# Lexical and Syntax Analysis. Bottom-Up Parsing

Size: px
Start display at page:

Transcription

1 Lexical and Syntax Analysis Bottom-Up Parsing

2 Parsing There are two ways to construct derivation of a grammar. Top-Down: begin with start symbol; repeatedly replace an instance of a production s LHS with its RHS. Bottom-Up: begin with terminal symbols; repeatedly replace an instance of a production s RHS with its LHS. (See animation.)

3 Derivation in reverse Bottom-up parsers construct a derivation in reverse. Example: ( x + x ) ( v + x ) ( e + x ) ( e + v ) ( e + e ) e (Here we have a rightmost derivation in reverse.)

4 Shift-Reduce Parsing A non-deterministic procedure for bottom-up parsing involving: a stack holding grammar symbols; an input buffer holding the rest of the string to be parsed. Symbol \$ is used to mark the bottom of the stack and the end of the input buffer.

5 Shift-Reduce Parsing There are four primary operations: 1. Shift. Consume the next input symbol and push it onto the stack. 2. Reduce. If the RHS of a production appears on top of the stack, then replace it with the LHS. 3. Accept. Announce success when the stack contains only the start symbol and the input is empty. 4. Error. Fail when the input is empty and no reduction can be applied.

6 Exercise 1 Consider the following grammar G. e e + t t t t * f f f ( e ) x Show steps taken by a shift-reduce parser to successfully parse the following input. x * x

7 Shift-reduce parsing is complete If an input string conforms to a grammar, then there exists at least one series of shift-reduce steps leading to acceptance. (See Aho et al. for a proof.)

8 Problem But how do we decide when to shift and when to reduce? Stack Input Action \$ x * x \$ Shift \$ x * x \$ Reduce by f x \$ f * x \$ Reduce by t f \$ t * x \$ Shift or Reduce? Both shift and reduce (by e t) are possible, but reduce leads to failure.

9 Possible solutions How do we decide when to shift and when to reduce? Solution 1: guess, and backtrack upon failure. (Inefficient!) Solution 2: LR parsing. L for left-to-right scan of the input, and R for constructing a rightmost derivation in reverse.

10 PART 1: LR(0) PARSING (When to shift and when to reduce) LR(0) Items Reducible Items LR(0) States LR(0) Automata Constructing an LR(0) Automaton LR(0) Parsing

11 LR(0) Items An item of a grammar H is a production of H with a dot at some point in the body. For example, the production e e + t has four possible items: e e + t e e + t e e + t e e + t

12 LR(0) Items Note that the production n ε has just one possible item: n

13 Intuition An item indicates how much of a production we have seen at some point during parsing. For example, the item e e + t indicates that we have just seen a substring derivable from e and that next we hope to see one derivable from + t.

14 Reducible items An item is reducible if it has a dot at the rightmost position. For example: t t * f Intuition: we have reached a point where we are ready to reduce t * f to t. Exception: an item defining the start symbol is not reducible.

15 LR(0) States A state of an LR parser is a set of items. For example, here is a state S 2 : S 2 e e + v v x v y In state S 2 we could be in the process of parsing one of three possible productions.

16 LR(0) Automaton An LR(0) automaton has states (sets of LR(0) items); and transitions labelled by grammar symbols. For example, here is a fragment of an LR(0) automaton: x S 2 e e + v v x v y S 5 v x v y S 6 v y S 3 e e + v

17 Constructing an LR(0) automaton An LR(0) automaton is defined by two main functions: GOTO(L, X): the LR(0) state reached by taking an X transition in state L. STATES(G): the set of all LR(0) states of grammar G. To define these we need an auxiliary function called CLOSURE.

18 The CLOSURE function If L is a set of items then CLOSURE(L) is the set of items such that: every item in L is in CLOSURE(L); if item n α m β is in CLOSURE(L) and m γ is a production then m γ is also in CLOSURE(L).

19 Exercise 2 Consider the following grammar P. s e e e + v v v x y Compute the CLOSURE of the set of items { s e }.

20 The GOTO function If L is a set of items and X is a grammar symbol and n α X β L then GOTO(L, X) is the CLOSURE of the set of all items n α X β

21 Exercise 3 Consider the following LR(0) state. S 0 s e e e + v e v v x v y Give the states that can be reached from S 0 on each of the following grammar symbols: e, v, x and y.

22 Exercise 4 Consider the following LR(0) state. S 1 s e e e + v Give the states that can be reached from S 1 on symbol +.

23 Constructing the LR(0) states Aim: to compute C, the set of all LR(0) states for some grammar G. Pre-processing step: if s is the start symbol of G, introduce a new start symbol s' and a new production s' s. (Motivation: success is detected when s is reduced to s'.)

24 The STATES function STATES(G) { } C := { CLOSURE({ s' s }) } repeat for each L C for each grammar symbol X C := C { GOTO(L, X) } until C is unchanging return C

25 Constructing the LR(0) automaton States: obtained by the STATES function. Transitions: for each state L and grammar symbol X compute GOTO(X, L). Final state: if s' is the start symbol and s' s is an item in state L then add a transition labelled \$ from L to the accepting state.

26 Exercise 5 Construct an LR(0) automaton for the following grammar. s e e e + v v v x y (A new start symbol s has already been introduced.)

27 LR(0) Parsing An LR(0) parser has: an LR(0) automaton (the GOTO function in particular); a pointer next to the next character in the input string; a stack of states S, initially containing the start state of the LR(0) automaton; a current state, always at the top of the stack.

28 LR(0) Parsing while top(s) accept if n α is a reducible item in top(s) then pop α elements push( GOTO(top(S), n ) ) else if GOTO(top(S), *next) = L then next++ push(l) else raise syntax error Shift! Reduce!

29 Exercise 6 (page 1) Consider the LR(0) automaton: start v S 0 s e e e + v e v v x v y S 1 s e e e + v \$ e accept + x y S 4 e v S 5 v x x S 2 e e + v v x v y v y S 6 v y S 3 e e + v

30 Exercise 6 (page 2) Show the steps taken by an LR(0) parser on the following input string. x + x For each step, show the stack, the input buffer, and the action taken.

31 Shift-Reduce Conflicts If at some state L there is a reducible item and a transition on a terminal symbol then: there exists a shift-reduce conflict; and the grammar is not an LR(0) grammar. Grammar P contains no shiftreduce conflicts.

32 Reduce-Reduce Conflicts If at some state L there is a more than one reducible item then: there exists a reduce-reduce conflict; and the grammar is not an LR(0) grammar. Grammar P contains no reducereduce conflicts.

33 PART 2: LR(1) PARSING (When to shift and when to reduce) LR(1) Items Reducible Items SLR(1) Parsing LR(1) Parsing LALR(1) Parsing

34 Motivation LR(0) automata say when to shift and when to reduce. But conflicts are very common: many grammars are not LR(0) grammars. If we enrich the structure of LR(0) items, we can decrease conflicts significantly.

35 LR(1) Items Idea: extend LR(0) items to have the form n α β { σ } where { σ } is a set of terminal symbols called the lookahead set.

36 Reducible items An item is reducible if it has a dot at the rightmost position and the next input symbol is in the lookahead set. Example: t t * f { *, +, ) } Here we have reached a point where we can reduce t * f to t provided that the next input symbol is *, + or ).

37 LR(1) parsing LR(1) parsing is like LR(0) parsing except that: LR(1) states contain LR(1) items rather than LR(0) items. An item is only reducible if the next input symbol is in the lookahead set.

38 Aside: an equivalence If an LR(1) state contains several items differing only in their lookahead sets, e.g. t t * f { *, + } t t * f { +, ) } then these are equivalent to the single item formed by unioning the lookahead sets, e.g. t t * f { *, +, ) }

39 LR(1) parsing There are three main forms of LR(1) parsing, each differing in how the lookahead sets of items are defined. LR(1) LALR(1) SLR(1)

40 SLR(1) PARSING SLR(1) stands for simple LR(1)

41 SLR(1) Automata An SLR(1) automaton is an LR(0) automaton with every item n α β replaced by n α β { σ } where {σ } is the follow set of n.

42 Exercise 7 Compute the follow set of each non-terminal in the following grammar. s e e e + v v v x y

43 Answer follow( s ) = { \$ } follow( e ) = { +, \$ } follow( v ) = { +, \$ }

44 Example of an SLR(1) automaton start v S 4 e v {+, \$} S 0 s e {\$} e e + v {+, \$} e v {+, \$} v x {+, \$} v y {+, \$} e S 1 s e {\$} e e + v {+, \$} \$ accept + x y S 5 v x {+, \$} S 6 v y {+, \$} x S y 2 e e + v {+, \$} v x {+, \$} v y {+, \$} v S 3 e e + v {+, \$}

45 Power of SLR(1) SLR(1) Grammars LR(0) Grammars An SLR(1) parser observes fewer reducible items than an LR(0) parser. Therefore, fewer reduce-reduce and shift-reduce conflicts.

46 LR(1) PARSING More powerful than SLR(1)

47 Idea of LR(1) In SLR(1), the lookahead set of an item is computed in the context of any possible derivation. Idea: have different lookahead sets for item n α β for each occurrence site of n in the grammar.

48 Example Consider the following grammar. s c c c c c d The follow sets are: follow( s ) = { \$ } follow( c ) = { c, d, \$ }

49 Example (continued) In SLR(1) parsing, we have items such as c d { c, d, \$ } But depending on whether we are parsing the first or second c in an s, we want items such as c d { c, d } or c d { \$ }

50 Construction an LR(1) automaton To construct an LR(1) automaton, we make minor modifications to the CLOSURE and GOTO functions.

51 The CLOSURE function every item in L is in CLOSURE(L); if item n α m β {σ} is in CLOSURE(L) and m γ is a production then m γ {σ'} is in CLOSURE(L) where σ' contains every terminal in first(β) and also, if ε first(β), every terminal in σ.

52 Exercise 8 Consider the following grammar Q. s' s s c c c c c d Compute the CLOSURE of the set of items { s' s {\$} }.

53 The GOTO function If L is a set of items and X is a grammar symbol and n α X β {σ} L then GOTO(L, X) is the CLOSURE of the set of all items n α X β {σ}

54 Exercise 9 Consider the following LR(1) state. S 0 s' s {\$} s c c {\$} c c c {c, d} c d {c, d} Give the states that can be reached from S 0 on each of the following grammar symbols: s, c, c and d.

55 Exercise 10 Construct an LR(1) automaton for the following grammar. s' s s c c c c c d (A new start symbol s' has already been introduced.)

56 LALR(1) PARSING Merging LR(1) States

57 Problem LR(1) automata can contain very many states, requiring large amounts of memory to store.

58 LALR(1) Parsing Idea: first construct an LR(1) automaton and then merge states where possible. Two LR(1) states are merged if, by ignoring the lookahead sets, they contain the same items. The merged state contains the union of all the items in the original two states.

59 Example Ignoring lookahead sets, states S 4 and S 7 have the same items. S 4 c d {c, d} S 7 c d {\$} After merging: S 47 c d {c, d} c d {\$} Or more simply: S 47 c d {\$, c, d}

60 Exercise 11 Construct an LALR(1) automaton for the following grammar. s' s s c c c c c d (A new start symbol s' has already been introduced.)

61 Facts about LALR(1) LALR(1) and LR(0) automata contain the same number of states. For the C language, the LALR(1) automaton contains hundreds of states whereas the LR(1) automaton contains thousands.

62 More facts about LALR(1) If the LR(1) automaton for a grammar contains no shiftreduce conflicts, then neither does the LALR(1) automaton. But, an LALR(1) automaton may contain reduce-reduce conflicts not present in an LR(1) automaton.

63 Expressive power of LR parsing techniques LR(1) LALR(1) SLR(1) LR(0)

64 Concluding remarks LR parsers can handle a larger class of grammars than LL parsers. But LR parsers are often too complex to construct by hand. So the main use of LR parsing is in automatic parser generator tools such as Bison.

65 Acknowledgements

### MIT Parse Table Construction. Martin Rinard Laboratory for Computer Science Massachusetts Institute of Technology

MIT 6.035 Parse Table Construction Martin Rinard Laboratory for Computer Science Massachusetts Institute of Technology Parse Tables (Review) ACTION Goto State ( ) \$ X s0 shift to s2 error error goto s1

### Bottom-Up Parsing. Lecture 11-12

Bottom-Up Parsing Lecture 11-12 (From slides by G. Necula & R. Bodik) 9/22/06 Prof. Hilfinger CS164 Lecture 11 1 Bottom-Up Parsing Bottom-up parsing is more general than topdown parsing And just as efficient

### S Y N T A X A N A L Y S I S LR

LR parsing There are three commonly used algorithms to build tables for an LR parser: 1. SLR(1) = LR(0) plus use of FOLLOW set to select between actions smallest class of grammars smallest tables (number

### Bottom-Up Parsing. Lecture 11-12

Bottom-Up Parsing Lecture 11-12 (From slides by G. Necula & R. Bodik) 2/20/08 Prof. Hilfinger CS164 Lecture 11 1 Administrivia Test I during class on 10 March. 2/20/08 Prof. Hilfinger CS164 Lecture 11

### LR Parsing LALR Parser Generators

Outline LR Parsing LALR Parser Generators Review of bottom-up parsing Computing the parsing DFA Using parser generators 2 Bottom-up Parsing (Review) A bottom-up parser rewrites the input string to the

### Formal Languages and Compilers Lecture VII Part 4: Syntactic A

Formal Languages and Compilers Lecture VII Part 4: Syntactic Analysis Free University of Bozen-Bolzano Faculty of Computer Science POS Building, Room: 2.03 artale@inf.unibz.it http://www.inf.unibz.it/

### LR Parsing LALR Parser Generators

LR Parsing LALR Parser Generators Outline Review of bottom-up parsing Computing the parsing DFA Using parser generators 2 Bottom-up Parsing (Review) A bottom-up parser rewrites the input string to the

### In One Slide. Outline. LR Parsing. Table Construction

LR Parsing Table Construction #1 In One Slide An LR(1) parsing table can be constructed automatically from a CFG. An LR(1) item is a pair made up of a production and a lookahead token; it represents a

### Formal Languages and Compilers Lecture VII Part 3: Syntactic A

Formal Languages and Compilers Lecture VII Part 3: Syntactic Analysis Free University of Bozen-Bolzano Faculty of Computer Science POS Building, Room: 2.03 artale@inf.unibz.it http://www.inf.unibz.it/

### Principle of Compilers Lecture IV Part 4: Syntactic Analysis. Alessandro Artale

Free University of Bolzano Principles of Compilers Lecture IV Part 4, 2003/2004 AArtale (1) Principle of Compilers Lecture IV Part 4: Syntactic Analysis Alessandro Artale Faculty of Computer Science Free

### Context-free grammars

Context-free grammars Section 4.2 Formal way of specifying rules about the structure/syntax of a program terminals - tokens non-terminals - represent higher-level structures of a program start symbol,

### LALR stands for look ahead left right. It is a technique for deciding when reductions have to be made in shift/reduce parsing. Often, it can make the

LALR parsing 1 LALR stands for look ahead left right. It is a technique for deciding when reductions have to be made in shift/reduce parsing. Often, it can make the decisions without using a look ahead.

### Compiler Construction: Parsing

Compiler Construction: Parsing Mandar Mitra Indian Statistical Institute M. Mitra (ISI) Parsing 1 / 33 Context-free grammars. Reference: Section 4.2 Formal way of specifying rules about the structure/syntax

### shift-reduce parsing

Parsing #2 Bottom-up Parsing Rightmost derivations; use of rules from right to left Uses a stack to push symbols the concatenation of the stack symbols with the rest of the input forms a valid bottom-up

### LR Parsing. Leftmost and Rightmost Derivations. Compiler Design CSE 504. Derivations for id + id: T id = id+id. 1 Shift-Reduce Parsing.

LR Parsing Compiler Design CSE 504 1 Shift-Reduce Parsing 2 LR Parsers 3 SLR and LR(1) Parsers Last modifled: Fri Mar 06 2015 at 13:50:06 EST Version: 1.7 16:58:46 2016/01/29 Compiled at 12:57 on 2016/02/26

### Let us construct the LR(1) items for the grammar given below to construct the LALR parsing table.

MODULE 18 LALR parsing After understanding the most powerful CALR parser, in this module we will learn to construct the LALR parser. The CALR parser has a large set of items and hence the LALR parser is

### 3. Syntax Analysis. Andrea Polini. Formal Languages and Compilers Master in Computer Science University of Camerino

3. Syntax Analysis Andrea Polini Formal Languages and Compilers Master in Computer Science University of Camerino (Formal Languages and Compilers) 3. Syntax Analysis CS@UNICAM 1 / 54 Syntax Analysis: the

### LR Parsing Techniques

LR Parsing Techniques Introduction Bottom-Up Parsing LR Parsing as Handle Pruning Shift-Reduce Parser LR(k) Parsing Model Parsing Table Construction: SLR, LR, LALR 1 Bottom-UP Parsing A bottom-up parser

### Bottom-Up Parsing II (Different types of Shift-Reduce Conflicts) Lecture 10. Prof. Aiken (Modified by Professor Vijay Ganesh.

Bottom-Up Parsing II Different types of Shift-Reduce Conflicts) Lecture 10 Ganesh. Lecture 10) 1 Review: Bottom-Up Parsing Bottom-up parsing is more general than topdown parsing And just as efficient Doesn

### UNIT III & IV. Bottom up parsing

UNIT III & IV Bottom up parsing 5.0 Introduction Given a grammar and a sentence belonging to that grammar, if we have to show that the given sentence belongs to the given grammar, there are two methods.

### Conflicts in LR Parsing and More LR Parsing Types

Conflicts in LR Parsing and More LR Parsing Types Lecture 10 Dr. Sean Peisert ECS 142 Spring 2009 1 Status Project 2 Due Friday, Apr. 24, 11:55pm The usual lecture time is being replaced by a discussion

### SLR parsers. LR(0) items

SLR parsers LR(0) items As we have seen, in order to make shift-reduce parsing practical, we need a reasonable way to identify viable prefixes (and so, possible handles). Up to now, it has not been clear

### Bottom-up parsing. Bottom-Up Parsing. Recall. Goal: For a grammar G, withstartsymbols, any string α such that S α is called a sentential form

Bottom-up parsing Bottom-up parsing Recall Goal: For a grammar G, withstartsymbols, any string α such that S α is called a sentential form If α V t,thenα is called a sentence in L(G) Otherwise it is just

### Lecture 8: Deterministic Bottom-Up Parsing

Lecture 8: Deterministic Bottom-Up Parsing (From slides by G. Necula & R. Bodik) Last modified: Fri Feb 12 13:02:57 2010 CS164: Lecture #8 1 Avoiding nondeterministic choice: LR We ve been looking at general

### LR Parsing - The Items

LR Parsing - The Items Lecture 10 Sections 4.5, 4.7 Robb T. Koether Hampden-Sydney College Fri, Feb 13, 2015 Robb T. Koether (Hampden-Sydney College) LR Parsing - The Items Fri, Feb 13, 2015 1 / 31 1 LR

### CSE P 501 Compilers. LR Parsing Hal Perkins Spring UW CSE P 501 Spring 2018 D-1

CSE P 501 Compilers LR Parsing Hal Perkins Spring 2018 UW CSE P 501 Spring 2018 D-1 Agenda LR Parsing Table-driven Parsers Parser States Shift-Reduce and Reduce-Reduce conflicts UW CSE P 501 Spring 2018

### CS 4120 Introduction to Compilers

CS 4120 Introduction to Compilers Andrew Myers Cornell University Lecture 6: Bottom-Up Parsing 9/9/09 Bottom-up parsing A more powerful parsing technology LR grammars -- more expressive than LL can handle

### Parsers. Xiaokang Qiu Purdue University. August 31, 2018 ECE 468

Parsers Xiaokang Qiu Purdue University ECE 468 August 31, 2018 What is a parser A parser has two jobs: 1) Determine whether a string (program) is valid (think: grammatically correct) 2) Determine the structure

### EDAN65: Compilers, Lecture 06 A LR parsing. Görel Hedin Revised:

EDAN65: Compilers, Lecture 06 A LR parsing Görel Hedin Revised: 2017-09-11 This lecture Regular expressions Context-free grammar Attribute grammar Lexical analyzer (scanner) Syntactic analyzer (parser)

### Lecture 7: Deterministic Bottom-Up Parsing

Lecture 7: Deterministic Bottom-Up Parsing (From slides by G. Necula & R. Bodik) Last modified: Tue Sep 20 12:50:42 2011 CS164: Lecture #7 1 Avoiding nondeterministic choice: LR We ve been looking at general

### MODULE 14 SLR PARSER LR(0) ITEMS

MODULE 14 SLR PARSER LR(0) ITEMS In this module we shall discuss one of the LR type parser namely SLR parser. The various steps involved in the SLR parser will be discussed with a focus on the construction

### Wednesday, August 31, Parsers

Parsers How do we combine tokens? Combine tokens ( words in a language) to form programs ( sentences in a language) Not all combinations of tokens are correct programs (not all sentences are grammatically

### Parsing Wrapup. Roadmap (Where are we?) Last lecture Shift-reduce parser LR(1) parsing. This lecture LR(1) parsing

Parsing Wrapup Roadmap (Where are we?) Last lecture Shift-reduce parser LR(1) parsing LR(1) items Computing closure Computing goto LR(1) canonical collection This lecture LR(1) parsing Building ACTION

### Wednesday, September 9, 15. Parsers

Parsers What is a parser A parser has two jobs: 1) Determine whether a string (program) is valid (think: grammatically correct) 2) Determine the structure of a program (think: diagramming a sentence) Agenda

### Parsers. What is a parser. Languages. Agenda. Terminology. Languages. A parser has two jobs:

What is a parser Parsers A parser has two jobs: 1) Determine whether a string (program) is valid (think: grammatically correct) 2) Determine the structure of a program (think: diagramming a sentence) Agenda

### Bottom up parsing. The sentential forms happen to be a right most derivation in the reverse order. S a A B e a A d e. a A d e a A B e S.

Bottom up parsing Construct a parse tree for an input string beginning at leaves and going towards root OR Reduce a string w of input to start symbol of grammar Consider a grammar S aabe A Abc b B d And

### Principles of Programming Languages

Principles of Programming Languages h"p://www.di.unipi.it/~andrea/dida2ca/plp- 14/ Prof. Andrea Corradini Department of Computer Science, Pisa Lesson 8! Bo;om- Up Parsing Shi?- Reduce LR(0) automata and

### LR Parsing. Table Construction

#1 LR Parsing Table Construction #2 Outline Review of bottom-up parsing Computing the parsing DFA Closures, LR(1) Items, States Transitions Using parser generators Handling Conflicts #3 In One Slide An

### Lecture Bottom-Up Parsing

Lecture 14+15 Bottom-Up Parsing CS 241: Foundations of Sequential Programs Winter 2018 Troy Vasiga et al University of Waterloo 1 Example CFG 1. S S 2. S AyB 3. A ab 4. A cd 5. B z 6. B wz 2 Stacks in

SYNTAX ANALYSIS 1. Define parser. Hierarchical analysis is one in which the tokens are grouped hierarchically into nested collections with collective meaning. Also termed as Parsing. 2. Mention the basic

### Example CFG. Lectures 16 & 17 Bottom-Up Parsing. LL(1) Predictor Table Review. Stacks in LR Parsing 1. Sʹ " S. 2. S " AyB. 3. A " ab. 4.

Example CFG Lectures 16 & 17 Bottom-Up Parsing CS 241: Foundations of Sequential Programs Fall 2016 1. Sʹ " S 2. S " AyB 3. A " ab 4. A " cd Matt Crane University of Waterloo 5. B " z 6. B " wz 2 LL(1)

### Bottom Up Parsing. Shift and Reduce. Sentential Form. Handle. Parse Tree. Bottom Up Parsing 9/26/2012. Also known as Shift-Reduce parsing

Also known as Shift-Reduce parsing More powerful than top down Don t need left factored grammars Can handle left recursion Attempt to construct parse tree from an input string eginning at leaves and working

### LR(0) Parsing Summary. LR(0) Parsing Table. LR(0) Limitations. A Non-LR(0) Grammar. LR(0) Parsing Table CS412/CS413

LR(0) Parsing ummary C412/C41 Introduction to Compilers Tim Teitelbaum Lecture 10: LR Parsing February 12, 2007 LR(0) item = a production with a dot in RH LR(0) state = set of LR(0) items valid for viable

### Review: Shift-Reduce Parsing. Bottom-up parsing uses two actions: Bottom-Up Parsing II. Shift ABC xyz ABCx yz. Lecture 8. Reduce Cbxy ijk CbA ijk

Review: Shift-Reduce Parsing Bottom-up parsing uses two actions: Bottom-Up Parsing II Lecture 8 Shift ABC xyz ABCx yz Reduce Cbxy ijk CbA ijk Prof. Aiken CS 13 Lecture 8 1 Prof. Aiken CS 13 Lecture 8 2

### LR Parsing E T + E T 1 T

LR Parsing 1 Introduction Before reading this quick JFLAP tutorial on parsing please make sure to look at a reference on LL parsing to get an understanding of how the First and Follow sets are defined.

### Monday, September 13, Parsers

Parsers Agenda Terminology LL(1) Parsers Overview of LR Parsing Terminology Grammar G = (Vt, Vn, S, P) Vt is the set of terminals Vn is the set of non-terminals S is the start symbol P is the set of productions

### Compiler Construction 2016/2017 Syntax Analysis

Compiler Construction 2016/2017 Syntax Analysis Peter Thiemann November 2, 2016 Outline 1 Syntax Analysis Recursive top-down parsing Nonrecursive top-down parsing Bottom-up parsing Syntax Analysis tokens

### Parsing. Handle, viable prefix, items, closures, goto s LR(k): SLR(1), LR(1), LALR(1)

TD parsing - LL(1) Parsing First and Follow sets Parse table construction BU Parsing Handle, viable prefix, items, closures, goto s LR(k): SLR(1), LR(1), LALR(1) Problems with SLR Aho, Sethi, Ullman, Compilers

### Review of CFGs and Parsing II Bottom-up Parsers. Lecture 5. Review slides 1

Review of CFGs and Parsing II Bottom-up Parsers Lecture 5 1 Outline Parser Overview op-down Parsers (Covered largely through labs) Bottom-up Parsers 2 he Functionality of the Parser Input: sequence of

### A left-sentential form is a sentential form that occurs in the leftmost derivation of some sentence.

Bottom-up parsing Recall For a grammar G, with start symbol S, any string α such that S α is a sentential form If α V t, then α is a sentence in L(G) A left-sentential form is a sentential form that occurs

### Compilers. Bottom-up Parsing. (original slides by Sam

Compilers Bottom-up Parsing Yannis Smaragdakis U Athens Yannis Smaragdakis, U. Athens (original slides by Sam Guyer@Tufts) Bottom-Up Parsing More general than top-down parsing And just as efficient Builds

### Bottom-Up Parsing II. Lecture 8

Bottom-Up Parsing II Lecture 8 1 Review: Shift-Reduce Parsing Bottom-up parsing uses two actions: Shift ABC xyz ABCx yz Reduce Cbxy ijk CbA ijk 2 Recall: he Stack Left string can be implemented by a stack

### LR Parsers. Aditi Raste, CCOEW

LR Parsers Aditi Raste, CCOEW 1 LR Parsers Most powerful shift-reduce parsers and yet efficient. LR(k) parsing L : left to right scanning of input R : constructing rightmost derivation in reverse k : number

### Syntax Analysis. Amitabha Sanyal. (www.cse.iitb.ac.in/ as) Department of Computer Science and Engineering, Indian Institute of Technology, Bombay

Syntax Analysis (www.cse.iitb.ac.in/ as) Department of Computer Science and Engineering, Indian Institute of Technology, Bombay September 2007 College of Engineering, Pune Syntax Analysis: 2/124 Syntax

### PART 3 - SYNTAX ANALYSIS. F. Wotawa TU Graz) Compiler Construction Summer term / 309

PART 3 - SYNTAX ANALYSIS F. Wotawa (IST @ TU Graz) Compiler Construction Summer term 2016 64 / 309 Goals Definition of the syntax of a programming language using context free grammars Methods for parsing

### 4. Lexical and Syntax Analysis

4. Lexical and Syntax Analysis 4.1 Introduction Language implementation systems must analyze source code, regardless of the specific implementation approach Nearly all syntax analysis is based on a formal

### Table-driven using an explicit stack (no recursion!). Stack can be viewed as containing both terminals and non-terminals.

Bottom-up Parsing: Table-driven using an explicit stack (no recursion!). Stack can be viewed as containing both terminals and non-terminals. Basic operation is to shift terminals from the input to the

### CSE 401 Compilers. LR Parsing Hal Perkins Autumn /10/ Hal Perkins & UW CSE D-1

CSE 401 Compilers LR Parsing Hal Perkins Autumn 2011 10/10/2011 2002-11 Hal Perkins & UW CSE D-1 Agenda LR Parsing Table-driven Parsers Parser States Shift-Reduce and Reduce-Reduce conflicts 10/10/2011

### LR Parsing Techniques

LR Parsing Techniques Bottom-Up Parsing - LR: a special form of BU Parser LR Parsing as Handle Pruning Shift-Reduce Parser (LR Implementation) LR(k) Parsing Model - k lookaheads to determine next action

### 4. Lexical and Syntax Analysis

4. Lexical and Syntax Analysis 4.1 Introduction Language implementation systems must analyze source code, regardless of the specific implementation approach Nearly all syntax analysis is based on a formal

### More Bottom-Up Parsing

More Bottom-Up Parsing Lecture 7 Dr. Sean Peisert ECS 142 Spring 2009 1 Status Project 1 Back By Wednesday (ish) savior lexer in ~cs142/s09/bin Project 2 Due Friday, Apr. 24, 11:55pm My office hours 3pm

Downloaded from http://himadri.cmsdu.org Page 1 LR Parsing We first understand Context Free Grammars. Consider the input string: x+2*y When scanned by a scanner, it produces the following stream of tokens:

### Chapter 4: LR Parsing

Chapter 4: LR Parsing 110 Some definitions Recall For a grammar G, with start symbol S, any string α such that S called a sentential form α is If α Vt, then α is called a sentence in L G Otherwise it is

### LR Parsing, Part 2. Constructing Parse Tables. An NFA Recognizing Viable Prefixes. Computing the Closure. GOTO Function and DFA States

TDDD16 Compilers and Interpreters TDDB44 Compiler Construction LR Parsing, Part 2 Constructing Parse Tables Parse table construction Grammar conflict handling Categories of LR Grammars and Parsers An NFA

### CS453 : JavaCUP and error recovery. CS453 Shift-reduce Parsing 1

CS453 : JavaCUP and error recovery CS453 Shift-reduce Parsing 1 Shift-reduce parsing in an LR parser LR(k) parser Left-to-right parse Right-most derivation K-token look ahead LR parsing algorithm using

### Lexical and Syntax Analysis. Top-Down Parsing

Lexical and Syntax Analysis Top-Down Parsing Easy for humans to write and understand String of characters Lexemes identified String of tokens Easy for programs to transform Data structure Syntax A syntax

### Syntax Analysis: Context-free Grammars, Pushdown Automata and Parsing Part - 4. Y.N. Srikant

Syntax Analysis: Context-free Grammars, Pushdown Automata and Part - 4 Department of Computer Science and Automation Indian Institute of Science Bangalore 560 012 NPTEL Course on Principles of Compiler

### Intro to Bottom-up Parsing. Lecture 9

Intro to Bottom-up Parsing Lecture 9 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

### Section A. A grammar that produces more than one parse tree for some sentences is said to be ambiguous.

Section A 1. What do you meant by parser and its types? A parser for grammar G is a program that takes as input a string w and produces as output either a parse tree for w, if w is a sentence of G, or

### How do LL(1) Parsers Build Syntax Trees?

How do LL(1) Parsers Build Syntax Trees? So far our LL(1) parser has acted like a recognizer. It verifies that input token are syntactically correct, but it produces no output. Building complete (concrete)

WWW.STUDENTSFOCUS.COM UNIT -3 SYNTAX ANALYSIS 3.1 ROLE OF THE PARSER Parser obtains a string of tokens from the lexical analyzer and verifies that it can be generated by the language for the source program.

### Context-Free Grammars and Parsers. Peter S. Housel January 2001

Context-Free Grammars and Parsers Peter S. Housel January 2001 Copyright This is the Monday grammar library, a set of facilities for representing context-free grammars and dynamically creating parser automata

### CS 2210 Sample Midterm. 1. Determine if each of the following claims is true (T) or false (F).

CS 2210 Sample Midterm 1. Determine if each of the following claims is true (T) or false (F). F A language consists of a set of strings, its grammar structure, and a set of operations. (Note: a language

### CS143 Handout 20 Summer 2011 July 15 th, 2011 CS143 Practice Midterm and Solution

CS143 Handout 20 Summer 2011 July 15 th, 2011 CS143 Practice Midterm and Solution Exam Facts Format Wednesday, July 20 th from 11:00 a.m. 1:00 p.m. in Gates B01 The exam is designed to take roughly 90

### UNIT-III BOTTOM-UP PARSING

UNIT-III BOTTOM-UP PARSING Constructing a parse tree for an input string beginning at the leaves and going towards the root is called bottom-up parsing. A general type of bottom-up parser is a shift-reduce

### Compiler Design 1. Bottom-UP Parsing. Goutam Biswas. Lect 6

Compiler Design 1 Bottom-UP Parsing Compiler Design 2 The Process The parse tree is built starting from the leaf nodes labeled by the terminals (tokens). The parser tries to discover appropriate reductions,

### Simple LR (SLR) LR(0) Drawbacks LR(1) SLR Parse. LR(1) Start State and Reduce. LR(1) Items 10/3/2012

LR(0) Drawbacks Consider the unambiguous augmented grammar: 0.) S E \$ 1.) E T + E 2.) E T 3.) T x If we build the LR(0) DFA table, we find that there is a shift-reduce conflict. This arises because the

### CSE 130 Programming Language Principles & Paradigms Lecture # 5. Chapter 4 Lexical and Syntax Analysis

Chapter 4 Lexical and Syntax Analysis Introduction - Language implementation systems must analyze source code, regardless of the specific implementation approach - Nearly all syntax analysis is based on

### Bottom Up Parsing Handout. 1 Introduction. 2 Example illustrating bottom-up parsing

Bottom Up Parsing Handout Compiled by: Nomair. Naeem dditional Material by: driel Dean-Hall and Brad Lushman his handout is intended to accompany material covered during lectures and is not consered a

### Lecture Notes on Bottom-Up LR Parsing

Lecture Notes on Bottom-Up LR Parsing 15-411: Compiler Design Frank Pfenning Lecture 9 September 23, 2009 1 Introduction In this lecture we discuss a second parsing algorithm that traverses the input string

### Top down vs. bottom up parsing

Parsing A grammar describes the strings that are syntactically legal A recogniser simply accepts or rejects strings A generator produces sentences in the language described by the grammar A parser constructs

### Top-Down Parsing and Intro to Bottom-Up Parsing. Lecture 7

Top-Down Parsing and Intro to Bottom-Up Parsing Lecture 7 1 Predictive Parsers Like recursive-descent but parser can predict which production to use Predictive parsers are never wrong Always able to guess

### Parsing III. CS434 Lecture 8 Spring 2005 Department of Computer Science University of Alabama Joel Jones

Parsing III (Top-down parsing: recursive descent & LL(1) ) (Bottom-up parsing) CS434 Lecture 8 Spring 2005 Department of Computer Science University of Alabama Joel Jones Copyright 2003, Keith D. Cooper,

### LALR Parsing. What Yacc and most compilers employ.

LALR Parsing Canonical sets of LR(1) items Number of states much larger than in the SLR construction LR(1) = Order of thousands for a standard prog. Lang. SLR(1) = order of hundreds for a standard prog.

### Lecture Notes on Bottom-Up LR Parsing

Lecture Notes on Bottom-Up LR Parsing 15-411: Compiler Design Frank Pfenning Lecture 9 1 Introduction In this lecture we discuss a second parsing algorithm that traverses the input string from left to

### Top-Down Parsing and Intro to Bottom-Up Parsing. Lecture 7

Top-Down Parsing and Intro to Bottom-Up Parsing Lecture 7 1 Predictive Parsers Like recursive-descent but parser can predict which production to use Predictive parsers are never wrong Always able to guess

### CSE302: 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 March 20, 2007 Outline Recap LR(0)

### Syntax Analysis Part I

Syntax Analysis Part I Chapter 4: Context-Free Grammars Slides adapted from : Robert van Engelen, Florida State University Position of a Parser in the Compiler Model Source Program Lexical Analyzer Token,

### Algorithms for NLP. LR Parsing. Reading: Hopcroft and Ullman, Intro. to Automata Theory, Lang. and Comp. Section , pp.

11-711 Algorithms for NL L arsing eading: Hopcroft and Ullman, Intro. to Automata Theory, Lang. and Comp. Section 10.6-10.7, pp. 248 256 Shift-educe arsing A class of parsers with the following principles:

### Parsing III. (Top-down parsing: recursive descent & LL(1) )

Parsing III (Top-down parsing: recursive descent & LL(1) ) Roadmap (Where are we?) Previously We set out to study parsing Specifying syntax Context-free grammars Ambiguity Top-down parsers Algorithm &

### CS2210: Compiler Construction Syntax Analysis Syntax Analysis

Comparison with Lexical Analysis The second phase of compilation Phase Input Output Lexer string of characters string of tokens Parser string of tokens Parse tree/ast What Parse Tree? CS2210: Compiler

### Bottom-up Parser. Jungsik Choi

Formal Languages and Compiler (CSE322) Bottom-up Parser Jungsik Choi chjs@khu.ac.kr * Some slides taken from SKKU SWE3010 (Prof. Hwansoo Han) and TAMU CSCE434-500 (Prof. Lawrence Rauchwerger) Bottom-up

### Lecture 14: Parser Conflicts, Using Ambiguity, Error Recovery. Last modified: Mon Feb 23 10:05: CS164: Lecture #14 1

Lecture 14: Parser Conflicts, Using Ambiguity, Error Recovery Last modified: Mon Feb 23 10:05:56 2015 CS164: Lecture #14 1 Shift/Reduce Conflicts If a DFA state contains both [X: α aβ, b] and [Y: γ, a],

VIVA QUESTIONS WITH ANSWERS 1. What is a compiler? A compiler is a program that reads a program written in one language the source language and translates it into an equivalent program in another language-the

### Lexical and Syntax Analysis

Lexical and Syntax Analysis (of Programming Languages) Top-Down Parsing Lexical and Syntax Analysis (of Programming Languages) Top-Down Parsing Easy for humans to write and understand String of characters

### Configuration Sets for CSX- Lite. Parser Action Table

Configuration Sets for CSX- Lite State s 6 s 7 Cofiguration Set Prog { Stmts } Eof Stmts Stmt Stmts State s s Cofiguration Set Prog { Stmts } Eof Prog { Stmts } Eof Stmts Stmt Stmts Stmts λ Stmt if ( Expr

### FROWN An LALR(k) Parser Generator

FROWN An LALR(k) Parser Generator RALF HINZE Institute of Information and Computing Sciences Utrecht University Email: ralf@cs.uu.nl Homepage: http://www.cs.uu.nl/~ralf/ September, 2001 (Pick the slides