Lecture 09 syntax analysis 05
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The document discusses LR(1) parsing and the construction of LR(1) parsing tables. It describes how LR(1) items include a lookahead terminal symbol to avoid invalid reductions. The closure and goto functions are used to construct the canonical collection of LR(1) item sets. From this, the action and goto tables of the LR(1) parser are derived. The document also discusses how LALR parsing tables are constructed by merging states that have the same core (first component) of LR(1) items, which can introduce reduce/reduce conflicts but not shift/reduce conflicts.
![CONSTRUCTION OF LR(1) PARSING TABLES
1. Construct the canonical collection of sets of LR(1) items for G’.
C{I0,...,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 AS’.
• If S’S.,$ is in Ii , then action[i,$] is accept.
• If any conflicting actions generated by these rules, the grammar is not
LR(1).
3. Create the parsing goto table
• for all non-terminals A, if goto(Ii,A)=Ij then goto[i,A]=j
4. All entries not defined by (2) and (3) are errors.
5. Initial state of the parser contains S’.S,$
12](https://image.slidesharecdn.com/lecture09syntaxanalysis05-151020082118-lva1-app6892/85/Lecture-09-syntax-analysis-05-12-320.jpg)
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Lecture 09 syntax analysis 05
- 2. ASSIGNMENT 01 (DUE ON 20TH) 1. Derive the (i) LL(1) parse table, (ii) LR(0) automation, (iii) LR(0) parse table of following grammar: S-> SS+ S-> SS* S-> a 2. Parse the following string using (i) LL (1) parse table, (ii) LR (0) parse table: “aa+a*a+” 2
- 3. 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.) 3
- 5. INTUITION BEHIND LR (1) ITEMS 5
- 6. INTUITION BEHIND LR (1) ITEMS 6
- 9. LR (1) EXAMPLE S -> CC C -> cC C -> d 9
- 10. 10
- 12. CONSTRUCTION OF LR(1) PARSING TABLES 1. Construct the canonical collection of sets of LR(1) items for G’. C{I0,...,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 AS’. • If S’S.,$ is in Ii , then action[i,$] is accept. • If any conflicting actions generated by these rules, the grammar is not LR(1). 3. Create the parsing goto table • for all non-terminals A, if goto(Ii,A)=Ij then goto[i,A]=j 4. All entries not defined by (2) and (3) are errors. 5. Initial state of the parser contains S’.S,$ 12
- 13. LALR Parsing Tables • LALR stands for LookAhead 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. • A state of LALR parser will be again a set of LR(1) items.
- 14. CREATING LALR PARSING TABLES Canonical LR(1) Parser € LALR Parser shrink # of states • 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.
- 15. 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,$. S L.=R R L.,$ R L. • 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. L id.,$ I1:L id.,= A new state:I12: L id.,= I2:L id.,$ • 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 Core Same Core Merge Them
- 16. 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={I0,...,In} € C’={J1,...,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=I1 ... Iksince I1,...,Ik have same cores € cores of goto(I1,X),...,goto(I2,X) must be same. – So, goto(J,X)=K where K is the union of all sets of items having same cores as goto(I1,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)
- 17. 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)
- 18. 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. I1 : A .,a B .,b I2: A .,b B .,c € reduce/reduce conflictI12: A .,a/b B .,b/c