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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)))