• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
    • Std/lists
    • Std/alists
    • Obags
    • Std/util
    • Std/strings
      • Pretty-printing
      • Printtree
      • Base64
      • Charset-p
      • Strtok!
      • Cases
        • Icharlisteqv
        • Upcase-charlist
        • Downcase-charlist
        • Upcase-string
        • Istreqv
        • Downcase-char
        • Upcase-char
        • Ichareqv
        • Downcase-string
        • Upcase-first-charlist
        • Downcase-first-charlist
        • Downcase-first
        • Upcase-first
        • Down-alpha-p
        • Up-alpha-p
        • Upcase-char-str
        • Downcase-char-str
        • Upcase-string-list
        • Downcase-string-list
      • Concatenation
      • Html-encoding
      • Character-kinds
      • Substrings
      • Strtok
      • Equivalences
      • Url-encoding
      • Lines
      • Explode-implode-equalities
      • Ordering
      • Numbers
      • Pad-trim
      • Coercion
      • Std/strings/digit-to-char
      • Substitution
      • Symbols
    • Std/io
    • Std/osets
    • Std/basic
    • Std/system
    • Std/typed-lists
    • Std/bitsets
    • Std/testing
    • Std/typed-alists
    • Std/stobjs
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Cases
• 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))))