Outline of Class 7: More Grammars

Held: Monday, February 2, 1998

Administrivia

• Assignment one is now graded (at least all that I received by Friday are graded).
  • A set of notes on that assignment are also available. I don't guarantee that I'll produce notes for all assignments.
  • Since it is nearly impossible to give numerical evaluations of textual answers, I used a check-based system. A check means that you got a question mostly right, perhaps with a few errors. A check plus means that you provided an especially insightful answer. A check minus means that there were significant problems with your answer. A zero means that your answer was unacceptable. I then tallied your results to come up with a letter grade.
• Don't forget about today's brown bag lunch. Today is the second part of the Java tutorial.
• Don't forget about tomorrow's exotic programming languages group meeting.
• This Thursday at 4:15, selected math and CS faculty will be discussing summer research opportunities. Come hear how you can get both money and credit while participating in interesting projects.
• This Thursday at 7:30, Mike Jipping from Hope college will be speaking on threads in Java. His talk is based in part on work done with undergraduates as part of Hope's REU program.
• Today we'll begin the class with a quiz. The quiz won't be available until class time.

The Expression Grammar, Revisited

• Recall that last class we worked on developing a grammar for arithmetical expressions and found a way to add precedence to the grammar.
• Today we'll look at associativity in the same grammar.

Adding Associativity to the Expression Grammar

• Have we solved the precedence problem? No. You'll observe that we can still misparse the original expression (although with a different tree).
• How do we handle precedence?
  • By considering which tree is correct.
  • By considering why the incorrect tree is incorrect.
  • By trying to change the grammar to eliminate the incorrect tree.
• Why is the incorrect tree incorrect? Because there is unparenthesized subtraction to "the right of" subtraction.
• What should we do? Come up with a category for "no unparenthesized subtraction".
• Do we have such a category? Yes, we called it Term.

  Exp ::= Exp AddOp Term
  

• Are there other similar areas we must worry about?. Yes, we'll need to worry about repeated division (or multiplication). We can use the same strategy.

  Term ::= Term MulOp Factor
  

• Have we changed the language? No, but the proof is more difficult.

The Final Grammar

• Here is our unambiguous grammar, so far.

  Exp ::= Exp AddOp Term
       |  Term
  Term ::= Term MulOp Factor
        |  Factor
  Factor ::= '(' Exp ')'
          |  num
          |  id
  

• We could further extend this grammar in many ways.
  • Include the unary operators. Note that each at most one unary operator is typically used (e.g., -+num is meaningless, as is ---num).
  • Include exponentiation. Is exponentiation left or right associative?
  • Include other operations.
  • Function calls.
  • ...
• These extensions are left as an exercise to the reader.