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Chapter 4 Parsing Sequences
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Recursive Descent Parsing expr() – term() lex() +/- lex() term() factor() – if id lex(), if ( expr() right lex(), term() – factor * or / lex() factor() a + b lex() -> nextToken (a) = ID expr()
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Recursive Descent Parsing expr() – term() lex() +/- lex() term() factor() – if id lex(), if ( expr() right lex(), term() – factor * or / lex() factor() a + b lex() -> nextToken = ID expr() term()
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Recursive Descent Parsing expr() – term() lex() +/- lex() term() factor() – if id lex(), if ( expr() right lex(), term() – factor * or / lex() factor() a + b lex() -> nextToken = ID expr() term() factor()
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Recursive Descent Parsing expr() – term() lex() +/- lex() term() factor() – if id lex(), if ( expr() right lex(), term() – factor * or / lex() factor() a + b lex() -> nextToken = ID expr() term() factor() nextToken is ID, so call lex() and return from factor, nextToken is +
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Recursive Descent Parsing expr() – term() lex() +/- lex() term() factor() – if id lex(), if ( expr() right lex(), term() – factor * or / lex() factor() a + b lex() -> nextToken = ID expr() term() factor() nextToken is ID, so call lex() and return from factor, nextToken is + not * or / so return from term
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Recursive Descent Parsing expr() – term() +/- lex() term() factor() – if id lex(), if ( expr() right lex(), term() – factor * or / lex() factor() a + b lex() -> nextToken = ID expr() term() factor() nextToken is ID, so call lex() and return from factor, nextToken is + not * or / so return from term nextToken is + so call lex() (nextToken is b)
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Recursive Descent Parsing expr() – term() +/- lex() term() factor() – if id lex(), if ( expr() right lex(), term() – factor * or / lex() factor() a + b lex() -> nextToken = ID expr() term() factor() nextToken is ID, so call lex() and return from factor, nextToken is + not * or / so return from term nextToken is + so call lex() (nextToken is b) now call term()
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Recursive Descent Parsing expr() – term() +/- lex() term() factor() – if id lex(), if ( expr() right lex(), term() – factor * or / lex() factor() a + b lex() -> nextToken = ID expr() term() factor() nextToken is ID, so call lex() and return from factor, nextToken is + not * or / so return from term nextToken is + so lex() (sets nextToken to b) now call term() call factor
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Recursive Descent Parsing expr() – term() +/- lex() term() factor() – if id lex(), if ( expr() right lex(), term() – factor * or / lex() factor() a + b lex() -> nextToken = ID expr() term() factor() nextToken is ID, so call lex() and return from factor, nextToken is + not * or / so return from term nextToken is + so lex() (sets nextToken to b) and call term() call factor nextToken (b) is ID, so call lex() and return from factor, nextToken is end
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Recursive Descent Parsing expr() – term() +/- lex() term() factor() – if id lex(), if ( expr() right lex(), term() – factor * or / lex() factor() a + b lex() -> nextToken = ID expr() term() factor() nextToken is ID, so call lex() and return from factor, nextToken is + not * or / so return from term nextToken is + so lex() (sets nextToken to b) and call term() call factor nextToken (b) is ID, so call lex() and return from factor, nextToken is end nextToken is not * or / so return from term
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Recursive Descent Parsing expr() – term() +/- lex() term() factor() – if id lex(), if ( expr() right lex(), term() – factor * or / lex() factor() a + b lex() -> nextToken = ID expr() term() factor() nextToken is ID, so call lex() and return from factor, nextToken is + not * or / so return from term nextToken is + so lex() (sets nextToken to b) and call term() call factor nextToken (b) is ID, so call lex() and return from factor, nextToken is end nextToken is not * or / so return from term return from expr() – have just recognized a + b as an expression!
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Recursive Descent Parsing expr() – term() +/- lex() term() factor() – if id lex(), if ( expr() right lex(), term() – factor * or / lex() factor() a + b lex() -> nextToken = ID expr() term() factor() nextToken is ID, so call lex() and return from factor, nextToken is + not * or / so return from term nextToken is + so lex() (sets nextToken to b) and call term() call factor nextToken (b) is ID, so call lex() and return from factor, nextToken is end nextToken is not * or / so return from term return from expr() – have just recognized a + b as an expression!
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14 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id
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15 Bottom-up Parsing/LR example Stack 0 0id5 0F3 0T2 0E1 0E1+6 0E1+6id5 0E1+6F3 0E1+6T9 0E1+6T9*7 0E1+6T9*7id5 0E1+6T9*7F10 0E1+6T9 0E1 Action S5 R6 (use GOTO[0.F]) R4 (use GOTO[0,T]) R2 (use GOTO[0,E]) S6 S5 R6 (use GOTO[6,F]) R4 (use GOTO[6,T] S7 S5 R6 (use GOTO[7.F]) R3 (use GOTO[6,T]) R1 (use GOTO[0.E]) accept Parse id + id * id Input id + id * id$ + id * id$ id * id$ * id$ id$ $
![15 Bottom-up Parsing/LR example Stack 0 0id5 0F3 0T2 0E1 0E1+6 0E1+6id5 0E1+6F3 0E1+6T9 0E1+6T9*7 0E1+6T9*7id5 0E1+6T9*7F10 0E1+6T9 0E1 Action S5 R6 (use GOTO[0.F]) R4 (use GOTO[0,T]) R2 (use GOTO[0,E]) S6 S5 R6 (use GOTO[6,F]) R4 (use GOTO[6,T] S7 S5 R6 (use GOTO[7.F]) R3 (use GOTO[6,T]) R1 (use GOTO[0.E]) accept Parse id + id * id Input id + id * id$ + id * id$ id * id$ * id$ id$ $](http://images.slideplayer.com./16/5244263/slides/slide_15.jpg "15 Bottom-up Parsing/LR example Stack 0 0id5 0F3 0T2 0E1 0E1+6 0E1+6id5 0E1+6F3 0E1+6T9 0E1+6T9*7 0E1+6T9*7id5 0E1+6T9*7F10 0E1+6T9 0E1 Action S5 R6 (use GOTO[0.F]) R4 (use GOTO[0,T]) R2 (use GOTO[0,E]) S6 S5 R6 (use GOTO[6,F]) R4 (use GOTO[6,T] S7 S5 R6 (use GOTO[7.F]) R3 (use GOTO[6,T]) R1 (use GOTO[0.E]) accept Parse id + id * id Input id + id * id$ + id * id$ id * id$ * id$ id$ $")
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16 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input id + id * id$ Stack 0 Action: Shift 5
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17 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input + id * id$ Stack id5 0 Action: Reduce 6, pops id5, state is now 0, so GOTO [State0, F] places in state 3 (push F3)
![17 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input + id * id$ Stack id5 0 Action: Reduce 6, pops id5, state is now 0, so GOTO [State0, F] places in state 3 (push F3)](http://images.slideplayer.com./16/5244263/slides/slide_17.jpg "17 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input + id * id$ Stack id5 0 Action: Reduce 6, pops id5, state is now 0, so GOTO [State0, F] places in state 3 (push F3)")
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18 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input + id * id$ Stack F3 0 Action: Reduce 4, pops F3 off stack, state is now 0, so GOTO [State0, T] places in state 2 (push T2)
![18 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input + id * id$ Stack F3 0 Action: Reduce 4, pops F3 off stack, state is now 0, so GOTO [State0, T] places in state 2 (push T2)](http://images.slideplayer.com./16/5244263/slides/slide_18.jpg "18 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input + id * id$ Stack F3 0 Action: Reduce 4, pops F3 off stack, state is now 0, so GOTO [State0, T] places in state 2 (push T2)")
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19 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input + id * id$ Stack T2 0 Action: Reduce 2, pops T2 off the stack, state is now 0, so GOTO [State0, E] places in state 1 (push E1)
![19 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input + id * id$ Stack T2 0 Action: Reduce 2, pops T2 off the stack, state is now 0, so GOTO [State0, E] places in state 1 (push E1)](http://images.slideplayer.com./16/5244263/slides/slide_19.jpg "19 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input + id * id$ Stack T2 0 Action: Reduce 2, pops T2 off the stack, state is now 0, so GOTO [State0, E] places in state 1 (push E1)")
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20 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input + id * id$ Stack E1 0 Action: Shift 6, gets the next input token and moves to state 6
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21 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input id * id$ Stack +6 E1 0 Action: Shift 5, gets the next input token and moves to state 5
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22 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input * id$ Stack id5 +6 E1 0 Action: Reduce 6, pops id5 off stack, state is now 6, so GOTO [State6, F] places in state 3 (pushes F3)
![22 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input * id$ Stack id5 +6 E1 0 Action: Reduce 6, pops id5 off stack, state is now 6, so GOTO [State6, F] places in state 3 (pushes F3)](http://images.slideplayer.com./16/5244263/slides/slide_22.jpg "22 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input * id$ Stack id5 +6 E1 0 Action: Reduce 6, pops id5 off stack, state is now 6, so GOTO [State6, F] places in state 3 (pushes F3)")
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23 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input * id$ Stack F3 +6 E1 0 Action: Reduce 4, pops F3 off stack, state is now 6, so GOTO [State6, T] places in state 9 (pushes T9)
![23 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input * id$ Stack F3 +6 E1 0 Action: Reduce 4, pops F3 off stack, state is now 6, so GOTO [State6, T] places in state 9 (pushes T9)](http://images.slideplayer.com./16/5244263/slides/slide_23.jpg "23 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input * id$ Stack F3 +6 E1 0 Action: Reduce 4, pops F3 off stack, state is now 6, so GOTO [State6, T] places in state 9 (pushes T9)")
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24 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input * id$ Stack T9 +6 E1 0 Action: Shift 7, gets the next input token and moves to state 7
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25 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input id $ Stack *7 T9 +6 E1 0 Action: Shift 5, gets the next input token and moves to state 5
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26 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input $ Stack id5 *7 T9 +6 E1 0 Action: Reduce 6, pops id5 off stack, state is now 7, so GOTO [State7, F] places in state 10 (pushes F10)
![26 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input $ Stack id5 *7 T9 +6 E1 0 Action: Reduce 6, pops id5 off stack, state is now 7, so GOTO [State7, F] places in state 10 (pushes F10)](http://images.slideplayer.com./16/5244263/slides/slide_26.jpg "26 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input $ Stack id5 *7 T9 +6 E1 0 Action: Reduce 6, pops id5 off stack, state is now 7, so GOTO [State7, F] places in state 10 (pushes F10)")
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27 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input $ Stack F10 *7 T9 +6 E1 0 Action: Reduce 3, pops F10*7T9 off stack, state is now 6, so GOTO [State6, T] places in state 9 (pushes T9)
![27 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input $ Stack F10 *7 T9 +6 E1 0 Action: Reduce 3, pops F10*7T9 off stack, state is now 6, so GOTO [State6, T] places in state 9 (pushes T9)](http://images.slideplayer.com./16/5244263/slides/slide_27.jpg "27 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input $ Stack F10 *7 T9 +6 E1 0 Action: Reduce 3, pops F10*7T9 off stack, state is now 6, so GOTO [State6, T] places in state 9 (pushes T9)")
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28 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input $ Stack T9 +6 E1 0 Action: Reduce 1, pops T9+6E1 off stack, state is now 0, so GOTO [State0, E] places in state 1 (pushes E1)
![28 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input $ Stack T9 +6 E1 0 Action: Reduce 1, pops T9+6E1 off stack, state is now 0, so GOTO [State0, E] places in state 1 (pushes E1)](http://images.slideplayer.com./16/5244263/slides/slide_28.jpg "28 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input $ Stack T9 +6 E1 0 Action: Reduce 1, pops T9+6E1 off stack, state is now 0, so GOTO [State0, E] places in state 1 (pushes E1)")
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29 LR Parsing Table 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input $ Stack E1 0 Action: Accept
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30 LR Parsing Table Quick Exercise 1.E -> E + T 2.E -> T 3.T -> T * F 4.T -> F 5.F -> (E) 6.F -> id Input (id + id) $ Stack 0 Action:
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