Lecture3.md

Lecture 3 (Jan 16, 2018)

Grammars

• Grammars are descriptions of languages

  • Used to generate sentences
  • Used to parse sentences

• Grammars are (almost) programs

• What can go wrong with grammars?

  • Nonterminal used but not defined (useless rule)
  • Nonterminal defined but not used (useless nonterminal)
  • Nonterminal not reachable from start symbol
  • Nonterminals that can never produce a string of terminals
  • Trying to use grammar to capture constraints that are best captured elsewhere
  • 1 token = 1 character
    • Using grammars to specify details best handled by technology
  • Ambiguous grammars (example)

    E -> E + E
    E -> E * E
    E -> ID
    E -> NUM
    E -> (E)
    

    • A terminal sandwiched between nonterminals indicates trouble (ex. E + E or E * E)

• Discover and Fix Ambiguity

  • Prove that a single string can produce two or more parses
  • Rewrite grammar to have associativity constraints (ex. left-associative operator)
  • Rewrite grammar to have precedence tules (ex. multiplication before addition)

• Multiple Notations for Grammars

  • BNF (Backus–Naur form)
  • EBNF (Extended BNF)
    • Recall
      • x* zero or more xs in a sequence
      • x+ one or more xs in a row
    • Used for RFC 5322 (Internet message format). Where / represents OR and specials are ()<>@;:\'"[]:

    msg-id = "<" word *("."word) "@" atom* ("." atom) ">"
    

    word = atom / quoted-string
    atom = 1*<any CHAR except specials, SPACE, and CTLs>
    quoted-string = <"> *(qtext / quoted-pair) <">
    qtext = <any CHAR except " \ CR> 
    quoted=pair = "\" CHAR
    

    • ISO standard for EVNF

    [options]
    {repetition}
    [grouping]
    (*comment*)
    x* (repetition)
    x-y (except)
    x,y (concatenate)
    x|y (or)
    = (defn in a rule)
    ; (end of rule)
    

    syntax = syntax rule, {syntax rule};
    syntax rule = meta id, "=", defns list, ";";
    defns list = defn, {"|", defn};