Compiler Construction


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1 Compiler Construction Regular expressions Scanning Görel Hedin Reviderad a 2013 Compiler Construction 2013 F021
2 Compiler overview source code lexical analysis tokens intermediate code generation intermediate code syntactic analysis attributed AST optimization AST semantic analysis analysis intermediate code machine code generation synthesis machine code Compiler Construction 2013 F022
3 Compiler phases source code scanner regular expressions tokens lexical analysis parser context free grammar parse tree (implicit) AST builder AST (explicit) syntactic analysis Compiler Construction 2013 F023
4 Typical tokens Reserved words (keywords) Identifiers example lexemes Literals Operators Separators Compiler Construction 2013 F024
5 Typical tokens Reserved words (keywords) Identifiers example lexemes if then else begin i alpha k10 Literals A text Operators + ++!= Separators ;, ( Compiler Construction 2013 F025
6 Nontokens whitespace example lexemes comments Compiler Construction 2013 F026
7 Nontokens whitespace comments example lexemes tab newline formfeed /* comment */ //eol comment Compiler Construction 2013 F027
8 Formal languages An alphabet, Σ, is a set of symbols. (Nonempty and finite) A string is a sequence of symbols. (Each string is finite) A formal language, L, is a set of strings. (Can be infinite) Compiler Construction 2013 F028
9 Formal languages An alphabet, Σ, is a set of symbols. (Nonempty and finite) A string is a sequence of symbols. (Each string is finite) A formal language, L, is a set of strings. (Can be infinite) We would like to have rules or algorithms for deciding if a certain string over the alphabet belongs to the language or not. Compiler Construction 2013 F028
10 Example: Languages over binary numbers Suppose we have the alphabet Σ = {0, 1} Example languages: The set of all possible combinations of zeros and ones: L 0 = {0, 1, 00, 01, 10, 11, 000,...} All binary numbers without unnecessary leading zeros: L 1 = {0, 1, 10, 11, 100, 101, 110, 111, 1000,...} All binary numbers with two digits: L 2 = {00, 01, 10, 11}... Compiler Construction 2013 F029
11 Example: Languages over UNICODE Here, the alphabet Σ is the set of UNICODE characters Example languages: All possible Java keywords: { class, import, public,...} All possible lexemes corresponding to Java tokens. All possible lexemes corresponding to Java whitespace. All binary numbers... Compiler Construction 2013 F0210
12 Example: Languages over Java tokens Here, the alphabet Σ is the set of Java tokens Example languages: All syntactically correct Java programs All that are syntactically incorrect All that are compiletime correct All that terminate Compiler Construction 2013 F0211
13 Example: Languages over Java tokens Here, the alphabet Σ is the set of Java tokens Example languages: All syntactically correct Java programs All that are syntactically incorrect All that are compiletime correct All that terminate (undecidable)... Compiler Construction 2013 F0211
14 Defining languages using rules Increasingly powerful: Regular expressions Contextfree grammars Attribute grammars Compiler Construction 2013 F0212
15 Regular expressions (core notation) RE read is called a a symbol M N M or N alternative M N M followed by N concatenation ɛ the empty string epsilon M zero or more M repetition (Kleene star) (M) where a is a symbol in the alphabet (e.g., {0, 1} or UNICODE) and M and N are regular expressions Each regular expression defines a language over the alphabet (a set of strings that belong to the language). Priorities: M N P = M (N (P )) Compiler Construction 2013 F0213
16 Example a b c means Compiler Construction 2013 F0214
17 Example a b c means {a, b, bc, bcc, bccc,...} Compiler Construction 2013 F0214
18 Regular expressions with extended notation RE read is called a a symbol M N M or N alternative M N M followed by N concatenation ɛ the empty string epsilon M zero or more M repetition (Kleene star) (M) means M + at least one... M M M? optional... ɛ M [a za Z] one of... a b... z A... Z [0 9] not... one character, but not anyone of those listed a+b the string... a \+ b Compiler Construction 2013 F0215
19 Exercise Write a regular expression that defines the language of all decimal numbers, like But not numbers lacking an integer part. And not numbers with a decimal point but lacking a fractional part. So not numbers like Leading and trailing zeros are allowed. So the following numbers are ok: a) Use the extended notation. b) Then translate the expression to the core notation. c) Then write an expression that disallows leading zeros. Compiler Construction 2013 F0216
20 Solution a) [0 9] + (. [0 9] + )? b) (0... 9) (0... 9) (ɛ (. ((0... 9) (0... 9) ))) c) 0 (. [0 9] + )? [1 9] [0 9] (. [0 9] + )? Compiler Construction 2013 F0217
21 JavaCC notation Appel JavaCC ɛ M + M+ M? M? [a za Z] [ a  z, A  Z ] [ 09 ] a b c abc \n \n Compiler Construction 2013 F0218
22 JavaCC example... /* Skip whitespace */ SKIP : { " " "\t" "\n" "\r" } /* Reserved words */ TOKEN [IGNORE_CASE]: { < IF: "if"> < THEN: "then"> } /* Identifiers */ TOKEN: { < ID: (["A""Z", "a""z"])+ > } Compiler Construction 2013 F0219
23 ... JavaCC example /* Literals */ TOKEN: { < INT: (["0""9"])+ > } /* Operators and separators */ TOKEN: { < ASSIGN: "=" > < MULT: "*" > < LT: "<" > < LE: "<=" >... } Compiler Construction 2013 F0220
24 Ambiguous lexical definitions The scanned text can match tokens in more than one way Which tokens match <=? Compiler Construction 2013 F0221
25 Ambiguous lexical definitions The scanned text can match tokens in more than one way Which tokens match <=? Which tokens match if? Compiler Construction 2013 F0221
26 Extra rules for resolving the ambiguities Longest match If one rule can be used to match a token, but there is another rule that will match a longer token, the latter rule will be chosen. This way, the scanner will match the longest token possible. Compiler Construction 2013 F0222
27 Extra rules for resolving the ambiguities Longest match If one rule can be used to match a token, but there is another rule that will match a longer token, the latter rule will be chosen. This way, the scanner will match the longest token possible. Rule priority If two rules can be used to match the same sequence of characters, the first one takes priority. Compiler Construction 2013 F0222
28 Implementation of scanners Finite automata 1 i f 2 3 state IF a transition start state INT final state Compiler Construction 2013 F0223
29 More automata WHITESPACE ID Compiler Construction 2013 F0224
30 More automata WHITESPACE 1 \t \n ID a z a z 1 2 Compiler Construction 2013 F0225
31 Automaton for the whole language Combine the automata for individual tokens merge the start states reenumerate the states so they get unique numbers mark each final state with the token that is matched Compiler Construction 2013 F0226
32 Example 1 Combine IF and INT Compiler Construction 2013 F0227
33 Example 1 1 i f IF INT Compiler Construction 2013 F0228
34 Example 2 Combine IF and ID Compiler Construction 2013 F0229
35 Example 2 1 i f 2 3 a z0 9 IF a z 4 ID Compiler Construction 2013 F0230
36 Is the automaton deterministic? Compiler Construction 2013 F0231
37 Translating a RE to an NFA a MN M N M ɛ Compiler Construction 2013 F0232
38 DFA vs. NFA Deterministic Finite Automaton (DFA) A finite automaton is deterministic if all outgoing edges from any given node have disjoint character sets there are no ɛ edges (the empty string) Can be implemented efficiently Compiler Construction 2013 F0233
39 DFA vs. NFA Deterministic Finite Automaton (DFA) A finite automaton is deterministic if all outgoing edges from any given node have disjoint character sets there are no ɛ edges (the empty string) Can be implemented efficiently Nondeterministic Finite Automaton (NFA) An NFA may have two outgoing edges with overlapping character sets ɛedges DFA NFA Compiler Construction 2013 F0233
40 Each NFA can be translated to a DFA Simulate the NFA keep track of a set of current NFAstates follow ɛ edges to extend the current set (take the closure) Construct the corresponding DFA Each such set of NFA states corresponds to one DFA state If any of the NFA states are final, the DFA state is also final, and is marked with the corresponding token. If there is more than one token to choose from, select the token that is defined first (rule priority) (Minimize the DFA for efficiency) Compiler Construction 2013 F0234
41 Translate an NFA to a DFA NFA start 1 f 2 3 i az az 4 ID IF Compiler Construction 2013 F0235
42 Translate an NFA to a DFA NFA 2 f 3 i IF start 1 az az 4 ID DFA 2,4 f 3,4 i aegz IF start 1 az az ahjz 4 ID Compiler Construction 2013 F0236
43 Construction of a Scanner Define all tokens as regular expressions Construct a finite automaton for each token Combine all these automata to a new automaton (an NFA in general) Translate to a corresponding DFA Minimize the DFA Implement the DFA Compiler Construction 2013 F0237
44 Implementation alternatives for DFAs Tabledriven Represent the automaton by a table Additional table to keep track of final states and token kinds A global variable keeps track of the current state Compiler Construction 2013 F0238
45 Implementation alternatives for DFAs Tabledriven Represent the automaton by a table Additional table to keep track of final states and token kinds A global variable keeps track of the current state Switch statements Each state is implemented as a switch statement Each case implements a state transition as a jump (to another switch statement). The current state is represented by the program counter Compiler Construction 2013 F0238
46 Error handling Add a dead state (state 0), corresponding to erroneous input Add transitions to the dead state for all erroneous input Generate an Error token when the dead state is reached Compiler Construction 2013 F0239
47 Tabledriven implementation DFA for IF and ID 1 2,4 3,4 4.. ae f gh i jz.. final kind true ERROR Compiler Construction 2013 F0240
48 Tabledriven implementation DFA for IF and ID.. ae f gh i jz.. final kind 0 true ERROR ,4 4 0 false 2, , true ID 3, true IF true ID Compiler Construction 2013 F0241
49 Design Token int kind String string Parser Scanner Token next() Reader int get() Compiler Construction 2013 F0242
50 Scanner (sketch) class Scanner { PushbackReader reader; boolean isfinal [ ]; int edges [ ] [ ]; int kind [ ]; Token next() { } } Compiler Construction 2013 F0243
51 Scanner (sketch) class Scanner { //does not handle: PushbackReader reader; //longest match boolean isfinal [ ]; //eof int edges [ ] [ ]; //whitespace int kind [ ]; //token strings Token next() { int state = 1; //start state while(!isfinal[state]) { char ch = reader.read(); state = edges[state][ch]; } return new Token(kind[state]); } } Compiler Construction 2013 F0244
52 Handling EndOfFile (EOF) and nontokens Compiler Construction 2013 F0245
53 Handling EndOfFile (EOF) and nontokens EOF construct an explicit EOF token when the EOF character is read Nontokens (Whitespace & Comments) Errors view as tokens of a special kind scan them as normal tokens, but don t create token objects for them loop in next() until a real token has been found construct an explicit ERROR token to be returned when no valid token can be found. Compiler Construction 2013 F0245
54 Handling longest match When a token is matched (a final state reached), don t stop scanning. Keep track of the latest matched token in a variable. Continue scanning until we reach the dead state Restore the input stream. Use PushbackReader to be able to do this. Return the latest matched token (or return the ERROR token if there was no latest matched token) Compiler Construction 2013 F0246
55 Scanner with longest match class Scanner {... Token next() { } } Compiler Construction 2013 F0247
56 Scanner with longest match class Scanner {... Token next() { int state = 1, lastfinalstate = 0; int lastfinalstr = "": StringBuilder builder = new StringBuilder(); while(state!=0) { char ch = reader.read(); builder.append(ch); state = edges[state][ch]; if(isfinal[state]) { lastfinalstate = state; lastfinalstr = builder.tostring(); } } reader.unread(... ); //unused characters return new Token(kind[lastFinalState], lastfinalstr); } Compiler Construction 2013 F0248
57 JavaCC as a scanner generator toy.jj sum.toy javacc ToyTokenManager.java ToyConstants.java...java tokens Compiler Construction 2013 F0249
58 Other scanner generators tool author implementation generates lex Schmidt, Lesk, 1975 tabledriven C code flex Paxon switch statements C code jlex tabledriven Java code jflex switch statements Java code Compiler Construction 2013 F0250
59 Additional functionality Lexical actions extra (Java) code written in the specification for adapting the generated scanner e.g., create special token objects, count tokens, keep track of position in input text (line and column numbers), etc. Compiler Construction 2013 F0251
60 Additional functionality Lexical actions extra (Java) code written in the specification for adapting the generated scanner e.g., create special token objects, count tokens, keep track of position in input text (line and column numbers), etc. Lexical states ( start states ) gives the possibility to switch automata during scanning makes it easier to scan certain tokens, e.g., multiline comments makes it possible to scan certain combined languages, e.g., HTML Compiler Construction 2013 F0251
61 Lexcial states, example Scanning of /*... */ Compiler Construction 2013 F0252
62 Summary questions What is meant by an ambiguous lexical definition? Give some typical examples of this and how they may be resolved. Construct an NFA for a given lexical definition Construct a DFA for a given NFA What is the difference between a DFA and an NFA? Implement a DFA in Java. How is rule priority handled in the implementation? How is longest match handled? EOF? Whitespace? Compiler Construction 2013 F0253
63 What s next? Tomorrow: Seminar 1 (Scanning) Next week: Parsing and Assignment 1 (Scanning) Compiler Construction 2013 F0254
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