Compiler theory learning (3) grammar and language

1. grammar G (Z): Z-> aZb | ab definition of what kind of language?

　　 Grammar G (Z) has two production rules:

　　（1）Z->aZb

　　（2）Z->ab

　　By using the n-1 times to generate a first type, and then use a formula to generate a second, to give Z-> aZb-> aaZbb-> aaaZbbb-> aaaZbbb -> ...... A ^n-1 B ^{n- -1} -> A ^n- B ^n-

 

2. Write grammar quaternion form materials 22 pages identifiers in example 2.2.

　　Grammar quad form:

　　Grammar = G (V _N , V _T , P, S)

　　V _n- = {W is (identifier), Q (letters), K (number)}

　　V_t={a,b,c,d...........z,0,1.......9}

　　P={W-->Q | K }

　　S={W}

 

3. Write the following expressions leftmost derivation and rightmost derivation syntax tree.

G (E):

E=> E + T | T

T=>T * F | F

F=>（E）| i

• i*i+i
• i+i*i
• i+(i+i)

 Observe different leftmost and rightmost derivation process, as well as the similarities and differences of the syntax tree.

　　（1）i*i+i

　　　　Leftmost derivation:

　　　　E=>E+T=>T*F+T=>F*F+T=>i*F+T=>i*i+T=>i*i+F=>i*i+i

　　　　Rightmost derivation:

　　　　E=>E+T=>E+F=>E+i=>T*i=>T*F+i=>T*T+i=>T*T+i=>T*i+i=>i*i+i

　　　　

　　　　

　　　（2）i+i*i

　　　　Leftmost derivation:

　　　　E=>E+T=>T+T=>F+T=>i+T=>i+T*F=>i+F*F=>i+i*i

　　　　最右推导：

　　　　E=>E+T=>E+F=>E+E=>E+E+T=>E+T*F=>E+T*F=>E+T*i=>E+F*i=>E+i*i=>T+i*i=>F+i*i=>i+i*i

            

　　　　

　　　　（3）i+(i+i)

　　　　最左推导：

　　　　E=>E+T=>T+T=>F+T=>i+T=>i+F=>i+(E)=>i+(E+T)=>i+(T+T)=>i+(F+T)=>i+(i+T)=>i+(i+F)=>i+(i+i)

　　　　最右推导：

　　　　E=>E+T=>E+F=>E+(E)=>E+(E+T)=>E+(E+F)=>E+(E+i)=>E+(T+i)=>E+(F+i)=>E+(i+i)=>T+(i+i)=>F+(i+i)=>i+(i+i)