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• Strprefixp

Strprefixp-impl

Fast implementation of strprefixp.

Definitions and Theorems

Function: strprefixp-impl

(defun strprefixp-impl (x y xn yn xl yl)
 (declare (type string x)
          (type string y)
          (type integer xn)
          (type integer yn)
          (type integer xl)
          (type integer yl)
          (xargs :guard (and (stringp x)
                             (stringp y)
                             (natp xn)
                             (natp yn)
                             (natp xl)
                             (natp yl)
                             (= xl (length x))
                             (= yl (length y))
                             (<= xn (length x))
                             (<= yn (length y)))))
 (cond
   ((mbe :logic (zp (- (nfix xl) (nfix xn)))
         :exec (int= xn xl))
    t)
   ((mbe :logic (zp (- (nfix yl) (nfix yn)))
         :exec (int= yn yl))
    nil)
   ((eql (the character (char x xn))
         (the character (char y yn)))
    (mbe :logic (strprefixp-impl x y (+ (nfix xn) 1)
                                 (+ (nfix yn) 1)
                                 xl yl)
         :exec (strprefixp-impl (the string x)
                                (the string y)
                                (the integer (+ (the integer xn) 1))
                                (the integer (+ (the integer yn) 1))
                                (the integer xl)
                                (the integer yl))))
   (t nil)))

Theorem: strprefixp-impl-elim

(defthm strprefixp-impl-elim
  (implies (and (force (stringp x))
                (force (stringp y))
                (force (natp xn))
                (force (natp yn))
                (force (= xl (length x)))
                (force (= yl (length y))))
           (equal (strprefixp-impl x y xn yn xl yl)
                  (prefixp (nthcdr xn (explode x))
                           (nthcdr yn (explode y))))))