CS 488
Spring 2012
Lecture 4
Bapa Rao
Cal State L.A.
Reverse rightmost derivation
• ETT*FT*idF*idid*id
• Reduction
– Replace RHS of production with LHS
• Handle
– Substring (terms and non-terms) that matches the body of
a production
– Reduction by handle represents one step along a reverse
rightmost derivation
• “a handle” vs “the handle”
– Ambiguity!
– >1 rightmost derivation of αβw
– w can only have terminals
Four possible actions of a shift-reduce
parser
• Shift
– Token on to top of stack
• Reduce
– Handle to non-terminal on right of production
– Handle always on top of stack
– Never need to go “inside” stack to find handle
• Accept
• Error
• Case 1: expand A via nonterminal B
• Case 2: expand A and B directly to terminal
• In both cases, handle on top of stack
Shift-reduce conflicts
• Dangling-else
Stmt  if expr then stmt
| if expr then stmt else stmt
| other
STACK has
… if expr then stmt
INPUT has
else … $
Should you shift the else or reduce?
• Array references and procedure calls have same syntas
– P(a,b)
– A(I,j)
Simple LR parsing
• Can handle nearly all programming languages
• Most general method of nonbacktracking
parsing, still efficient
• Earliest syntax error detection
• Proper superset of LL parsable grammars
• Hard to construct by hand
Items and Closure
• LR(0) item is a production of grammar with a dot somewhere on
RHS
– How much have you seen on RHS
•
•
•
•
Canonical LR(0) collection
Build a DFSA: LR(0) automaton
States represent set of items
Augmented Grammar
– S’  S
• Closure is Recursive-transitive closure of an item from the grammar
• GOTO transition function
• Kernel and non-kernel items
– Kernel: S’  .S and all items whose dots are not at left end
– Non-kernel: all items with dots at left end except for S’ S
• GOTO transition function
– GOTO(Item,GrammarSymbol)  Closure of set of
all items such GrammarSymbol is reduced
• Kernel and non-kernel items
– Kernel: S’  .S and all items whose dots are not at
left end
– Non-kernel: all items with dots at left end except
for S’ S