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• Initialization

System-init-loop

Signature

(system-init-loop correct-vals vstates) → new-vstates

Arguments

correct-vals — Guard (address-setp correct-vals).

vstates — Guard (validators-statep vstates).

Returns

new-vstates — Type (validators-statep new-vstates), given (validators-statep vstates).

Definitions and Theorems

Function: system-init-loop

(defun system-init-loop (correct-vals vstates)
  (declare (xargs :guard (and (address-setp correct-vals)
                              (validators-statep vstates))))
  (let ((__function__ 'system-init-loop))
    (declare (ignorable __function__))
    (b* (((when (or (not (mbt (address-setp correct-vals)))
                    (emptyp correct-vals)))
          (validators-state-fix vstates))
         (vstates (omap::update (head correct-vals)
                                (validator-init)
                                vstates)))
      (system-init-loop (tail correct-vals)
                        vstates))))

Theorem: validators-statep-of-system-init-loop

(defthm validators-statep-of-system-init-loop
  (implies
       (validators-statep vstates)
       (b* ((new-vstates (system-init-loop correct-vals vstates)))
         (validators-statep new-vstates)))
  :rule-classes :rewrite)

Theorem: system-init-loop-of-address-set-fix-correct-vals

(defthm system-init-loop-of-address-set-fix-correct-vals
  (equal (system-init-loop (address-set-fix correct-vals)
                           vstates)
         (system-init-loop correct-vals vstates)))

Theorem: system-init-loop-address-set-equiv-congruence-on-correct-vals

(defthm
      system-init-loop-address-set-equiv-congruence-on-correct-vals
  (implies (address-set-equiv correct-vals correct-vals-equiv)
           (equal (system-init-loop correct-vals vstates)
                  (system-init-loop correct-vals-equiv vstates)))
  :rule-classes :congruence)

Theorem: in-of-keys-of-system-init-loop

(defthm in-of-keys-of-system-init-loop
 (implies
    (validators-statep vstates)
    (equal (in val
               (omap::keys (system-init-loop correct-vals vstates)))
           (or (in val (address-set-fix correct-vals))
               (in val (omap::keys vstates))))))

Theorem: keys-of-system-init-loop

(defthm keys-of-system-init-loop
  (implies
       (validators-statep vstates)
       (equal (omap::keys (system-init-loop correct-vals vstates))
              (union (address-set-fix correct-vals)
                     (omap::keys vstates)))))

Theorem: lookup-of-system-init-loop

(defthm lookup-of-system-init-loop
  (implies
       (validators-statep vstates)
       (equal (omap::lookup val
                            (system-init-loop correct-vals vstates))
              (if (in val (address-set-fix correct-vals))
                  (validator-init)
                (omap::lookup val vstates)))))