Polynomial definition and conversion to Horner form

hornify.scm

(import (scheme base))

(define-syntax hornify
  (syntax-rules ()
    ((_ x an) an)
    ((_ x a pn ...)
     (+ a (* x (hornify x pn ...))))))

(define-syntax poly
  (syntax-rules ()
    ((_ (x y ...) (pn ...))
     (lambda (x y ...) (hornify x pn ...)))))

(define (quadratic a b c)
  (poly (x) (c b a)))

((quadratic 1 -1 -1) 1.618) ; => =~ 0.0