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Compiler Construction Sohail Aslam Lecture 26

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2 Finite Automaton of Items Then for every item A → X we must add an -transition for every production X → A → X X →

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3 Finite Automaton of Items The initial DFA state I 0 we computed is the -closure of the set consisting of item S → E

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4 Recall the stage in the closure s ={ [S → E, $], [E → E + (E), $], [E → int, $] } Finite Automaton of Items

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5 NFA states [S → E,$] [E → E+(E),$] [E → int,$]

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6 Algorithm: Construction of collection of canonical sets of LR(1) items. Input: An augmented grammar G' Output: Collection of canonical ( CC ) sets of LR(1)

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7 Algorithm: Construction of collection of canonical sets of LR(1) items. Input: An augmented grammar G' Output: Collection of canonical ( CC ) sets of LR(1)

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8 Algorithm: Construction of collection of canonical sets of LR(1) items. Input: An augmented grammar G' Output: Collection of canonical ( CC ) sets of LR(1)

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9 CC( G' ) I 0 ← {closure( [S' → S, $] )} CC ← { I 0 } repeat for each unmarked set I j CC mark I j as processed for each X following in an item in I j I k ← goto( I j, X ) if I k CC then CC ← CC I k record transition from I j to I k on X until CC is not changing

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10 Sets of LR(1) Items Augmented grammar G' S → E E → E + (E) | int

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11 Sets of LR(1) Items We now compute goto( I 0, X ) for various values of X X can be E, int, +, ( and )

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12 goto(s, y ) m { } for each item [X → y , b] s m ← m { [X → y , b] } return closure(m)

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13 I 1 = goto( I 0, int ) m ← {} for each [X → int , b] I 0 [E → int, $ / +] I 0 m = m { [E → int , $ / +] } return closure({ [E → int ,$ / +] })

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14 closure({ [E → int ,$ / +] }) No additional closure is possible since the dot is at the right end of the production

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15 Thus I 1 = { [E → int , $ / +] } And we have the transition from I 0 to I 1 on int

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16 Thus I 1 = { [E → int , $ / +] } And we have the transition from I 0 to I 1 on int I0I0 int I1I1

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17 I 2 = goto( I 0, E ) m ← {} for each [X → E , b] I 0 [S → E, $] [E → E+(E), $ / +]

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18 m = m { [S → E , $] } { [E → E +(E), $ / +] } return closure(m)

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19 I 2 = { [S → E , $], [E → E +(E), $ / +] } No further closure for the first item because is at the end In the second item, a terminal + appears after so no further closure

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20 I 2 = { [S → E , $], [E → E +(E), $ / +] } No further closure for the first item because is at the end In the second item, a terminal + appears after so no further closure

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21 I 3 = goto( I 2, + ) = { [E → E + (E), $ / +] } I 4 = goto( I 3, ( ) = { [E → E + ( E), $ / +] [E → E + (E), ) / +] [E → int, ) / +] }

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22 I 3 = goto( I 2, + ) = { [E → E + (E), $ / +] } I 4 = goto( I 3, ( ) = { [E → E + ( E), $ / +] [E → E + (E), ) / +] [E → int, ) / +] }

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23 I 5 = goto( I 4, int ) = { [E → int , ) / +] } I 6 = goto( I 4, E ) = { [E → E + (E ), $ / +] [E → E + (E), ) / +] } and so on....

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24 I 5 = goto( I 4, int ) = { [E → int , ) / +] } I 6 = goto( I 4, E ) = { [E → E + (E ), $ / +] [E → E + (E), ) / +] } and so on....

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25 I 5 = goto( I 4, int ) = { [E → int , ) / +] } I 6 = goto( I 4, E ) = { [E → E + (E ), $ / +] [E → E + (E), ) / +] } and so on....

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26 0 E → int on ), + int E + ( E E → int on $, + accept on $ S → E, $ E → E+(E), $/+ E → int, $/+ 1 E → int , $/+ 2 S → E , $ E → E +(E), $/+ 3 E → E+ (E), $/+ 4 E → E+( E), $/+ E → E+(E), )/+ E → int, )/+ 6 E → E+( E), $/+ E → E+(E), )/+ E → int, )/+ 5 E → int , )/+

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27 NFA of LR(0) Items Consider the augmented grammar E ' → E E → E + n | n

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28 E E + E' → EE' → E E' → EE' → E E → E+nE → n E → E+ nE → E +n E → n E → E+n n n

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29 E E + E' → EE' → E E' → EE' → E E → E+nE → n E → E+ nE → E +n E → n E → E+n n n

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30 E + E ' → E E → E+n E → n E' → EE' → E E → E+ nE → E +n E → n E → E+n n n E

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31 E + E ' → E E → E+n E → n E ' → E E → E +n n n 0 1 2 3 4 E → E+ n E → n E → E+n

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32 LR(1) Transitions Given an LR(1) item [ A → B a ] where B is a non-terminal, there are -transitions to items [B → b] for every production B → and for every token b in FIRST ( a )

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33 LR Table Construction Construct CC = { I 0, I 1, I 2,..., I n }, for G' State i of the parser is constructed from the set I i The parsing actions for state i are determined as follows:

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34 LR Table Construction Construct CC = { I 0, I 1, I 2,..., I n }, for G' State i of the parser is constructed from the set I i The parsing actions for state i are determined as follows:

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35 LR Table Construction Construct CC = { I 0, I 1, I 2,..., I n }, for G' State i of the parser is constructed from the set I i The parsing actions for state i are determined as follows:

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