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• Charset-p

Count-leading-charset

Count how many characters at the start of a list are members of a particular character set.

Signature

(count-leading-charset x set) → num

Arguments

x — Guard (character-listp x).

set — Guard (charset-p set).

Returns

num — Type (natp num).

Definitions and Theorems

Function: count-leading-charset

(defun count-leading-charset (x set)
  (declare (xargs :guard (and (character-listp x)
                              (charset-p set))))
  (let ((acl2::__function__ 'count-leading-charset))
    (declare (ignorable acl2::__function__))
    (cond ((atom x) 0)
          ((char-in-charset-p (car x) set)
           (+ 1 (count-leading-charset (cdr x) set)))
          (t 0))))

Theorem: natp-of-count-leading-charset

(defthm natp-of-count-leading-charset
  (b* ((num (count-leading-charset x set)))
    (natp num))
  :rule-classes :type-prescription)

Theorem: upper-bound-of-count-leading-charset

(defthm upper-bound-of-count-leading-charset
  (<= (count-leading-charset x set)
      (len x))
  :rule-classes ((:rewrite) (:linear)))

Theorem: count-leading-charset-len

(defthm count-leading-charset-len
  (equal (equal (len x)
                (count-leading-charset x set))
         (chars-in-charset-p x set))
  :rule-classes
  ((:rewrite)
   (:rewrite :corollary (equal (< (count-leading-charset x set)
                                  (len x))
                               (not (chars-in-charset-p x set))))
   (:linear :corollary (implies (not (chars-in-charset-p x set))
                                (< (count-leading-charset x set)
                                   (len x))))))

Theorem: count-leading-charset-zero

(defthm count-leading-charset-zero
  (equal (equal 0 (count-leading-charset x set))
         (not (char-in-charset-p (car x) set)))
  :rule-classes
  ((:rewrite)
   (:rewrite :corollary (equal (< 0 (count-leading-charset x set))
                               (char-in-charset-p (car x) set)))
   (:linear
        :corollary (implies (char-in-charset-p (car x) set)
                            (< 0 (count-leading-charset x set))))))

Theorem: count-leading-charset-sound

(defthm count-leading-charset-sound
  (let ((n (count-leading-charset x set)))
    (chars-in-charset-p (take n x) set)))

Theorem: count-leading-charset-complete

(defthm count-leading-charset-complete
  (b* ((n (count-leading-charset x set))
       (next-char (nth n x)))
    (not (char-in-charset-p next-char set))))