Exercício 07.96

Apresente uma derivação à extrema direita (DED) da sentença x = (a * b + c) / (b / c - a) sobre a gramática a seguir.

G = ({A, B, C, D, E, F, G}, {a, b, c, d, x, =, +, -, *, /, (, )}, P, A)
P = {< A >  ->  < G > = < B >
     < B >  ->  < D > < C >  |  < D >
     < C >  ->  + < D > < C >  |  - < D > < C >  |  + < D >  |  - < D >
     < D >  ->  < F > < E >  |  < F >
     < E >  ->  * < F > < E >  |  / < F > < E >  |  * < F >  |  / < F >
     < F >  ->  ( < B > )  |  < G >
     < G >  ->  a  |  b  |  c  |  d  |  x }

Resposta

< A >
< G > = < B >
< G > = < D >
< G > = < F > < E >
< G > = < F > / < F >
< G > = < F > / ( < B > )
< G > = < F > / ( < D > < C > )
< G > = < F > / ( < D > - < D > )
< G > = < F > / ( < D > - < F > )
< G > = < F > / ( < D > - < G > )
< G > = < F > / ( < D > - a )
< G > = < F > / ( < F > < E > - a )
< G > = < F > / ( < F > / < F > - a )
< G > = < F > / ( < F > / < G > - a )
< G > = < F > / ( < F > / c - a )
< G > = < F > / ( < G > / c - a )
< G > = < F > / ( b / c - a )
< G > = ( < B > ) / ( b / c - a )
< G > = ( < D > < C > ) / ( b / c - a )
< G > = ( < D > + < D > ) / ( b / c - a )
< G > = ( < D > + < F > ) / ( b / c - a )
< G > = ( < D > + < G > ) / ( b / c - a )
< G > = ( < D > + c ) / ( b / c - a )
< G > = ( < F > < E > + c ) / ( b / c - a )
< G > = ( < F > * < F > + c ) / ( b / c - a )
< G > = ( < F > * < G > + c ) / ( b / c - a )
< G > = ( < F > * b + c ) / ( b / c - a )
< G > = ( < G > * b + c ) / ( b / c - a )
< G > = ( a * b + c ) / ( b / c - a )
x = ( a * b + c ) / ( b / c - a )