Ambiguity. Grammar E E + E E * E ( E ) int. The string int * int + int has two parse trees. * int


 Ronald Bradley
 3 years ago
 Views:
Transcription
1 Administrivia Ambiguity, Precedence, Associativity & opdown Parsing eam assignments this evening for all those not listed as having one. HW#3 is now available, due next uesday morning (Monday is a holiday). Lecture 910 (From slides by G. Necula & R. Bodik) 2/13/2008 Prof. Hilfinger CS164 Lecture 9 1 2/13/2008 Prof. Hilfinger CS164 Lecture 9 2 Remaining Issues How do we find a derivation of s? Ambiguity: what there is more than one parse tree (erpretation) for some string s? rrors: what there is no parse tree for some string s? Given a derivation, how do we construct an abstract syntax tree from it? Ambiguity Grammar ( ) Strings 2/13/2008 Prof. Hilfinger CS164 Lecture 9 3 2/13/2008 Prof. Hilfinger CS164 Lecture 9 4 Ambiguity. xample he string has two parse trees Ambiguity. xample he string has two parse trees is leftassociative 2/13/2008 Prof. Hilfinger CS164 Lecture 9 5 has higher precedence than 2/13/2008 Prof. Hilfinger CS164 Lecture 9 6 1
2 Ambiguity (Cont.) A grammar is ambiguous it has more than one parse tree for some string quivalently, there is more than one rightmost or leftmost derivation for some string Ambiguity is bad Leaves meaning of some programs illdefined Ambiguity is common in programming languages Arithmetic expressions IFHNLS 2/13/2008 Prof. Hilfinger CS164 Lecture 9 7 Dealing with Ambiguity here are several ways to handle ambiguity Most direct method is to rewrite the grammar unambiguously ( ) nforces precedence of over nforces leftassociativity of and 2/13/2008 Prof. Hilfinger CS164 Lecture 9 8 Ambiguity. xample he has only one parse tree now Ambiguity: he Dangling lse Consider the grammar then then else OHR his grammar is also ambiguous 2/13/2008 Prof. Hilfinger CS164 Lecture 9 9 2/13/2008 Prof. Hilfinger CS164 Lecture 9 10 he Dangling lse: xample he expression 1 then 2 then 3 else 4 has two parse trees ypically we want the second form 2/13/2008 Prof. Hilfinger CS164 Lecture he Dangling lse: A Fix else matches the closest unmatched then We can describe this in the grammar (distinguish between matched and unmatched then ) MIF / all then are matched / UIF / some then are unmatched / MIF then MIF else MIF OHR UIF then then MIF else UIF Describes the same set of strings 2/13/2008 Prof. Hilfinger CS164 Lecture
3 he Dangling lse: xample Revisited he expression 1 then 2 then 3 else A valid parse tree (for a UIF) 2/13/2008 Prof. Hilfinger CS164 Lecture Not valid because the then expression is not a MIF Ambiguity Impossible to convert automatically an ambiguous grammar to an unambiguous one Used with care, ambiguity can simply the grammar Sometimes allows more natural definitions But we need disambiguation mechanisms Instead of rewriting the grammar Use the more natural (ambiguous) grammar Along with disambiguating declarations Most tools allow precedence and associativity declarations to disambiguate grammars xamples 2/13/2008 Prof. Hilfinger CS164 Lecture 9 14 Associativity Declarations Consider the grammar Ambiguous: two parse trees of Leftassociativity declaration: %left 2/13/2008 Prof. Hilfinger CS164 Lecture 9 15 Precedence Declarations Consider the grammar And the string 2/13/2008 Prof. Hilfinger CS164 Lecture 9 16 Precedence declarations: %left %left How It s Done I: Intro to opdown Parsing opdown DepthFirst Parsing erminals are seen in order of appearance in the token stream: t 1 t 2 t 3 t 4 t 5 he parse tree is constructed From the top From left to right As for leftmost derivation t 1 A B C t 2 t 3 D t 4 t 4 Consider the grammar ( ) oken stream is: Start with toplevel nonterminal ry the rules for in order 2/13/2008 Prof. Hilfinger CS164 Lecture /13/2008 Prof. Hilfinger CS164 Lecture
4 DepthFirst Parsing. xample DepthFirst Parsing. xample Start with start symbol ry hen try a rule for ( ) () But ( input ; backtrack to ry. oken matches. But input ; back to ry But (skipping some steps) can t be matched Must backtrack to 2/13/2008 Prof. Hilfinger CS164 Lecture 9 19 ry Follow same steps as before for And succeed with and With the following parse tree 2/13/2008 Prof. Hilfinger CS164 Lecture 9 20 DepthFirst Parsing Parsing: given a string of tokens t 1 t 2... t n, find a leftmost derivation (and thus, parse tree) Depthfirst parsing: Beginning with start symbol, try each production exhaustively on leftmost nonterminal in current sentential form and recurse. 2/13/2008 Prof. Hilfinger CS164 Lecture 9 21 DepthFirst Parsing of t 1 t 2 t n At a given moment, have sentential form that looks like this: t 1 t 2 t k A, 0 k n Initially, k=0 and A is just start symbol ry a production for A: A BC is a production, the new form is t 1 t 2 t k B C Backtrack when leading terminals aren t prefix of t 1 t 2 t n and try another production Stop when no more nonterminals and terminals all matched (accept) or no more productions left (reject) 2/13/2008 Prof. Hilfinger CS164 Lecture 9 22 When DepthFirst Doesn t Work Well Consider productions S S a a: In the process of parsing S we try the above rules Applied consistently in this order, get infinite loop Could reorder productions, but search will have lots of backtracking and general rule for ordering is complex Problem here is leftrecursive grammar: one that has a nonterminal S S Sα for some α limination of Left Recursion Consider the leftrecursive grammar S S α β S generates all strings starting with a β and followed by any number of α s Can rewrite using rightrecursion S β S S α S 2/13/2008 Prof. Hilfinger CS164 Lecture /13/2008 Prof. Hilfinger CS164 Lecture
5 limination of left Recursion. xample Consider the grammar S 1 S 0 ( β = 1 and α = 0 ) can be rewritten as S 1 S S 0 S More limination of Left Recursion In general S S α 1 S α n β 1 β m All strings derived from S start with one of β 1,,β m and continue with several instances of α 1,,α n Rewrite as S β 1 S β m S S α 1 S α n S 2/13/2008 Prof. Hilfinger CS164 Lecture /13/2008 Prof. Hilfinger CS164 Lecture 9 26 General Left Recursion he grammar S A α δ (1) A S β (2) is also leftrecursive because S S β α his left recursion can also be eliminated by first substituting (2) o (1) here is a general algorithm (e.g. Aho, Sethi, Ullman 4.3) But personally, I d just do this by hand. 2/13/2008 Prof. Hilfinger CS164 Lecture 9 27 An Alternative Approach Instead of reordering or rewriting grammar, can use topdown breadthfirst search. S S a a String: aaa S a a a S a a S S a a (not all matched) a a a a a 2/13/2008 Prof. Hilfinger CS164 Lecture 9 28 Summary of opdown Parsing So Far Simple and general parsing strategy Left recursion must be eliminated first but that can be done automatically Or can use breadthfirst search But backtracking (depthfirst) or maaining list of possible sentential forms (breadthfirst) can make it slow Often, though, we can avoid both Predictive Parsers Modication of depthfirst parsing in which parser predicts which production to use By looking at the next few tokens No backtracking Predictive parsers accept LL(k) grammars L means lefttoright scan of input L means leftmost derivation k means need k tokens of lookahead to predict In practice, LL(1) is used 2/13/2008 Prof. Hilfinger CS164 Lecture /13/2008 Prof. Hilfinger CS164 Lecture
6 Recursive Descent: Grammar as Program In recursive descent, we think of a grammar as a program. Here, we ll look at predictive version. ach nonterminal is turned o a procedure ach righthand side transliterated o part of the procedure body for its nonterminal First, define next() current token of input scan(t) check that next()=t (else RROR), and then read new token. 2/13/2008 Prof. Hilfinger CS164 Lecture 9 31 Recursive Descent: xample P S $ S S S S ( S ) def P (): S(); scan($) def S(): (); S () def S (): predict next() == : scan( ); S() el next() in [ ), $]: pass else: RROR def (): next () == : scan() el next() == ( : scan( ( ); S(); scan ( ) ) else: RROR ($ = end marker) But where do prediction tests come from? 2/13/2008 Prof. Hilfinger CS164 Lecture 9 32 Predicting Righthand Sides he tests are conditions by which parser predicts which righthand side to use. In our example, used only next symbol (LL(1)); but could use more. Can be specied as a 2D table One dimension for current nonterminal to expand One dimension for next token A table entry contains one production But First: Left Factoring With the grammar ( ) Impossible to predict because For two productions start with For it is not clear how to predict A grammar must be leftfactored before use for predictive parsing 2/13/2008 Prof. Hilfinger CS164 Lecture /13/2008 Prof. Hilfinger CS164 Lecture 9 34 LeftFactoring xample Starting with the grammar ( ) Factor out common prefixes of productions X X ( ) Y Y Recursive Descent for Real So far, have presented a purist view. In fact, use of recursive descent makes le simpler in many ways we cheat a bit. Here s how you really handle left recursion in recursive descent, for S S A R: def S(): R () while next() FIRS(A): A() It s a program: all kinds of shortcuts possible. 2/13/2008 Prof. Hilfinger CS164 Lecture /13/2008 Prof. Hilfinger CS164 Lecture
7 LL(1) Parsing able xample Leftfactored grammar X ( ) Y X Y he LL(1) parsing table ($ is a special end marker): X Y Y X ( ( ) X ) $ LL(1) Parsing able xample (Cont.) Consider the [, ] entry Means When current nonterminal is and next input is, use production X X can generate string with in front Consider the [Y,] entry When current nonterminal is Y and current token is, get rid of Y We ll see later why this is right 2/13/2008 Prof. Hilfinger CS164 Lecture /13/2008 Prof. Hilfinger CS164 Lecture 9 38 LL(1) Parsing ables. rrors Blank entries indicate error situations Consider the [,] entry here is no way to derive a string starting with from nonterminal Using Parsing ables ssentially tabledriven recursive descent, except We use a stack to keep track of pending nonterminals We reject when we encounter an error state We accept when we encounter endofinput 2/13/2008 Prof. Hilfinger CS164 Lecture /13/2008 Prof. Hilfinger CS164 Lecture 9 40 LL(1) Parsing Algorithm initialize stack = <S,$> repeat case stack of <X, rest> : [X,next()] == Y 1 Y n : stack <Y 1 Y n rest>; else: error (); <t, rest> : scan (t); stack <rest>; until stack == < > LL(1) Parsing xample Stack Input Action $ $ X X $ $ Y Y X $ $ terminal Y X $ $ X $ $ terminal X $ $ Y Y X $ $ terminal Y X $ $ X $ $ $ $ ACCP 2/13/2008 Prof. Hilfinger CS164 Lecture /13/2008 Prof. Hilfinger CS164 Lecture
8 Constructing Parsing ables LL(1) languages are those definable by a parsing table for the LL(1) algorithm such that no table entry is multiply defined Once we have the table Can create tabledriver or recursivedescent parser he parsing algorithms are simple and fast No backtracking is necessary We want to generate parsing tables from CFG 2/13/2008 Prof. Hilfinger CS164 Lecture 9 43 Predicting Productions I opdown parsing expands a parse tree from the start symbol to the leaves Always expand the leftmost nonterminal 2/13/2008 Prof. Hilfinger CS164 Lecture 9 44 Predicting Productions II Predicting Productions III opdown parsing expands a parse tree from the start symbol to the leaves Always expand the leftmost nonterminal he leaves at any po form a string βaγ β contains only terminals he input string is βbδ he prefix β matches he next token is b 2/13/2008 Prof. Hilfinger CS164 Lecture 9 45 opdown parsing expands a parse tree from the start symbol to the leaves Always expand the leftmost nonterminal he leaves at any po form a string βaγ (A=, γ=) β contains only terminals γ contains any symbols he input string is βbδ (b=) So Aγ must derive bδ 2/13/2008 Prof. Hilfinger CS164 Lecture 9 46 Predicting Productions IV Predicting Productions V opdown parsing expands a parse tree from the start symbol to the leaves Always expand the leftmost nonterminal So choose production for that can eventually derive something that starts with 2/13/2008 Prof. Hilfinger CS164 Lecture 9 47 Go back to previous grammar, with X X ( ) Y Y Y X Here, YX must match Since doesn t start with, can t use Y 2/13/2008 Prof. Hilfinger CS164 Lecture
9 Predicting Productions V Go back to previous grammar, with X X ( ) Y Y Y X But can follow Y, so we choose Y FIRS and FOLLOW o summarize, we are trying to predict how to expand A with b the next token, then either: b belongs to an expansion of A Any A α can be used b can start a string derived from α In this case we say that b First(α) or b does not belong to an expansion of A, A has an expansion that derives, and b belongs to something that can follow A (so S βabω) We say that b Follow(A) in this case. 2/13/2008 Prof. Hilfinger CS164 Lecture /13/2008 Prof. Hilfinger CS164 Lecture 9 50 Summary of Definitions Computing First Sets For b, the set of terminals; α a sequence of terminal & nonterminal symbols, S the start symbol, A N, the set of nonterminals: FIRS(α) { } b FIRS(α) f α b FIRS(α) f α FOLLOW(A) b FOLLOW(A) f S A b 2/13/2008 Prof. Hilfinger CS164 Lecture 9 51 Definition First(X) = { b X bα} { X }, X any grammar symbol. 1. First(b) = { b } for b any terminal symbol 2. For all productions X A 1 A n Add First(A 1 ) {} to First(X). Stop First(A 1 ) Add First(A 2 ) {} to First(X). Stop First(A 2 ) Add First(A n ) {} to First(X). Stop First(A n ) Add to First(X) 3. Repeat 2 until nothing changes ( compute fixed po ) 2/13/2008 Prof. Hilfinger CS164 Lecture 9 52 Computing First Sets, Contd. hat takes care of singlesymbol case. In general: FIRS(X 1 X 2 X k ) = FIRS(X 1 ) FIRS(X 2 ) FIRS(X 1 ) FIRS(X k ) FIRS(X 1 X 2 X k1 )  { } unless FIRS(X i ) i First Sets. xample For the grammar X X ( ) Y Y First sets First( ( ) = { ( } First( ) = {, ( } First( ) ) = { ) } First( ) = {, ( } First( ) = { } First( X ) = {, } First( ) = { } First( Y ) = {, } First( ) = { } 2/13/2008 Prof. Hilfinger CS164 Lecture /13/2008 Prof. Hilfinger CS164 Lecture
10 Computing Follow Sets Follow Sets. xample Definition Follow(X) = { b S β X b ω } 1. Compute the First sets for all nonterminals first 2. Add $ to Follow(S) ( S is the start nonterminal) 3. For all productions Y X A 1 A n Add First(A 1 ) {} to Follow(X). Stop First(A 1 ) Add First(A 2 ) {} to Follow(X). Stop First(A 2 ) Add First(A n ) {} to Follow(X). Stop First(A n ) Add Follow(Y) to Follow(X) 4. Repeat 3 until nothing changes. For the grammar X ( ) Y Follow sets Follow( ) = {), $} Follow( X ) = {$, ) } Follow( Y ) = {, ), $} Follow( ) = {, ), $} X Y 2/13/2008 Prof. Hilfinger CS164 Lecture /13/2008 Prof. Hilfinger CS164 Lecture 9 56 Constructing LL(1) Parsing ables LL(1) Parsing able xample Construct a parsing table for CFG G X ( ) Y X Y For each production A α in G do: For each terminal b First(α) do [A, b] = α If α, for each b Follow(A) do [A, b] = α 2/13/2008 Prof. Hilfinger CS164 Lecture 9 57 X Y Y X ( ) X Follow( ) = {), $} First( ) = {, ( } Follow( X ) = {$, ) } First( ) = {, ( } Follow( Y ) = {, ), $} First( X ) = {, } Follow( ) = {, ), $} First( Y ) = {, } 2/13/2008 Prof. Hilfinger CS164 Lecture 9 58 ( ) $ Notes on LL(1) Parsing ables If any entry is multiply defined then G is not LL(1). his happens If G is ambiguous If G is left recursive If G is not leftfactored And in other cases as well Most programming language grammars are not LL(1) here are tools that build LL(1) tables Review For some grammars there is a simple parsing strategy Predictive parsing (LL(1)) Once you build the LL(1) table (or know the FIRS and FOLLOW sets), you can write the parser by hand: recursive descent. Next: a more powerful parsing strategy for grammars that are not LL(1) 2/13/2008 Prof. Hilfinger CS164 Lecture /13/2008 Prof. Hilfinger CS164 Lecture
Ambiguity, Precedence, Associativity & TopDown Parsing. Lecture 910
Ambiguity, Precedence, Associativity & TopDown Parsing Lecture 910 (From slides by G. Necula & R. Bodik) 9/18/06 Prof. Hilfinger CS164 Lecture 9 1 Administrivia Please let me know if there are continued
More informationAdministrativia. WA1 due on Thu PA2 in a week. Building a Parser III. Slides on the web site. CS164 3:305:00 TT 10 Evans.
Administrativia Building a Parser III CS164 3:305:00 10 vans WA1 due on hu PA2 in a week Slides on the web site I do my best to have slides ready and posted by the end of the preceding logical day yesterday,
More informationBuilding a Parser III. CS164 3:305:00 TT 10 Evans. Prof. Bodik CS 164 Lecture 6 1
Building a Parser III CS164 3:305:00 TT 10 Evans 1 Overview Finish recursive descent parser when it breaks down and how to fix it eliminating left recursion reordering productions Predictive parsers (aka
More informationGrammars and ambiguity. CS164 3:305:00 TT 10 Evans. Prof. Bodik CS 164 Lecture 8 1
Grammars and ambiguity CS164 3:305:00 TT 10 vans 1 Overview derivations and parse trees different derivations produce may produce same parse tree ambiguous grammars what they are and how to fix them 2
More informationCS1622. Today. A Recursive Descent Parser. Preliminaries. Lecture 9 Parsing (4)
CS1622 Lecture 9 Parsing (4) CS 1622 Lecture 9 1 Today Example of a recursive descent parser Predictive & LL(1) parsers Building parse tables CS 1622 Lecture 9 2 A Recursive Descent Parser. Preliminaries
More informationParsing: Derivations, Ambiguity, Precedence, Associativity. Lecture 8. Professor Alex Aiken Lecture #5 (Modified by Professor Vijay Ganesh)
Parsing: Derivations, Ambiguity, Precedence, Associativity Lecture 8 (Modified by Professor Vijay Ganesh) 1 Topics covered so far Regular languages and Finite automaton Parser overview Contextfree grammars
More informationAbstract Syntax Trees & TopDown Parsing
Review of Parsing Abstract Syntax Trees & TopDown Parsing Given a language L(G), a parser consumes a sequence of tokens s and produces a parse tree Issues: How do we recognize that s L(G)? A parse tree
More informationE E+E E E (E) id. id + id E E+E. id E + E id id + E id id + id. Overview. derivations and parse trees. Grammars and ambiguity. ambiguous grammars
Overview Grammars and ambiguity CS164 3:305:00 TT 10 vans derivations and parse trees dferent derivations produce may produce same parse tree ambiguous grammars what they are and how to fix them 1 2 Recall:
More informationAbstract Syntax Trees & TopDown Parsing
Abstract Syntax Trees & TopDown Parsing Review of Parsing Given a language L(G), a parser consumes a sequence of tokens s and produces a parse tree Issues: How do we recognize that s L(G)? A parse tree
More informationAbstract Syntax Trees & TopDown Parsing
Review of Parsing Abstract Syntax Trees & TopDown Parsing Given a language L(G), a parser consumes a sequence of tokens s and produces a parse tree Issues: How do we recognize that s L(G)? A parse tree
More informationExtra Credit Question
TopDown Parsing #1 Extra Credit Question Given this grammar G: E E+T E T T T * int T int T (E) Is the string int * (int + int) in L(G)? Give a derivation or prove that it is not. #2 Revenge of Theory
More informationTopDown Parsing and Intro to BottomUp Parsing. Lecture 7
TopDown Parsing and Intro to BottomUp Parsing Lecture 7 1 Predictive Parsers Like recursivedescent but parser can predict which production to use Predictive parsers are never wrong Always able to guess
More informationOutline. Parser overview Contextfree grammars (CFG s) Derivations SyntaxDirected Translation
Outline Introduction to Parsing (adapted from CS 164 at Berkeley) Parser overview Contextfree grammars (CFG s) Derivations SyntaxDirected ranslation he Functionality of the Parser Input: sequence of
More informationTopDown Parsing and Intro to BottomUp Parsing. Lecture 7
TopDown Parsing and Intro to BottomUp Parsing Lecture 7 1 Predictive Parsers Like recursivedescent but parser can predict which production to use Predictive parsers are never wrong Always able to guess
More information( ) i 0. Outline. Regular languages revisited. Introduction to Parsing. Parser overview. Contextfree grammars (CFG s) Lecture 5.
Outline Regular languages revisited Introduction to Parsing Lecture 5 Parser overview Contextfree grammars (CFG s) Derivations Prof. Aiken CS 143 Lecture 5 1 Ambiguity Prof. Aiken CS 143 Lecture 5 2 Languages
More informationOutline. Regular languages revisited. Introduction to Parsing. Parser overview. Contextfree grammars (CFG s) Lecture 5. Derivations.
Outline Regular languages revisited Introduction to Parsing Lecture 5 Parser overview Contextfree grammars (CFG s) Derivations Prof. Aiken CS 143 Lecture 5 1 Ambiguity Prof. Aiken CS 143 Lecture 5 2 Languages
More informationAmbiguity. Lecture 8. CS 536 Spring
Ambiguity Lecture 8 CS 536 Spring 2001 1 Announcement Reading Assignment ContextFree Grammars (Sections 4.1, 4.2) Programming Assignment 2 due Friday! Homework 1 due in a week (Wed Feb 21) not Feb 25!
More informationIntroduction to Parsing Ambiguity and Syntax Errors
Introduction to Parsing Ambiguity and Syntax rrors Outline Regular languages revisited Parser overview Contextfree grammars (CFG s) Derivations Ambiguity Syntax errors Compiler Design 1 (2011) 2 Languages
More informationTop 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
More informationIntroduction to Parsing. Lecture 5. Professor Alex Aiken Lecture #5 (Modified by Professor Vijay Ganesh)
Introduction to Parsing Lecture 5 (Modified by Professor Vijay Ganesh) 1 Outline Regular languages revisited Parser overview Contextfree grammars (CFG s) Derivations Ambiguity 2 Languages and Automata
More information8 Parsing. Parsing. Top Down Parsing Methods. Parsing complexity. Top down vs. bottom up parsing. Top down vs. bottom up parsing
8 Parsing Parsing A grammar describes syntactically legal strings in a language A recogniser simply accepts or rejects strings A generator produces strings A parser constructs a parse tree for a string
More informationCompilers. Predictive Parsing. Alex Aiken
Compilers Like recursivedescent but parser can predict which production to use By looking at the next fewtokens No backtracking Predictive parsers accept LL(k) grammars L means lefttoright scan of input
More informationIntroduction to Parsing. Lecture 5
Introduction to Parsing Lecture 5 1 Outline Regular languages revisited Parser overview Contextfree grammars (CFG s) Derivations Ambiguity 2 Languages and Automata Formal languages are very important
More informationTypes of parsing. CMSC 430 Lecture 4, Page 1
Types of parsing Topdown parsers start at the root of derivation tree and fill in picks a production and tries to match the input may require backtracking some grammars are backtrackfree (predictive)
More informationIntroduction to Parsing Ambiguity and Syntax Errors
Introduction to Parsing Ambiguity and Syntax rrors Outline Regular languages revisited Parser overview Contextfree grammars (CFG s) Derivations Ambiguity Syntax errors 2 Languages and Automata Formal
More informationParsing. Roadmap. > Contextfree grammars > Derivations and precedence > Topdown parsing > Leftrecursion > Lookahead > Tabledriven parsing
Roadmap > Contextfree grammars > Derivations and precedence > Topdown parsing > Leftrecursion > Lookahead > Tabledriven parsing The role of the parser > performs contextfree syntax analysis > guides
More informationLL Parsing: A piece of cake after LR
LL Parsing: A piece of cake after LR Lecture 11 Dr. Sean Peisert ECS 142 Spring 2009 1 LL Parsing Still specified using a CFG Still reads lefttoright (Lx) Now is leftmost derivation (xl) rather than
More informationNote that for recursive descent to work, if A ::= B1 B2 is a grammar rule we need First k (B1) disjoint from First k (B2).
LL(k) Grammars We need a bunch of terminology. For any terminal string a we write First k (a) is the prefix of a of length k (or all of a if its length is less than k) For any string g of terminal and
More information3. Parsing. Oscar Nierstrasz
3. Parsing Oscar Nierstrasz Thanks to Jens Palsberg and Tony Hosking for their kind permission to reuse and adapt the CS132 and CS502 lecture notes. http://www.cs.ucla.edu/~palsberg/ http://www.cs.purdue.edu/homes/hosking/
More informationIntroduction to Parsing. Lecture 5
Introduction to Parsing Lecture 5 1 Outline Regular languages revisited Parser overview Contextfree grammars (CFG s) Derivations Ambiguity 2 Languages and Automata Formal languages are very important
More informationCS502: Compilers & Programming Systems
CS502: Compilers & Programming Systems Topdown Parsing Zhiyuan Li Department of Computer Science Purdue University, USA There exist two wellknown schemes to construct deterministic topdown parsers:
More informationLL(k) Parsing. Predictive Parsers. LL(k) Parser Structure. Sample Parse Table. LL(1) Parsing Algorithm. Push RHS in Reverse Order 10/17/2012
Predictive Parsers LL(k) Parsing Can we avoid backtracking? es, if for a given input symbol and given nonterminal, we can choose the alternative appropriately. his is possible if the first terminal of
More informationLecture 8: Deterministic BottomUp Parsing
Lecture 8: Deterministic BottomUp 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
More informationParsing Part II. (Ambiguity, Topdown parsing, Leftrecursion Removal)
Parsing Part II (Ambiguity, Topdown parsing, Leftrecursion Removal) Ambiguous Grammars Definitions If a grammar has more than one leftmost derivation for a single sentential form, the grammar is ambiguous
More informationOutline. Limitations of regular languages Parser overview Contextfree grammars (CFG s) Derivations SyntaxDirected Translation
Outline Introduction to Parsing Lecture 8 Adapted from slides by G. Necula and R. Bodik Limitations of regular languages Parser overview Contextfree grammars (CG s) Derivations SyntaxDirected ranslation
More informationLecture 7: Deterministic BottomUp Parsing
Lecture 7: Deterministic BottomUp 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
More informationFormal Languages and Compilers Lecture V: Parse Trees and Ambiguous Gr
Formal Languages and Compilers Lecture V: Parse Trees and Ambiguous Grammars Free University of BozenBolzano Faculty of Computer Science POS Building, Room: 2.03 artale@inf.unibz.it http://www.inf.unibz.it/
More informationCS 321 Programming Languages and Compilers. VI. Parsing
CS 321 Programming Languages and Compilers VI. Parsing Parsing Calculate grammatical structure of program, like diagramming sentences, where: Tokens = words Programs = sentences For further information,
More informationError Handling SyntaxDirected Translation Recursive Descent Parsing
Announcements rror Handling SyntaxDirected ranslation Lecture 6 PA1 & WA1 Due today at midnight PA2 & WA2 Assigned today Prof. Aiken CS 143 Lecture 6 1 Prof. Aiken CS 143 Lecture 6 2 Outline xtensions
More informationError Handling SyntaxDirected Translation Recursive Descent Parsing
Announcements rror Handling SyntaxDirected ranslation Lecture 6 PA1 & WA1 Due today at midnight PA2 & WA2 Assigned today Prof. Aiken CS 14 Lecture 6 1 Prof. Aiken CS 14 Lecture 6 2 Outline xtensions of
More informationLexical and Syntax Analysis. TopDown Parsing
Lexical and Syntax Analysis TopDown 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
More informationCS 314 Principles of Programming Languages
CS 314 Principles of Programming Languages Lecture 5: Syntax Analysis (Parsing) Zheng (Eddy) Zhang Rutgers University January 31, 2018 Class Information Homework 1 is being graded now. The sample solution
More information1 Introduction. 2 Recursive descent parsing. Predicative parsing. Computer Language Implementation Lecture Note 3 February 4, 2004
CMSC 51086 Winter 2004 Computer Language Implementation Lecture Note 3 February 4, 2004 Predicative parsing 1 Introduction This note continues the discussion of parsing based on context free languages.
More informationLexical and Syntax Analysis
Lexical and Syntax Analysis (of Programming Languages) TopDown Parsing Lexical and Syntax Analysis (of Programming Languages) TopDown Parsing Easy for humans to write and understand String of characters
More informationSometimes an ambiguous grammar can be rewritten to eliminate the ambiguity.
Eliminating Ambiguity Sometimes an ambiguous grammar can be rewritten to eliminate the ambiguity. Example: consider the following grammar stat if expr then stat if expr then stat else stat other One can
More informationCA Compiler Construction
CA4003  Compiler Construction David Sinclair A topdown parser starts with the root of the parse tree, labelled with the goal symbol of the grammar, and repeats the following steps until the fringe of
More informationBottomUp Parsing. Lecture 1112
BottomUp Parsing Lecture 1112 (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
More informationIntro To Parsing. Step By Step
#1 Intro To Parsing Step By Step #2 SelfTest from Last Time Are practical parsers and scanners based on deterministic or nondeterministic automata? How can regular expressions be used to specify nested
More informationAdministrativia. PA2 assigned today. WA1 assigned today. Building a Parser II. CS164 3:305:00 TT 10 Evans. First midterm. Grammars.
Administrativia Building a Parser II CS164 3:305:00 TT 10 Evans PA2 assigned today due in 12 days WA1 assigned today due in a week it s a practice for the exam First midterm Oct 5 will contain some projectinspired
More informationReview: ShiftReduce Parsing. Bottomup parsing uses two actions: BottomUp Parsing II. Shift ABC xyz ABCx yz. Lecture 8. Reduce Cbxy ijk CbA ijk
Review: ShiftReduce Parsing Bottomup parsing uses two actions: BottomUp 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
More informationBottomUp Parsing II (Different types of ShiftReduce Conflicts) Lecture 10. Prof. Aiken (Modified by Professor Vijay Ganesh.
BottomUp Parsing II Different types of ShiftReduce Conflicts) Lecture 10 Ganesh. Lecture 10) 1 Review: BottomUp Parsing Bottomup parsing is more general than topdown parsing And just as efficient Doesn
More informationParsing III. CS434 Lecture 8 Spring 2005 Department of Computer Science University of Alabama Joel Jones
Parsing III (Topdown parsing: recursive descent & LL(1) ) (Bottomup parsing) CS434 Lecture 8 Spring 2005 Department of Computer Science University of Alabama Joel Jones Copyright 2003, Keith D. Cooper,
More informationCompilerconstructie. najaar Rudy van Vliet kamer 140 Snellius, tel rvvliet(at)liacs(dot)nl. college 3, vrijdag 22 september 2017
Compilerconstructie najaar 2017 http://www.liacs.leidenuniv.nl/~vlietrvan1/coco/ Rudy van Vliet kamer 140 Snellius, tel. 071527 2876 rvvliet(at)liacs(dot)nl college 3, vrijdag 22 september 2017 + werkcollege
More informationMore BottomUp Parsing
More BottomUp 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
More information4 (c) parsing. Parsing. Top down vs. bo5om up parsing
4 (c) parsing Parsing A grammar describes syntac2cally legal strings in a language A recogniser simply accepts or rejects strings A generator produces strings A parser constructs a parse tree for a string
More informationIntroduction to BottomUp Parsing
Introduction to BottomUp Parsing Lecture 11 CS 536 Spring 2001 1 Outline he strategy: shiftreduce parsing Ambiguity and precedence declarations Next lecture: bottomup parsing algorithms CS 536 Spring
More informationCSCI312 Principles of Programming Languages
Copyright 2006 The McGrawHill Companies, Inc. CSCI312 Principles of Programming Languages! LL Parsing!! Xu Liu Derived from Keith Cooper s COMP 412 at Rice University Recap Copyright 2006 The McGrawHill
More informationSyntax Analysis Check syntax and construct abstract syntax tree
Syntax Analysis Check syntax and construct abstract syntax tree if == = ; b 0 a b Error reporting and recovery Model using context free grammars Recognize using Push down automata/table Driven Parsers
More informationSyntactic Analysis. TopDown Parsing
Syntactic Analysis TopDown Parsing Copyright 2017, Pedro C. Diniz, all rights reserved. Students enrolled in Compilers class at University of Southern California (USC) have explicit permission to make
More informationCS2210: 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
More informationCompilers. Yannis Smaragdakis, U. Athens (original slides by Sam
Compilers Parsing Yannis Smaragdakis, U. Athens (original slides by Sam Guyer@Tufts) Next step text chars Lexical analyzer tokens Parser IR Errors Parsing: Organize tokens into sentences Do tokens conform
More informationParsing. 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
More informationCS415 Compilers. Syntax Analysis. These slides are based on slides copyrighted by Keith Cooper, Ken Kennedy & Linda Torczon at Rice University
CS415 Compilers Syntax Analysis These slides are based on slides copyrighted by Keith Cooper, Ken Kennedy & Linda Torczon at Rice University Limits of Regular Languages Advantages of Regular Expressions
More informationOutline. The strategy: shiftreduce parsing. Introduction to BottomUp Parsing. A key concept: handles
Outline Introduction to BottomUp Parsing Lecture Notes by Profs. Alex Aiken and George Necula (UCB) he strategy: reduce parsing A key concept: handles Ambiguity and precedence declarations CS780(Prasad)
More informationBottomUp Parsing. Lecture 1112
BottomUp Parsing Lecture 1112 (From slides by G. Necula & R. Bodik) 9/22/06 Prof. Hilfinger CS164 Lecture 11 1 BottomUp Parsing Bottomup parsing is more general than topdown parsing And just as efficient
More informationBottomUp Parsing II. Lecture 8
BottomUp Parsing II Lecture 8 1 Review: ShiftReduce Parsing Bottomup 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
More informationSyntax Analysis. COMP 524: Programming Language Concepts Björn B. Brandenburg. The University of North Carolina at Chapel Hill
Syntax Analysis Björn B. Brandenburg The University of North Carolina at Chapel Hill Based on slides and notes by S. Olivier, A. Block, N. Fisher, F. HernandezCampos, and D. Stotts. The Big Picture Character
More informationSyntaxDirected Translation. Lecture 14
SyntaxDirected Translation Lecture 14 (adapted from slides by R. Bodik) 9/27/2006 Prof. Hilfinger, Lecture 14 1 Motivation: parser as a translator syntaxdirected translation stream of tokens parser ASTs,
More informationSyntax Analysis. The Big Picture. The Big Picture. COMP 524: Programming Languages Srinivas Krishnan January 25, 2011
Syntax Analysis COMP 524: Programming Languages Srinivas Krishnan January 25, 2011 Based in part on slides and notes by Bjoern Brandenburg, S. Olivier and A. Block. 1 The Big Picture Character Stream Token
More informationCompiler Design 1. TopDown Parsing. Goutam Biswas. Lect 5
Compiler Design 1 TopDown Parsing Compiler Design 2 Nonterminal as a Function In a topdown parser a nonterminal may be viewed as a generator of a substring of the input. We may view a nonterminal
More informationSyntax Analysis. Martin Sulzmann. Martin Sulzmann Syntax Analysis 1 / 38
Syntax Analysis Martin Sulzmann Martin Sulzmann Syntax Analysis 1 / 38 Syntax Analysis Objective Recognize individual tokens as sentences of a language (beyond regular languages). Example 1 (OK) Program
More informationBuilding a Parser II. CS164 3:305:00 TT 10 Evans. Prof. Bodik CS 164 Lecture 6 1
Building a Parser II CS164 3:305:00 TT 10 Evans 1 Grammars Programming language constructs have recursive structure. which is why our handwritten parser had this structure, too An expression is either:
More informationTableDriven Parsing
TableDriven Parsing It is possible to build a nonrecursive predictive parser by maintaining a stack explicitly, rather than implicitly via recursive calls [1] The nonrecursive parser looks up the production
More informationFall Compiler Principles Lecture 2: LL parsing. Roman Manevich BenGurion University of the Negev
Fall 20172018 Compiler Principles Lecture 2: LL parsing Roman Manevich BenGurion University of the Negev 1 Books Compilers Principles, Techniques, and Tools Alfred V. Aho, Ravi Sethi, Jeffrey D. Ullman
More informationCompilers: CS31003 Computer Sc & Engg: IIT Kharagpur 1. TopDown Parsing. Lect 5. Goutam Biswas
Compilers: CS31003 Computer Sc & Engg: IIT Kharagpur 1 TopDown Parsing Compilers: CS31003 Computer Sc & Engg: IIT Kharagpur 2 Nonterminal as a Function In a topdown parser a nonterminal may be viewed
More informationContextFree Grammars
CFG2: Ambiguity ContextFree Grammars CMPT 379: Compilers Instructor: Anoop Sarkar anoopsarkar.github.io/compilersclass Ambiguity  /  / ( )  / /  160622 2 Ambiguity Grammar is ambiguous if more
More informationCS Parsing 1
CS4142003403 Parsing 1 030: Parsing Once we have broken an input file into a sequence of tokens, the next step is to determine if that sequence of tokens forms a syntactically correct program parsing
More informationCompilers Course Lecture 4: Context Free Grammars
Compilers Course Lecture 4: Context Free Grammars Example: attempt to define simple arithmetic expressions using named regular expressions: num = [09]+ sum = expr "+" expr expr = "(" sum ")" num Appears
More informationCS 406/534 Compiler Construction Parsing Part I
CS 406/534 Compiler Construction Parsing Part I Prof. Li Xu Dept. of Computer Science UMass Lowell Fall 2004 Part of the course lecture notes are based on Prof. Keith Cooper, Prof. Ken Kennedy and Dr.
More informationIntroduction to Parsing. Lecture 8
Introduction to Parsing Lecture 8 Adapted from slides by G. Necula Outline Limitations of regular languages Parser overview Contextfree grammars (CFG s) Derivations Languages and Automata Formal languages
More informationMonday, 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 nonterminals S is the start symbol P is the set of productions
More informationWednesday, 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
More informationParsers. 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
More informationSome Basic Definitions. Some Basic Definitions. Some Basic Definitions. Language Processing Systems. Syntax Analysis (Parsing) Prof.
Language Processing Systems Prof. Mohamed Hamada Software ngineering Lab. he University of Aizu Japan Syntax Analysis (Parsing) Some Basic Definitions Some Basic Definitions syntax: the way in which words
More informationParsing. Note by Baris Aktemur: Our slides are adapted from Cooper and Torczon s slides that they prepared for COMP 412 at Rice.
Parsing Note by Baris Aktemur: Our slides are adapted from Cooper and Torczon s slides that they prepared for COMP 412 at Rice. Copyright 2010, Keith D. Cooper & Linda Torczon, all rights reserved. Students
More informationChapter 3. Parsing #1
Chapter 3 Parsing #1 Parser source file get next character scanner get token parser AST token A parser recognizes sequences of tokens according to some grammar and generates Abstract Syntax Trees (ASTs)
More informationParsing #1. Leonidas Fegaras. CSE 5317/4305 L3: Parsing #1 1
Parsing #1 Leonidas Fegaras CSE 5317/4305 L3: Parsing #1 1 Parser source file get next character scanner get token parser AST token A parser recognizes sequences of tokens according to some grammar and
More informationParsers. 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
More informationPrelude COMP 181 Tufts University Computer Science Last time Grammar issues Key structure meaning Tufts University Computer Science
Prelude COMP Lecture Topdown Parsing September, 00 What is the Tufts mascot? Jumbo the elephant Why? P. T. Barnum was an original trustee of Tufts : donated $0,000 for a natural museum on campus Barnum
More informationOutline. Limitations of regular languages. Introduction to Parsing. Parser overview. Contextfree grammars (CFG s)
Outline Limitations of regular languages Introduction to Parsing Parser overview Lecture 8 Adapted from slides by G. Necula Contextfree grammars (CFG s) Derivations Languages and Automata Formal languages
More informationCompiler Design Concepts. Syntax Analysis
Compiler Design Concepts Syntax Analysis Introduction First task is to break up the text into meaningful words called tokens. newval=oldval+12 id = id + num Token Stream Lexical Analysis Source Code (High
More informationAmbiguity and Errors SyntaxDirected Translation
Outline Ambiguity (revisited) Ambiguity and rrors SyntaxDirected Translation xtensions of CFG for parsing Precedence declarations rror handling Semantic actions Constructing a parse tree CS780(Prasad)
More informationParsing Part II (Topdown parsing, leftrecursion removal)
Parsing Part II (Topdown parsing, leftrecursion removal) Copyright 2003, Keith D. Cooper, Ken Kennedy & Linda Torczon, all rights reserved. Students enrolled in Comp 412 at Rice University have explicit
More informationParsing. Lecture 11: Parsing. Recursive Descent Parser. Arithmetic grammar.  drops irrelevant details from parse tree
Parsing Lecture 11: Parsing CSC 131 Fall, 2014 Kim Bruce Build parse tree from an expression Interested in abstract syntax tree  drops irrelevant details from parse tree Arithmetic grammar ::=
More informationSYNTAX 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
More informationCOP4020 Programming Languages. Syntax Prof. Robert van Engelen
COP4020 Programming Languages Syntax Prof. Robert van Engelen Overview Tokens and regular expressions Syntax and contextfree grammars Grammar derivations More about parse trees Topdown and bottomup
More informationSyntactic Analysis. TopDown Parsing. Parsing Techniques. TopDown Parsing. Remember the Expression Grammar? Example. Example
Syntactic Analysis opdown Parsing Parsing echniques opdown Parsers (LL(1), recursive descent) Start at the root of the parse tree and grow toward leaves Pick a production & try to match the input Bad
More informationLL(1) predictive parsing
LL(1) predictive parsing Informatics 2A: Lecture 11 John Longley School of Informatics University of Edinburgh jrl@staffmail.ed.ac.uk 13 October, 2011 1 / 12 1 LL(1) grammars and parse tables 2 3 2 / 12
More informationCSE431 Translation of Computer Languages
CSE431 Translation of Computer Languages Top Down Parsers Doug Shook Top Down Parsers Two forms: Recursive Descent Table Also known as LL(k) parsers: Read tokens from Left to right Produces a Leftmost
More informationPart 3. Syntax analysis. Syntax analysis 96
Part 3 Syntax analysis Syntax analysis 96 Outline 1. Introduction 2. Contextfree grammar 3. Topdown parsing 4. Bottomup parsing 5. Conclusion and some practical considerations Syntax analysis 97 Structure
More information