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• Reasoning-about-memory-reads-and-writes

Rb

Signature

(rb n addr r-x x86) → (mv flg val new-x86)

Arguments

n — Number of bytes to be read.
    Guard (natp n).

addr — First linear address.
    Guard (integerp addr).

r-x — Type of memory access.

Returns

val — Type (integerp val).

new-x86 — Type (x86p new-x86), given (x86p x86).

Definitions and Theorems

Function: rb

(defun rb (n addr r-x x86)
  (declare (xargs :stobjs (x86)))
  (declare (type (member :r :x) r-x))
  (declare (xargs :guard (and (natp n) (integerp addr))))
  (declare (xargs :guard (canonical-address-p (+ -1 n addr))))
  (let ((__function__ 'rb))
    (declare (ignorable __function__))
    (if (app-view x86)
        (rb-1 n addr r-x x86)
      (b* (((mv flg p-addrs x86)
            (las-to-pas n addr r-x x86))
           ((when flg) (mv flg 0 x86))
           (val (read-from-physical-memory p-addrs x86)))
        (mv nil val x86)))))

Theorem: integerp-of-rb.val

(defthm integerp-of-rb.val
  (b* (((mv ?flg ?val ?new-x86)
        (rb n addr r-x x86)))
    (integerp val))
  :rule-classes :type-prescription)

Theorem: x86p-of-rb.new-x86

(defthm x86p-of-rb.new-x86
  (implies (x86p x86)
           (b* (((mv ?flg ?val ?new-x86)
                 (rb n addr r-x x86)))
             (x86p new-x86)))
  :rule-classes :rewrite)

Theorem: natp-of-mv-nth-1-rb

(defthm natp-of-mv-nth-1-rb
  (b* (((mv ?flg ?val ?new-x86)
        (rb n addr r-x x86)))
    (natp val))
  :rule-classes :type-prescription)

Theorem: rb-no-reads-when-zp-n

(defthm rb-no-reads-when-zp-n
  (b* (((mv ?flg ?val ?new-x86)
        (rb n addr r-x x86)))
    (implies (zp n) (equal val 0))))

Theorem: rb-is-rb-1-for-app-view

(defthm rb-is-rb-1-for-app-view
  (implies (app-view x86)
           (equal (rb n addr r-x x86)
                  (rb-1 n addr r-x x86))))

Theorem: rb-returns-no-error-app-view

(defthm rb-returns-no-error-app-view
  (implies (and (app-view x86)
                (canonical-address-p addr)
                (canonical-address-p (+ -1 n addr)))
           (equal (mv-nth 0 (rb n addr r-x x86))
                  nil)))

Theorem: rb-returns-x86-app-view

(defthm rb-returns-x86-app-view
  (implies (app-view x86)
           (equal (mv-nth 2 (rb n addr r-x x86))
                  x86)))

Theorem: size-of-rb

(defthm size-of-rb
 (implies (and (equal m (ash n 3)) (natp n))
          (unsigned-byte-p m (mv-nth 1 (rb n addr r-x x86))))
 :rule-classes
 (:rewrite
  (:linear
   :corollary (implies (and (equal m (ash n 3)) (natp n))
                       (and (<= 0 (mv-nth 1 (rb n addr r-x x86)))
                            (< (mv-nth 1 (rb n addr r-x x86))
                               (expt 2 m))))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))

Theorem: size-of-rb-in-app-view

(defthm size-of-rb-in-app-view
 (implies (and (app-view x86) (natp n))
          (unsigned-byte-p (ash n 3)
                           (mv-nth 1 (rb n addr r-x x86))))
 :rule-classes
 (:rewrite
  (:linear
   :corollary (implies (and (app-view x86) (natp n))
                       (and (<= 0 (mv-nth 1 (rb n addr r-x x86)))
                            (< (mv-nth 1 (rb n addr r-x x86))
                               (expt 2 (ash n 3)))))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))

Theorem: rb-values-and-xw-rflags-in-sys-view

(defthm rb-values-and-xw-rflags-in-sys-view
 (implies
     (and (equal (rflagsbits->ac (double-rewrite value))
                 (rflagsbits->ac (rflags x86)))
          (not (app-view x86))
          (x86p x86))
     (and (equal (mv-nth 0
                         (rb n addr r-x (xw :rflags nil value x86)))
                 (mv-nth 0 (rb n addr r-x (double-rewrite x86))))
          (equal (mv-nth 1
                         (rb n addr r-x (xw :rflags nil value x86)))
                 (mv-nth 1
                         (rb n addr r-x (double-rewrite x86)))))))

Theorem: 64-bit-modep-of-rb

(defthm 64-bit-modep-of-rb
  (equal (64-bit-modep (mv-nth 2 (rb n addr r-x x86)))
         (64-bit-modep x86)))

Theorem: x86-operation-mode-of-rb

(defthm x86-operation-mode-of-rb
  (equal (x86-operation-mode (mv-nth 2 (rb n addr r-x x86)))
         (x86-operation-mode x86)))