• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Debugging
  • Projects
  • Std
    • Std/lists
    • Std/alists
    • Obags
    • Std/util
    • Std/strings
      • Pretty-printing
      • Printtree
      • Base64
      • Charset-p
      • Strtok!
      • Cases
      • Concatenation
      • Html-encoding
      • Character-kinds
      • Substrings
      • Strtok
      • Equivalences
      • Url-encoding
      • Lines
      • Explode-implode-equalities
      • Ordering
      • Numbers
        • Decimal
        • Hex
        • Octal
        • Binary
          • Parse-bits-from-string
          • Parse-bits-from-charlist
          • Nat-to-bin-chars
          • Bin-digit-chars-value
          • Take-leading-bin-digit-chars
          • Bin-digit-char-listp
          • Skip-leading-bit-digits
          • Bin-digit-char-list*p
          • Bin-digit-string-p
          • Bin-digit-char-value
          • Strval2
          • Nat-to-bin-string
          • Bin-digit-char-p
          • Nat-to-bin-string-list
          • Nat-to-bin-string-size
          • Revappend-nat-to-bin-chars
          • Binify-width
          • Binify
      • 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

• Binary

Nat-to-bin-string-list

Convert a list of natural numbers into a list of bit strings.

Signature

(nat-to-bin-string-list x) → strs

Arguments

x — Guard (nat-listp x).

Returns

strs — Type (string-listp strs).

Definitions and Theorems

Function: nat-to-bin-string-list

(defun nat-to-bin-string-list (x)
  (declare (xargs :guard (nat-listp x)))
  (let ((acl2::__function__ 'nat-to-bin-string-list))
    (declare (ignorable acl2::__function__))
    (if (atom x)
        nil
      (cons (nat-to-bin-string (car x))
            (nat-to-bin-string-list (cdr x))))))

Theorem: string-listp-of-nat-to-bin-string-list

(defthm string-listp-of-nat-to-bin-string-list
  (b* ((strs (nat-to-bin-string-list x)))
    (string-listp strs))
  :rule-classes :rewrite)

Theorem: nat-to-bin-string-list-when-atom

(defthm nat-to-bin-string-list-when-atom
  (implies (atom x)
           (equal (nat-to-bin-string-list x) nil)))

Theorem: nat-to-bin-string-list-of-cons

(defthm nat-to-bin-string-list-of-cons
  (equal (nat-to-bin-string-list (cons a x))
         (cons (nat-to-bin-string a)
               (nat-to-bin-string-list x))))