(def litnum (r (o i srzero))
  (list 'lit 'num r i))

(def number (x)
  (let r (fn (y)
           (match y (list [in _ '+ '-] proper proper)))
    (match x `(lit num ,r ,r))))

(set numr car:cddr
     numi cadr:cddr)

(set rpart litnum:numr
     ipart litnum:numi)

(def real (x)
  (and (number x) (= (numi x) srzero)))

(def inv (x)
  (litnum (srinv:numr x) (srinv:numi x)))

(def abs (x)
  (litnum (cons '+ (cdr (numr x)))))

(def simplify ((s n d))
  (if (= n i0) (list '+ n i1)
      (= n d)  (list s i1 i1)
               (let g (apply i* ((of common factor) n d))
                 (list s (car:i/ n g) (car:i/ d g)))))

(def factor (x (o d i2))
  (if (i< x d)
      nil
      (let (q r) (i/ x d)
        (if (= r i0)
            (cons d (factor q d))
            (factor x (i+ d i1))))))

(def common (xs ys)
  (if (in nil xs ys)
      nil
      (let (a b) (split (is (car xs)) ys)
        (if b
            (cons (car xs)
                  (common (cdr xs) (append a (cdr b))))
            (common (cdr xs) ys)))))

(set buildnum (of litnum simplify))

(def recip (x)
  (with (r (numr x)
         i (numi x))
    (let d (sr+ (sr* r r) (sr* i i))
      (buildnum (sr/ r d)
                (sr/ (srinv i) d)))))