13, bottom-up parsing

1. Known grammar:

E→E+T | T

T→T*F | F

F → (E) | i

Reducible to handle as a string, a symbol string write 'i + i * i #' of "Shift - reduce" analysis.

 

2.P121 Exercise 1 (1) (2).

1) calculating and FIRSTVT LASTVT.

2) find a three relationships right.

3) construction operator precedence table.

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solution:

1、

Symbol string	Input string	action
#	i+i*i#	Moved into
#i	+i*i#	Reduction
#F	+i*i#	Reduction
#T	+i*i#	Reduction
#E	+i*i#	Reduction
#E+	+i*i#	Moved into
# E + I	*i#	Moved into
#E+F	*i#	Reduction
#E+T	*i#	Reduction
#E+T*	i#	Moved into
#E+T*i	#	Moved into
#E+T*F	#	Reduction
#E+T	#	Reduction
#E	#	Moved into

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 2、

   1) calculating and FIRSTVT LASTVT

　　S1→ #S#

　　S → a | L | (T)

　　T→ T，S|S

 

　　FIRSTVT(S)={a,Λ,(}

　　FIRSTVT(T)={，,a,Λ,(}

　　LASTVT(S)={a,Λ,)}

　　LASTVT(T)={，,a,Λ,)}

   2) to find the three relationships

①　=

　　(T)

　　#S#

------------------------------------

②　<

　　#S

　　，S

　　(T

------------------------------------

③　>

　　S#

　　T)

　　T，

------------------------------------

   3) construction operator precedence table

	a	L.	(	)	,	#
a				>	>	>
L.				>	>	>
(	<	<	<	=	<
)				>	>	>
,	<	<	<	>	>
#	<	<	<