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• Lower-case-p

Down-alpha-p

Determine if a character is a lower-case letter (a-z).

Signature

(down-alpha-p x) → bool

ACL2 has a built-in alternative to this function, common-lisp::lower-case-p, which however can also recognize characters that are not standard characters. (Historical note: Before May 2024, the guard for acl2::lower-case-p required standard-char-p yet also converted only standard characters; this provided motivation for the development of down-alpha-p.)

Definitions and Theorems

Function: down-alpha-p$inline

(defun down-alpha-p$inline (x)
  (declare (type character x))
  (let ((acl2::__function__ 'down-alpha-p))
    (declare (ignorable acl2::__function__))
    (b* (((the (unsigned-byte 8) code)
          (char-code x)))
      (and (<= (little-a) code)
           (<= code (little-z))))))

Theorem: chareqv-implies-equal-down-alpha-p-1

(defthm chareqv-implies-equal-down-alpha-p-1
  (implies (chareqv x x-equiv)
           (equal (down-alpha-p x)
                  (down-alpha-p x-equiv)))
  :rule-classes (:congruence))

Theorem: lower-case-p-is-down-alpha-p

(defthm lower-case-p-is-down-alpha-p
  (implies (standard-char-p x)
           (equal (common-lisp::lower-case-p x)
                  (down-alpha-p (double-rewrite x)))))

Theorem: down-alpha-p-when-up-alpha-p

(defthm down-alpha-p-when-up-alpha-p
  (implies (up-alpha-p x)
           (not (down-alpha-p x))))