SLR Parser (with Examples) (original) (raw)

Last Updated : 23 Jul, 2025

**LR parsers is an efficient bottom-up syntax analysis technique that can be used to parse large classes of context-free grammar is called LR(k) parsing.
L stands for left-to-right scanning
R stands for rightmost derivation in reverse
k is several input symbols. when k is omitted k is assumed to be 1.

**Advantages of LR parsing

• LR parsers handle context-free grammars. These grammars describe the structure of programming languages-how statements, expressions, and other language constructs fit together.
• LR parsers ensure that your code adheres to these rules.
• It is able to detect syntactic errors
• It is an efficient non-backtracking shift shift-reducing parsing method.

**Types of LR Parsing Methods

• SLR parser
• LALR parser
• Canonical LR parser

**SLR Parser

• LR parser is also called as SLR parser
• it is weakest of the three methods but easier to implement
• a grammar for which SLR parser can be constructed is called SLR grammar

**Steps for constructing the SLR parsing table

1. Writing augmented grammar
2. LR(0) collection of items to be found
3. Find FOLLOW of LHS of production
4. Defining 2 functions:goto[list of terminals] and action[list of non-terminals] in the parsing table

**EXAMPLE - Construct LR parsing table for the given context-free grammar

S-->AA
A-->aA|b

**Solution:

**STEP1: Find augmented grammar
The augmented grammar of the given grammar is:-

S'-->.S [0th production]
S-->.AA [1st production]
A-->.aA [2nd production]
A-->.b [3rd production]

**STEP2: Find LR(0) collection of items
Below is the figure showing the LR(0) collection of items. We will understand everything one by one.

The terminals of this grammar are {a,b}.
The non-terminals of this grammar are {S,A}

**RULE -
If any non-terminal has ' . ' preceding it, we have to write all its production and add ' . ' preceding each of its production.

**RULE -
from each state to the next state, the ' . ' shifts to one place to the right.

• In the figure, I0 consists of augmented grammar.
• Io goes to I1 when ' . ' of 0th production is shifted towards the right of S(S'->S.). this state is the accepted state. S is seen by the compiler.
• Io goes to I2 when ' . ' of 1st production is shifted towards right (S->A.A) . A is seen by the compiler
• I0 goes to I3 when ' . ' of the 2nd production is shifted towards right (A->a.A) . a is seen by the compiler.
• I0 goes to I4 when ' . ' of the 3rd production is shifted towards right (A->b.) . b is seen by the compiler.
• I2 goes to I5 when ' . ' of 1st production is shifted towards right (S->AA.) . A is seen by the compiler
• I2 goes to I4 when ' . ' of 3rd production is shifted towards right (A->b.) . b is seen by the compiler.
• I2 goes to I3 when ' . ' of the 2nd production is shifted towards right (A->a.A) . a is seen by the compiler.
• I3 goes to I4 when ' . ' of the 3rd production is shifted towards right (A->b.) . b is seen by the compiler.
• I3 goes to I6 when ' . ' of 2nd production is shifted towards the right (A->aA.) . A is seen by the compiler
• I3 goes to I3 when ' . ' of the 2nd production is shifted towards right (A->a.A) . a is seen by the compiler.

**STEP3: Find FOLLOW of LHS of production

FOLLOW(S)=$
FOLLOW(A)=a,b,$

To find FOLLOW of non-terminals, please read follow set in syntax analysis.

**STEP 4: Defining 2 functions:goto[list of non-terminals] and action[list of terminals] in the parsing table. Below is the SLR parsing table.

• $ is by default a nonterminal that takes accepting state.
• 0,1,2,3,4,5,6 denotes I0,I1,I2,I3,I4,I5,I6
• I0 gives A in I2, so 2 is added to the A column and 0 rows.
• I0 gives S in I1,so 1 is added to the S column and 1 row.
• similarly 5 is written in A column and 2 row, 6 is written in A column and 3 row.
• I0 gives a in I3 .so S3(shift 3) is added to a column and 0 row.
• I0 gives b in I4 .so S4(shift 4) is added to the b column and 0 row.
• Similarly, S3(shift 3) is added on a column and 2,3 row ,S4(shift 4) is added on b column and 2,3 rows.
• I4 is reduced state as ' . ' is at the end. I4 is the 3rd production of grammar(A-->.b).LHS of this production is A. FOLLOW(A)=a,b,$ . write r3(reduced 3) in the columns of a,b,$ and 4th row
• I5 is reduced state as ' . ' is at the end. I5 is the 1st production of grammar(S-->.AA). LHS of this production is S.
  FOLLOW(S)=$ . write r1(reduced 1) in the column of $ and 5th row
• I6 is a reduced state as ' . ' is at the end. I6 is the 2nd production of grammar( A-->.aA). The LHS of this production is A.
  FOLLOW(A)=a,b,$ . write r2(reduced 2) in the columns of a,b,$ and 6th row

**APPLICATIONS GALORE:

• Compiler
• Data Validation
• Natural Language Processing(NLP)
• Protocol Parsing