2.34¶

; Evaluating a polynomial in x at a given value of x can be formulated as an 
; accumulation. We evaluate the polynomial,
; a_nx^n + a_(n-1)x^n + ... + a_1x + a_0
; using a well-known algorithm called Horner’s rule, which structures the 
; computation as,
; (... (a_nx + a_(n-1))x + ... a1)x + a_0
; In other words, we start with an, multiply by x, add a_(n−1), multiply by x, 
; and so on, until we reach a0
; Fill in the following template to produce a procedure that evaluates a polynomial 
; using Horner’s rule. Assume that the coefficients of the polynomial are arranged 
; in a sequence, from a0 through an.
; (define (horner-eval x coefficient-sequence) 
;   (accumulate (lambda (this-coeff higher-terms) ⟨??⟩)
;               0
;               coefficient-sequence))
; For example, to compute 1 + 3x + 5x^3 + x^5 at x = 2 you would evaluate
; (horner-eval 2 (list 1 3 0 5 0 1))

(define nil '())
(define (accumulate op initial sequence)
    (if (null? sequence) 
        initial
        (op (car sequence) (accumulate op initial (cdr sequence)))))

(define (horner-eval x coefficient-sequence)
    (accumulate
        (lambda (this-coeff higher-terms) 
            (+ (* higher-terms x) this-coeff))
        0
        coefficient-sequence))
(horner-eval 2 (list 1 3 0 5 0 1)) ;Value: 79