LR Parsing – The Items

1. LR Parsing – The Items Lecture 10 Fri, Feb 13, 2004

2. LR Parsers • A bottom-up parser follows a rightmost derivation from the bottom up. • Such parsers typically use the LR algorithm and are called LR parsers. • L means process tokens from Left to right. • R means follow a Rightmost derivation.

3. LR Parsers • Furthermore, in LR parsing, the production is applied only after the pattern has been matched. • In LL (predictive) parsing, the production was selected, and then the tokens were matched to it.

4. Rightmost Derivations • Let the grammar be EE + T | T TT * F | F F (E) | id | num

5. Rightmost Derivations • A rightmost derivation of (id + num)*id is E T  T*F  T*id  F*id  (E)*id  (E + T)*id  (E + F)*id  (E + num)*id  (T + num)*id  (F + num)*id  (id + num)*id.

6. LR Parsers • An LR parser uses a parsing table, an input buffer, and a stack of “states.” • If performs three operations. • Shift a token from the input buffer to the stack. • Reduce the content of the stack by applying a production. • Go to a new state.

7. LR(0) Items • To build an LR parsing table, we must first find the LR(0) items. • An LR(0) item is a production with a special marker () marking a position within the string on the right side of the production. • LR(0) parsing is also called SLR parsing (“simple” LR).

8. Example: LR(0) Items • If the production is EE + T, then the possible LR(0) items are • [EE + T] • [EE + T] • [EE + T] • [EE + T]

9. LR(0) Items • The interpretation of [A  ] is “We have processed  and we might process  next.” • Whether we do actually process  will be borne out by the subsequent sequence of tokens.

10. LR Parsing • We will build a PDA whose states are sets of LR(0) items. • First we augment the grammar with a new start symbol S'. S'S. • This guarantees that the start symbol will not recurse.

11. States of the PDA • The initial state is called I0. • State I0 is the closure of the set {[S'S]}. • To form the closure of a set of items • For each item [A  B] in the set and for each production B, add the item [B] to the set. • Let us call [B] an initial B-item. • Continue in this manner until there is no further change.

12. Example: LR Parsing • Continuing with the example, the augmented grammar is E'E EE + T | T TT * F | F F (E) | id | num

13. Example: LR Parsing • The state I0 consists of the items the closure of item [E'E]. [E'E] [EE + T] [ET] [TT * F] [TF] [F (E)] [Fid] [Fnum]

14. Transitions • There will be a transition from one state to another state for each grammar symbol in an item that immediately follows the marker  in an item in that state. • If an item in the state is [A  X], then • The transition from that state occurs when the symbol X is processed. • The transition is to the state that is the closure of the item [AX  ].

15. Example: LR Parsing • Thus, from the state I0, there will be transitions for the symbols E, T, F, (, id, and num. • On processing E, the items [E'E] and [E E + T] become [E'E] and [EE + T].

16. E I0 I1 Example: LR Parsing • Let state I1 be the closure of these items. I1: [E'E] [EE + T] • Thus the PDA has the transition

17. Example: LR Parsing • Similarly we determine the other transitions from I0. • Process T: I2: [ET] [TT * F] • Process F: I3: [TF]

18. Example: LR Parsing • Process (: I4: [F (  E)] [EE + T] [ET] [TT + F] [TF] [F (E)] [Fid] [Fnum]

19. Example: LR Parsing • Process id: I5: [Fid] • Process num: I6: [Fnum]

20. Example: LR Parsing • Now find the transitions from states I1 through I6 to other states, and so on, until no new states appear.

21. Example: LR Parsing • I7: [EE + T] [T T * F] [T F] [F  (E)] [F id] [F num]

22. Example: LR Parsing • I8: [T T * F] [F  (E)] [F id] [F num] • I9: [F (E )] [EE + T]

23. Example: LR Parsing • I10: [E E + T] [T T * F] • I11: [T T * F] • I12: [F (E) ]