1. Compilers ABHISHEK REDDY PAM (11CS30002) DATE : 07/10/2013

2. Viable Prefix  The set of prefixes of right sentential forms that can appear on the stack of a shift-reduce parser are called viable prefixes.  Right-Sentential Form : A sentential form that can be derived by a rightmost derivation  The prefix of the sentential form may not be the content of the stack.

3. Example Consider: S  aABe A  Abc | b B  d Rightmost Derivation of the string abbcde: S  aABe  aAde  aAbcde  abbcde The (unique) handle is underlined for each step.

4. Continuation… A viable prefix is : (1) a string that equals a prefix of a right- sentential form up to (and including) its unique handle. (2) any prefix of a string that satisfies (1) For given example : Viable prefixes: a, aA, aAd, aAbc, ab, aAb,… Not viable prefixes: aAde, Abc, aAA,…

5. Shift/Reduce Parser StackInputRemark $abbcde$SHIFT $abbcde$SHIFT $abbcde$REDUCE $aAbcde$SHIFT $aAbcde$SHIFT $aAbcde$REDUCE $aAde$SHIFT $aAde$e$REDUCE $aABe$e$SHIFT $aABe$REDUCE $S$ACCEPT All strings in the stack are viable prefixes

6. When to shift/reduce ? Sometimes on top of the stack something appears to be a handle (i.e., matches the RHS of a production). But: maybe we have not shifted enough elements to identify the handle. Observe the correct sequence of Shift and Reduce steps preserves the property that the stack IS a viable prefix. Example : $aAb cde$Shift or Reduce? If we shift we obtain aAbc in the stack (aA is the valid item for the viable prefix aAbc). Recall that Abc is a handle. Instead if we reduce we obtain aAA in the stack. (this is NOT a viable prefix!!!)

7. Valid Items DEFINITION: A  α.β, {a} is a valid LR(1)-item for a viable prefix γα if there exists a right-most derivation. S  γAy  γαβy Such that i.a is the first symbol of y (or) ii.y = ε and a = $

8. THE END A DFA accepting viable prefixes. Its states are sets of LR(1)-items (that are valid for the corresponding viable prefixes) Canonical LR Parser(LR(1) Parser), States and encoding of valid items and viable prefixes are discussed in the next lecture.