13 compiler theory 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.

Symbols Stack	Input string	action
#	i+i*i#	Moved into
#i	+i*i#	Reduction
#F	+i*i#	Reduction
#T	+i*i#	Reduction
#E	+i*i#	Moved into
#E+	i*i#	Moved into
# E + i	*i#	Reduction
#E+F	*i#	Reduction
#E+T	*i#	Moved into
#E+T*	i#	Moved into
#E+T*i	#	Reduction
#E+T*F	#	Reduction
#E+T	#	Reduction
#E	#	accept

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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

1) calculating and FIRSTVT LASTVT.

2) find a three relationships right.

3) construction operator precedence table.

（1）

FIRSTVT(S) = {a , ^ , ( }

FIRSTVT(T) = {，, a , ^ , ( }

LASTVT(S) = {a , ^ , ) }

Lastva (T) = {,, the, ^,)}

（2）

=	<	>
(T) #S#	#S (T ,S	S# T) T,

 

 

 

 

 

（3）

	a	^	,	(	)	#
a			>		>	>
^			>		>	>
,	<	<	>	<	>
(	<	<	<	<	=
)			>		>	>
#	<	<		<		=