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Gentle
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We now look at a more interesting algorithm that works on the abstract syntax. We introduce the placeholder x and interpret an expression as a function in x. Given such an expression E, we will compute an expression E' that represents the derivative of the function. We extend the abstract syntax by the alternative xand add to the concrete syntax the rule 'rule' expr3(> x): "x" The root clause now takes the form 'root' expression(> X) deriv(X > D) print(D) The procedure deriv is then defined as follows 'action' deriv (Expr > Expr) 'rule' deriv(mult (U,V) > plus(mult(Ud,V), mult(U,Vd))): deriv(U > Ud) deriv(V > Vd) 'rule' deriv(div(U,V) > div(minus(mult(Ud,V),mult(U,Vd)),mult(V,V))): deriv(U > Ud) deriv(V > Vd) 'rule' deriv(plus(U,V) > plus(Ud, Vd)): deriv(U > Ud) deriv(V > Vd) 'rule' deriv(minus(U,V) > minus(Ud, Vd)): deriv(U > Ud) deriv(V > Vd) 'rule' deriv(num(N) > num(0)) 'rule' deriv(x > num(1)) 