BottomUp Parsing A bottomup parser creates the parse
Bottom-Up Parsing • A bottom-up parser creates the parse tree of the given input starting from leaves towards the root. • A bottom-up parser tries to find the right-most derivation of the given input in the reverse order. S . . . (the right-most derivation of ) (the bottom-up parser finds the right-most derivation in the reverse order) • Bottom-up parsing is also known as shift-reduce parsing because its two main actions are shift and reduce. – At each shift action, the current symbol in the input string is pushed to a stack. – At each reduction step, the symbols at the top of the stack (this symbol sequence is the right side of a production) will replaced by the non-terminal at the left side of that production. – There also two more actions: accept and error. CS 416 Compiler Design 1
Shift-Reduce Parsing • A shift-reduce parser tries to reduce the given input string into the starting symbol. a string the starting symbol reduced to • At each reduction step, a substring of the input matching to the right side of a production rule is replaced by the non-terminal at the left side of that production rule. • If the substring is chosen correctly, the right most derivation of that string is created in the reverse order. Rightmost Derivation: Shift-Reduce Parser finds: * S rm rm CS 416 Compiler Design . . . S rm 2
Shift-Reduce Parsing -- Example S a. ABb A a. A | a B b. B | b input string: aaabb aa. Abb a. ABb S reduction S rm a. ABb aa. Abb rm a. Abb rm rm aaabb Right Sentential Forms • How do we know which substring to be replaced at each reduction step? CS 416 Compiler Design 3
Handle • Informally, a handle of a string is a substring that matches the right side of a production rule. – But not every substring matches the right side of a production rule is handle • A handle of a right sentential form ( ) is a production rule A and a position of where the string may be found and replaced by A to produce the previous right-sentential form in a rightmost derivation of . * A S rm • If the grammar is unambiguous, then every right-sentential form of the grammar has exactly one handle. • We will see that is a string of terminals. CS 416 Compiler Design 4
Handle Pruning • A right-most derivation in reverse can be obtained by handle-pruning. S= 0 2 rm . . . rm n-1 rm 1 rm rm n= input string • Start from n, find a handle An n in n, and replace n in by An to get n-1. • Then find a handle An-1 in n-1, replace n-1 in by An-1 to get n-2. • Repeat this, until we reach S. CS 416 Compiler Design and 5
A Shift-Reduce Parser E E+T | T T T*F | F F (E) | id Right-Most Derivation of id+id*id E E+T*F E+T*id E+F*id E+id*id T+id*id F+id*id id+id*id Right-Most Sentential Form Reducing Production id+id*id F id F+id*id T F T+id*id E T E+id*id F id E+F*id T F E+T*id F id E+T*F T T*F E+T E Handles are red and underlined in the right-sentential forms. CS 416 Compiler Design 6
A Stack Implementation of A Shift-Reduce Parser • There are four possible actions of a shift-parser action: 1. Shift : The next input symbol is shifted onto the top of the stack. 2. Reduce: Replace the handle on the top of the stack by the nonterminal. 3. Accept: Successful completion of parsing. 4. Error: Parser discovers a syntax error, and calls an error recovery routine. • • Initial stack just contains only the end-marker $. The end of the input string is marked by the end-marker $. CS 416 Compiler Design 7
A Stack Implementation of A Shift-Reduce Parser Stack Input Action $ $id $F $T $E $E+id $E+F $E+T*id $E+T*F $E+T $E id+id*id$ shift +id*id$ id*id$ id$ $ $ reduce by F id reduce by T F reduce by E T shift reduce by F id reduce by T F shift reduce by F id reduce by T T*F reduce by E E+T accept CS 416 Compiler Design Parse Tree E 8 E 3 + T 7 T 2 T 5 * F 1 F 4 id id F 6 id 8
Conflicts During Shift-Reduce Parsing • There are context-free grammars for which shift-reduce parsers cannot be used. • Stack contents and the next input symbol may not decide action: – shift/reduce conflict: Whether make a shift operation or a reduction. – reduce/reduce conflict: The parser cannot decide which of several reductions to make. • If a shift-reduce parser cannot be used for a grammar, that grammar is called as non-LR(k) grammar. left to right scanning right-most derivation k lookhead • An ambiguous grammar can never be a LR grammar. CS 416 Compiler Design 9
Shift-Reduce Parsers • There are two main categories of shift-reduce parsers 1. Operator-Precedence Parser – simple, but only a small class of grammars. CFG CLR LALR 2. LR-Parsers SLR – covers wide range of grammars. • SLR – simple LR parser • Canonical LR – most general LR parser • LALR – intermediate LR parser (lookhead LR parser) – SLR, CLR and LALR work same, only their parsing tables are different. CS 416 Compiler Design 10
LR Parsers • The most powerful shift-reduce parsing (yet efficient) is: LR(k) parsing. left to right scanning right-most derivation k lookhead (k is omitted it is 1) • LR parsing is attractive because: – LR parsing is most general non-backtracking shift-reduce parsing, yet it is still efficient. – The class of grammars that can be parsed using LR methods is a proper superset of the class of grammars that can be parsed with predictive parsers. LL(1)-Grammars LR(1)-Grammars – An LR-parser can detect a syntactic error as soon as it is possible to do so a left-to-right scan of the input. CS 416 Compiler Design 11
LR Parsers • LR-Parsers – covers wide range of grammars. – SLR – simple LR parser – CLR – most general LR parser – LALR – intermediate LR parser (look-head LR parser) – SLR, CLR and LALR work same (they used the same algorithm), only their parsing tables are different. CS 416 Compiler Design 12
LR Parsing Algorithm input a 1 . . . ai . . . an $ stack Sm Xm LR Parsing Algorithm Sm-1 output Xm-1. . Action Table S 1 X 1 S 0 Goto Table terminals and $ s t a t e s four different actions CS 416 Compiler Design non-terminal s t a t e s each item is a state number 13
A Configuration of LR Parsing Algorithm • A configuration of a LR parsing is: ( So X 1 S 1. . . Xm Sm, ai ai+1. . . an $ ) Stack Rest of Input • Sm and ai decides the parser action by consulting the parsing action table. (Initial Stack contains just So ) • A configuration of a LR parsing represents the right sentential form: X 1. . . Xm ai ai+1. . . an $ CS 416 Compiler Design 14
Actions of A LR-Parser 1. shift s -- shifts the next input symbol and the state s onto the stack ( So X 1 S 1. . . Xm Sm, ai ai+1. . . an $ ) ( So X 1 S 1. . . Xm Sm ai s, ai+1. . . an $ ) 2. reduce A (or rn where n is a production number) – pop 2| | (=r) items from the stack; – then push A and s where s=goto[sm-r, A] ( So X 1 S 1. . . Xm Sm, ai ai+1. . . an $ ) ( So X 1 S 1. . . Xm-r Sm-r A s, ai. . . an $ ) – Output is the reducing production reduce A 3. Accept – Parsing successfully completed 4. Error -- Parser detected an error (an empty entry in the action table) CS 416 Compiler Design 15
Reduce Action • pop 2| | (=r) items from the stack; let us assume that = Y 1 Y 2. . . Yr • then push A and s where s=goto[sm-r, A] ( So X 1 S 1. . . Xm-r Sm-r Y 1 Sm-r. . . Yr Sm, ai ai+1. . . an $ ) ( So X 1 S 1. . . Xm-r Sm-r A s, ai. . . an $ ) • In fact, Y 1 Y 2. . . Yr is a handle. X 1. . . Xm-r A ai. . . an $ X 1. . . Xm Y 1. . . Yr ai ai+1. . . an $ CS 416 Compiler Design 16
(SLR) Parsing Tables for Expression Grammar Action Table 1) 2) 3) 4) 5) 6) E E+T E T T T*F T F F (E) F id state id 0 s 5 + * ( Goto Table ) $ s 4 1 s 6 2 r 2 s 7 r 2 3 r 4 r 4 4 s 4 r 6 T F 1 2 3 8 2 3 9 3 acc s 5 5 E r 6 6 s 5 s 4 7 s 5 s 4 r 6 10 8 s 6 s 11 9 r 1 s 7 r 1 10 r 3 r 3 11 r 5 r 5 CS 416 Compiler Design 17
Actions of A (S)LR-Parser -- Example stack 0 0 id 5 0 F 3 0 T 2*7 id 5 0 T 2*7 F 10 0 T 2 0 E 1+6 id 5 0 E 1+6 F 3 0 E 1+6 T 9 0 E 1 input id*id+id$ id+id$ +id$ $ $ action shift 5 reduce by F id reduce by T F shift 7 shift 5 reduce by F id reduce by T T*F reduce by E T shift 6 shift 5 reduce by F id reduce by T F reduce by E E+T accept CS 416 Compiler Design output F id T F F id T T*F E T F id T F E E+T 18
Constructing SLR Parsing Tables – LR(0) Item • An LR(0) item of a grammar G is a production of G a dot at the some position of the right side. • Ex: A a. Bb Possible LR(0) Items: A a. Bb (four different possibility) A a Bb A a. Bb • Sets of LR(0) items will be the states of action and goto table of the SLR parser. • A collection of sets of LR(0) items (the canonical LR(0) collection) is the basis for constructing SLR parsers. • Augmented Grammar: G’ is G with a new production rule S’ S where S’ is the new starting symbol. . . CS 416 Compiler Design 19
The Closure Operation • If I is a set of LR(0) items for a grammar G, then closure(I) is the set of LR(0) items constructed from I by the two rules: . . 1. Initially, every LR(0) item in I is added to closure(I). 2. If A B is in closure(I) and B is a production rule of G; then B will be in the closure(I). We will apply this rule until no more new LR(0) items can be added to closure(I). CS 416 Compiler Design 20
The Closure Operation -- Example E’ E E E+T E T T T*F T F F (E) F id . closure({E’ E}) = { E’ E E E+T E T T T*F T F F (E) F id } CS 416 Compiler Design . . . . kernel items 21
Goto Operation • If I is a set of LR(0) items and X is a grammar symbol (terminal or nonterminal), then goto(I, X) is defined as follows: – If A X in I then every item in closure({A X }) will be in goto(I, X). . Example: . . I ={ E’ E, E E+T, E T, T T*F, T F, F (E), F id } goto(I, E) = { E’ E , E E +T } goto(I, T) = { E T , T T *F } goto(I, F) = {T F } goto(I, () = { F ( E), E E+T, E F (E), F id } goto(I, id) = { F id } T, T CS 416 Compiler Design T*F, T . F, 22
Construction of The Canonical LR(0) Collection • To create the SLR parsing tables for a grammar G, we will create the canonical LR(0) collection of the grammar G’. • Algorithm: . C is { closure({S’ S}) } repeat the followings until no more set of LR(0) items can be added to C. for each I in C and each grammar symbol X if goto(I, X) is not empty and not in C add goto(I, X) to C • goto function is a DFA on the sets in C. CS 416 Compiler Design 23
The Canonical LR(0) Collection -- Example I 0: E’ . EI 1: E’ E. I 6: E E+. T E . E+T E E. +T E . T T . T*F I 2: E T. T . F T T. *F F . (E) F . id I 3: T F. I 4: F (. E) E . E+T E . T T . T*F T . F F . (E) F . id I 9: E E+T. T . T*F T . F F . (E) F . id I 7: T T*. F F . (E) F . id T T. *F I 10: T T*F. I 11: F (E). I 8: F (E. ) E E. +T I 5: F id. CS 416 Compiler Design 24
Transition Diagram (DFA) of Goto Function I 0 E I 1 + I 6 T F ( T id I 2 F ( * I 7 F ( id I 3 I 4 id id I 5 E T F ( I 8 to I 2 to I 3 to I 4 ) + I 9 to I 3 to I 4 to I 5 * to I 7 I 10 to I 4 to I 5 I 11 to I 6 CS 416 Compiler Design 25
Constructing SLR Parsing Table (of an augumented grammar G’) 1. Construct the canonical collection of sets of LR(0) items for G’. C {I 0, . . . , In} 2. Create the parsing action table as follows • If a is a terminal, A . a in Ii and goto(Ii, a)=Ij then action[i, a] is shift j. • If A . is in Ii , then action[i, a] is reduce A for all a in FOLLOW(A) where A S’. • If S’ S. is in Ii , then action[i, $] is accept. • If any conflicting actions generated by these rules, the grammar is not SLR(1). 3. Create the parsing goto table • for all non-terminals A, if goto(Ii, A)=Ij then goto[i, A]=j 4. All entries not defined by (2) and (3) are errors. 5. Initial state of the parser contains S’. S CS 416 Compiler Design 26
Parsing Tables of Expression Grammar Action Table state id 0 s 5 + * ( Goto Table ) $ s 4 1 s 6 2 r 2 s 7 r 2 3 r 4 r 4 4 s 4 r 6 T F 1 2 3 8 2 3 9 3 acc s 5 5 E r 6 6 s 5 s 4 7 s 5 s 4 r 6 10 8 s 6 s 11 9 r 1 s 7 r 1 10 r 3 r 3 11 r 5 r 5 CS 416 Compiler Design 27
SLR(1) Grammar • An LR parser using SLR(1) parsing tables for a grammar G is called as the SLR(1) parser for G. • If a grammar G has an SLR(1) parsing table, it is called SLR(1) grammar (or SLR grammar in short). • Every SLR grammar is unambiguous, but every unambiguous grammar is not a SLR grammar. CS 416 Compiler Design 28
shift/reduce and reduce/reduce conflicts • If a state does not know whether it will make a shift operation or reduction for a terminal, we say that there is a shift/reduce conflict. • If a state does not know whether it will make a reduction operation using the production rule i or j for a terminal, we say that there is a reduce/reduce conflict. • If the SLR parsing table of a grammar G has a conflict, we say that grammar is not SLR grammar. CS 416 Compiler Design 29
Conflict Example S L=R S R L *R L id R L I 0: S’ . S S . L=R S . R L . *R L . id R . L Problem FOLLOW(R)={=, $} = shift 6 reduce by R L shift/reduce conflict I 1: S’ S. I 2: S L. =R R L. I 6: S L=. R R . L L . *R L . id I 9: S L=R. I 3: S R. I 4: L *. R R . L L . *R L . id I 7: L *R. I 8: R L. I 5: L id. CS 416 Compiler Design 30
Conflict Example 2 S Aa. Ab S Bb. Ba A B I 0: S’ . S S . Aa. Ab S . Bb. Ba A. B. Problem FOLLOW(A)={a, b} FOLLOW(B)={a, b} a reduce by A reduce by B reduce/reduce conflict b CS 416 Compiler Design 31
Constructing Canonical LR(1) Parsing Tables • In SLR method, the state i makes a reduction by A when the current token is a: – if the A . in the Ii and a is FOLLOW(A) • In some situations, A cannot be followed by the terminal a in a right-sentential form when and the state i are on the top stack. This means that making reduction in this case is not correct. S Aa. Ab S Bb. Ba A B S Aa. Ab Aab ab S Bb. Ba Bba ba Aab ab Aa. Ab Aa b Bba ba Bb. Ba Bb a CS 416 Compiler Design 32
LR(1) Item • To avoid some of invalid reductions, the states need to carry more information. • Extra information is put into a state by including a terminal symbol as a second component in an item. • A LR(1) item is: . A , a where a is the look-head of the LR(1) item (a is a terminal or end-marker. ) CS 416 Compiler Design 33
LR(1) Item (cont. ) . • When ( in the LR(1) item A , a ) is not empty, the look-head does not have any affect. . • When is empty (A , a ), we do the reduction by A only if the next input symbol is a (not for any terminal in FOLLOW(A)). . • A state will contain A , a 1 where {a 1, . . . , an} FOLLOW(A). . A , an CS 416 Compiler Design 34
Canonical Collection of Sets of LR(1) Items • The construction of the canonical collection of the sets of LR(1) items are similar to the construction of the canonical collection of the sets of LR(0) items, except that closure and goto operations work a little bit different. closure(I) is: ( where I is a set of LR(1) items) – every LR(1) item in I is in closure(I) . – if A B , a in closure(I) and B is a production rule of G; then B. , b will be in the closure(I) for each terminal b in FIRST( a). CS 416 Compiler Design 35
goto operation • If I is a set of LR(1) items and X is a grammar symbol (terminal or non-terminal), then goto(I, X) is defined as follows: – If A . X , a in I then every item in closure({A X. , a}) will be in goto(I, X). CS 416 Compiler Design 36
Construction of The Canonical LR(1) Collection • Algorithm: C is { closure({S’. S, $}) } repeat the followings until no more set of LR(1) items can be added to C. for each I in C and each grammar symbol X if goto(I, X) is not empty and not in C add goto(I, X) to C • goto function is a DFA on the sets in C. CS 416 Compiler Design 37
A Short Notation for The Sets of LR(1) Items • A set of LR(1) items containing the following items . A , a 1. . A , an can be written as . A , a 1/a 2/. . . /an CS 416 Compiler Design 38
Canonical LR(1) Collection -- Example S Aa. Ab S Bb. Ba A B I 0: S’ . S , $ S . Aa. Ab , $ S . Bb. Ba , $ A . , a B . , b I 1: S’ S. , $ S A B I 2: S A. a. Ab , $ a I 3: S B. b. Ba , $ b I 4: S Aa. Ab , $ A . , b A I 6: S Aa. A. b , $ b I 8: S Aa. Ab. , $ I 5: S Bb. Ba , $ B . , a B I 7: S Bb. B. a , $ a I 9: S Bb. Ba. , $ CS 416 Compiler Design to I 4 to I 5 39
Canonical LR(1) Collection – Example 2 S’ S 1) S L=R 2) S R 3) L *R 4) L id 5) R L I 0: S’ . S, $ S . L=R, $ S . R, $ L . *R, $/= L . id, $/= R . L, $ I 6: S L=. R, $ R . L, $ L . *R, $ L . id, $ R L * I 1: S’ S. , $ S * L I 2: S L. =R, $ R L. , $ R I 3: S R. , $ id to I 9 to I 10 to I 11 I 8: R L. , $/= I 12: L id. , $ CS 416 Compiler Design to I 7 L * to I 8 id to I 4 to I 5 I 13: L *R. , $ I 10: R L. , $ I 7: L *R. , $/= to I 12 R I 5: L id. , $/= I 9: S L=R. , $ I 11: L *. R, $ R . L, $ L . *R, $ L . id, $ id I 4: L *. R, $/= R . L, $/= to I 6 L . *R, $/= L . id, $/= I 4 and I 11 R L * id to I 13 to I 10 I 5 and I 12 to I 11 I 7 and I 13 to I 12 I 8 and I 10 40
Construction of LR(1) Parsing Tables 1. Construct the canonical collection of sets of LR(1) items for G’. C {I 0, . . . , In} 2. Create the parsing action table as follows • • . If a is a terminal, A a , b in Ii and goto(Ii, a)=Ij then action[i, a] is shift j. If A , a is in Ii , then action[i, a] is reduce A where A S’. If S’ S , $ is in Ii , then action[i, $] is accept. If any conflicting actions generated by these rules, the grammar is not LR(1). . . 3. Create the parsing goto table • for all non-terminals A, if goto(Ii, A)=Ij then goto[i, A]=j 4. All entries not defined by (2) and (3) are errors. 5. Initial state of the parser contains S’. S, $ CS 416 Compiler Design 41
LR(1) Parsing Tables – (for Example 2) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 id s 5 * s 4 = $ s 6 acc r 5 r 2 s 4 r 4 s 12 L 2 R 3 8 7 10 9 r 4 s 11 r 3 r 5 S 1 r 3 r 5 r 1 r 5 s 11 no shift/reduce or no reduce/reduce conflict so, it is a LR(1) grammar 10 13 r 4 r 3 CS 416 Compiler Design 42
LALR Parsing Tables • LALR stands for Look. Ahead LR. • LALR parsers are often used in practice because LALR parsing tables are smaller than LR(1) parsing tables. • The number of states in SLR and LALR parsing tables for a grammar G are equal. • But LALR parsers recognize more grammars than SLR parsers. • yacc creates a LALR parser for the given grammar. • A state of LALR parser will be again a set of LR(1) items. CS 416 Compiler Design 43
Creating LALR Parsing Tables Canonical LR(1) Parser shrink # of states LALR Parser • This shrink process may introduce a reduce/reduce conflict in the resulting LALR parser (so the grammar is NOT LALR) • But, this shrink process does not produce a shift/reduce conflict. CS 416 Compiler Design 44
The Core of A Set of LR(1) Items • The core of a set of LR(1) items is the set of its first component. Ex: . . S L =R, $ R L , $ . . S L =R R L Core • We will find the states (sets of LR(1) items) in a canonical LR(1) parser with same cores. Then we will merge them as a single state. . . I 1: L id , = I 2: L id , $ A new state: . . I 12: L id , = L id , $ have same core, merge them • We will do this for all states of a canonical LR(1) parser to get the states of the LALR parser. • In fact, the number of the states of the LALR parser for a grammar will be equal to the number of states of the SLR parser for that grammar. CS 416 Compiler Design 45
Creation of LALR Parsing Tables • Create the canonical LR(1) collection of the sets of LR(1) items for the given grammar. • Find each core; find all sets having that same core; replace those sets having same cores with a single set which is their union. C={I 0, . . . , In} C’={J 1, . . . , Jm} where m n • Create the parsing tables (action and goto tables) same as the construction of the parsing tables of LR(1) parser. – Note that: If J=I 1 . . . Ik since I 1, . . . , Ik have same cores of goto(I 1, X), . . . , goto(I 2, X) must be same. – So, goto(J, X)=K where K is the union of all sets of items having same cores as goto(I 1, X). • If no conflict is introduced, the grammar is LALR(1) grammar. (We may only introduce reduce/reduce conflicts; we cannot introduce a shift/reduce conflict) CS 416 Compiler Design 46
Shift/Reduce Conflict • We say that we cannot introduce a shift/reduce conflict during the shrink process for the creation of the states of a LALR parser. • Assume that we can introduce a shift/reduce conflict. In this case, a state of LALR parser must have: . . A , a and B a , b • This means that a state of the canonical LR(1) parser must have: A , a and B a , c But, this state has also a shift/reduce conflict. i. e. The original canonical LR(1) parser has a conflict. (Reason for this, the shift operation does not depend on lookaheads) CS 416 Compiler Design 47
Reduce/Reduce Conflict • But, we may introduce a reduce/reduce conflict during the shrink process for the creation of the states of a LALR parser. . . I 1 : A , a I 2: A , b B , c . . I 12: A , a/b reduce/reduce conflict B , b/c CS 416 Compiler Design 48
Canonical LALR(1) Collection – Example 2 S’ S 1) S L=R 2) S R 3) L *R 4) L id 5) R L . . . I 0: S’ S S L L R I 6: S L= R, $ R L, $ L *R, $ L id, $ R L * id S, $ L=R, $ *R, $/= id, $/= L, $ to I 9 . . I 1: S’ S , $ I 411: L * R, $/= S * R L, $/= L I 2: S L =R, $ to I 6 L *R, $/= R L , $ L id, $/= R id I 3: S R , $ I : L id , $/= 512 . I 9: S L=R , $ to I 810 to I 411 R to I 713 L * to I 810 id to I 411 to I 512 Same Cores I 4 and I 11 I 5 and I 12 to I 512 I 7 and I 13 I 713: L *R , $/= I 8 and I 10 I 810: R L , $/= CS 416 Compiler Design 49
LALR(1) Parsing Tables – (for Example 2) 0 1 2 3 4 5 6 7 8 9 id s 5 * s 4 = $ s 6 acc r 5 r 2 s 4 r 4 s 12 L 2 R 3 8 7 10 9 r 4 s 11 r 3 r 5 S 1 no shift/reduce or no reduce/reduce conflict r 3 r 5 r 1 so, it is a LALR(1) grammar CS 416 Compiler Design 50
Using Ambiguous Grammars • All grammars used in the construction of LR-parsing tables must be un -ambiguous. • Can we create LR-parsing tables for ambiguous grammars ? – Yes, but they will have conflicts. – We can resolve these conflicts in favor of one of them to disambiguate the grammar. – At the end, we will have again an unambiguous grammar. • Why we want to use an ambiguous grammar? – Some of the ambiguous grammars are much natural, and a corresponding unambiguous grammar can be very complex. – Usage of an ambiguous grammar may eliminate unnecessary reductions. • Ex. E E+T | T E E+E | E*E | (E) | id CS 416 Compiler Design T T*F | F F (E) | id 51
Sets of LR(0) Items for Ambiguous Grammar . . E+E E. . E*E (E). id I 0: E’ E E . . . E I 1: E’ E E E +E E E *E ( + ( . . E+E E). . E*E (E). id I 2 : E ( E E E id E I 3: E id id . . . I : E E *. E E . E+E E . E*E E . (E) E . id I 4 : E E + E E E+E E E*E * E (E) E id E ( id 5 E . . . I 6: E (E ) E E +E E E *E CS 416 Compiler Design I 2 I 3 ( id . . . I 7: E E+E + I 4 E E +E * I 5 E E *E E I 2 I 3 ) + * I 4 I 5 . . . I 8: E E*E + I 4 E E +E * I 5 E E *E I 9: E (E) . 52
SLR-Parsing Tables for Ambiguous Grammar FOLLOW(E) = { $, +, *, ) } State I 7 has shift/reduce conflicts for symbols + and *. I 0 E I 1 + I 4 E I 7 when current token is + shift + is right-associative reduce + is left-associative when current token is * shift * has higher precedence than + reduce + has higher precedence than * CS 416 Compiler Design 53
SLR-Parsing Tables for Ambiguous Grammar FOLLOW(E) = { $, +, *, ) } State I 8 has shift/reduce conflicts for symbols + and *. I 0 E I 1 * I 5 E I 7 when current token is * shift * is right-associative reduce * is left-associative when current token is + shift + has higher precedence than * reduce * has higher precedence than + CS 416 Compiler Design 54
SLR-Parsing Tables for Ambiguous Grammar 0 1 2 3 4 5 6 7 8 9 id s 3 Action + * s 4 ( s 2 ) s 5 s 3 $ acc s 2 r 4 s 3 6 r 4 s 2 s 4 r 1 r 2 r 3 Goto E 1 s 5 r 2 r 3 7 8 s 9 r 1 r 2 r 3 CS 416 Compiler Design r 1 r 2 r 3 55
Error Recovery in LR Parsing • An LR parser will detect an error when it consults the parsing action table and finds an error entry. All empty entries in the action table are error entries. • Errors are never detected by consulting the goto table. • An LR parser will announce error as soon as there is no valid continuation for the scanned portion of the input. • A canonical LR parser (LR(1) parser) will never make even a single reduction before announcing an error. • The SLR and LALR parsers may make several reductions before announcing an error. • But, all LR parsers (LR(1), LALR and SLR parsers) will never shift an erroneous input symbol onto the stack. CS 416 Compiler Design 56
Panic Mode Error Recovery in LR Parsing • Scan down the stack until a state s with a goto on a particular nonterminal A is found. (Get rid of everything from the stack before this state s). • Discard zero or more input symbols until a symbol a is found that can legitimately follow A. – The symbol a is simply in FOLLOW(A), but this may not work for all situations. • The parser stacks the nonterminal A and the state goto[s, A], and it resumes the normal parsing. • This nonterminal A is normally is a basic programming block (there can be more than one choice for A). – stmt, expr, block, . . . CS 416 Compiler Design 57
Phrase-Level Error Recovery in LR Parsing • Each empty entry in the action table is marked with a specific error routine. • An error routine reflects the error that the user most likely will make in that case. • An error routine inserts the symbols into the stack or the input (or it deletes the symbols from the stack and the input, or it can do both insertion and deletion). – missing operand – unbalanced right parenthesis CS 416 Compiler Design 58
SLR-Parsing Tables for Ambiguous Grammar E E + E | E * E | (E) | id 0 1 2 id s 3 e 3 s 3 Action + * e 1 s 4 s 5 e 1 ( s 2 e 3 s 2 ) e 2 e 2 $ e 1 acc e 1 3 4 5 6 7 8 9 r 4 s 3 e 3 r 1 r 2 r 3 r 4 e 1 s 4 r 1 r 2 r 3 r 4 s 2 e 3 r 1 r 2 r 3 r 4 e 2 s 9 r 1 r 2 r 3 r 4 e 1 e 4 r 1 r 2 r 3 r 4 e 1 s 5 r 2 r 3 CS 416 Compiler Design Goto E 1 6 7 8 59
Error Recovery 1. We have changed each state that calls for a particular reduction on some input symbols by replacing error entries in that state by the reduction. 2. The remaining blank entries have been replaced by calls to error routines. CS 416 Compiler Design 60
The error routines are as follows 1. e 1: this routine expect the beginning of an operand, either id or left parenthesis. Routine: push an imaginary id onto the stack issue diagnostic: “missing operand” 2. e 2: finding right parenthesis remove the right parenthesis. issue diagnostic: “unbalance right parenthesis” CS 416 Compiler Design 61
3. e 3: expecting an operator and an id or right parenthesis found. routine: push + onto the stack issue diagnostic: “missing operator” 4. e 4: expected an operator or a right parenthesis and the end of input is found Routine: Push the right parenthesis onto the stack issue diagnostic: “Missing right parenthesis” CS 416 Compiler Design 62
Continue Stack 0 0 id 3 0 E 1+4 Input id + )$ +)$ )$ $ 0 E 1+4 id 3 $ 0 E 1+4 E 7 0 E 1 $ $ Error Message & Action “unbalance right parenthesis” e 2 removes right parenthesis “missing operand” e 1 pushes id 3 on stack CS 416 Compiler Design 63
Operator precedence parser Operator precedence grammar have the property that 1. no production right side is ε or 2. has two adjacent nonterminals. E EAE | (E) | -E | id A +|-|*|/|↑ The above grammar is not operator grammar, because the right side EAE has two nonterminals. If we substitute for a each of its alternatives, we obtain the following operator grammar: E E+E | E-E | E*E | E/E | E↑E | (E) | -E | id CS 416 Compiler Design 64
Three disjoint precedence relations <, > and = a<b means a “yields precedence to” b a=b means a “has the same precedence as b” a>b means a “takes precedence over” b id id + * $ > > > + < > * < > > > $ < < < CS 416 Compiler Design 65
Precedence Function id id + * $ > > > + < > * < > > > $ < < < gi d + * id $ f 2 4 4 0 g 1 3 5 0 fi d f* g g f+ f$ g * + $ CS 416 Compiler Design 67
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