• Top
  • Documentation
  • Books
  • Recursion-and-induction
  • 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
        • Upcase-string
        • Downcase-charlist
        • Istreqv
        • Ichareqv
        • Downcase-char
        • Downcase-string
          • String-has-some-up-alpha-p
          • Downcase-string-aux
        • Upcase-char
        • Upcase-first-charlist
        • Downcase-first-charlist
        • Downcase-first
        • Upcase-first
        • Upcase-char-str
        • Downcase-char-str
        • Down-alpha-p
        • Downcase-string-list
        • Upcase-string-list
        • Up-alpha-p
      • Concatenation
      • Html-encoding
      • Character-kinds
      • Substrings
      • Strtok
      • Equivalences
      • Url-encoding
      • Lines
      • Ordering
      • Numbers
      • Pad-trim
      • Coercion
      • Std/strings-extensions
      • Std/strings/digit-to-char
      • Substitution
      • Symbols
    • Std/io
    • Std/osets
    • Std/system
    • Std/basic
    • Std/typed-lists
    • Std/bitsets
    • Std/testing
    • Std/typed-alists
    • Std/stobjs
    • Std-extensions
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Testing-utilities
  • Math

• Cases
• String-downcase

Downcase-string

Convert a string to lower case.

Signature

(downcase-string x) → *

(downcase-string x) converts a string to lower case, effectively by transforming each of its characters with downcase-char.

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

See also upcase-string, which has more discussion on how we try to make this fast.

Definitions and Theorems

Function: downcase-string

(defun
 downcase-string (x)
 (declare (type string x))
 (let
  ((acl2::__function__ 'downcase-string))
  (declare (ignorable acl2::__function__))
  (mbe
   :logic (implode (downcase-charlist (explode x)))
   :exec
   (let ((xl (length x)))
        (if (not (string-has-some-up-alpha-p x 0 xl))
            x
            (rchars-to-string (downcase-string-aux x 0 xl nil)))))))

Theorem: istreqv-implies-equal-downcase-string-1

(defthm istreqv-implies-equal-downcase-string-1
        (implies (istreqv x x-equiv)
                 (equal (downcase-string x)
                        (downcase-string x-equiv)))
        :rule-classes (:congruence))

Theorem: len-of-downcase-string

(defthm len-of-downcase-string
        (equal (len (explode (downcase-string x)))
               (len (explode x))))

Theorem: length-of-downcase-string

(defthm length-of-downcase-string
        (equal (length (downcase-string x))
               (len (explode x))))

Theorem: equal-of-empty-string-with-downcase-string

(defthm equal-of-empty-string-with-downcase-string
        (equal (equal "" (downcase-string x))
               (atom (explode x))))

Theorem: string-downcase-is-downcase-string

(defthm string-downcase-is-downcase-string
        (equal (common-lisp::string-downcase x)
               (downcase-string (double-rewrite x))))

Subtopics

String-has-some-up-alpha-p

Downcase-string-aux