Compiler Design Spring 2017
|
|
- Wesley Jones
- 5 years ago
- Views:
Transcription
1 Compiler Design Spring Bottom-up parsing Dr. Zoltán Majó Compiler Group Java HotSpot Virtual Machine Oracle Corporation 1
2 Bottom up parsing Goal: Obtain rightmost derivation in reverse w S Reduce input string w to start symbol S Parser (stack machine) supports four actions Accept Error Shift Read input, push onto stack (and add appropriate control symbols) Reduce Using A à b b = X 1 X 2 X m X i T NT Remove b = X 1 X 2 X m from the stack, add A to stack (And add/remove appropriate control symbols) 3
3 Handles Key issue: How to identify b to be used in reduction A à b? b is the handle if it can be used in the next reduction step On the way from w to S In the reverse right-most derivation Bottom up parsing = handle pruning 4
4 or signal error 5
5 Idea: Simulate derivations Simulate all possible derivations b to determine if b is the handle for A à b Use item to lay out simulation Item: production with dot ( ) in right hand side Item uses a dot to mark progress (i.e., to mark parts of b that have been already explored) Part of b to the left of the dot has already been explored Item example [A à b ] We ve not explored any part of the right hand side of this production Generic example [A à a b ] We ve explored a and are about to explore b 6
6 Item set construction Given grammar G, (new) start symbol S Three steps to construct item sets 1. Put item [S à S] into initial item set I 0. I 0 = {[S à S]} 2. Compute closure of (any) item set I k Start with I 0 Closure: simulate possible derivations 3. Generate new item sets according to the goto transition function Simulate building up handle Continue until no more changes No more sets can be generated with goto or closed with closure 7
7 Example S à S S à b X Y c X à b X b Y à d Consider this grammar: S à b X Y c X à b X b Y à d First step: insert new start symbol S S à S S à b X Y c X à b X b Y à d 10
8 Item set construction Given grammar G, (new) start symbol S Three steps to construct item sets 1. Put item [S à S] into initial item set I 0. I 0 = {[S à S]} 2. Compute closure of (any) item set I k Start with I 0 Closure: simulate possible derivations 3. Generate new item sets according to the goto transition function Simulate building up handle Continue until no more changes No more sets can be generated or closed with closure 11
9 3.4.1 Closure (for Rule 2) Given an item set I k To compute Closure(I k ) consider all items [ A à a Z b ] in I k such that Z NT For all productions with Z on the left hand side (e.g., Z à z) add the item [ Z à z ] to I k Until no more items can be added to I k Informally: Closure(I k ) = I k { items that can be formed with productions of Z NT if there is an item with the dot in front of Z in the set } 14
10 3.4.2 Goto transition function Given an item set I k, Z T NT Goto (I k, Z) = I j is defined as follows: For all items [ A à a Z b ] in I k add [ A à a Z b ] to I j Recall that a, b may be e 17
11 Example S à S S à b X Y c X à b X b Y à d I 0 = { [S à S]} Closure(I 0 ) = { [S à S], [ S à b X Y c] } Goto(I 0, S) = { [S à S ] } = I 1 Goto(I 0, b) = { [S à b X Y c] } = I 2 18
12 Example S à S S à b X Y c X à b X b Y à d I 0 = { [S à S]} Closure(I 0 ) = { [S à S], [ S à b X Y c] } Goto(I 0, S) = { [S à S ] } = I 1 Goto(I 0, b) = { [S à b X Y c] } = I 2 Closure(I 2 ) = { [S à b X Y c], [X à b X], [X à b] } Goto(I 2, X) = { [S à b X Y c] } = I 3 Closure(I 3 ) = { [S à b X Y c], [ Y à d] } Goto(I 3, Y) = { [S à b X Y c] } = I 4 Goto(I 3, d) = { [Y à d ] } = I 5 Goto(I 4, c) = { [S à b X Y c ] } = I 6 Goto(I 2,b) = { [X à b X], [X à b ] } = I 7 Closure(I 7 ) = { [X à b X], [X à b ], [X à b X], [X à b] } Goto(I 7,X) = { [X à b X ]} = I 8 Goto(I 7,b) = { [X à b X], [X à b ] } = I 9 Closure(I 9 ) = { [X à b X], [X à b ], [X à b X], [X à b] } = I 7 Goto(I 7,b) = I 7 20
13 Transition diagram Remember: Item sets represent states of a FSM 21
14 23
15 24
16 What we ve done so far Constructed item sets and resulting FSM Item sets are states of the FSM FSM represents simulation of all possible derivations of grammar G Next: Use item sets and FSM to build control table M Remember: M is the grammar-specific part of the parser 25
17 Control table and states Item sets (states) and goto function (transitions) determine the setup of M Four rules 1. If item [ A à a a b ] I j, a T, and goto(i j, a) = I k then action(i j, a) : shift a; new state I k 2. If item [ A à a ] I j and t FOLLOW(A) then action(i j, t) : reduce A à a New state determined by goto(i k, A) with I k on top of the stack after removing a (and states interspersed with a) 26
18 27
19 Control table and states (continued) 3. If item [ S à S ] is in I j then action(i j, $) : accept 4. All other entries are error 29
20 Example Productions S à S S à b X Y c X à b X b Y à d Follow sets: FOLLOW(S ) = FOLLOW(S) = {$} FOLLOW(X) = {d} FOLLOW(Y) = {c} 30
21 32
22 Productions S à S S à b X Y c X à b X b Y à d Follow sets: FOLLOW(S ) = {$} FOLLOW(S) = {$} FOLLOW(X) = {d} FOLLOW(Y) = {c} State Action Goto b c d $ S X Y 33
23 34
24 35
25 36
26 37
27 38
28 39
29 40
30 41
31 8 42
32 45
33 46
34 Predictive parsing There cannot be a conflict between shifting and reducing, e.g. action(i j, t) : shift and action(i j, t) : reduce This is called a shift-reduce conflict It must be clear which production to use when reducing action(i j, t) : reduce X à a and action(i j, t) : reduce Y à b This is called a reduce-reduce conflict 47
35 Bottom-up parsing in perspective Items LR(0) items Did not use any info about context when constructing the items FOLLOW() entered the picture when we set up the parsing table M Parser: simple LR(1) parser 1 because one input symbol is used Simple because we take the LR(0) items Known as SLR (or SLR(1)) parser Grammar said to be an SLR(1) grammar 48
36 SLR(1) grammars SLR(1) grammars are unambiguous Proof by construction SLR parsers don t work for many programming language constructs 49
37 51
38 Is G SLR(1)? S à S S à X x X y Y y Y x X à e Y à e Item set I 0 : { } [S à S], [S à X x X y] [S à Y y Y x] [X à ] [Y à ] FOLLOW(X) = FOLLOW(Y) = {x, y} M[I 0, x ] = M[I 0, y ] : {reduce X à e, reduce Y à e } A reduce-reduce conflict Parser cannot decide which production to use 52
39 More on G What would the top-down predictive parser of 3.3 do? S à X x X y Y y Y x X à e Y à e G is unambiguous G is LL(1) (But not SLR(1)) 53
40 Boundaries Problem is construction of LR(0) items LR(0) does not consider (left) context (Over)approximate by using FOLLOW(X) to decide when to reduce X à e Solution: More accurate construction of item sets Introduce context information into item Context: Next input Canonical LR parsing Canonical LR often referred to as LR 54
41 Canonical LR parsing Use LR(1) items Like LR(0) but with look-ahead LR(1) has look-ahead of 1 Larger look-aheads are possible LR(1) item format: [ A à a, t ] (Instead of [ A à a ] as in case of LR(0)) t T t is the look-ahead symbol Reduce with a on top of the stack only if the next input symbol is t If item is [A à a b, t ] with b e : look-ahead has no effect Parsing table for M [ X, t] set to reduce A à a only for those t where [A à a, t ] item set X Subset of FOLLOW(A) 55
42 57
43 58
44 61
45 Canonical LR parsing Same approach as explained for SLR parsing However, the number of states generated is higher SLR ~100s of states, canonical LR: ~1000s of states (for a language like C) Memory usage is (was) an issue 63
46 Variations Lookahead LR(1) LALR Reduced number of states Same number of states as SLR(1) Very popular (yacc and bison) 64
47 Grammar world From 65
48 Parser generators Parsers are not constructed by hand Generation of LR(0) items, LR(1) items can be automated Also generation of LL(1), LL(2), parsers Parser generator: Takes grammar and constructs parser Or reports shift/reduce or reduce/reduce conflicts Time to rework the grammar or use other parser generator Popular parser generators Yacc Bison ANTLR JavaCUP ( Construction of Useful Parsers ) 66
49 Further topics Error handling Report meaningful information in case w L(G) At least line number of suspected error Not syntax error Should the parser repair input? Efficiency Missing semi-colon Grammar massaging LL(1) tends to require more work as common prefixes must be factored out Syntax analysis as you type ( on the fly ) 67
I 1 : {S S } I 2 : {S X ay, Y X } I 3 : {S Y } I 4 : {X b Y, Y X, X by, X c} I 5 : {X c } I 6 : {S Xa Y, Y X, X by, X c} I 7 : {X by } I 8 : {Y X }
Let s try building an SLR parsing table for another simple grammar: S XaY Y X by c Y X S XaY Y X by c Y X Canonical collection: I 0 : {S S, S XaY, S Y, X by, X c, Y X} I 1 : {S S } I 2 : {S X ay, Y X }
More informationShift-Reduce parser E + (E + (E) E [a-z] In each stage, we shift a symbol from the input to the stack, or reduce according to one of the rules.
Bottom-up Parsing Bottom-up Parsing Until now we started with the starting nonterminal S and tried to derive the input from it. In a way, this isn t the natural thing to do. It s much more logical to start
More informationSyntax Analysis (Part 2)
Syntax Analysis (Part 2) Martin Sulzmann Martin Sulzmann Syntax Analysis (Part 2) 1 / 42 Bottom-Up Parsing Idea Build right-most derivation. Scan input and seek for matching right hand sides. Terminology
More informationParsing -3. A View During TD Parsing
Parsing -3 Deterministic table-driven parsing techniques Pictorial view of TD and BU parsing BU (shift-reduce) Parsing Handle, viable prefix, items, closures, goto s LR(k): SLR(1), LR(1) Problems with
More informationBottom-Up Parsing. Ÿ rm E + F *idÿ rm E +id*idÿ rm T +id*id. Ÿ rm F +id*id Ÿ rm id + id * id
Bottom-Up Parsing Attempts to traverse a parse tree bottom up (post-order traversal) Reduces a sequence of tokens to the start symbol At each reduction step, the RHS of a production is replaced with LHS
More informationCS 406: Bottom-Up Parsing
CS 406: Bottom-Up Parsing Stefan D. Bruda Winter 2016 BOTTOM-UP PUSH-DOWN AUTOMATA A different way to construct a push-down automaton equivalent to a given grammar = shift-reduce parser: Given G = (N,
More informationCA Compiler Construction
CA4003 - Compiler Construction Bottom Up Parsing David Sinclair Bottom Up Parsing LL(1) parsers have enjoyed a bit of a revival thanks to JavaCC. LL(k) parsers must predict which production rule to use
More informationLR2: LR(0) Parsing. LR Parsing. CMPT 379: Compilers Instructor: Anoop Sarkar. anoopsarkar.github.io/compilers-class
LR2: LR(0) Parsing LR Parsing CMPT 379: Compilers Instructor: Anoop Sarkar anoopsarkar.github.io/compilers-class Parsing - Roadmap Parser: decision procedure: builds a parse tree Top-down vs. bottom-up
More informationCompiler Design 1. LR Parsing. Goutam Biswas. Lect 7
Compiler Design 1 LR Parsing Compiler Design 2 LR(0) Parsing An LR(0) parser can take shift-reduce decisions entirely on the basis of the states of LR(0) automaton a of the grammar. Consider the following
More informationBottom up parsing. General idea LR(0) SLR LR(1) LALR To best exploit JavaCUP, should understand the theoretical basis (LR parsing);
Bottom up parsing General idea LR(0) SLR LR(1) LALR To best exploit JavaCUP, should understand the theoretical basis (LR parsing); 1 Top-down vs Bottom-up Bottom-up more powerful than top-down; Can process
More informationAnnouncements. H6 posted 2 days ago (due on Tue) Midterm went well: Very nice curve. Average 65% High score 74/75
Announcements H6 posted 2 days ago (due on Tue) Mterm went well: Average 65% High score 74/75 Very nice curve 80 70 60 50 40 30 20 10 0 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106
More informationCompiler Construction Lectures 13 16
Compiler Construction Lectures 13 16 Lent Term, 2013 Lecturer: Timothy G. Griffin 1 Generating Lexical Analyzers Source Program Lexical Analyzer tokens Parser Lexical specification Scanner Generator LEX
More informationComputer Science 160 Translation of Programming Languages
Computer Science 160 Translation of Programming Languages Instructor: Christopher Kruegel Building a Handle Recognizing Machine: [now, with a look-ahead token, which is LR(1) ] LR(k) items An LR(k) item
More informationΕΠΛ323 - Θεωρία και Πρακτική Μεταγλωττιστών. Lecture 7a Syntax Analysis Elias Athanasopoulos
ΕΠΛ323 - Θεωρία και Πρακτική Μεταγλωττιστών Lecture 7a Syntax Analysis Elias Athanasopoulos eliasathan@cs.ucy.ac.cy Operator-precedence Parsing A class of shiq-reduce parsers that can be writen by hand
More informationAdministrivia. Test I during class on 10 March. Bottom-Up Parsing. Lecture An Introductory Example
Administrivia Test I during class on 10 March. Bottom-Up Parsing Lecture 11-12 From slides by G. Necula & R. Bodik) 2/20/08 Prof. Hilfinger CS14 Lecture 11 1 2/20/08 Prof. Hilfinger CS14 Lecture 11 2 Bottom-Up
More informationCompiler Construction Lent Term 2015 Lectures (of 16)
Compiler Construction Lent Term 2015 Lectures 13 --- 16 (of 16) 1. Return to lexical analysis : application of Theory of Regular Languages and Finite Automata 2. Generating Recursive descent parsers 3.
More informationSyntax Analysis Part I
1 Syntax Analysis Part I Chapter 4 COP5621 Compiler Construction Copyright Robert van Engelen, Florida State University, 2007-2013 2 Position of a Parser in the Compiler Model Source Program Lexical Analyzer
More informationCompiler Construction Lent Term 2015 Lectures (of 16)
Compiler Construction Lent Term 2015 Lectures 13 --- 16 (of 16) 1. Return to lexical analysis : application of Theory of Regular Languages and Finite Automata 2. Generating Recursive descent parsers 3.
More informationSyntax Analysis Part I
1 Syntax Analysis Part I Chapter 4 COP5621 Compiler Construction Copyright Robert van Engelen, Florida State University, 2007-2013 2 Position of a Parser in the Compiler Model Source Program Lexical Analyzer
More informationTHEORY OF COMPILATION
Lecture 04 Syntax analysis: top-down and bottom-up parsing THEORY OF COMPILATION EranYahav 1 You are here Compiler txt Source Lexical Analysis Syntax Analysis Parsing Semantic Analysis Inter. Rep. (IR)
More informationLR(1) Parsers Part III Last Parsing Lecture. Copyright 2010, Keith D. Cooper & Linda Torczon, all rights reserved.
LR(1) Parsers Part III Last Parsing Lecture Copyright 2010, Keith D. Cooper & Linda Torczon, all rights reserved. LR(1) Parsers A table-driven LR(1) parser looks like source code Scanner Table-driven Parser
More informationEXAM. CS331 Compiler Design Spring Please read all instructions, including these, carefully
EXAM Please read all instructions, including these, carefully There are 7 questions on the exam, with multiple parts. You have 3 hours to work on the exam. The exam is open book, open notes. Please write
More informationEXAM. CS331 Compiler Design Spring Please read all instructions, including these, carefully
EXAM Please read all instructions, including these, carefully There are 7 questions on the exam, with multiple parts. You have 3 hours to work on the exam. The exam is open book, open notes. Please write
More informationSyntax Analysis Part I. Position of a Parser in the Compiler Model. The Parser. Chapter 4
1 Syntax Analysis Part I Chapter 4 COP5621 Compiler Construction Copyright Robert van ngelen, Flora State University, 2007 Position of a Parser in the Compiler Model 2 Source Program Lexical Analyzer Lexical
More informationBottom-Up Syntax Analysis
Bottom-Up Syntax Analysis Mooly Sagiv http://www.cs.tau.ac.il/~msagiv/courses/wcc13.html Textbook:Modern Compiler Design Chapter 2.2.5 (modified) 1 Pushdown automata Deterministic fficient Parsers Report
More informationIntroduction to Bottom-Up Parsing
Introduction to Bottom-Up Parsing Outline Review LL parsing Shift-reduce parsing The LR parsing algorithm Constructing LR parsing tables Compiler Design 1 (2011) 2 Top-Down Parsing: Review Top-down parsing
More information1. For the following sub-problems, consider the following context-free grammar: S AA$ (1) A xa (2) A B (3) B yb (4)
ECE 468 & 573 Problem Set 2: Contet-free Grammars, Parsers 1. For the following sub-problems, consider the following contet-free grammar: S $ (1) (2) (3) (4) λ (5) (a) What are the terminals and non-terminals
More informationIntroduction to Bottom-Up Parsing
Outline Introduction to Bottom-Up Parsing Review LL parsing Shift-reduce parsing he LR parsing algorithm Constructing LR parsing tables Compiler Design 1 (2011) 2 op-down Parsing: Review op-down parsing
More informationn Top-down parsing vs. bottom-up parsing n Top-down parsing n Introduction n A top-down depth-first parser (with backtracking)
Announcements n Quiz 1 n Hold on to paper, bring over at the end n HW1 due today n HW2 will be posted tonight n Due Tue, Sep 18 at 2pm in Submitty! n Team assignment. Form teams in Submitty! n Top-down
More informationLecture VII Part 2: Syntactic Analysis Bottom-up Parsing: LR Parsing. Prof. Bodik CS Berkley University 1
Lecture VII Part 2: Syntactic Analysis Bottom-up Parsing: LR Parsing. Prof. Bodik CS 164 -- Berkley University 1 Bottom-Up Parsing Bottom-up parsing is more general than topdown parsing And just as efficient
More informationIntroduction to Bottom-Up Parsing
Introduction to Bottom-Up Parsing Outline Review LL parsing Shift-reduce parsing The LR parsing algorithm Constructing LR parsing tables 2 Top-Down Parsing: Review Top-down parsing expands a parse tree
More informationParsing Algorithms. CS 4447/CS Stephen Watt University of Western Ontario
Parsing Algorithms CS 4447/CS 9545 -- Stephen Watt University of Western Ontario The Big Picture Develop parsers based on grammars Figure out properties of the grammars Make tables that drive parsing engines
More informationCreating a Recursive Descent Parse Table
Creating a Recursive Descent Parse Table Recursive descent parsing is sometimes called LL parsing (Left to right examination of input, Left derivation) Consider the following grammar E TE' E' +TE' T FT'
More informationIntroduction to Bottom-Up Parsing
Outline Introduction to Bottom-Up Parsing Review LL parsing Shift-reduce parsing he LR parsing algorithm Constructing LR parsing tables 2 op-down Parsing: Review op-down parsing expands a parse tree from
More informationLR(1) Parsers Part II. Copyright 2010, Keith D. Cooper & Linda Torczon, all rights reserved.
LR(1) Parsers Part II Copyright 2010, Keith D. Cooper & Linda Torczon, all rights reserved. Building LR(1) Tables : ACTION and GOTO How do we build the parse tables for an LR(1) grammar? Use grammar to
More informationCompiler Construction
Compiler Construction Thomas Noll Software Modeling and Verification Group RWTH Aachen University https://moves.rwth-aachen.de/teaching/ss-16/cc/ Recap: LR(0) Grammars LR(0) Grammars The case k = 0 is
More informationSyntax Analysis, VI Examples from LR Parsing. Comp 412
COMP 412 FALL 2017 Syntax Analysis, VI Examples from LR Parsing Comp 412 source code IR IR target code Front End Optimizer Back End Copyright 2017, Keith D. Cooper & Linda Torczon, all rights reserved.
More informationEXAM. Please read all instructions, including these, carefully NAME : Problem Max points Points 1 10 TOTAL 100
EXAM Please read all instructions, including these, carefully There are 7 questions on the exam, with multiple parts. You have 3 hours to work on the exam. The exam is open book, open notes. Please write
More information1. For the following sub-problems, consider the following context-free grammar: S AB$ (1) A xax (2) A B (3) B yby (5) B A (6)
ECE 468 & 573 Problem Set 2: Contet-free Grammars, Parsers 1. For the following sub-problems, consider the following contet-free grammar: S AB$ (1) A A (2) A B (3) A λ (4) B B (5) B A (6) B λ (7) (a) What
More informationLecture 11 Sections 4.5, 4.7. Wed, Feb 18, 2009
The s s The s Lecture 11 Sections 4.5, 4.7 Hampden-Sydney College Wed, Feb 18, 2009 Outline The s s 1 s 2 3 4 5 6 The LR(0) Parsing s The s s There are two tables that we will construct. The action table
More informationINF5110 Compiler Construction
INF5110 Compiler Construction Parsing Spring 2016 1 / 131 Outline 1. Parsing Bottom-up parsing Bibs 2 / 131 Outline 1. Parsing Bottom-up parsing Bibs 3 / 131 Bottom-up parsing: intro LR(0) SLR(1) LALR(1)
More informationParsing VI LR(1) Parsers
Parsing VI LR(1) Parsers N.B.: This lecture uses a left-recursive version of the SheepNoise grammar. The book uses a rightrecursive version. The derivations (& the tables) are different. Copyright 2005,
More informationCurs 8. LR(k) parsing. S.Motogna - FL&CD
Curs 8 LR(k) parsing Terms Reminder: rhp = right handside of production lhp = left handside of production Prediction see LL(1) Handle = symbols from the head of the working stack that form (in order) a
More informationLR(1) Parsers Part II. Copyright 2010, Keith D. Cooper & Linda Torczon, all rights reserved.
LR(1) Parsers Part II Copyright 2010, Keith D. Cooper & Linda Torczon, all rights reserved. LR(1) Parsers A table-driven LR(1) parser looks like source code Scanner Table-driven Parser IR grammar Parser
More informationBriefly on Bottom-up
Briefly on Bottom-up Paola Quaglia University of Trento November 11, 2017 Abstract These short notes provide descriptions and references relative to the construction of parsing tables for SLR(1), for LR(1),
More informationTop-Down Parsing and Intro to Bottom-Up Parsing
Predictive Parsers op-down Parsing and Intro to Bottom-Up Parsing Lecture 7 Like recursive-descent but parser can predict which production to use By looking at the next few tokens No backtracking Predictive
More informationWhy augment the grammar?
Why augment the grammar? Consider -> F + F FOLLOW F -> i ---------------- 0:->.F+ ->.F F->.i i F 2:F->i. Action Goto + i $ F ----------------------- 0 s2 1 1 s3? 2 r3 r3 3 s2 4 1 4? 1:->F.+ ->F. i 4:->F+.
More informationCS415 Compilers Syntax Analysis Bottom-up Parsing
CS415 Compilers Syntax Analysis Bottom-up Parsing These slides are based on slides copyrighted by Keith Cooper, Ken Kennedy & Linda Torczon at Rice University Review: LR(k) Shift-reduce Parsing Shift reduce
More informationTranslator Design Lecture 16 Constructing SLR Parsing Tables
SLR Simple LR An LR(0) item (item for short) of a grammar G is a production of G with a dot at some position of the right se. Thus, production A XYZ yields the four items AA XXXXXX AA XX YYYY AA XXXX ZZ
More informationChapter 4: Bottom-up Analysis 106 / 338
Syntactic Analysis Chapter 4: Bottom-up Analysis 106 / 338 Bottom-up Analysis Attention: Many grammars are not LL(k)! A reason for that is: Definition Grammar G is called left-recursive, if A + A β for
More informationSyntax Analysis, VII The Canonical LR(1) Table Construction. Comp 412
COMP 412 FALL 2018 Syntax Analysis, VII The Canonical LR(1) Table Construction Comp 412 source code IR IR target Front End Optimizer Back End code Copyright 2018, Keith D. Cooper & Linda Torczon, all rights
More informationCMSC 330: Organization of Programming Languages. Pushdown Automata Parsing
CMSC 330: Organization of Programming Languages Pushdown Automata Parsing Chomsky Hierarchy Categorization of various languages and grammars Each is strictly more restrictive than the previous First described
More informationCS20a: summary (Oct 24, 2002)
CS20a: summary (Oct 24, 2002) Context-free languages Grammars G = (V, T, P, S) Pushdown automata N-PDA = CFG D-PDA < CFG Today What languages are context-free? Pumping lemma (similar to pumping lemma for
More informationComputing if a token can follow
Computing if a token can follow first(b 1... B p ) = {a B 1...B p... aw } follow(x) = {a S......Xa... } There exists a derivation from the start symbol that produces a sequence of terminals and nonterminals
More informationBottom-up syntactic parsing. LR(k) grammars. LR(0) grammars. Bottom-up parser. Definition Properties
Course 9-10 1 Bottom-up syntactic parsing Bottom-up parser LR(k) grammars Definition Properties LR(0) grammars Characterization theorem for LR(0) LR(0) automaton 2 a 1... a i... a n # X 1 X 1 Control Parsing
More informationProf. Mohamed Hamada Software Engineering Lab. The University of Aizu Japan
Language Processing Systems Prof. Mohamed Hamada Software Engineering La. The University of izu Japan Syntax nalysis (Parsing) 1. Uses Regular Expressions to define tokens 2. Uses Finite utomata to recognize
More informationBottom-Up Syntax Analysis
Bottom-Up Syntax Analysis Wilhelm/Maurer: Compiler Design, Chapter 8 Reinhard Wilhelm Universität des Saarlandes wilhelm@cs.uni-sb.de and Mooly Sagiv Tel Aviv University sagiv@math.tau.ac.il Subjects Functionality
More informationBottom-up syntactic parsing. LR(k) grammars. LR(0) grammars. Bottom-up parser. Definition Properties
Course 8 1 Bottom-up syntactic parsing Bottom-up parser LR(k) grammars Definition Properties LR(0) grammars Characterization theorem for LR(0) LR(0) automaton 2 a 1... a i... a n # X 1 X 1 Control Parsing
More informationBottom-up syntactic parsing. LR(k) grammars. LR(0) grammars. Bottom-up parser. Definition Properties
Course 8 1 Bottom-up syntactic parsing Bottom-up parser LR(k) grammars Definition Properties LR(0) grammars Characterization theorem for LR(0) LR(0) automaton 2 a 1... a i... a n # X 1 X 1 Control Parsing
More informationSyntax Analysis, VII The Canonical LR(1) Table Construction. Comp 412 COMP 412 FALL Chapter 3 in EaC2e. source code. IR IR target.
COMP 412 FALL 2017 Syntax Analysis, VII The Canonical LR(1) Table Construction Comp 412 source code IR IR target Front End Optimizer Back End code Copyright 2017, Keith D. Cooper & Linda Torczon, all rights
More informationSyntax Analysis Part III
Syntax Analysis Part III Chapter 4: Top-Down Parsing Slides adapted from : Robert van Engelen, Florida State University Eliminating Ambiguity stmt if expr then stmt if expr then stmt else stmt other The
More informationSyntactic Analysis. Top-Down Parsing
Syntactic Analysis Top-Down Parsing Copyright 2015, Pedro C. Diniz, all rights reserved. Students enrolled in Compilers class at University of Southern California (USC) have explicit permission to make
More informationBottom-Up Syntax Analysis
Bottom-Up Syntax Analysis Wilhelm/Seidl/Hack: Compiler Design Syntactic and Semantic Analysis, Chapter 3 Reinhard Wilhelm Universität des Saarlandes wilhelm@cs.uni-saarland.de and Mooly Sagiv Tel Aviv
More informationCS415 Compilers Syntax Analysis Top-down Parsing
CS415 Compilers Syntax Analysis Top-down Parsing These slides are based on slides copyrighted by Keith Cooper, Ken Kennedy & Linda Torczon at Rice University Announcements Midterm on Thursday, March 13
More informationCompilerconstructie. najaar Rudy van Vliet kamer 124 Snellius, tel rvvliet(at)liacs.
Compilerconstructie najaar 2012 http://www.liacs.nl/home/rvvliet/coco/ Rudy van Vliet kamer 124 Snellius, tel. 071-527 5777 rvvliet(at)liacs.nl werkcollege 9, dinsdag 27 november 2012 SLR Parsing / Backpatching
More informationContext free languages
Context free languages Syntatic parsers and parse trees E! E! *! E! (! E! )! E + E! id! id! id! 2 Context Free Grammars The CF grammar production rules have the following structure X α being X N and α
More informationCSE302: Compiler Design
CSE302: Compiler Design Instructor: Dr. Liang Cheng Department of Computer Science and Engineering P.C. Rossin College of Engineering & Applied Science Lehigh University February 27, 2007 Outline Recap
More informationSyntax Analysis: Context-free Grammars, Pushdown Automata and Parsing Part - 3. Y.N. Srikant
Syntax Analysis: Context-free Grammars, Pushdown Automata and Part - 3 Department of Computer Science and Automation Indian Institute of Science Bangalore 560 012 NPTEL Course on Principles of Compiler
More informationCompiling Techniques
Lecture 6: 9 October 2015 Announcement New tutorial session: Friday 2pm check ct course webpage to find your allocated group Table of contents 1 2 Ambiguity s Bottom-Up Parser A bottom-up parser builds
More informationAmbiguity, Precedence, Associativity & Top-Down Parsing. Lecture 9-10
Ambiguity, Precedence, Associativity & Top-Down Parsing Lecture 9-10 (From slides by G. Necula & R. Bodik) 2/13/2008 Prof. Hilfinger CS164 Lecture 9 1 Administrivia Team assignments this evening for all
More informationContext-Free and Noncontext-Free Languages
Examples: Context-Free and Noncontext-Free Languages a*b* is regular. A n B n = {a n b n : n 0} is context-free but not regular. A n B n C n = {a n b n c n : n 0} is not context-free The Regular and the
More informationBottom-Up Syntax Analysis
Bottom-Up Syntax Analysis Wilhelm/Seidl/Hack: Compiler Design Syntactic and Semantic Analysis Reinhard Wilhelm Universität des Saarlandes wilhelm@cs.uni-saarland.de and Mooly Sagiv Tel Aviv University
More information1. For the following sub-problems, consider the following context-free grammar: S A$ (1) A xbc (2) A CB (3) B yb (4) C x (6)
ECE 468 & 573 Problem Set 2: Contet-free Grammars, Parsers (Solutions) 1. For the following sub-problems, consider the following contet-free grammar: S A$ (1) A C (2) A C (3) y (4) λ (5) C (6) (a) What
More informationCompiler Design. Spring Syntactic Analysis. Sample Exercises and Solutions. Prof. Pedro C. Diniz
Compiler Design Spring 2015 Syntactic Analysis Sample Exercises and Solutions Prof. Pedro C. Diniz USC / Information Sciences Institute 4676 Admiralty Way, Suite 1001 Marina del Rey, California 90292 pedro@isi.edu
More informationFollow sets. LL(1) Parsing Table
Follow sets. LL(1) Parsing Table Exercise Introducing Follow Sets Compute nullable, first for this grammar: stmtlist ::= ε stmt stmtlist stmt ::= assign block assign ::= ID = ID ; block ::= beginof ID
More informationCompiler Principles, PS4
Top-Down Parsing Compiler Principles, PS4 Parsing problem definition: The general parsing problem is - given set of rules and input stream (in our case scheme token input stream), how to find the parse
More informationPredictive parsing as a specific subclass of recursive descent parsing complexity comparisons with general parsing
Plan for Today Recall Predictive Parsing when it works and when it doesn t necessary to remove left-recursion might have to left-factor Error recovery for predictive parsers Predictive parsing as a specific
More informationINF5110 Compiler Construction
INF5110 Compiler Construction Parsing Spring 2016 1 / 84 Overview First and Follow set: general concepts for grammars textbook looks at one parsing technique (top-down) [Louden, 1997, Chap. 4] before studying
More informationCS153: Compilers Lecture 5: LL Parsing
CS153: Compilers Lecture 5: LL Parsing Stephen Chong https://www.seas.harvard.edu/courses/cs153 Announcements Proj 1 out Due Thursday Sept 20 (2 days away) Proj 2 out Due Thursday Oct 4 (16 days away)
More informationType 3 languages. Type 2 languages. Regular grammars Finite automata. Regular expressions. Type 2 grammars. Deterministic Nondeterministic.
Course 7 1 Type 3 languages Regular grammars Finite automata Deterministic Nondeterministic Regular expressions a, a, ε, E 1.E 2, E 1 E 2, E 1*, (E 1 ) Type 2 languages Type 2 grammars 2 Brief history
More informationCompiler Principles, PS7
Top-Down Parsing Compiler Principles, PS7 Parsing problem definition: The general parsing problem is - given set of rules and input stream (in our case scheme token input stream), how to find the parse
More informationComputer Science 160 Translation of Programming Languages
Computer Science 160 Translation of Programming Languages Instructor: Christopher Kruegel Top-Down Parsing Top-down Parsing Algorithm Construct the root node of the parse tree, label it with the start
More informationBottom-up Analysis. Theorem: Proof: Let a grammar G be reduced and left-recursive, then G is not LL(k) for any k.
Bottom-up Analysis Theorem: Let a grammar G be reduced and left-recursive, then G is not LL(k) for any k. Proof: Let A Aβ α P and A be reachable from S Assumption: G is LL(k) A n A S First k (αβ n γ) First
More informationSyntactical analysis. Syntactical analysis. Syntactical analysis. Syntactical analysis
Context-free grammars Derivations Parse Trees Left-recursive grammars Top-down parsing non-recursive predictive parsers construction of parse tables Bottom-up parsing shift/reduce parsers LR parsers GLR
More informationTheory of Computation (IV) Yijia Chen Fudan University
Theory of Computation (IV) Yijia Chen Fudan University Review language regular context-free machine DFA/ NFA PDA syntax regular expression context-free grammar Pushdown automata Definition A pushdown automaton
More informationEverything You Always Wanted to Know About Parsing
Everything You Always Wanted to Know About Parsing Part V : LR Parsing University of Padua, Italy ESSLLI, August 2013 Introduction Parsing strategies classified by the time the associated PDA commits to
More informationINF5110 Compiler Construction
INF5110 Compiler Construction Spring 2017 1 / 330 Outline 1. Parsing First and follow sets Top-down parsing Bottom-up parsing References 2 / 330 INF5110 Compiler Construction Parsing Spring 2017 3 / 330
More informationCompiler Design Spring 2017
Compiler Design Spring 2017 8.5 Reaching definitions Dr. Zoltán Majó Compiler Group Java HotSpot Virtual Machine Oracle Corporation Admin issues Brief reminder: Code review takes place today @ 15:15 You
More informationCISC4090: Theory of Computation
CISC4090: Theory of Computation Chapter 2 Context-Free Languages Courtesy of Prof. Arthur G. Werschulz Fordham University Department of Computer and Information Sciences Spring, 2014 Overview In Chapter
More informationEquivalence of TMs and Multitape TMs. Theorem 3.13 and Corollary 3.15 By: Joseph Lauman
Equivalence of TMs and Multitape TMs Theorem 3.13 and Corollary 3.15 By: Joseph Lauman Turing Machines First proposed by Alan Turing in 1936 Similar to finite automaton, but with an unlimited and unrestricted
More informationContext-Free Grammars (and Languages) Lecture 7
Context-Free Grammars (and Languages) Lecture 7 1 Today Beyond regular expressions: Context-Free Grammars (CFGs) What is a CFG? What is the language associated with a CFG? Creating CFGs. Reasoning about
More informationIntroduction to ANTLR (ANother Tool for Language Recognition)
Introduction to ANTLR (ANother Tool for Language Recognition) Jon Eyolfson University of Waterloo September 27 - October 1, 2010 Outline Introduction Usage Example Demonstration Conclusion Jon Eyolfson
More informationUNIT-VIII COMPUTABILITY THEORY
CONTEXT SENSITIVE LANGUAGE UNIT-VIII COMPUTABILITY THEORY A Context Sensitive Grammar is a 4-tuple, G = (N, Σ P, S) where: N Set of non terminal symbols Σ Set of terminal symbols S Start symbol of the
More informationCS 314 Principles of Programming Languages
CS 314 Principles of Programming Languages Lecture 7: LL(1) Parsing Zheng (Eddy) Zhang Rutgers University February 7, 2018 Class Information Homework 3 will be posted this coming Monday. 2 Review: Top-Down
More informationPushdown Automata (2015/11/23)
Chapter 6 Pushdown Automata (2015/11/23) Sagrada Familia, Barcelona, Spain Outline 6.0 Introduction 6.1 Definition of PDA 6.2 The Language of a PDA 6.3 Euivalence of PDA s and CFG s 6.4 Deterministic PDA
More informationContext-free Languages and Pushdown Automata
Context-free Languages and Pushdown Automata Finite Automata vs CFLs E.g., {a n b n } CFLs Regular From earlier results: Languages every regular language is a CFL but there are CFLs that are not regular
More informationMA/CSSE 474 Theory of Computation
MA/CSSE 474 Theory of Computation CFL Hierarchy CFL Decision Problems Your Questions? Previous class days' material Reading Assignments HW 12 or 13 problems Anything else I have included some slides online
More informationSyntax Directed Transla1on
Syntax Directed Transla1on Syntax Directed Transla1on CMPT 379: Compilers Instructor: Anoop Sarkar anoopsarkar.github.io/compilers-class Syntax directed Translation Models for translation from parse trees
More informationComputation Theory Finite Automata
Computation Theory Dept. of Computing ITT Dublin October 14, 2010 Computation Theory I 1 We would like a model that captures the general nature of computation Consider two simple problems: 2 Design a program
More informationLL conflict resolution using the embedded left LR parser
DOI: 10.2298/CSIS111216023S LL conflict resolution using the embedded left LR parser Boštjan Slivnik University of Ljubljana Faculty of Computer and Information Science Tržaška cesta 25, 1000 Ljubljana,
More information