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• Physical-memory

Rm-low-32

Signature

(rm-low-32 addr x86) → *

Definitions and Theorems

Function: rm-low-32$inline

(defun rm-low-32$inline (addr x86)
  (declare (xargs :stobjs (x86)))
  (declare (type (unsigned-byte 52) addr))
  (declare (xargs :guard (and (not (app-view x86))
                              (integerp addr)
                              (<= 0 addr)
                              (< (+ 3 addr) *mem-size-in-bytes*))))
  (if (mbt (not (app-view x86)))
      (let ((addr (mbe :logic (ifix addr) :exec addr)))
        (b* (((the (unsigned-byte 8) byte0)
              (mbe :logic (loghead 8 (memi addr x86))
                   :exec (memi addr x86)))
             ((the (unsigned-byte 8) byte1)
              (mbe :logic (loghead 8 (memi (1+ addr) x86))
                   :exec (memi (1+ addr) x86)))
             ((the (unsigned-byte 16) word0)
              (logior (the (unsigned-byte 16) (ash byte1 8))
                      byte0))
             ((the (unsigned-byte 8) byte2)
              (mbe :logic (loghead 8 (memi (+ 2 addr) x86))
                   :exec (memi (+ 2 addr) x86)))
             ((the (unsigned-byte 8) byte3)
              (mbe :logic (loghead 8 (memi (+ 3 addr) x86))
                   :exec (memi (+ 3 addr) x86)))
             ((the (unsigned-byte 16) word1)
              (the (unsigned-byte 16)
                   (logior (the (unsigned-byte 16) (ash byte3 8))
                           byte2)))
             ((the (unsigned-byte 32) dword)
              (logior (the (unsigned-byte 32) (ash word1 16))
                      word0)))
          dword))
    0))

Theorem: rm-low-32-in-app-view

(defthm rm-low-32-in-app-view
  (implies (app-view x86)
           (equal (rm-low-32 p-addr x86) 0)))

Theorem: n32p-rm-low-32

(defthm n32p-rm-low-32
 (unsigned-byte-p 32 (rm-low-32 addr x86))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (rm-low-32 addr x86))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0 (rm-low-32 addr x86))
                   (< (rm-low-32 addr x86) 4294967296))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))

Theorem: rm-low-32-xw

(defthm rm-low-32-xw
  (implies (and (not (equal fld :mem))
                (not (equal fld :app-view)))
           (equal (rm-low-32 addr (xw fld index val x86))
                  (rm-low-32 addr x86))))