First assignment for SICM, Excercises 8.1 and 8.2

assignment0.scm

(define (f x y)
  (* (square x) (cube y)))

(define (g x y)
  (up (f x y) 'y))

; just for giggles
(define (helix t)
  (up (cos t) (sin t) t))

(print-expression ((D helix) 't))
;>> (up (* -1 (sin t)) (cos t) 1)

(define (h x y)
  (f (f x y) y))

; typing partial is no fun
(define (pf f n)
  (((partial n) f) 'x 'y))


;;; 8.1 a

(pf f 0)
#|
(* 2 x (expt y 3))
|#

(pf f 1)
#|
(* 3 (expt x 2) (expt y 2))
|#

;;; 8.1 b

(((partial 0) f) (f 'x 'y) 'y)
#|
(* 2 (expt x 2) (expt y 6))
|#

;; NOT the same as:
(pf h 0)
#|
(* 4 (expt x 3) (expt y 9))
|#

(((partial 1) f) (f 'x 'y) 'y)
#|
(* 3 (expt x 4) (expt y 8))
|#


;;; 8.1 c

(pf g 0)
#|
(up (* 2 x (expt y 3)) 0)
|#

(pf g 1)
#|
(up (* 3 (expt x 2) (expt y 2)) 0)
|#


::; 8.1 d
((D f) 'a 'b)
#|
(down (* 2 a (expt b 3)) (* 3 (expt a 2) (expt b 2)))
|#

((D g) 3 5)
#|
(down (up 750 0) (up 675 0))
|#

((D h) (* 3 (square 'a)) 
       (* 5 (cube 'b)))
#|
(down (* 210937500 (expt a 6) (expt b 27)) (* 284765625 (expt a 8) (expt b 24)))
|#

;;; 8.2
; and now for the vector argument formulation

(define (f* v)
  (let ((x (ref v 0))
	(y (ref v 1)))
    (* (square x) (cube y))))

; this one looks like a profanity
(f* (up 'x 'y))

; I really need to examine macros in scheme
; these let statements feel like code smell.
(define (g* v)
  (let ((x (ref v 0))
	(y (ref v 1)))
    (up (f* v) y)))

(g* (up 'x 'y))

; ah, a breath of fresh air
(define h* (compose f* g*))

(h* (up 4 2))

((D h*) (up (* 3 (square 'a)) (* 5 (cube 'b))))
#|
(down (* 210937500 (expt a 6) (expt b 27)) (* 284765625 (expt a 8) (expt b 24)))
|#
; hooray, it's the same