Today in CS362: Shift-Reduce Parsing, Concluded

Missing
  Mark, Nathan

Admin
* Do small tasks immediately
* Parser delayed until after break
* Class ends early

Overview
* Review
* Using LR(0) tables
* SLR parsers
* LR(1) parsers
* Done

Building LR(0) parsing tables/automata.
Each state in an LR(0) autom. is a collection of
  extended productions.
Each extended production is a production augmented
  by a note as to postition in RHS
Transitions are labeled by both nonterminals and
  terminals

How to use an LR(0) automataon
  Push start state
  repeat
    look at the state at the top of the stack and
      the current input symbol
    if the state on the top of the stack contains
    an ep with a complete RHS, then REDUCE:
      pop the RHS off the stack
      s1 = top of the stack // a state, s1
      push LHS on the stack
      push goto(s1,LHS) on the stack
    otherwise, // follow the edge labeled by the input symbol 
    SHIFT
      push current input symbol on stack
      push goto(old-top,input-symbol) on stack
      advance input
  until either
    (a) The state on top of the stack contains [S' -> S $ .]
        ACCEPT
    (b) The state on top of the stack contains no eps.
        REJECT

A few potential problems:
(1) In some states, you might be tempted to shift or reduce.
    Which do you do?  SHIFT-REDUCE conflict
    (a) LR(0) soloution: reduce
    (b) "Fix" the grammar
    (c) Reduce only when the next symbol is in Follow(LHS)
        This modification to LR(0) is called SLR
(2) In some states, you might have choices of two things to
    reduce  REDUCE-REDUCE conflict
    (a) "Fix" the grammar b/c it's probably ambiguous
(3) Can you have a SHIFT-SHIFT conflict?  NO

SLR has problems on some grammars b/c over aggressive in
using Follow

LR(1): A better way of computing more restrictive follows