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Nthcdr-bytes

Skip past some number of bytes in an open file.

(nthcdr-bytes n channel state) is like nthcdr for an :byte input channel. That is, it just reads n bytes and ignores them, returning the updated state.

This is notably useful as a way to express the post-state after take-bytes.

Definitions and Theorems

Function: nthcdr-bytes

(defun nthcdr-bytes (n channel state)
  (declare (xargs :guard (and (natp n)
                              (state-p state)
                              (symbolp channel)
                              (open-input-channel-p channel
                                                    :byte state))))
  (b* (((when (zp n)) state)
       ((mv ?byte state)
        (read-byte$ channel state)))
    (nthcdr-bytes (- n 1) channel state)))

Theorem: state-p1-of-nthcdr-bytes

(defthm state-p1-of-nthcdr-bytes
  (implies (and (force (state-p1 state))
                (force (symbolp channel))
                (force (open-input-channel-p1 channel
                                              :byte state)))
           (state-p1 (nthcdr-bytes n channel state))))

Theorem: open-input-channel-p1-of-nthcdr-bytes

(defthm open-input-channel-p1-of-nthcdr-bytes
 (implies
      (and (force (state-p1 state))
           (force (symbolp channel))
           (force (open-input-channel-p1 channel
                                         :byte state)))
      (open-input-channel-p1 channel
                             :byte (nthcdr-bytes n channel state))))

Theorem: read-byte$-all-of-nthcdr-bytes

(defthm read-byte$-all-of-nthcdr-bytes
 (implies
  (and (force (state-p1 state))
       (force (symbolp channel))
       (force (open-input-channel-p1 channel
                                     :byte state)))
  (equal
    (mv-nth 0
            (read-byte$-all channel (nthcdr-bytes n channel state)))
    (nthcdr n
            (mv-nth 0 (read-byte$-all channel state))))))

Theorem: nthcdr-bytes-1

(defthm nthcdr-bytes-1
  (equal (nthcdr-bytes 1 channel state)
         (mv-nth 1 (read-byte$ channel state))))

Theorem: nthcdr-bytes-2

(defthm nthcdr-bytes-2
  (equal
       (nthcdr-bytes 2 channel state)
       (mv-nth 1
               (read-byte$ channel
                           (mv-nth 1 (read-byte$ channel state))))))

Theorem: nthcdr-bytes-3

(defthm nthcdr-bytes-3
 (equal
  (nthcdr-bytes 3 channel state)
  (mv-nth
   1
   (read-byte$
     channel
     (mv-nth 1
             (read-byte$ channel
                         (mv-nth 1 (read-byte$ channel state))))))))

Theorem: nthcdr-bytes-4

(defthm nthcdr-bytes-4
 (equal
  (nthcdr-bytes 4 channel state)
  (mv-nth
   1
   (read-byte$
    channel
    (mv-nth
     1
     (read-byte$
      channel
      (mv-nth
           1
           (read-byte$ channel
                       (mv-nth 1 (read-byte$ channel state))))))))))

Theorem: nthcdr-bytes-measure-weak

(defthm nthcdr-bytes-measure-weak
  (implies (and (force (state-p1 state))
                (force (open-input-channel-p1 channel
                                              :byte state))
                (force (symbolp channel)))
           (<= (file-measure channel (nthcdr-bytes n channel state))
               (file-measure channel state)))
  :rule-classes (:rewrite :linear))

Theorem: nthcdr-bytes-measure-strong

(defthm nthcdr-bytes-measure-strong
  (implies (and (mv-nth 0 (read-byte$ channel state))
                (not (zp n))
                (force (state-p1 state))
                (force (open-input-channel-p1 channel
                                              :byte state))
                (force (symbolp channel)))
           (< (file-measure channel (nthcdr-bytes n channel state))
              (file-measure channel state)))
  :rule-classes (:rewrite :linear))