• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
    • X86isa
      • Program-execution
      • Sdm-instruction-set-summary
      • Tlb
        • Tlb-key
          • !tlb-key->implicit-supervisor-access
          • Tlb-key-fast
          • Tlb-key-p
          • !tlb-key->r-w-x
          • !tlb-key->vpn
          • !tlb-key->smep
          • !tlb-key->smap
          • !tlb-key->cpl
          • !tlb-key->nxe
          • Tlb-key->implicit-supervisor-access
          • !tlb-key->wp
          • !tlb-key->ac
          • Tlb-key->vpn
          • Tlb-key->smep
          • Tlb-key->smap
          • Tlb-key->r-w-x
          • Tlb-key->cpl
          • Tlb-key-fix
          • Tlb-key->wp
          • Tlb-key->nxe
          • Tlb-key->ac
          • Good-tlb-key-p
        • Tlbp
        • Tlb-entryp
      • Running-linux
      • Introduction
      • Asmtest
      • X86isa-build-instructions
      • Publications
      • Contributors
      • Machine
      • Implemented-opcodes
      • To-do
      • Proof-utilities
      • Peripherals
      • Model-validation
      • Modelcalls
      • Concrete-simulation-examples
      • Utils
      • Debugging-code-proofs
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Tlb-key

!tlb-key->ac

Update the |X86ISA|::|AC| field of a tlb-key bit structure.

Signature

(!tlb-key->ac ac x) → new-x

Arguments

ac — Guard (bitp ac).

x — Guard (tlb-key-p x).

Returns

new-x — Type (tlb-key-p new-x).

Definitions and Theorems

Function: !tlb-key->ac$inline

(defun !tlb-key->ac$inline (ac x)
 (declare (xargs :guard (and (bitp ac) (tlb-key-p x))))
 (mbe
     :logic
     (b* ((ac (mbe :logic (bfix ac) :exec ac))
          (x (tlb-key-fix x)))
       (part-install ac x :width 1 :low 3))
     :exec (the (unsigned-byte 46)
                (logior (the (unsigned-byte 46)
                             (logand (the (unsigned-byte 46) x)
                                     (the (signed-byte 5) -9)))
                        (the (unsigned-byte 4)
                             (ash (the (unsigned-byte 1) ac) 3))))))

Theorem: tlb-key-p-of-!tlb-key->ac

(defthm tlb-key-p-of-!tlb-key->ac
  (b* ((new-x (!tlb-key->ac$inline ac x)))
    (tlb-key-p new-x))
  :rule-classes :rewrite)

Theorem: !tlb-key->ac$inline-of-bfix-ac

(defthm !tlb-key->ac$inline-of-bfix-ac
  (equal (!tlb-key->ac$inline (bfix ac) x)
         (!tlb-key->ac$inline ac x)))

Theorem: !tlb-key->ac$inline-bit-equiv-congruence-on-ac

(defthm !tlb-key->ac$inline-bit-equiv-congruence-on-ac
  (implies (bit-equiv ac ac-equiv)
           (equal (!tlb-key->ac$inline ac x)
                  (!tlb-key->ac$inline ac-equiv x)))
  :rule-classes :congruence)

Theorem: !tlb-key->ac$inline-of-tlb-key-fix-x

(defthm !tlb-key->ac$inline-of-tlb-key-fix-x
  (equal (!tlb-key->ac$inline ac (tlb-key-fix x))
         (!tlb-key->ac$inline ac x)))

Theorem: !tlb-key->ac$inline-tlb-key-equiv-congruence-on-x

(defthm !tlb-key->ac$inline-tlb-key-equiv-congruence-on-x
  (implies (tlb-key-equiv x x-equiv)
           (equal (!tlb-key->ac$inline ac x)
                  (!tlb-key->ac$inline ac x-equiv)))
  :rule-classes :congruence)

Theorem: !tlb-key->ac-is-tlb-key

(defthm !tlb-key->ac-is-tlb-key
  (equal (!tlb-key->ac ac x)
         (change-tlb-key x :ac ac)))

Theorem: tlb-key->ac-of-!tlb-key->ac

(defthm tlb-key->ac-of-!tlb-key->ac
  (b* ((?new-x (!tlb-key->ac$inline ac x)))
    (equal (tlb-key->ac new-x) (bfix ac))))

Theorem: !tlb-key->ac-equiv-under-mask

(defthm !tlb-key->ac-equiv-under-mask
  (b* ((?new-x (!tlb-key->ac$inline ac x)))
    (tlb-key-equiv-under-mask new-x x -9)))