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Topic #3: Lexical Analysis
CSC 338 – Compiler Design and implementation Dr. Mohamed Ben Othman
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Lexical Analyzer and Parser
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Why Separate? Reasons to separate lexical analysis from parsing:
Simpler design Improved efficiency Portability Tools exist to help implement lexical analyzers and parsers independently
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Tokens, Lexemes, and Patterns
Tokens include keywords, operators, identifiers, constants, literal strings, punctuation symbols A lexeme is a sequence of characters in the source program representing a token A pattern is a rule describing a set of lexemes that can represent a particular token
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Attributes Attributes provide additional information about tokens
Technically speaking, lexical analyzers usually provide a single attribute per token (might be pointer into symbol table)
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Buffer Most lexical analyzers use a buffer
Often buffers are divided into two N character halves Two pointers used to indicate start and end of lexeme If pointer walks past end of either half of buffer, other half of buffer is reloaded A sentinel character can be used to decrease number of checks necessary
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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 Other terms relating to strings: prefix; suffix; substring; proper prefix, suffix, or substring (non-empty, not entire string); subsequence
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Operations on Languages
Union: Concatenation: Kleene closure: Zero or more concatenations Positive closure: One or more concatenations
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Regular Expressions Defined over an alphabet Σ
ε represents {ε}, the set containing the empty string If a is a symbol in Σ, then a is a regular expression denoting {a}, the set containing the string a If r and s are regular expressions denoting the languages L(r) and L(s), then: (r)|(s) is a regular expression denoting L(r)U L(s) (r)(s) is a regular expression denoting L(r)L(s) (r)* is a regular expression denoting (L(r))* (r) is a regular expression denoting L(r) Precedence: * (left associative), then concatenation (left associative), then | (left associative)
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Regular Definitions 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)*
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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 )? optional_exponent (E(+|-)? digits )? num digits optional_fraction optional_exponent
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Limitations Can not describe balanced or nested constructs
Example, all valid strings of balanced parentheses This can be done with CFG Can not describe repeated strings Example: {wcw|w is a string of a’s and b’s} Can not denote with CFG either!
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Grammar Fragment (Pascal)
stmt if expr then stmt | if expr then stmt else stmt | ε expr term relop term | term term id | num
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Related Regular Definitions
if if then then else else relop < | <= | = | <> | > | >= id letter ( letter | digit )* num digit+ (. digit+ )? (E(+|-)? digit+ )? delim blank | tab | newline ws delim+
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Tokens and Attributes Regular Expression Token Attribute Value ws - if
then else id pointer to entry num < relop LT <= LE = EQ <> NE > GT => GE
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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 Some states may have associated actions At some final states, need to retract a character
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Transition Diagram for “relop”
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Identifiers and Keywords
Share a transition diagram After reaching accepting state, code determines if lexeme is keyword or identifier Easier than encoding exceptions in diagram Simple technique is to appropriately initialize symbol table with keywords
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Numbers
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Order of Transition Diagrams
Transition diagrams tested in order Diagrams with low numbered start states tried before diagrams with high numbered start states Order influences efficiency of lexical analyzer
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Trying Transition Diagrams
int next_td(void) { switch (start) { case 0: start = 9; break; case 9: start = 12; break; case 12: start = 20; break; case 20: start = 25; break; case 25: recover(); break; default: error("invalid start state"); } /* Possibly additional actions here */ return start;
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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; … /* 27 other cases here */
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The End of a Token token nexttoken(void) { while (1) {
switch (state) { … /* First 19 cases */ case 19: retract(); install_num(); return(NUM); break; … /* Final 8 cases */
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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
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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
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Transition Tables State Input Symbol a b {0,1} {0} 1 --- {2} 2 {3}
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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
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