Class 14: Parsing, concluded

Held Wednesday, September 30, 1998

Notes

• Don't forget that assignment 6 is due today at 5pm. I'll be available after class for questions.
  • Those of you who need a free extension until next Wednesday may have that extension.
  • Extra credit for those who turn it in by class time on Friday.
• Your answers to assignment 4 suggested that English is a particularly bad language for describing languages.
  • ``Strings of a,b,c with first a before first b'' -- What happens if there are no a's?
  • ``Binary numbers that are multiples of 4'' -- Can binary numbers start with 0? Is 0 a multiple of 4?
  • ``Numbers with an integer solution of aⁿ + bⁿ = cⁿ'' -- Can a,b, and c be 0? Negative?

LR parsing, concluded

Construction of LR(0) automata, revisited

• Recall that we build LR(0) automata using the following guidelines
• A state in an LR(0) automaton is a collection of LR(0) items
• An LR(0) item is a production augmented by a ``position marker'' that indicates where in the production we might be.
• The grammar is augmented with a new start state, S', and production,

    S' ::= S $
  

• The initial state is the closure of S' ::= . S $
• The closure of a state fills in the other possible items. For example, if we're waiting to see an N (indicated by a position marker before N in some item), then we need to include all the items for ``how to parse an N, given that you've seen nothing of the right-hand side''.
• The edge labels of the automaton are given by the nonterminals and terminals of the grammar.
• The edges of the automaton correspond to seeing one more symbol in the right-hand sides. After moving the position marker appropriately, one computes the closure of the new items.
• The final states are the states in which the position marker has reached the end of the right-hand side.
• When reaching a final state in some contexts, one does the reduction given by the final state, returns to the state in effect when we started matching the right-hand side, and restarts the automaton.
  • A stack keeps track of the state history.

Conflicts in LR automata

• At times, there are conflicts in LR automata. What kinds of conflicts?
• A state may include a ``final'' item (one in which the position marker is at the end) and a nonfinal item.
  • This is called a shift-reduce conflict
• A state may include two different ``final'' items.
  • This is called a reduce-reduce conflict
  • Can we have reduce-reduce conflicts in unambiguous grammars?
• Can we have a shift-shift conflict?

SLR Automata

• You may have noted (e.g., from our example yesterday) that LR(0) automata can be overly aggressive in choosing to reduce.
  • Such automata typically reduce whenever we've reached the end of a right-hand side.
• SLR automata only reduce when the next token is in Follow of the left-hand side of the reduction.

LR(1) Automata

• LR(1) automata require a more complicated construction process, one that involves lookahead.
• In effect, instead of using the Follow table (as SLR automata do), LR(1) automata build more specific follow tables that correspond to the possible follow symbols according to a particular context.
• Each LR(1) item contains not just an augmented production, but also a token that can follow the nonterminal when we've reached the current state.
• The tokens are inserted by the closure routine.
  • If we have N ::= alpha . M beta then when we insert the M items, we indicate that each of them can be followed by the tokens in first(beta)
  • If beta is nullable, then the M items can also be followed by whatever can follow N (in the given LR(1) item).
• See the book and the errata sheets for more details.

History

• Created Monday, September 28, 1998 (no content).
• Selected text on SLR automata copied from the previous outline and was added on Wednesday, September 30, 1998.
• The attribute grammar for expressions is slightly modified from one I wrote for CS302 last semester. It was added on Wednesday, September 30, 1998. The original was developed on our near May 7, 1998.
• On Friday, October 2, I moved all of the attribute materials to the next outline.