Top-Down Parsing and Intro to Bottom-Up Parsing
|
|
- Daniela Perkins
- 5 years ago
- Views:
Transcription
1 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 parsers accept LL(k) grammars L means left-to-right scan of input L means leftmost derivation k means predict based on k tokens of lookahead In practice, LL(1) is used Prof. Aiken CS 143 Lecture 7 1 Prof. Aiken CS 143 Lecture 7 2 LL(1) vs. Recursive Descent Predictive Parsing and Left Factoring In recursive-descent, At each step, many choices of production to use Backtracking used to undo bad choices In LL(1), At each step, only one choice of production hat is When a non-terminal A is leftmost in a derivation he next input symbol is t here is a unique production A α to use Or no production to use (an error state) LL(1) is a recursive descent variant without backtracking Prof. Aiken CS 143 Lecture 7 3 Recall the grammar + ( ) Hard to predict because For two productions start with For it is not clear how to predict We need to left-factor the grammar Prof. Aiken CS 143 Lecture 7 4 Left-Factoring xample LL(1) Parsing able xample Recall the grammar + ( ) Factor out common prefixes of productions X X + ε ( ) Y Y ε Prof. Aiken CS 143 Lecture 7 5 Left-factored grammar X ( ) Y he LL(1) parsing table: X + ε Y ε next input token + ( ) $ X X X + ε ε Y ( ) Y ε ε ε leftmost non-terminal rhs of production to use Prof. Aiken CS 143 Lecture 7 6 1
2 LL(1) Parsing able xample (Cont.) Consider the [, ] entry When current non-terminal is and next input is, use production X his can generate an in the first position Consider the [Y,+] entry When current non-terminal is Y and current token is +, get rid of Y Y can be followed by + only if Y ε LL(1) Parsing ables. rrors Blank entries indicate error situations Consider the [,] entry here is no way to derive a string starting with from non-terminal Prof. Aiken CS 143 Lecture 7 7 Prof. Aiken CS 143 Lecture 7 8 Using Parsing ables Method similar to recursive descent, except For the leftmost non-terminal S We look at the next input token a And choose the production shown at [S,a] A stack records frontier of parse tree Non-terminals that have yet to be expanded erminals that have yet to matched against the input op of stack = leftmost pending terminal or non-terminal Reject on reaching error state Accept on end of input & empty stack Prof. Aiken CS 143 Lecture 7 9 LL(1) Parsing Algorithm initialize stack = <S $> and next repeat case stack of <X, rest> : if [X,next] = Y 1 Y n then stack <Y 1 Y n rest>; else error (); <t, rest> : if t == next ++ then stack <rest>; else error (); until stack == < > Prof. Aiken CS 143 Lecture 7 10 LL(1) Parsing Algorithm $ marks bottom of stack LL(1) Parsing xample initialize stack = <S $> and next repeat For non-terminal X on top of stack, lookup production case stack of <X, rest> : if [X,next] = Y 1 Y n then stack <Y 1 Y n rest>; else error (); <t, rest> : if t == next ++ For terminal t on top of then stack <rest>; stack, check t matches next else error (); input token. until stack == < > Pop X, push production rhs on stack. Note leftmost symbol of rhs is on top of the stack. Prof. Aiken CS 143 Lecture 7 11 Stack Input Action $ $ X X $ $ Y Y X $ $ terminal Y X $ $ X $ $ terminal X $ $ Y Y X $ $ terminal Y X $ $ ε X $ $ ε $ $ ACCP Prof. Aiken CS 143 Lecture
3 Constructing Parsing ables: he Intuition Computing First Sets Consider non-terminal A, production A α, & token t [A,t] = α in two cases: If α t β α can derive a t in the first position We say that t First(α) If A α and α ε and S β A t δ Useful if stack has A, input is t, and A cannot derive t In this case only option is to get rid of A (by deriving ε) Can work only if t can follow A in at least one derivation We say t Follow(A) Definition First(X) = { t X tα} {ε X ε} Algorithm sketch: 1. First(t) = { t } 2. ε First(X) if X ε if X A 1 A n and ε First(A i ) for 1 i n 3. First(α) First(X) if X A 1 A n α and ε First(A i ) for 1 i n Prof. Aiken CS 143 Lecture 7 13 Prof. Aiken CS 143 Lecture 7 14 First Sets. xample Computing Follow Sets Recall the grammar X ( ) Y X + ε Y ε Definition: Follow(X) = { t S β X t δ } First sets First( ( ) = { ( } First( ) = {, ( } First( ) ) = { ) } First( ) = {, ( } First( ) = { } First( X ) = {+, ε } First( + ) = { + } First( Y ) = {, ε } First( ) = { } Intuition If X A B then First(B) Follow(A) and Follow(X) Follow(B) if B ε then Follow(X) Follow(A) If S is the start symbol then $ Follow(S) Prof. Aiken CS 143 Lecture 7 15 Prof. Aiken CS 143 Lecture 7 16 Computing Follow Sets (Cont.) Algorithm sketch: 1. $ Follow(S) 2. First(β) - {ε} Follow(X) For each production A α X β 3. Follow(A) Follow(X) For each production A α X β where ε First(β) Follow Sets. xample Recall the grammar X ( ) Y X + ε Y ε Follow sets Follow( + ) = {, ( } Follow( ) = {, ( } Follow( ( ) = {, ( } Follow( ) = {), $} Follow( X ) = {$, ) } Follow( ) = {+, ), $} Follow( ) ) = {+, ), $} Follow( Y ) = {+, ), $} Follow( ) = {, +, ), $} Prof. Aiken CS 143 Lecture 7 17 Prof. Aiken CS 143 Lecture
4 Constructing LL(1) Parsing ables Construct a parsing table for CFG G For each production A α in G do: For each terminal t First(α) do [A, t] = α If ε First(α), for each t Follow(A) do [A, t] = α If ε First(α) and $ Follow(A) do [A, $] = α Notes on LL(1) Parsing ables If any entry is multiply defined then G is not LL(1) If G is ambiguous If G is left recursive If G is not left-factored And in other cases as well Most programming language CFGs are not LL(1) Prof. Aiken CS 143 Lecture 7 19 Prof. Aiken CS 143 Lecture 7 20 Bottom-Up Parsing Bottom-up parsing is more general than topdown parsing And just as efficient Builds on ideas in top-down parsing Bottom-up is the preferred method Concepts today, algorithms next time An Introductory xample Bottom-up parsers don t need left-factored grammars Revert to the natural grammar for our example: + () Consider the string: + Prof. Aiken CS 143 Lecture 7 21 Prof. Aiken CS 143 Lecture 7 22 he Idea Bottom-up parsing reduces a string to the start symbol by inverting productions: Prof. Aiken CS 143 Lecture 7 23 Observation Read the productions in reverse (from bottom to top) his is a rightmost derivation! Prof. Aiken CS 143 Lecture
5 Important Fact #1 A Bottom-up Parse Important Fact #1 about bottom-up parsing: A bottom-up parser traces a rightmost derivation in reverse Prof. Aiken CS 143 Lecture 7 25 Prof. Aiken CS 143 Lecture 7 26 A Bottom-up Parse in Detail (1) A Bottom-up Parse in Detail (2) Prof. Aiken CS 143 Lecture 7 27 Prof. Aiken CS 143 Lecture 7 28 A Bottom-up Parse in Detail (3) A Bottom-up Parse in Detail (4) Prof. Aiken CS 143 Lecture 7 29 Prof. Aiken CS 143 Lecture
6 A Bottom-up Parse in Detail (5) A Bottom-up Parse in Detail (6) Prof. Aiken CS 143 Lecture 7 31 Prof. Aiken CS 143 Lecture 7 32 A rivial Bottom-Up Parsing Algorithm Let I = input string repeat pick a non-empty substring β of I where X β is a production if no such β, backtrack replace one β by X in I until I = S (the start symbol) or all possibilities are exhausted Questions Does this algorithm terminate? How fast is the algorithm? Does the algorithm handle all cases? How do we choose the substring to reduce at each step? Prof. Aiken CS 143 Lecture 7 33 Prof. Aiken CS 143 Lecture 7 34 Where Do Reductions Happen? Important Fact #1 has an eresting consequence: Let αβω be a step of a bottom-up parse Assume the next reduction is by X β hen ω is a string of terminals Why? Because αxω αβω is a step in a rightmost derivation Notation Idea: Split string o two substrings Right substring is as yet unexamined by parsing (a string of terminals) Left substring has terminals and non-terminals he dividing po is marked by a he is not part of the string Initially, all input is unexamined x 1 x 2... x n Prof. Aiken CS 143 Lecture 7 35 Prof. Aiken CS 143 Lecture
7 Shift-Reduce Parsing Bottom-up parsing uses only two kinds of actions: Shift Shift Shift: Move one place to the right Shifts a terminal to the left string ABC xyz ABCx yz Reduce Prof. Aiken CS 143 Lecture 7 37 Prof. Aiken CS 143 Lecture 7 38 Reduce he xample with Reductions Only Apply an inverse production at the right end of the left string If A xy is a production, then Cbxy ijk CbA ijk + + reduce reduce Prof. Aiken CS 143 Lecture reduce reduce reduce + Prof. Aiken CS 143 Lecture 7 40 he xample with Shift-Reduce Parsing A Shift-Reduce Parse in Detail (1) reduce reduce reduce reduce reduce Prof. Aiken CS 143 Lecture 7 41 Prof. Aiken CS 143 Lecture
8 A Shift-Reduce Parse in Detail (2) + + A Shift-Reduce Parse in Detail (3) Prof. Aiken CS 143 Lecture 7 43 Prof. Aiken CS 143 Lecture 7 44 A Shift-Reduce Parse in Detail (4) A Shift-Reduce Parse in Detail (5) Prof. Aiken CS 143 Lecture 7 45 Prof. Aiken CS 143 Lecture 7 46 A Shift-Reduce Parse in Detail (6) A Shift-Reduce Parse in Detail (7) Prof. Aiken CS 143 Lecture 7 47 Prof. Aiken CS 143 Lecture
9 A Shift-Reduce Parse in Detail (8) A Shift-Reduce Parse in Detail (9) Prof. Aiken CS 143 Lecture 7 49 Prof. Aiken CS 143 Lecture 7 50 A Shift-Reduce Parse in Detail (10) A Shift-Reduce Parse in Detail (11) Prof. Aiken CS 143 Lecture Prof. Aiken CS 143 Lecture 7 52 he Stack Conflicts Left string can be implemented by a stack op of the stack is the Shift pushes a terminal on the stack Reduce pops 0 or more symbols off of the stack (production rhs) and pushes a nonterminal on the stack (production lhs) In a given state, more than one action ( or reduce) may lead to a valid parse If it is legal to or reduce, there is a reduce conflict If it is legal to reduce by two different productions, there is a reduce-reduce conflict You will see such conflicts in your project! More next time... Prof. Aiken CS 143 Lecture 7 53 Prof. Aiken CS 143 Lecture
Introduction 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationCompiling Techniques
Lecture 5: Top-Down Parsing 26 September 2017 The Parser Context-Free Grammar (CFG) Lexer Source code Scanner char Tokeniser token Parser AST Semantic Analyser AST IR Generator IR Errors Checks the stream
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 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 informationCompiling Techniques
Lecture 5: Top-Down Parsing 6 October 2015 The Parser Context-Free Grammar (CFG) Lexer Source code Scanner char Tokeniser token Parser AST Semantic Analyser AST IR Generator IR Errors Checks the stream
More informationTop-Down Parsing, Part II
op-down Parsing, Part II Announcements Programming Project 1 due Friday, 11:59PM Office hours every day until then. ubmission instructions will be emailed out tonight. Where We Are ource Code Lexical Analysis
More informationCONTEXT FREE GRAMMAR AND
CONTEXT FREE GRAMMAR AND PARSING STATIC ANALYSIS - PARSING Source language Scanner (lexical analysis) tokens Parser (syntax analysis) Syntatic structure Semantic Analysis (IC generator) Syntatic/sema ntic
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 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 informationAnnouncement: Midterm Prep
Announcement: Midterm Prep Midterm is Tuesday, 3/13 at 11 in three classrooms - Last name A-C Van Vleck B115 - Last name D-J Van Vleck B135 - Last name K-Z CS1240 List of topics Up to and including lecture
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 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 informationExercises. Exercise: Grammar Rewriting
Exercises Text adapted from : Alessandro Artale, Free University of Bolzano Exercise: Grammar Rewriting Consider the following grammar for Boolean expressions: Bexp Bexp or Bterm Bterm Bterm Bterm and
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 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 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 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 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 informationThe Parser. CISC 5920: Compiler Construction Chapter 3 Syntactic Analysis (I) Grammars (cont d) Grammars
The Parser CISC 5920: Compiler Construction Chapter 3 Syntactic Analysis (I) Arthur. Werschulz Fordham University Department of Computer and Information Sciences Copyright c Arthur. Werschulz, 2017. All
More informationLL(1) Grammar and parser
Crafting a Compiler with C (XI) 資科系 林偉川 LL(1) Grammar and parser LL(1) grammar is the class of CFG and is suitable for RDP. Define LL(1) parsers which use an LL(1) parse table rather than recursive procedures
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 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 informationPushdown Automata (Pre Lecture)
Pushdown Automata (Pre Lecture) Dr. Neil T. Dantam CSCI-561, Colorado School of Mines Fall 2017 Dantam (Mines CSCI-561) Pushdown Automata (Pre Lecture) Fall 2017 1 / 41 Outline Pushdown Automata Pushdown
More informationI 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 informationTalen en Compilers. Johan Jeuring , period 2. October 29, Department of Information and Computing Sciences Utrecht University
Talen en Compilers 2015-2016, period 2 Johan Jeuring Department of Information and Computing Sciences Utrecht University October 29, 2015 12. LL parsing 12-1 This lecture LL parsing Motivation Stack-based
More informationComputability Theory
CS:4330 Theory of Computation Spring 2018 Computability Theory Decidable Problems of CFLs and beyond Haniel Barbosa Readings for this lecture Chapter 4 of [Sipser 1996], 3rd edition. Section 4.1. Decidable
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 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 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 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 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 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 informationComputational Models - Lecture 4
Computational Models - Lecture 4 Regular languages: The Myhill-Nerode Theorem Context-free Grammars Chomsky Normal Form Pumping Lemma for context free languages Non context-free languages: Examples Push
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 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 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 informationSyntax Analysis - Part 1. Syntax Analysis
Syntax Analysis Outline Context-Free Grammars (CFGs) Parsing Top-Down Recursive Descent Table-Driven Bottom-Up LR Parsing Algorithm How to Build LR Tables Parser Generators Grammar Issues for Programming
More informationCompiler Design Spring 2017
Compiler Design Spring 2017 3.4 Bottom-up parsing Dr. Zoltán Majó Compiler Group Java HotSpot Virtual Machine Oracle Corporation 1 Bottom up parsing Goal: Obtain rightmost derivation in reverse w S Reduce
More informationCSC 4181Compiler Construction. Context-Free Grammars Using grammars in parsers. Parsing Process. Context-Free Grammar
CSC 4181Compiler Construction Context-ree Grammars Using grammars in parsers CG 1 Parsing Process Call the scanner to get tokens Build a parse tree from the stream of tokens A parse tree shows the syntactic
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 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 informationRecursive descent for grammars with contexts
39th International Conference on Current Trends in Theory and Practice of Computer Science Špindleruv Mlýn, Czech Republic Recursive descent parsing for grammars with contexts Ph.D. student, Department
More informationLanguages. Languages. An Example Grammar. Grammars. Suppose we have an alphabet V. Then we can write:
Languages A language is a set (usually infinite) of strings, also known as sentences Each string consists of a sequence of symbols taken from some alphabet An alphabet, V, is a finite set of symbols, e.g.
More informationHarvard CS 121 and CSCI E-207 Lecture 10: Ambiguity, Pushdown Automata
Harvard CS 121 and CSCI E-207 Lecture 10: Ambiguity, Pushdown Automata Salil Vadhan October 4, 2012 Reading: Sipser, 2.2. Another example of a CFG (with proof) L = {x {a, b} : x has the same # of a s and
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 informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION Spring 2016 http://cseweb.ucsd.edu/classes/sp16/cse105-ab/ Today's learning goals Sipser Ch 2 Define push down automata Trace the computation of a push down automaton Design
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 informationCS Rewriting System - grammars, fa, and PDA
Restricted version of PDA If (p, γ) δ(q, a, X), a Σ {ε}, p. q Q, X Γ. restrict γ Γ in three ways: i) if γ = YX, (q, ay, Xβ) (p, y, YXβ) push Y Γ, ii) if γ = X, (q, ay, Xβ) (p, y, Xβ) no change on stack,
More informationCSE 105 THEORY OF COMPUTATION
CSE 105 THEORY OF COMPUTATION Spring 2017 http://cseweb.ucsd.edu/classes/sp17/cse105-ab/ Review of CFG, CFL, ambiguity What is the language generated by the CFG below: G 1 = ({S,T 1,T 2 }, {0,1,2}, { S
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 informationDefinition: A grammar G = (V, T, P,S) is a context free grammar (cfg) if all productions in P have the form A x where
Recitation 11 Notes Context Free Grammars Definition: A grammar G = (V, T, P,S) is a context free grammar (cfg) if all productions in P have the form A x A V, and x (V T)*. Examples Problem 1. Given the
More informationSection 1 (closed-book) Total points 30
CS 454 Theory of Computation Fall 2011 Section 1 (closed-book) Total points 30 1. Which of the following are true? (a) a PDA can always be converted to an equivalent PDA that at each step pops or pushes
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 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 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 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 informationCourse Script INF 5110: Compiler construction
Course Script INF 5110: Compiler construction INF5110, spring 2018 Martin Steffen ii Contents Contents 4 Parsing 1 4.1 Introduction to parsing........................ 1 4.2 Top-down parsing...........................
More informationCompiler construction
Compiler construction Martin Steffen February 20, 2017 Contents 1 Abstract 1 1.1 Parsing.................................................. 1 1.1.1 First and follow sets.....................................
More informationTHEORY OF COMPUTATION (AUBER) EXAM CRIB SHEET
THEORY OF COMPUTATION (AUBER) EXAM CRIB SHEET Regular Languages and FA A language is a set of strings over a finite alphabet Σ. All languages are finite or countably infinite. The set of all languages
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 informationTheory of Computation (VI) Yijia Chen Fudan University
Theory of Computation (VI) Yijia Chen Fudan University Review Forced handles Definition A handle h of a valid string v = xhy is a forced handle if h is the unique handle in every valid string xhŷ where
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 informationFrom EBNF to PEG. Roman R. Redziejowski. Concurrency, Specification and Programming Berlin 2012
Concurrency, Specification and Programming Berlin 2012 EBNF: Extended Backus-Naur Form A way to define grammar. EBNF: Extended Backus-Naur Form A way to define grammar. Literal = Decimal Binary Decimal
More informationIntroduction to Theory of Computing
CSCI 2670, Fall 2012 Introduction to Theory of Computing Department of Computer Science University of Georgia Athens, GA 30602 Instructor: Liming Cai www.cs.uga.edu/ cai 0 Lecture Note 3 Context-Free Languages
More informationLecture 11 Context-Free Languages
Lecture 11 Context-Free Languages COT 4420 Theory of Computation Chapter 5 Context-Free Languages n { a b : n n { ww } 0} R Regular Languages a *b* ( a + b) * Example 1 G = ({S}, {a, b}, S, P) Derivations:
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 informationFundamentele Informatica II
Fundamentele Informatica II Answer to selected exercises 5 John C Martin: Introduction to Languages and the Theory of Computation M.M. Bonsangue (and J. Kleijn) Fall 2011 5.1.a (q 0, ab, Z 0 ) (q 1, b,
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 informationPushdown Automata: Introduction (2)
Pushdown Automata: Introduction Pushdown automaton (PDA) M = (K, Σ, Γ,, s, A) where K is a set of states Σ is an input alphabet Γ is a set of stack symbols s K is the start state A K is a set of accepting
More informationOctober 6, Equivalence of Pushdown Automata with Context-Free Gramm
Equivalence of Pushdown Automata with Context-Free Grammar October 6, 2013 Motivation Motivation CFG and PDA are equivalent in power: a CFG generates a context-free language and a PDA recognizes a context-free
More informationMA/CSSE 474 Theory of Computation
MA/CSSE 474 Theory of Computation Bottom-up parsing Pumping Theorem for CFLs Recap: Going One Way Lemma: Each context-free language is accepted by some PDA. Proof (by construction): The idea: Let the stack
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 informationHarvard CS 121 and CSCI E-207 Lecture 10: CFLs: PDAs, Closure Properties, and Non-CFLs
Harvard CS 121 and CSCI E-207 Lecture 10: CFLs: PDAs, Closure Properties, and Non-CFLs Harry Lewis October 8, 2013 Reading: Sipser, pp. 119-128. Pushdown Automata (review) Pushdown Automata = Finite automaton
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 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 informationCPS 220 Theory of Computation Pushdown Automata (PDA)
CPS 220 Theory of Computation Pushdown Automata (PDA) Nondeterministic Finite Automaton with some extra memory Memory is called the stack, accessed in a very restricted way: in a First-In First-Out fashion
More information