LR Parser

The LR parser is a non-recursive, shift-reduce, bottom-up parser. It uses a wide class of context-free grammar which makes it the most efficient syntax analysis technique. LR parsers are also known as LR(k) parsers, where L stands for left-to-right scanning of the input stream; R stands for the construction of right-most derivation in reverse, and k denotes the number of lookahead symbols to make decisions.

There are three widely used algorithms available for constructing an LR parser:

• SLR(1) – Simple LR Parser:
  • Works on smallest class of grammar
  • Few number of states, hence very small table
  • Simple and fast construction
• LR(1) – LR Parser:
  • Works on complete set of LR(1) Grammar
  • Generates large table and large number of states
  • Slow construction
• LALR(1) – Look-Ahead LR Parser:
  • Works on intermediate size of grammar
  • Number of states are same as in SLR(1)

LR Parsing Algorithm

Here we describe a skeleton algorithm of an LR parser:

token = next_token()

repeat forever
   s = top of stack
   
   if action[s, token] = “shift si” then
      PUSH token
      PUSH si 
      token = next_token()
      
   else if action[s, token] = “reduce A::= β“ then 
      POP 2 * |β| symbols
      s = top of stack
      PUSH A
      PUSH goto[s,A]
      
   else if action[s, token] = “accept” then
      return
      
   else
      error()

LL vs. LR