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Istrprefixp

Case-insensitive string prefix test.

(istrprefixp x y) determines if the string x is a case-insensitive prefix of the string y.

Logically, this is identical to

(iprefixp (explode x) (explode y))

But we use a more efficient implementation which avoids coercing the strings to lists.

Definitions and Theorems

Function: istrprefixp-impl

(defun istrprefixp-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)
        ((ichareqv (char x xn) (char y yn))
         (istrprefixp-impl x y (+ 1 (lnfix xn))
                           (+ 1 (lnfix yn))
                           xl yl))
        (t nil)))

Function: istrprefixp$inline

(defun istrprefixp$inline (x y)
 (declare (type string x)
          (type string y))
 (mbe
    :logic (iprefixp (explode x) (explode y))
    :exec (istrprefixp-impl (the string x)
                            (the string y)
                            (the integer 0)
                            (the integer 0)
                            (the integer (length (the string x)))
                            (the integer (length (the string y))))))

Theorem: istrprefixp-impl-elim

(defthm istrprefixp-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 (istrprefixp-impl x y xn yn xl yl)
                  (iprefixp (nthcdr xn (coerce x 'list))
                            (nthcdr yn (coerce y 'list))))))

Theorem: istreqv-implies-equal-istrprefixp-1

(defthm istreqv-implies-equal-istrprefixp-1
  (implies (istreqv x x-equiv)
           (equal (istrprefixp x y)
                  (istrprefixp x-equiv y)))
  :rule-classes (:congruence))

Theorem: istreqv-implies-equal-istrprefixp-2

(defthm istreqv-implies-equal-istrprefixp-2
  (implies (istreqv y y-equiv)
           (equal (istrprefixp x y)
                  (istrprefixp x y-equiv)))
  :rule-classes (:congruence))