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• Strrpos

Strrpos-fast

Fast implementation of strrpos.

Definitions and Theorems

Function: strrpos-fast

(defun strrpos-fast (x y n xl yl)
  (declare (type string x y)
           (type (integer 0 *) n xl yl)
           (xargs :guard (and (stringp x)
                              (stringp y)
                              (natp xl)
                              (natp yl)
                              (natp n)
                              (<= n (length y))
                              (= xl (length x))
                              (= yl (length y)))))
  (cond ((mbe :logic (prefixp (explode x)
                              (nthcdr n (explode y)))
              :exec (strprefixp-impl (the string x)
                                     (the string y)
                                     (the integer 0)
                                     (the (integer 0 *) n)
                                     (the (integer 0 *) xl)
                                     (the (integer 0 *) yl)))
         (lnfix n))
        ((zp n) nil)
        (t (strrpos-fast (the string x)
                         (the string y)
                         (the (integer 0 *) (+ -1 (lnfix n)))
                         (the (integer 0 *) xl)
                         (the (integer 0 *) yl)))))

Theorem: strrpos-fast-type

(defthm strrpos-fast-type
  (or (and (integerp (strrpos-fast x y n xl yl))
           (<= 0 (strrpos-fast x y n xl yl)))
      (not (strrpos-fast x y n xl yl)))
  :rule-classes :type-prescription)

Theorem: strrpos-fast-upper-bound

(defthm strrpos-fast-upper-bound
  (implies (force (natp n))
           (<= (strrpos-fast x y n xl yl) n))
  :rule-classes :linear)

Theorem: strrpos-fast-when-empty

(defthm strrpos-fast-when-empty
  (implies (and (not (consp (explode x)))
                (equal xl (length x))
                (equal yl (length y))
                (natp n))
           (equal (strrpos-fast x y n xl yl) n)))