Exercício 07.102

Apresente uma derivação à extrema direita (DED) da sentença x = a - (b * c - d) * (d - c / b) - 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 > < C >
< G > = < D > - < D > < C >
< G > = < D > - < D > - < D >
< G > = < D > - < D > - < F >
< G > = < D > - < D > - < G >
< G > = < D > - < D > - a
< G > = < D > - < F > < E > - a
< G > = < D > - < F > * < F > - a
< G > = < D > - < F > * ( < B > ) - a
< G > = < D > - < F > * ( < D > < C > ) - a
< G > = < D > - < F > * ( < D > - < D > ) - a
< G > = < D > - < F > * ( < D > - < F > < E > ) - a
< G > = < D > - < F > * ( < D > - < F > / < F > ) - a
< G > = < D > - < F > * ( < D > - < F > / < G > ) - a
< G > = < D > - < F > * ( < D > - < F > / b ) - a
< G > = < D > - < F > * ( < D > - < G > / b ) - a
< G > = < D > - < F > * ( < D > - c / b ) - a
< G > = < D > - < F > * ( < F > - c / b ) - a
< G > = < D > - < F > * ( < G > - c / b ) - a
< G > = < D > - < F > * ( d - c / b ) - a
< G > = < D > - ( < B > ) * ( d - c / b ) - a
< G > = < D > - ( < D > < C > ) * ( d - c / b ) - a
< G > = < D > - ( < D > - < D > ) * ( d - c / b ) - a
< G > = < D > - ( < D > - < F > ) * ( d - c / b ) - a
< G > = < D > - ( < D > - < G > ) * ( d - c / b ) - a
< G > = < D > - ( < D > - d ) * ( d - c / b ) - a
< G > = < D > - ( < F > < E > - d ) * ( d - c / b ) - a
< G > = < D > - ( < F > * < F > - d ) * ( d - c / b ) - a
< G > = < D > - ( < F > * < G > - d ) * ( d - c / b ) - a
< G > = < D > - ( < F > * c - d ) * ( d - c / b ) - a
< G > = < D > - ( < G > * c - d ) * ( d - c / b ) - a
< G > = < D > - ( b * c - d ) * ( d - c / b ) - a
< G > = < F > - ( b * c - d ) * ( d - c / b ) - a
< G > = < G > - ( b * c - d ) * ( d - c / b ) - a
< G > = a - ( b * c - d ) * ( d - c / b ) - a
x = a - ( b * c - d ) * ( d - c / b ) - a