexttoken(void) { while (1) { switch (state) { case 0: c = nextchar(); if (c == ' ' || c=='\t' || c == '\n') { state = 0; lexeme_beginning++; } else if (c == '<') state = 1; else if (c == '=') state = 5 else if (c == '>') state = 6 else state = next_td(); break; … /* other cases here */

Trying Transition Diagrams int next_td(void) { switch (start) { case 0: start = 9; break; case 9: start = 20; break; case 20: start = 25; break; case 25: recover(); break; default: error("invalid start state"); } /* Possibly additional actions here */ return start;

Finite Automata Generalized transition diagrams that act as “recognizer” for a language Can be nondeterministic (NFA) or deterministic (DFA) NFAs can have ε-transitions, DFAs can not NFAs can have multiple edges with same symbol leaving a state, DFAs can not Both can recognize exactly what regular expressions can denote

NFAs A set of states S A set of input symbols Σ (input alphabet) A transition function move that maps state, symbol pairs to a set of states A single start state s0 A set of accepting (or final) states F An NFA accepts a string s if and only if there exists a path from the start state to an accepting state such that the edge labels spell out s

NFA (Example) The language recognized by this NFA is (a|b) * ab 1 2 a b start 0 is the start state s0 {2} is the set of final states F = {a,b} S = {0,1,2} Transition graph of the NFA The language recognized by this NFA is (a|b) * ab

Transition Tables State Input Symbol a b {0,1} {0} 1 --- {2} 2 {3}

DFAs No state has an ε-transition For each state s and input symbol a, there as at most one edge labeled a leaving s

Example: r = (a|b)*abb

Functions ε-closure and move ε-closure(s) is the set of NFA states reachable from NFA state s on ε-transitions alone move(T,a) is the set of NFA states to which there is a transition on input a from any NFA state s in T

Constructed DFA

Simulating a DFA s := s0 c := nextchar while c != eof do s := move(s, c) end if s is in F then return “yes” else return “no”

Simulating an NFA S := ε-closure({s0}) a := nextchar while a != eof do S := ε-closure(move(S,a)) if S ∩ F != Ø return “yes” else return “no”

Space/Time Tradeoff (Worst Case) NFA O(|r|) O(|r|*|x|) DFA O(2|r|) O(|x|)

Simulating a Regular Expression First use Thompson’s Construction to convert RE to NFA Then there are two choices: Use subset construction to convert NFA to DFA, then simulate the DFA Simulate the NFA directly

Some Other Issues in Lexical Analyzer The lexical analyzer has to recognize the longest possible string. Ex: identifier newval -- n ne new newv newva newval What is the end of a token? Is there any character which marks the end of a token?

Some Other Issues in Lexical Analyzer (cont.) Skipping comments Normally we don’t return a comment as a token. So, the comments are only processed by the lexical analyzer, and don’t complicate the syntax of the language. Symbol table interface symbol table holds information about tokens (at least lexeme of identifiers) how to implement the symbol table, and what kind of operations. hash table – open addressing, chaining putting into the hash table, finding the position of a token from its lexeme. Positions of the tokens in the file (for the error handling).