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• Abstract-syntax

Hex-digit-list->chars

Extract the characters from a list of hex digits.

Signature

(hex-digit-list->chars x) → chars

Arguments

x — Guard (hex-digit-listp x).

Returns

chars — Type (str::hex-digit-char-list*p chars).

This is an ordinary std::defprojection.

Definitions and Theorems

Function: hex-digit-list->chars-exec

(defun hex-digit-list->chars-exec (x acc)
 (declare (xargs :guard (hex-digit-listp x)))
 (declare (xargs :guard t))
 (let ((__function__ 'hex-digit-list->chars-exec))
   (declare (ignorable __function__))
   (if
    (consp x)
    (hex-digit-list->chars-exec (cdr x)
                                (cons (hex-digit->get (car x)) acc))
    acc)))

Function: hex-digit-list->chars-nrev

(defun hex-digit-list->chars-nrev (x acl2::nrev)
  (declare (xargs :stobjs (acl2::nrev)))
  (declare (xargs :guard (hex-digit-listp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'hex-digit-list->chars-nrev))
    (declare (ignorable __function__))
    (if (atom x)
        (acl2::nrev-fix acl2::nrev)
      (let ((acl2::nrev (acl2::nrev-push (hex-digit->get (car x))
                                         acl2::nrev)))
        (hex-digit-list->chars-nrev (cdr x)
                                    acl2::nrev)))))

Function: hex-digit-list->chars

(defun hex-digit-list->chars (x)
  (declare (xargs :guard (hex-digit-listp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'hex-digit-list->chars))
    (declare (ignorable __function__))
    (mbe :logic
         (if (consp x)
             (cons (hex-digit->get (car x))
                   (hex-digit-list->chars (cdr x)))
           nil)
         :exec
         (if (atom x)
             nil
           (acl2::with-local-nrev
                (hex-digit-list->chars-nrev x acl2::nrev))))))

Theorem: hex-digit-char-list*p-of-hex-digit-list->chars

(defthm hex-digit-char-list*p-of-hex-digit-list->chars
  (b* ((chars (hex-digit-list->chars x)))
    (str::hex-digit-char-list*p chars))
  :rule-classes :rewrite)

Theorem: hex-digit-list->chars-nrev-removal

(defthm hex-digit-list->chars-nrev-removal
  (equal (hex-digit-list->chars-nrev acl2::x acl2::nrev)
         (append acl2::nrev
                 (hex-digit-list->chars acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: hex-digit-list->chars-exec-removal

(defthm hex-digit-list->chars-exec-removal
  (equal (hex-digit-list->chars-exec acl2::x acl2::acc)
         (revappend (hex-digit-list->chars acl2::x)
                    acl2::acc))
  :rule-classes ((:rewrite)))

Theorem: hex-digit-list->chars-of-take

(defthm hex-digit-list->chars-of-take
  (implies (<= (nfix acl2::n) (len acl2::x))
           (equal (hex-digit-list->chars (take acl2::n acl2::x))
                  (take acl2::n
                        (hex-digit-list->chars acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: set-equiv-congruence-over-hex-digit-list->chars

(defthm set-equiv-congruence-over-hex-digit-list->chars
  (implies (set-equiv acl2::x acl2::y)
           (set-equiv (hex-digit-list->chars acl2::x)
                      (hex-digit-list->chars acl2::y)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-hex-digit-list->chars-when-subsetp

(defthm subsetp-of-hex-digit-list->chars-when-subsetp
  (implies (subsetp acl2::x acl2::y)
           (subsetp (hex-digit-list->chars acl2::x)
                    (hex-digit-list->chars acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: member-of-hex-digit->get-in-hex-digit-list->chars

(defthm member-of-hex-digit->get-in-hex-digit-list->chars
  (implies (member acl2::k acl2::x)
           (member (hex-digit->get acl2::k)
                   (hex-digit-list->chars acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: hex-digit-list->chars-of-rev

(defthm hex-digit-list->chars-of-rev
  (equal (hex-digit-list->chars (rev acl2::x))
         (rev (hex-digit-list->chars acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: hex-digit-list->chars-of-list-fix

(defthm hex-digit-list->chars-of-list-fix
  (equal (hex-digit-list->chars (list-fix acl2::x))
         (hex-digit-list->chars acl2::x))
  :rule-classes ((:rewrite)))

Theorem: hex-digit-list->chars-of-append

(defthm hex-digit-list->chars-of-append
  (equal (hex-digit-list->chars (append acl2::a acl2::b))
         (append (hex-digit-list->chars acl2::a)
                 (hex-digit-list->chars acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-hex-digit-list->chars

(defthm cdr-of-hex-digit-list->chars
  (equal (cdr (hex-digit-list->chars acl2::x))
         (hex-digit-list->chars (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-hex-digit-list->chars

(defthm car-of-hex-digit-list->chars
  (equal (car (hex-digit-list->chars acl2::x))
         (and (consp acl2::x)
              (hex-digit->get (car acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: hex-digit-list->chars-under-iff

(defthm hex-digit-list->chars-under-iff
  (iff (hex-digit-list->chars acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-hex-digit-list->chars

(defthm consp-of-hex-digit-list->chars
  (equal (consp (hex-digit-list->chars acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-hex-digit-list->chars

(defthm len-of-hex-digit-list->chars
  (equal (len (hex-digit-list->chars acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-hex-digit-list->chars

(defthm true-listp-of-hex-digit-list->chars
  (true-listp (hex-digit-list->chars acl2::x))
  :rule-classes :type-prescription)

Theorem: hex-digit-list->chars-when-not-consp

(defthm hex-digit-list->chars-when-not-consp
  (implies (not (consp acl2::x))
           (equal (hex-digit-list->chars acl2::x)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: hex-digit-list->chars-of-cons

(defthm hex-digit-list->chars-of-cons
  (equal (hex-digit-list->chars (cons acl2::a acl2::b))
         (cons (hex-digit->get acl2::a)
               (hex-digit-list->chars acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: hex-digit-list->chars-of-hex-digit-list-fix-x

(defthm hex-digit-list->chars-of-hex-digit-list-fix-x
  (equal (hex-digit-list->chars (hex-digit-list-fix x))
         (hex-digit-list->chars x)))

Theorem: hex-digit-list->chars-hex-digit-list-equiv-congruence-on-x

(defthm hex-digit-list->chars-hex-digit-list-equiv-congruence-on-x
  (implies (hex-digit-list-equiv x x-equiv)
           (equal (hex-digit-list->chars x)
                  (hex-digit-list->chars x-equiv)))
  :rule-classes :congruence)