Exercício 07.111

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

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

Resposta

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