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• Decimal

Nat-to-dec-string-width

Convert a natural number into a string with the given width.

Signature

(nat-to-dec-string-width n width) → str

Arguments

n — Guard (natp n).

width — Guard (posp width).

Returns

str — Type (stringp str).

Similar to nat-to-dec-string but produces a fixed number of decimal digits. If the input number is smaller it is padded with 0s, and if larger its more-significant bits are truncated.

Definitions and Theorems

Function: nat-to-dec-string-width

(defun nat-to-dec-string-width (n width)
 (declare (xargs :guard (and (natp n) (posp width))))
 (let ((acl2::__function__ 'nat-to-dec-string-width))
   (declare (ignorable acl2::__function__))
   (b*
     ((width (mbe :logic (if (posp width) width 1)
                  :exec width))
      (chars (nat-to-dec-chars n))
      (width-chars (cond ((<= width (len chars))
                          (nthcdr (- (len chars) width) chars))
                         (t (append (make-list (- width (len chars))
                                               :initial-element #\0)
                                    chars)))))
     (implode width-chars))))

Theorem: stringp-of-nat-to-dec-string-width

(defthm stringp-of-nat-to-dec-string-width
  (b* ((str (nat-to-dec-string-width n width)))
    (stringp str))
  :rule-classes :type-prescription)

Theorem: dec-digit-char-list*p-of-nat-to-dec-string-width

(defthm dec-digit-char-list*p-of-nat-to-dec-string-width
  (dec-digit-char-list*p
       (explode (nat-to-dec-string-width n width))))

Theorem: nat-to-dec-string-width-nonempty

(defthm nat-to-dec-string-width-nonempty
  (not (equal (nat-to-dec-string-width n width)
              "")))