; http://cap-lore.com/MathPhys/Algebras/Clifford/CliffProg4.html
(list
(lambda (f)
(apply (lambda (sg / tr bar alpha zer one + - * rls basis) (list
  (lambda () (cons (sg) (sg))) ; sg
  (lambda (x) (let* ((a (car x))(b (cdr x))(ai (/ a))) ; / Inverse
    (if ai (let* ((aib (* ai b))(c (/ (+ a (* b (alpha aib))))))
       (and c (cons c (- (* aib (alpha c))))))
    (let ((bi (/ b))) ; (write (list 'Boo bi)) (newline)
       (and bi (let* ((bia (* bi a))(d (/ (- (+ (* (alpha a) bia) (alpha b)))))
         (c (alpha (- (* bia d))))) (and d (cons c d))))))))
  (lambda (x) (cons (tr (car x)) (bar (cdr x)))) ; tr
  (lambda (x) (cons (bar (car x)) (- (tr (cdr x))))) ; bar
  (lambda (x) (cons (alpha (car x)) (- (alpha (cdr x))))) ; alpha
  (cons zer zer) ; zer
  (cons one zer) ; one
  (lambda (a b) (cons (+ (car a)(car b))(+ (cdr a)(cdr b)))) ; +
  (lambda (a) (cons (-(car a))(-(cdr a)))) ; - (negation)
  (lambda (a b) (cons (+ (* (car a)(car b))(-(* (cdr a)(alpha (cdr b))))) ; *
                     (+ (* (car a)(cdr b))(* (cdr a)(alpha (car b))))))
  (lambda (x)(cons (rls x) zer)) ; rls
  (cons (cons zer one) (map (lambda (x) (cons x zer)) basis)) ; basis
  )) f))

(let ((i (lambda (x) x))) (list (lambda (x)(and (not (zero? x)) (/ x))) i i i 
   0 1 + - * i '())))

; test
(ylppa (fileVal "Clifford2") (lambda (G reals) (map (lambda (rn)
  (ylppa (G (G (G (G (cons rn reals)))))
    (lambda (sg / tr bar alpha zer one + ng * rls basis)
      (let ((= equal?))
        (let lp ((n 100)) (or (zero? n) (and 
          (let ((a (sg))(b (sg))(c (sg))) (and
            (= (+ a b)(+ b a))
            (= (+ a (+ b c)) (+ (+ a b) c))
            (= (* a (* b c)) (* (* a b) c))
            (equal? zer (* a zer))
            (= (* a one) a)
            (= (* (+ a b) c) (+ (* a c) (* b c)))
            (= (* (tr a)(tr b))(tr (* b a)))
            (= (+ (tr a)(tr b))(tr (+ a b)))
            (= (* (alpha a)(alpha b))(alpha (* a b)))
            (= (+ (alpha a)(alpha b))(alpha (+ a b)))
            (= (* (bar a)(bar b))(bar (* b a)))
            (= (+ (bar a)(bar b))(bar (+ a b)))
            (let ((bi (/ b))) (if bi (and (= a (* b (* bi a)))
                 (= (* b bi) one) (= (* bi b) one))
               (begin (write (list 'ZD b)) (newline) #t)))))
          (lp (- n 1)))))))))

(list
((fileVal "rr") "fli2")
(let ((U (((fileVal "RC4") "Fool6") 'U)))
  (lambda () (let ((x (U))) (if (< x 0.3) -1 (if (< x 0.7) 0 1)))))))))