Grossman fall initializefall 2011 empty 2011 r to for

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Unformatted text preview: = true L Variable Bindings ML from 1 to Mnd each for each i VariablekBindingsj from i +1 to k a if Y1 … Yi- 1 are all nullable (or if i = 1) Dan Grossman Dan Grossman add FIRST[Yi ] to FIRST[X ] Fall 2011 Fall nullable if Yi+1 … Yk are all 2011 (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 Winter 2013 UW CSE 401 (Michael Ringenburg) 14 2/4/13 Example Z ::= d Z ::= X Y Z Y ::= ε Y ::= c X ::= Y X ::= a repeat for each produc]on X := Y1 Y2 … Yk if Y1 … Yk are all nullable (or if k = 0, i.e., empty 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 LR(0) Reduce Ac]ons (review) CSE341: Programming Languages CSE341: •  In a LR(0) pProgramming Languages a reduc]on, it arser, if a state contains Lecture 1 L of the n is uncondi]onal regardless ecture 1 ext input Course Mechanics symbol Course Mechanics ML Variable Bindings ML Variable Bindings •  Algorithm, where R is the set of reduc]on ac]ons: Dan Grossman Dan Grossman Fall InitializeFall 2011 empty! 2011 R to for each state I in T ! for each item [A ::= α .] in I ! add (I, A ::= α) to R ! Winter 2013 UW CSE 401 (Michael Ringenburg) 17 2/4/13 SLR Construc]on CSE341: Programming CSE341: Programming Languages Languages •  This is iden]cal to LR(0) – states, etc., except Lecture 1 Lecture 1 for the calcula]on of reduce ac]ons. Course Mechanics Course Mechanics:= α •  Algorithm, where (I, a, Variable) means reduce ML A : Bindings ML Variable α to A in state I if tBindings he lookahead is ‘a’: Dan Grossman Dan Grossman Fall InitializeFall 2011 empty! 2011 R to for each state I in T ! for each item [A ::= α .] in I ! for each terminal a in FOLLOW(A) ! !add (I, a, A ::= α) to R ! Winter 2013 18 UW CSE 401 (Michael Ringenburg) S ::= E $ E ::= T + E E ::= T T ::= x CSE341: Programming CSE341: Programming Languages Languages FIRST/FOLLOW for 0. 1. 2. 3. Lecture 1 Lecture 1 Course Course Mechanics Mechanics ML Variable Bindings ML Variable Bindings Dan Grossman Dan Grossman repeat Fall 2011 for each produc]on X := Y1 Y2 … Yk Fall 2011 if Y1 … Yk are all nullable (or if k = 0, i.e., empty...
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