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• <<

Fast-<<

Probably faster alternative to <<.

(fast-<< x y) is logically the same as (<< x y). However, it is probably faster because:

1. it rearranges the check as in fast-lexorder, and
2. it folds in the not-equal check.

Definitions and Theorems

Function: fast-<<

(defun fast-<< (x y)
 (declare (xargs :guard t))
 (cond
    ((atom x)
     (if (atom y)
         (cond ((integerp x)
                (cond ((integerp y) (< x y))
                      ((real/rationalp y) (< x y))
                      (t t)))
               ((symbolp x)
                (if (symbolp y)
                    (and (not (eq x y)) (symbol< x y) t)
                  (not (or (integerp y)
                           (stringp y)
                           (characterp y)
                           (real/rationalp y)
                           (complex/complex-rationalp y)))))
               ((stringp x)
                (cond ((stringp y) (and (string< x y) t))
                      ((integerp y) nil)
                      ((symbolp y) t)
                      (t (not (or (characterp y)
                                  (real/rationalp y)
                                  (complex/complex-rationalp y))))))
               ((characterp x)
                (cond ((characterp y)
                       (< (char-code x) (char-code y)))
                      (t (not (or (integerp y)
                                  (real/rationalp y)
                                  (complex/complex-rationalp y))))))
               ((real/rationalp x)
                (cond ((integerp y) (< x y))
                      ((real/rationalp y) (< x y))
                      (t t)))
               ((real/rationalp y) nil)
               ((complex/complex-rationalp x)
                (cond ((complex/complex-rationalp y)
                       (or (< (realpart x) (realpart y))
                           (and (= (realpart x) (realpart y))
                                (< (imagpart x) (imagpart y)))))
                      (t t)))
               ((or (symbolp y)
                    (stringp y)
                    (characterp y)
                    (complex/complex-rationalp y))
                nil)
               (t (and (bad-atom<= x y)
                       (not (equal x y)))))
       t))
    ((atom y) nil)
    ((equal (car x) (car y))
     (fast-<< (cdr x) (cdr y)))
    (t (fast-<< (car x) (car y)))))

Theorem: fast-<<-is-<<

(defthm fast-<<-is-<<
  (equal (fast-<< x y) (<< x y)))