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Cases

Upcase-first-charlist

Convert the first character of a character list to upper case.

Signature
(upcase-first-charlist x) → upcased
Arguments: x — Guard (character-listp x).
Returns: upcased — Type (character-listp upcased).

Definitions and Theorems

Function: upcase-first-charlist

(defun upcase-first-charlist (x)
  (declare (xargs :guard (character-listp x)))
  (let ((acl2::__function__ 'upcase-first-charlist))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (if (atom x)
             nil
           (cons (upcase-char (car x))
                 (make-character-list (cdr x))))
         :exec (cond ((atom x) nil)
                     ((down-alpha-p (car x))
                      (cons (upcase-char (car x)) (cdr x)))
                     (t x)))))

Theorem: character-listp-of-upcase-first-charlist

(defthm character-listp-of-upcase-first-charlist
  (b* ((upcased (upcase-first-charlist x)))
    (character-listp upcased))
  :rule-classes :rewrite)

Theorem: charlisteqv-implies-equal-upcase-first-charlist-1

(defthm charlisteqv-implies-equal-upcase-first-charlist-1
  (implies (charlisteqv x x-equiv)
           (equal (upcase-first-charlist x)
                  (upcase-first-charlist x-equiv)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-icharlisteqv-upcase-first-charlist-1

(defthm icharlisteqv-implies-icharlisteqv-upcase-first-charlist-1
  (implies (icharlisteqv x x-equiv)
           (icharlisteqv (upcase-first-charlist x)
                         (upcase-first-charlist x-equiv)))
  :rule-classes (:congruence))

Theorem: upcase-first-charlist-when-atom

(defthm upcase-first-charlist-when-atom
  (implies (atom x)
           (equal (upcase-first-charlist x) nil)))

Theorem: len-of-upcase-first-charlist

(defthm len-of-upcase-first-charlist
  (equal (len (upcase-first-charlist x))
         (len x)))

Theorem: consp-of-upcase-first-charlist

(defthm consp-of-upcase-first-charlist
  (equal (consp (upcase-first-charlist x))
         (consp x)))

Theorem: upcase-first-charlist-under-iff

(defthm upcase-first-charlist-under-iff
  (iff (upcase-first-charlist x)
       (consp x)))