Application of a number not allowed (Scheme)

Question

I'm working a little with SCMUTILS package that implements MIT SCHEME. I'm running it from Emacs and I'm having trouble when using a function, can you help me?

My code is:

(define ((((delta eta) f) q) t)
  (let ((fmas (f (+ q (* 0.001 eta))))
         (efe (f q)))
       (/ (- (fmas t) (efe t)) 0.001)))


(define ((G q) t)
       (dot-product (q t) (q t)))


(((((delta  test-path) G)  test-path) 5))

Where test-path is:

(define (test-path t)
 (up (+ (* 4 t) 7)
     (+ (* 3 t) 5)
     (+ (* 2 t) 1)))

And I'm getting this error:

Loading "mecanica"...
;Application of a number not allowed 2501.2500000000273 (())

what could be the problem?

At first I thought that scheme couldn't divide a structure like test-path by a number, so I put the dot product to make it a function that returns a number; but that didn't work.

I've tried printing expression in the delta-eta function and the error comes in while doing this part:

(/ (- (fmas t) (efe t)) 0.001)))

And if I take out the quotient part, there is no error.

Surely I am missing something. Hope you can help. Thanks!

Answer 1

Assume this

(define ((((delta eta) f) q) t)
  (let ((fmas (f (+ q (* 0.001 eta))))
         (efe (f q)))
       (/ (- (fmas t) (efe t)) 0.001)))

is equivalent to this

(define (delta eta)
  (lambda (f)
    (lambda (q)
      (lambda (t)
        (let ((fmas (f (+ q (* 0.001 eta))))
              (efe (f q)))
          (/ (- (fmas t) (efe t)) 0.001))))))

Then (((((delta test-path) G) test-path) 5)) is multiplying 0.001 and test-path at (* 0.001 eta). And also inside of the G, it expects q as a procedure however, fmas is retrieving a procedure from G passing a number to G. Thus this would try to apply calculated number passing t.