Programming Languages Class: Given the grammar (1) E Prefix ( E ) (2) E V Tail (

Question

Programming Languages Class:

Given the grammar

(1)            E Prefix ( E )

(2)            E V Tail

(3)            Prefix F

(4)            Prefix

(5)            Tail + E                                                                    

(6)            Tail - E                                 

(7)            Tail                

( is defined as the empty set, NULL or ->    )        

Determine whether F(V-V) is syntactically correct using left-most derivation.   Show your work.

Explanation / Answer

Yes F(V-V) is syntactically correct. The following shows the left most derivation.

Since there is no starting variable given I would assume E to be the start as it is the first varaible. So in the left most derivation we have to replace the left most variable by its productions. So beginning now:

E ->Prefix(E) Beginning Production as we want F outside the parenthesis

E->F(E) By using Prefix->F

E->F(V Tail) By using E->V Tail

E->F(V - E) By using Tail->-E

E->F(V - V Tail) By using E->V Tail

E->F(V-V) By using Tail->null

This proves that we can derive E->F(V-V) using the left most derivation.

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