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• Char-fix

Charlist-fix

(charlist-fix x) maps ACL2::char-fix across a list.

Signature

(charlist-fix x) → *

This is an ordinary defprojection.

Definitions and Theorems

Function: charlist-fix-exec

(defun
    charlist-fix-exec (x acc)
    (declare (xargs :guard t))
    (let ((__function__ 'charlist-fix-exec))
         (declare (ignorable __function__))
         (if (consp x)
             (charlist-fix-exec (cdr x)
                                (cons (acl2::char-fix (car x)) acc))
             acc)))

Function: charlist-fix-nrev

(defun
 charlist-fix-nrev (x acl2::nrev)
 (declare (xargs :stobjs (acl2::nrev)))
 (declare (xargs :guard t))
 (let
     ((__function__ 'charlist-fix-nrev))
     (declare (ignorable __function__))
     (if (atom x)
         (acl2::nrev-fix acl2::nrev)
         (let ((acl2::nrev (acl2::nrev-push (acl2::char-fix (car x))
                                            acl2::nrev)))
              (charlist-fix-nrev (cdr x)
                                 acl2::nrev)))))

Function: charlist-fix

(defun
 charlist-fix (x)
 (declare (xargs :guard t))
 (let
  ((__function__ 'charlist-fix))
  (declare (ignorable __function__))
  (mbe
    :logic (if (consp x)
               (cons (acl2::char-fix (car x))
                     (charlist-fix (cdr x)))
               nil)
    :exec
    (if (atom x)
        nil
        (acl2::with-local-nrev (charlist-fix-nrev x acl2::nrev))))))

Theorem: charlist-fix-of-rev

(defthm charlist-fix-of-rev
        (equal (charlist-fix (acl2::rev acl2::x))
               (acl2::rev (charlist-fix acl2::x)))
        :rule-classes ((:rewrite)))

Theorem: charlist-fix-nrev-removal

(defthm charlist-fix-nrev-removal
        (equal (charlist-fix-nrev acl2::x acl2::nrev)
               (append acl2::nrev (charlist-fix acl2::x)))
        :rule-classes ((:rewrite)))

Theorem: charlist-fix-exec-removal

(defthm charlist-fix-exec-removal
        (equal (charlist-fix-exec acl2::x acl2::acc)
               (revappend (charlist-fix acl2::x)
                          acl2::acc))
        :rule-classes ((:rewrite)))

Theorem: charlist-fix-of-list-fix

(defthm charlist-fix-of-list-fix
        (equal (charlist-fix (list-fix acl2::x))
               (charlist-fix acl2::x))
        :rule-classes ((:rewrite)))

Theorem: charlist-fix-of-append

(defthm charlist-fix-of-append
        (equal (charlist-fix (append acl2::a acl2::b))
               (append (charlist-fix acl2::a)
                       (charlist-fix acl2::b)))
        :rule-classes ((:rewrite)))

Theorem: cdr-of-charlist-fix

(defthm cdr-of-charlist-fix
        (equal (cdr (charlist-fix acl2::x))
               (charlist-fix (cdr acl2::x)))
        :rule-classes ((:rewrite)))

Theorem: car-of-charlist-fix

(defthm car-of-charlist-fix
        (equal (car (charlist-fix acl2::x))
               (and (consp acl2::x)
                    (acl2::char-fix (car acl2::x))))
        :rule-classes ((:rewrite)))

Theorem: charlist-fix-under-iff

(defthm charlist-fix-under-iff
        (iff (charlist-fix acl2::x)
             (consp acl2::x))
        :rule-classes ((:rewrite)))

Theorem: consp-of-charlist-fix

(defthm consp-of-charlist-fix
        (equal (consp (charlist-fix acl2::x))
               (consp acl2::x))
        :rule-classes ((:rewrite)))

Theorem: len-of-charlist-fix

(defthm len-of-charlist-fix
        (equal (len (charlist-fix acl2::x))
               (len acl2::x))
        :rule-classes ((:rewrite)))

Theorem: true-listp-of-charlist-fix

(defthm true-listp-of-charlist-fix
        (true-listp (charlist-fix acl2::x))
        :rule-classes :type-prescription)

Theorem: charlist-fix-when-not-consp

(defthm charlist-fix-when-not-consp
        (implies (not (consp acl2::x))
                 (equal (charlist-fix acl2::x) nil))
        :rule-classes ((:rewrite)))

Theorem: charlist-fix-of-cons

(defthm charlist-fix-of-cons
        (equal (charlist-fix (cons acl2::a acl2::b))
               (cons (acl2::char-fix acl2::a)
                     (charlist-fix acl2::b)))
        :rule-classes ((:rewrite)))