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Items cse341 a is c lr1 item a programming

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Unformatted text preview: string) set nullable[X] = true for each i from 1 to k and each j from i +1 to k if Y1 … Yi- 1 are all nullable (or if i = 1) add FIRST[Yi ] to FIRST[X ] if Yi+1 … Yk are all nullable (or if i = k ) add FOLLOW[X ] to FOLLOW[Yi ] if Yi+1 … Yj- 1 are all nullable (or if i+1=j) add FIRST[Yj ] to FOLLOW[Yi ] Un]l FIRST, FOLLOW, and nullable do not change 2/4/13 S ::= E $ E ::= T + E E ::= T T ::= x CSE341: Programming CSE341: Programming Languages Languages LR(0) Parser for 0. 1. 2. 3. x $ Lecture 1 Lecture 1 + 1 s5 S ::= E . $ Course S ::= . E $ Course Mechanics Mechanics 2 acc E ::= . T + E ML Variable Bindings 3 E ::= . T ML Variable Bindings r2 3 s4,r2 r2 1 2 T ::= . x x 5 T ::= x . 6 E ::= T + E. T E ::= T . + E DE ::= T . an Grossman Fall 2011T + x E 4 E E E E Winter 2013 ::= ::= ::= ::= 4 s5 Dan Grossman 5 r3 Fall 2011 r3 6 T+.E .T+E .T .x r1 r1 E T g2 g3 g6 E g3 r3 r1 FOLLOW(T) = { +, $ } FOLLOW(E) = { $ } 21 UW CSE 401 (Michael Ringenburg) S ::= E $ E ::= T + E E ::= T T ::= x CSE341: Programming CSE341: Programming Languages Languages SLR Parser for 0. 1. 2. 3. x $ Lecture 1 Lecture 1 + 1 s5 S ::= E . $ Course S ::= . E $ Course Mechanics Mechanics 2 acc E ::= . T + E ML Variable Bindings 3 E ::= . T ML Variable Bindings r2 3 s4,r2 r2 1 2 T ::= . x x 5 T ::= x . 6 E ::= T + E. Winter 2013 T E ::= T . + E DE ::= T . an Grossman Fall 2011T + x E 4 E E E E ::= ::= ::= ::= T+.E .T+E .T .x 4 s5 Dan Grossman 5 r3 Fall 2011 r3 6 r1 r1 E T g2 g3 g6 E g3 r3 r1 FOLLOW(T) = { +, $ } FOLLOW(E) = { $ } UW CSE 401 (Michael Ringenburg) 22 2/4/13 LR(1) grammars CSE341: Programming CSE341: Programming Languages Languages •  Many prac]cal grammars are SLR Lecture 1 Lecture 1 •  LR(1) is more powerful yet Mechanics Course Course Mechanics ML ut no]on of an item is •  Similar construc]on, bVariable Bindings ML Variable Bindings more complex, incorpora]ng lookahead Dan Grossman Dan Grossman Fall 2011 informa]on Fall 2011 Winter 2013 UW CSE 401 (Michael Ringenburg) 23 LR(1) Items CSE341: β, a] is C LR(1) item [A ::= α . Programming •  An SE341: Programming Languages Languages –  A grammar pLecture 1(A ::= αβ) 1 roduc]on Lecture –  A right hand side posi]on (the Mechanics Course dot) Course Mechanics –  A lookahead symbol ML Variable Bindings (a) M i Variable Bindings •  Idea: This Ltem indicates that an A followed by an a would be consistent with the input the parser Dan Grossman has seen up tDanhis point. Fall 2011 o t Grossman •  Item [A ::= α . , Fall means reduce to A if the next a] 2011 symbol (...
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