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• Cases
• Char-upcase

Upcase-char

Convert a character to upper-case.

Signature

(upcase-char x) → char

Returns

char — Type (characterp char).

(upcase-char x) converts lower-case characters into their upper-case equivalents, and returns other characters unchanged.

ACL2 has a built-in alternative to this function, common-lisp::char-upcase, but it is irritating to use because it has standard-char-p guards. In contrast, upcase-char works on arbitrary characters.

Definitions and Theorems

Function: upcase-char$inline

(defun upcase-char$inline (x)
       (declare (type character x))
       (let ((acl2::__function__ 'upcase-char))
            (declare (ignorable acl2::__function__))
            (b* (((the (unsigned-byte 8) code)
                  (char-code x)))
                (if (and (<= (little-a) code)
                         (<= code (little-z)))
                    (code-char (the (unsigned-byte 8)
                                    (- code (case-delta))))
                    (mbe :logic (char-fix x) :exec x)))))

Theorem: characterp-of-upcase-char

(defthm characterp-of-upcase-char
        (b* ((char (upcase-char$inline x)))
            (characterp char))
        :rule-classes :type-prescription)

Theorem: chareqv-implies-equal-upcase-char-1

(defthm chareqv-implies-equal-upcase-char-1
        (implies (chareqv x x-equiv)
                 (equal (upcase-char x)
                        (upcase-char x-equiv)))
        :rule-classes (:congruence))

Theorem: upcase-char-does-nothing-unless-down-alpha-p

(defthm upcase-char-does-nothing-unless-down-alpha-p
        (implies (not (down-alpha-p x))
                 (equal (upcase-char x) (char-fix x))))

Theorem: upcase-char-of-upcase-char

(defthm upcase-char-of-upcase-char
        (equal (upcase-char (upcase-char x))
               (upcase-char x)))

Theorem: char-upcase-is-upcase-char

(defthm char-upcase-is-upcase-char
        (equal (common-lisp::char-upcase x)
               (upcase-char (double-rewrite x))))

Theorem: not-down-alpha-p-of-upcase-char

(defthm not-down-alpha-p-of-upcase-char
        (not (down-alpha-p (upcase-char x))))