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

Rb-1

Signature

(rb-1 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 (natp val).

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

Definitions and Theorems

Function: rb-1

(defun rb-1 (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-1))
    (declare (ignorable __function__))
    (if (zp n)
        (mv nil 0 x86)
      (b* (((unless (canonical-address-p addr))
            (mv 'rb-1 0 x86))
           ((mv flg0 byte0 x86) (rvm08 addr x86))
           ((when flg0) (mv flg0 0 x86))
           ((mv rest-flg rest-bytes x86)
            (rb-1 (1- n) (1+ addr) r-x x86)))
        (mv rest-flg
            (logior byte0 (ash rest-bytes 8))
            x86)))))

Theorem: natp-of-rb-1.val

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

Theorem: x86p-of-rb-1.new-x86

(defthm x86p-of-rb-1.new-x86
  (implies (x86p x86)
           (b* (((mv ?flg ?val ?new-x86)
                 (rb-1 n addr r-x x86)))
             (x86p new-x86)))
  :rule-classes :rewrite)

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

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

Theorem: rb-1-returns-x86

(defthm rb-1-returns-x86
  (b* (((mv ?flg ?val ?new-x86)
        (rb-1 n addr r-x x86)))
    (implies t (equal new-x86 x86))))

Theorem: rb-1-returns-no-error

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

Theorem: size-of-rb-1

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