1 / 51

530 likes | 706 Vues

Chapter 3-3. Chang Chi-Chung 2015.07.03. Bottom-Up Parsing. L R methods ( Left-to-right , Rightmost derivation ) LR(0), SLR, Canonical LR = LR(1), LALR 最右推導 沒有右遞迴 明確性文法 Other special cases: Shift-reduce parsing Operator-precedence parsing. Bottom-Up Parsing. reduction.

Télécharger la présentation
## Chapter 3-3

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**Chapter 3-3**Chang Chi-Chung 2015.07.03**Bottom-Up Parsing**• LR methods (Left-to-right, Rightmost derivation) • LR(0), SLR, Canonical LR = LR(1), LALR • 最右推導 • 沒有右遞迴 • 明確性文法 • Other special cases: • Shift-reduce parsing • Operator-precedence parsing**Bottom-Up Parsing**reduction E→ T → T * F → T * id → F * id → id * id rightmost derivation E → E + T | T T → T * F | F F → ( E ) | id**LR(0)**• An LR parser makes shift-reduce decisions by maintaining states to keep track. • An item of a grammar G is a production of G with a dot at some position of the body. • Example A → X Y Z A → ．X Y Z A → X．Y Z A → X Y ．Z A → X Y Z ． A → X．Y Z items stack next derivations with input strings Note that production A has one item [A •]**LR(0)**• Canonical LR(0) Collection • One collection of sets of LR(0) items • Provide the basis for constructing a DFA that is used to make parsing decisions. • LR(0) automation • The canonical LR(0) collection for a grammar • Augmented the grammar • If G is a grammar with start symbol S, then G’ is the augmented grammar for G with new start symbol S’ and new production S’ → S • Closure function • Goto function**Shift-Reduce Parsing**• Shift-Reduce Parsing is a form of bottom-up parsing • A stack holds grammar symbols • An input buffer holds the rest of the string to parsed. • Shift-Reduce parser action • shift • reduce • accept • error**Shift-Reduce Parsing**• Shift • Shift the next input symbol onto the top of the stack. • Reduce • The right end of the string to be reduced must be at the top of the stack. • Locate the left end of the string within the stack and decide with what nonterminal to replace the string. • Accept • Announce successful completion of parsing • Error • Discover a syntax error and call recovery routine**Conflicts During Shift-Reduce Parsing**• Conflicts Type • shift-reduce • reduce-reduce • Shift-reduce and reduce-reduce conflicts are caused by • The limitations of the LR parsing method (even when the grammar is unambiguous) • Ambiguity of the grammar**Function Closure**• If I is a set of items for a grammar G, then closure(I) is the set of items constructed from I. • Create closure(I) by the two rules: • add every item in I to closure(I) • IfA→α．Bβ is in closure(I) andB→γis a production, then add the item B→．γtoclosure(I). Applythis rule untill no more new items can be added toclosure(I). • Divide all the sets of items into two classes • Kernel items • initial item S’ → ．S, and all items whose dots are not at the left end. • Nonkernel items • All items with their dots at the left end, except for S’ → ．S**Example**• The grammar G E’ → E E → E + T | T T → T * F | F F → ( E ) | id • LetI = { E’ → ．E} , then closure(I) = { E’ →．E E →．E + T E →．T T →．T * F T →．F F →．( E ) F →．id}**Exercise**• The grammar G E’ → E E → E + T | T T → T * F | F F → ( E ) | id • LetI = { E → E +．T }**Function Goto**• Function Goto(I, X) • I is a set of items • X is a grammar symbol • Goto(I, X) is defined to be the closure of the set of all items [A α X‧β] such that [A α‧Xβ] is in I. • Goto function is used to define the transitions in the LR(0) automation for a grammar.**Example**• The grammar G • E’ → E • E → E + T | T • T → T * F | F • F → ( E ) | id • I = { E’ → E ． E → E ．+ T } • Goto (I, +) = { E → E +．T T →．T * F T →．F F →．(E) F →．id }**Constructing the LR(0) Collection**• The grammar is augmented with a new start symbol S’ and production S’S • Initially, set C = closure({[S’•S]})(this is the start state of the DFA) • For each set of items I C and each grammar symbol X (NT) such thatGOTO(I, X) Cand goto(I, X) , add the set of items GOTO(I, X) to C • Repeat 3 until no more sets can be added to C**Structure of the LR Parsing Table**• Parsing Table consists of two parts: • A parsing-action function ACTION • A goto function GOTO • The Action function, Action[i, a], have one of four forms: • Shift j, where j is a state. • The action taken by the parser shifts input a to the stack, but use state j to represent a. • Reduce A→β. • The action of the parser reduces β on the top of the stack to head A. • Accept • The parser accepts the input and finishes parsing. • Error**Structure of the LR Parsing Table(1)**• The GOTO Function, GOTO[Ii, A], defined on sets of items. • If GOTO[Ii, A] = Ij, then GOTO also maps a state i and a nonterminal A to state j.**Configuration ( = LR parser state):**($s0s1s2 … sm,aiai+1 … an$) stack input ($ X1 X2 … Xm,aiai+1 … an$) LR-Parser Configurations Ifaction[sm, ai] = shift sthen push s (ai), and advance input (s0 s1 s2 … sm, aiai+1 … an $)(s0s1s2 … sms, ai+1 … an$) Ifaction[sm, ai] = reduce A and goto[sm-r, A] = s with r = || then pop r symbols, and push s ( push A )( (s0 s1 s2 … sm, ai ai+1 … an $) (s0s1 s2 … sm-rs, aiai+1 … an$) Ifaction[sm, ai] = accept then stop Ifaction[sm, ai] = error then attempt recovery**Example LR Parse Table**action goto Grammar:1. E E+T2. E T3. T T*F4. T F5. F (E)6. F id state shift & goto 5 reduce byproduction #1**Example**Grammar0. S E 1. E E+T2. E T3. T T*F4. T F5. F (E)6. F id**SLR Grammars**• SLR (Simple LR): a simple extension of LR(0) shift-reduce parsing • SLR eliminates some conflicts by populating the parsing table with reductions A on symbols in FOLLOW(A) Shift on + State I2:E id•+EE id• State I0:S •EE •id+EE •id goto(I0,id) goto(I3,+) S EE id+EE id FOLLOW(E)={$}thus reduce on $**SLR Parsing Table**• Reductions do not fill entire rows • Otherwise the same as LR(0) 1. S E2. E id+E3. E id Shift on + FOLLOW(E)={$}thus reduce on $**Constructing SLR Parsing Tables**• Augment the grammar with S’ S • Construct the set C={I0, I1, …, In} of LR(0) items • State i is constructed from Ii • If [A•a] Iiand goto(Ii, a)=Ij then set action[i, a]=shiftj • If [A•] Iithen set action[i,a]=reduce A for all a FOLLOW(A) (apply only if AS’) • If [S’S•] is in Ii then set action[i,$]=accept • If goto(Ii, A)=Ij then set goto[i, A]=jset goto table • Repeat 3-4 until no more entries added • The initial state iis the Iiholding item [S’•S]**Example SLR Grammar and LR(0) Items**Augmentedgrammar:0. C’ C1. C A B2. A a3. B a I0 = closure({[C’ •C]})I1 = goto(I0,C) = closure({[C’ C•]})… State I1:C’ C• State I4:C A B• final goto(I0,C) goto(I2,B) State I0:C’ •CC •A BA •a State I2:C A•BB •a start goto(I0,A) goto(I2,a) State I5:B a• goto(I0,a) State I3:A a•**Example SLR Parsing Table**State I0:C’ •CC •A BA •a State I1:C’ C• State I2:C A•BB •a State I3:A a• State I4:C A B• State I5:B a• 1 Grammar:0. C’ C1. C A B2. A a3. B a C 4 B start A 2 0 a 5 a 3**SLR and Ambiguity**• Every SLR grammar is unambiguous, but not every unambiguous grammar is SLR, maybe LR(1) • Consider for example the unambiguous grammarS L=R | RL *R | idR L FOLLOW(R) = {=, $} I0:S’ •SS •L=RS •RL •*RL •idR •L I1:S’ S• I2:S L•=RR L• I3:S R• I4:L *•RR •L L •*RL •id I5:L id• I6:S L=•RR •L L •*RL •id I7:L *R• I8:R L• I9:S L=R• action[2,=]=s6action[2,=]=r5 Has no SLRparsing table no**LR(1) Grammars**• SLR too simple • LR(1) parsing uses lookahead to avoid unnecessary conflicts in parsing table • LR(1) item = LR(0) item + lookahead LR(0) item[A•] LR(1) item [A•, a]**SLR Versus LR(1)**• Split the SLR states by adding LR(1) lookahead • Unambiguous grammarS L = R | RL * R | idR L I2:S L•=RR L• split S L•=R R L• action[2,=]=s6 Should not reduce, because noright-sentential form begins with R=**LR(1) Items**• An LR(1) item [A•,a]contains a lookahead terminal a, meaning already on top of the stack, expect to seea • For items of the form[A•,a]the lookahead a is used to reduce A only if the next input is a • For items of the form[A•, a]with the lookahead has no effect**The Closure Operation for LR(1) Items**• Start with closure(I) = I • If [A•B, a] closure(I) then for each production B in the grammar and each terminal b FIRST(a) add the item [B•, b] to I if not already in I • Repeat 2 until no new items can be added**The Goto Operation for LR(1) Items**• For each item [A•X, a] I, add the set of items closure({[AX•, a]}) to goto(I,X) if not already there • Repeat step 1 until no more items can be added to goto(I,X)**The grammar G**• S’ → S • S → C C • C → cC | d Example • Let I= { (S’ → •S, $) } • I0 = closure(I) = { S’ → •S, $ S → • C C, $ C → •cC, c/d C → •d, c/d } • goto(I0, S) = closure( {S’ → S •, $ } ) = {S’ → S •, $ } = I1**Exercise**• The grammar G • S’ → S • S → C C • C → cC | d • Let I= { (S → C •C, $) } • I2 = closure(I) = ? • I3 = goto(I2, c) = ?**Construction of the sets of LR(1) Items**• Augment the grammar with a new start symbol S’ and production S’S • Initially, set C = closure({[S’•S,$]})(this is the start state of the DFA) • For each set of items I C and each grammar symbol X (NT) such that goto(I, X) Cand goto(I, X) , add the set of items goto(I, X) to C • Repeat 3 until no more sets can be added to C**Construction of the Canonical LR(1) Parsing Tables**• Augment the grammar with S’S • Construct the set C={I0,I1,…,In} of LR(1) items • State i of the parser is constructed from Ii • If [A•a, b] Iiand goto(Ii,a)=Ij then set action[i,a]=shift j • If [A•, a] Ii then set action[i,a]=reduce A (apply only if AS’) • If [S’S•, $] is in Ii then set action[i,$]=accept • If goto(Ii,A)=Ij then set goto[i,A]=j • Repeat 3 until no more entries added • The initial state i is the Ii holding item [S’•S,$]**Example**• The grammar G • S’ → S • S → C C • C → cC | d**Example Grammar and LR(1) Items**• Unambiguous LR(1) grammar:S L=R | RL *R | idR L • Augment with S’ S • LR(1) items (next slide)**I0:**[S’ •S, $] goto(I0,S)=I1[S •L=R, $] goto(I0,L)=I2[S •R, $] goto(I0,R)=I3[L •*R, =/$] goto(I0,*)=I4[L •id, =/$] goto(I0,id)=I5[R •L, $] goto(I0,L)=I2[S’ S•, $][S L•=R, $] goto(I0,=)=I6[R L•, $][S R•, $][L *•R, =/$] goto(I4,R)=I7[R •L, =/$] goto(I4,L)=I8[L •*R, =/$] goto(I4,*)=I4[L •id, =/$] goto(I4,id)=I5 [L id•, =/$] I6: [S L=•R, $] goto(I6,R)=I9[R •L, $] goto(I6,L)=I10 [L •*R, $] goto(I6,*)=I11[L •id, $] goto(I6,id)=I12[L *R•, =/$] [R L•, =/$] [S L=R•, $] [R L•, $][L *•R, $] goto(I11,R)=I13[R •L, $] goto(I11,L)=I10[L •*R, $] goto(I11,*)=I11[L •id, $] goto(I11,id)=I12[L id•, $] [L *R•, $] I7: I1: I8: I2: I9: I10: I3: I11: I4: I12: I5: I13:**Example LR(1) Parsing Table**Grammar:1. S’ S2. S L=R3. S R4. L *R5. L id6. R L**LALR(1) Grammars**• LR(1) parsing tables have many states • LALR(1) parsing (Look-Ahead LR) combines LR(1) states to reduce table size • Less powerful than LR(1) • Will not introduce shift-reduce conflicts, because shifts do not use lookaheads • May introduce reduce-reduce conflicts, but seldom do so for grammars of programming languages • SLR and LALR tables for a grammar always have the same number of states, and less than LR(1) tables. • Like C, SLR and LALR >100, LR(1) > 1000**Constructing LALR Parsing Tables**• Two ways • Construction of the LALR parsing table from the sets of LR(1) items. • Union the states • Requires much space and time • Construction of the LALR parsing table from the sets of LR(0) items • Efficient • Use in practice.**Example**LALR(1) LR(1)**Constructing LALR(1) Parsing Tables**• Construct sets of LR(1) items • Combine LR(1) sets with sets of items that share the same first part I4: [L *•R, =][R •L, =] [L •*R, =] [L •id, =] Shorthandfor two itemsin the same set [L *•R, =/$][R •L, =/$][L •*R, =/$][L •id, =/$] I11: [L *•R, $][R •L, $][L •*R, $][L •id, $]**Example LALR(1) Grammar**• Unambiguous LR(1) grammar:S L=R | RL *R | idR L • Augment with S’ S • LALR(1) items (next slide)**I0:**[S’ •S, $] goto(I0,S)=I1[S •L=R, $] goto(I0,L)=I2[S •R, $] goto(I0,R)=I3[L •*R, =/$] goto(I0,*)=I4[L •id, =/$] goto(I0,id)=I5[R •L, $] goto(I0,L)=I2[S’ S•, $][S L•=R, $] goto(I0,=)=I6[R L•, $][S R•, $][L *•R, =/$] goto(I4,R)=I7[R •L, =/$] goto(I4,L)=I9[L •*R, =/$] goto(I4,*)=I4[L •id, =/$] goto(I4,id)=I5 [L id•, =/$] I6: [S L=•R, $] goto(I6,R)=I8[R •L, $] goto(I6,L)=I9 [L •*R, $] goto(I6,*)=I4[L •id, $] goto(I6,id)=I5[L *R•, =/$] [S L=R•, $][R L•, =/$] I7: I1: I8: I2: I9: Shorthandfor two items I3: I4: [R L•, =][R L•, $] I5:**Example LALR(1) Parsing Table**Grammar:1. S’ S2. S L=R3. S R4. L *R5. L id6. R L**LL, SLR, LR, LALR Summary**• LL parse tables computed using FIRST/FOLLOW • Nonterminals terminals productions • Computed using FIRST/FOLLOW • LR parsing tables computed using closure/goto • LR states terminals shift/reduce actions • LR states nonterminals goto state transitions • A grammar is • LL(1) if its LL(1) parse table has no conflicts • SLR if its SLR parse table has no conflicts • LR(1) if its LR(1) parse table has no conflicts • LALR(1) if its LALR(1) parse table has no conflicts**LL, SLR, LR, LALR Grammars**LR(1) LL(1) LALR(1) SLR LR(0)

More Related