#lang scheme
(define pi 3.141592)

;part a
(define (sigmoid n)
  (/ 1 (+ 1 (exp (- n)))))

(define (neuralNode list sigmoid)
  (lambda (inputlist) (sigmoid (+ (car list) (nn (cdr list) inputlist)))))

(define (nn list1 list2)
  (cond
    ((null? list1) 0)
    (else (+ (* (car list1) (car list2)) (nn (cdr list1) (cdr list2))))))


;part b
(define (neuralLayer listoflist) (lambda (list) (nl listoflist list)))

(define (nl listoflist list)
  (cond
    ((null? listoflist) '())
    (else (cons ((neuralNode (car listoflist) sigmoid) list) (nl (cdr listoflist) list)))))

;part c
(define (neuralNet list)
  ((neuralNode '(0.5 0.3 0.7 0.1) sigmoid) ((neuralLayer '((0.1 0.3 0.4)(0.5 0.8 0.3)(0.7 0.6 0.6))) list)))

;part d
(define (applyNet n)
  (let ((answer '()))
    (let rec ((i n))
      (cond ((not (= i 0))
             (set! answer (cons (neuralNet (list (sin (/ (* 2 pi (- i 1)) n)) (cos (/ (* 2 pi (- i 1)) n)))) answer)) (rec (- i 1))))) answer))