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Compiler Principles Winter Compiler Principles Lexical Analysis (Scanning) Mayer Goldberg and Roman Manevich Ben-Gurion University

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General stuff Topics taught by me Lexical analysis (scanning) Syntax analysis (parsing) … Dataflow analysis Register allocation Slides will be available from web-site after lecture Request: please mute mobiles, tablets, super-cool squeaking devices 2

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Today Understand role of lexical analysis Lexical analysis theory Implementing modern scanner 3

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Role of lexical analysis First part of compiler front-end Convert stream of characters into stream of tokens Split text into most basic meaningful strings Simplify input for syntax analysis 4 High-level Language (scheme) Executable Code Lexical Analysis Syntax Analysis Parsing ASTSymbol Table etc. Inter. Rep. (IR) Code Generation

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From scanning to parsing (7 * x) )id*num(+ Lexical Analyzer program text token stream Parser Grammar: E id E num E E + E E E * E E ( E ) + num x * Abstract Syntax Tree valid syntax error

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Javascript example 6 var currOption = 0; // Choose content to display in lower pane. function choose ( id ) { var menu = ["about-me", "publications", "teaching", "software", "activities"]; for (i = 0; i < menu.length; i++) { currOption = menu[i]; var elt = document.getElementById(currOption); if (currOption == id && elt.style.display == "none") { elt.style.display = "block"; } else { elt.style.display = "none"; } Identify basic units in this code

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Javascript example 7 var currOption = 0; // Choose content to display in lower pane. function choose ( id ) { var menu = ["about-me", "publications", "teaching", "software", "activities"]; for (i = 0; i < menu.length; i++) { currOption = menu[i]; var elt = document.getElementById(currOption); if (currOption == id && elt.style.display == "none") { elt.style.display = "block"; } else { elt.style.display = "none"; } Identify basic units in this code

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Javascript example Identify basic units in this code 8 var currOption = 0; // Choose content to display in lower pane. function choose ( id ) { var menu = ["about-me", "publications", "teaching", "software", "activities"]; for (i = 0; i < menu.length; i++) { currOption = menu[i]; var elt = document.getElementById(currOption); if (currOption == id && elt.style.display == "none") { elt.style.display = "block"; } else { elt.style.display = "none"; } keyword numeric literal operator string literal punctuation identifier whitespace

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Scanner output 9 var currOption = 0; // Choose content to display in lower pane. function choose ( id ) { var menu = ["about-me", "publications“, "teaching", "software", "activities"]; for (i = 0; i < menu.length; i++) { currOption = menu[i]; var elt = document.getElementById(currOption); if (currOption == id && elt.style.display == "none") { elt.style.display = "block"; } else { elt.style.display = "none"; } 1: VAR 1: ID(currOption) 1: EQ 1: INT_LITERAL(0) 1: SEMI 3: FUNCTION 3: ID(choose) 3: LP 3: ID(id) 3: EP 3: LCB... Stream of Tokens LINE: ID(value)

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What is a token? Lexeme – substring of original text constituting an identifiable unit Identifiers, Values, reserved words, … Record type storing: Kind Value (when applicable) Start-position/end-position Any information that is useful for the parser Different for different languages 10

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C++ example 1 Splitting text into tokens can be tricky How should the code below be split? 11 vector > myVector >> operator >, > two tokens or ?

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C++ example 2 Splitting text into tokens can be tricky How should the code below be split? 12 vector > myVector >, > two tokens

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Example tokens TypeExamples Identifierx, y, z, foo, bar NUM42 FLOATNUM STRING“so long, and thanks for all the fish” LPAREN( RPAREN) IFif … 13

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Separating tokens 14 TypeExamples Comments/* ignore code */ // ignore until end of line White spaces\t \n Lexemes are recognized but get consumed rather than transmitted to parser if i f i/*comment*/f

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Preprocessor directives in C 15 TypeExamples Inlude directives#include Macros#define THE_ANSWER 42

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Designing a scanner Define each type of lexeme Reserved words: var, if, for, while Operators: < = ++ Identifiers: myFunction Literals: 123 “hello” But how do we define lexemes of unbounded length? 16

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Designing a scanner Define each type of lexeme Reserved words: var, if, for, while Operators: < = ++ Identifiers: myFunction Literals: 123 “hello” But how do we define lexemes of unbounded length? Regular expressions 17

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Regular languages refresher Formal languages Alphabet = finite set of letters Word = sequence of letter Language = set of words Regular languages defined equivalently by Regular expressions Finite-state automata 18

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Regular expressions Empty string: Є Letter: a Concatenation: R 1 R 2 Union: R 1 | R 2 Kleene-star: R* Shorthand: R + stands for R R* scope: (R) Example: (0* 1*) | (1* 0*) What is this language? 19

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Exercise 1 - Question Language of Java identifiers Identifiers start with either an underscore ‘_’ or a letter Continue with either underscore, letter, or digit 20

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Exercise 1 - Answer Language of Java identifiers Identifiers start with either an underscore ‘_’ or a letter Continue with either underscore, letter, or digit (_|a|b|…|z|A|…|Z)(_|a|b|…|z|A|…|Z|0|…|9)* Using shorthand macros First= _|a|b|…|z|A|…|Z Next= First|0|…|9 R= First Next* 21

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Exercise 2 - Question Language of rational numbers in decimal representation (no leading, ending zeros) Not 007 Not

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Exercise 2 - Answer Language of rational numbers in decimal representation (no leading, ending zeros) Digit= 1|2|…|9 Digit0 = 0|Digit Num= Digit Digit0* Frac= Digit0* Digit Pos= Num |.Frac | 0.Frac| Num.Frac PosOrNeg = (Є|-)Pos R= 0 | PosOrNeg 23

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Exercise 3 - Question Equal number of opening and closing parenthesis: [ n ] n = [], [[]], [[[]]], … 24

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Exercise 3 - Answer Equal number of opening and closing parenthesis: [ n ] n = [], [[]], [[[]]], … Not regular Context-free Grammar: S ::= [] | [S] 25

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Finite automata 26 start a b b c accepting state start state transition An automaton is defined by states and transitions

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Automaton running example 27 start a b b c Words are read left-to-right cba

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Automaton running example 28 start a b b c Words are read left-to-right cba

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Automaton running example 29 start a b b c Words are read left-to-right cba

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Automaton running example 30 start a b b c Words are read left-to-right word accepted cba

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Word outside of language 31 start a b b c cbb

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Word outside of language Missing transition means non-acceptance 32 start a b b c cbb

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Exercise - Question What is the language defined by the automaton below? 33 start a b b c

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Exercise - Answer What is the language defined by the automaton below? a b* c Generally: all paths leading to accepting states 34 start a b b c

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Non-deterministic automata Allow multiple transitions from given state labeled by same letter 35 start a a b c b c

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NFA run example 36 cba start a a b c b c

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NFA run example Maintain set of states 37 cba start a a b c b c

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NFA run example 38 cba start a a b c b c

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NFA run example Accept word if any of the states in the set is accepting 39 cba start a a b c b c

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NFA+Є automata Є transitions can “fire” without reading the input 40 start a b c Є

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NFA+Є run example 41 start a b c cba Є

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NFA+Є run example Now Є transition can non-deterministically take place 42 start a b c cba Є

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NFA+Є run example 43 start a b c cba Є

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NFA+Є run example 44 start a b c cba Є

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NFA+Є run example 45 start a b c cba Є

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NFA+Є run example 46 start a b c cba Є Word accepted

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Reg-exp vs. automata Regular expressions are declarative Offer compact way to define a regular language by humans Don’t offer direct way to check whether a given word is in the language Automata are operative Define an algorithm for deciding whether a given word is in a regular language Not a natural notation for humans 47

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From reg. exp. to automata Theorem: there is an algorithm to build an NFA+Є automaton for any regular expression Proof: by induction on the structure of the regular expression For each sub-expression R we build an automaton with exactly one start state and one accepting state Start state has no incoming transitions Accepting state has no outgoing transitions 48

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From reg. exp. to automata Theorem: there is an algorithm to build an NFA+Є automaton for any regular expression Proof: by induction on the structure of the regular expression 49 start

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Base cases 50 R = R = a start a

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Construction for R 1 | R 2 51 start R1R1 R2R2

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Construction for R 1 R 2 52 start R1R1 R2R2

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Construction for R* 53 start R

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From NFA+Є to DFA Construction requires O(n) states for a reg- exp of length n Running an NFA+Є with n states on string of length m takes O(m·n 2 ) time Solution: determinization via subset construction Number of states worst-case exponential in n Running time O(m) 54

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Subset construction For an NFA+Є with states M={s 1,…,s k } Construct a DFA with one state per set of states of the corresponding NFA M’={ [], [s 1 ], [s 1,s 2 ], [s 2,s 3 ], [s 1,s 2,s 3 ], …} Simulate transitions between individual states for every letter 55 a s1s1 s2s2 a [s 1,s 4 ] [s 2,s 7 ] NFA+Є DFA a s4s4 s7s7

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Subset construction For an NFA+Є with states M={s 1,…,s k } Construct a DFA with one state per set of states of the corresponding NFA M’={ [], [s 1 ], [s 1,s 2 ], [s 2,s 3 ], [s 1,s 2,s 3 ], …} Extend macro states by states reachable via Є transitions 56 Є s1s1 s4s4 [s 1,s 2 ] [s 1,s 2,s 4 ] NFA+Є DFA

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Scanning challenges Regular expressions allow us to define the language of all sequences of tokens Automata theory provides an algorithm for checking membership of words But we are interested in splitting the text not just deciding on membership How do we determine lexemes? How do we handle ambiguities – lexemes matching more than one token? 57

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Separating lexemes ID= (a+b+…+z) (a+b+…+z)* ONE= 1 Input: abb1 How do we identify ID(abb), ONE? 58

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Separating lexemes ID= (a+b+…+z) (a+b+…+z)* ONE= 1 Input: abb1 How do we identify ID(abb), ONE? 59 start a-z 1 ID ONE

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Maximal munch ID= (a+b+…+z) (a+b+…+z)* ONE= 1 Input: abb1 How do we identify ID(abb), ONE? Solution: find longest matching lexeme Keep reading text until automaton leaves accepting state Return token corresponding to accepting state Reset – go back to start state and continue reading input from there 60

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Handling ambiguities ID = (a+b+…+z) (a+b+…+z)* IF = if Input: if Matches both tokens What should the scanner output? 61 start a-z i ID IF f NFA

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Handling ambiguities ID = (a+b+…+z) (a+b+…+z)* IF = if Input: if Matches both tokens What should the scanner output? 62 start a-z\i i a-z ID IF ID f ID a-z\f DFA a-z

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Handling ambiguities ID = (a+b+…+z) (a+b+…+z)* IF = if Input: if Matches both tokens What should the scanner output? Solution: break tie using order of definitions Output: ID(if) 63 start a-z\i i a-z ID IF ID f ID a-z\f a-z

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Handling ambiguities IF = if ID = (a+b+…+z) (a+b+…+z)* Input: if Matches both tokens What should the scanner output? Solution: break tie using order of definitions Output: IF 64 Conclusion: list keyword token definitions before identifier definition start a-z\i i a-z ID IF ID f ID a-z\f a-z

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Implementing scanners in practice 65

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Implementing scanners Manual construction of automata + determinization is Very tedious Error-prone Non-incremental Fortunately there are tools that automatically generate code from a specification for most languages C: Lex, Flex Java: JLex, JFlex 66

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Using JFlex Define tokens (and states) Run Jflex to generate Java implementation Usually MyScanner.nextToken() will be called in a loop by parser 67 Regular Expressions JFlexMyScanner.java Stream of characters Tokens MyScanner.lex

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Common format for reg-exps 68

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Escape characters What is the expression for one or more + symbols? (+)+ won’t work (\+)+ will backslash \ before an operator turns it to standard character \*, \?, \+, … Newline: \n or \r\n depending on OS Tab: \t 69

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Shorthands Use names for expressions letter = a | b | … | z | A | B | … | Z letter_ = letter | _ digit = 0 | 1 | 2 | … | 9 id = letter_ (letter_ | digit)* Use hyphen to denote a range letter = a-z | A-Z digit =

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Catching errors What if input doesn’t match any token definition? Trick: Add a “catch-all” rule that matches any character and reports an error Add after all other rules 71

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72 Next lecture: parsing

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