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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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