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|
(in-package "ACL2")
(include-book "jvm-model")
(include-book "djvm-model")
(include-book "bcv-simple-model")
(include-book "bcv-model")
(include-book "generic")
(include-book "state-equiv-def")
;; in this example, the only difference between djvm-s and a jvm-s is that
;; jvm-s does not contain the stack map annotations not jvm-s checks for such
;; annotations.
;;
;; m-step does not check whether preconditions are met!!
;;
;;
;; usually we would assert class-table-equiv is pairwise method-equiv
;; However this is not the property that we really want,
;;
;; We want all method defined in djvm-method, looking up the method in the
;; jvm-class-table, we get a method-equiv method!
;;
;----------------------------------------------------------------------
(encapsulate ()
(local (include-book "bcv-simple-check-implies-djvm-check"))
(defthm bcv-simple-check-implies-djvm-check
(implies (and (consistent-state djvm-s)
(bcv-simple-check-step-pre (next-inst djvm-s)
(extract-sig-frame
(TOPX (G 'CALL-STACK DJVM-S))
(G 'METHOD-TABLE DJVM-S))))
(djvm-check-step djvm-s))))
;; (encapsulate ()
;; (local (include-book "bcv-simple-check-implies-djvm-check"))
;; (defthm bcv-simple-check-implies-djvm-check
;; (implies (bcv-simple-check-step-pre (next-inst djvm-s)
;; (extract-sig-frame
;; (TOPX (G 'CALL-STACK DJVM-S))
;; (G 'METHOD-TABLE DJVM-S)))
;; (djvm-check-step djvm-s))))
;; Sat Nov 19 15:08:28 2005
;;
;; wrong conjecture!
(encapsulate ()
(local (include-book "djvm-check-succeed-implies-jvm-equiv-state"))
(defthm djvm-check-succeed-implies-jvm-equiv-state
(implies (and (state-equiv jvm-s djvm-s)
(djvm-check-step djvm-s))
(state-equiv (m-step jvm-s)
(djvm-step djvm-s)))))
(encapsulate ()
(local (include-book "bcv-simple-check-monotonic"))
(defthm bcv-simple-check-step-pre-bcv-simple-check-step-pre
(implies (and (sig-frame-compatible frame1 frame2)
(bcv-simple-check-step-pre inst frame2))
(bcv-simple-check-step-pre inst frame1))))
;;;
;;; this following are top level properties.
;;;
(encapsulate ()
(local (include-book "bcv-simple-method-implies-bcv-simple-check-step-pre"))
(defthm method-verified-implies-bcv-simple-check-step-pre-on-recorded-signature-lemma
(implies (and (bcv-simple-method method method-table)
(integerp pc)
(<= 0 pc)
(< pc (len (g 'code method)))
(equal inst (nth pc (g 'code method)))
(member inst (g 'code method)))
(bcv-simple-check-step-pre inst
(cdr (assoc-equal pc (g 'sig-vector method)))))))
(encapsulate ()
(local (include-book "bcv-succeed-implies-bcv-simple-succeed"))
(defthm bcv-succeed-implies-bcv-simple-succeed
(implies (and (bcv-method method method-table)
(equal method (binding (g 'method-name method)
method-table))
(bcv-verified-method-table method-table))
(bcv-simple-method
(s 'sig-vector
(collect-witness-bcv-method
method method-table)
method)
method-table))))
;;; the above lemma is the most difficult one! Tue Nov 29 10:23:10 2005
(defthm method-verified-implies-bcv-simple-check-step-pre-on-recorded-signature
(implies (and (bcv-method method method-table)
(equal method (binding (g 'method-name method) method-table))
(bcv-verified-method-table method-table)
(integerp pc)
(<= 0 pc)
(< pc (len (g 'code method)))
(equal inst (nth pc (g 'code method)))
(member inst (g 'code method)))
(bcv-simple-check-step-pre inst
(cdr (assoc-equal pc
(collect-witness-bcv-method method method-table)))))
:hints (("Goal" :in-theory (disable collect-witness-bcv-method
bcv-verified-method-table
bcv-method
bcv-simple-method)
:use ((:instance
method-verified-implies-bcv-simple-check-step-pre-on-recorded-signature-lemma
(method (s 'sig-vector
(collect-witness-bcv-method method method-table) method))))
:do-not-induct t)))
;----------------------------------------------------------------------
(encapsulate ()
(local (include-book "djvm-is-safe"))
(defthm method-table-does-not-change
(equal (g 'method-table (djvm-step st))
(g 'method-table st))))
;----------------------------------------------------------------------
(encapsulate ()
(local (include-book "djvm-is-safe"))
(defthm djvm-step-preserve-consistent-state
(implies (consistent-state st)
(consistent-state (djvm-step st))))
(defthm djvm-run-preserve-consistent-state
(implies (consistent-state st)
(consistent-state (djvm-run st any)))))
;----------------------------------------------------------------------
(in-theory (disable state-equiv
m-step
djvm-step
djvm-check-step
bcv-simple-check-step-pre
next-inst
extract-sig-frame
consistent-state
bcv-verified-method-table
bcv-simple-method))
;; (i-am-here) ;; Fri Nov 18 22:24:27 2005
(defthm consistent-state-implies-pc-in-range
(implies (consistent-state djvm-s)
(pc-in-range djvm-s))
:hints (("Goal" :in-theory (enable consistent-state))))
;;;
;;; Sat Nov 19 14:56:39 2005 need to extend the consistent-state definition!!
;;; to assert that PC is in range!
;;;
;;; Will need to redo that bcv-simple-check-step-pre will ensure that!!
;;;
(defthm consistent-state-implies-bcv-method
(implies (consistent-state djvm-s)
(bcv-method (cdr (assoc-equal (g 'method-name (car (g 'call-stack djvm-s)))
(g 'method-table djvm-s)))
(g 'method-table djvm-s)))
:hints (("Goal" :in-theory (e/d (consistent-state current-method) (bcv-method)))))
(defthm consistent-state-implies-sig-frame-compatible
(implies (consistent-state djvm-s)
(SIG-FRAME-COMPATIBLE
(EXTRACT-SIG-FRAME (CAR (G 'CALL-STACK DJVM-S))
(G 'METHOD-TABLE DJVM-S))
(CDR (ASSOC-EQUAL (G 'PC (CAR (G 'CALL-STACK DJVM-S)))
(COLLECT-WITNESS-BCV-METHOD
(CDR (ASSOC-EQUAL (G 'METHOD-NAME
(CAR (G 'CALL-STACK DJVM-S)))
(G 'METHOD-TABLE DJVM-S)))
(G 'METHOD-TABLE DJVM-S))))))
:hints (("Goal" :in-theory (e/d (consistent-state current-method) (bcv-method)))))
(defthm consistent-state-method-name-equal
(implies (consistent-state djvm-s)
(equal (G 'METHOD-NAME
(CDR (ASSOC-EQUAL (G 'METHOD-NAME
(CAR (G 'CALL-STACK DJVM-S)))
(G 'METHOD-TABLE DJVM-S))))
(g 'method-name (car (g 'call-stack djvm-s)))))
:hints (("Goal" :in-theory (e/d (consistent-state current-method) (bcv-method)))))
(defthm in-range-then-member
(implies (and (<= 0 pc)
(< pc (len l)))
(member (nth pc l) l)))
(defthm pc-in-range-implies-member
(implies (pc-in-range djvm-s)
(member (nth (g 'pc (car (g 'call-stack djvm-s)))
(g 'code (cdr (assoc-equal
(g 'method-name (car (g 'call-stack
djvm-s)))
(g 'method-table djvm-s)))))
(g 'code (cdr (assoc-equal (g 'method-name (car (g
'call-stack djvm-s)))
(g 'method-table djvm-s))))))
:hints (("Goal" :in-theory (enable pc-in-range))))
(defthm consistent-state-implies-pc-in-range-f
(implies (consistent-state djvm-s)
(pc-in-range djvm-s)))
(defthm pc-in-range-f-pc-f
(implies (pc-in-range djvm-s)
(integerp (g 'pc (car (g 'call-stack djvm-s)))))
:rule-classes :forward-chaining)
(defthm pc-in-range-f-pc-b
(implies (pc-in-range djvm-s)
(integerp (g 'pc (car (g 'call-stack djvm-s))))))
(defthm pc-in-range-f-pc-f-2
(implies (pc-in-range djvm-s)
(<= 0 (g 'pc (car (g 'call-stack djvm-s)))))
:hints (("Goal" :in-theory (enable pc-in-range)))
:rule-classes :forward-chaining)
(defthm pc-in-range-f-pc-b-2
(implies (pc-in-range djvm-s)
(<= 0 (g 'pc (car (g 'call-stack djvm-s)))))
:hints (("Goal" :in-theory (enable pc-in-range))))
(defthm pc-in-range-f-pc-f-3
(implies (pc-in-range djvm-s)
(< (g 'pc (car (g 'call-stack djvm-s)))
(len (g 'code
(cdr (assoc-equal
(g 'method-name
(car (g 'call-stack djvm-s)))
(g 'method-table djvm-s)))))))
:hints (("Goal" :in-theory (enable pc-in-range)))
:rule-classes :forward-chaining)
(defthm pc-in-range-f-pc-b-3
(implies (pc-in-range djvm-s)
(< (g 'pc (car (g 'call-stack djvm-s)))
(len (g 'code
(cdr (assoc-equal
(g 'method-name
(car (g 'call-stack djvm-s)))
(g 'method-table djvm-s))))))))
(defthm bcv-simple-check-succeed-in-consistent-state
(implies (and (CONSISTENT-STATE DJVM-S)
(bcv-verified-method-table (g 'method-table djvm-s)))
(BCV-SIMPLE-CHECK-STEP-PRE (NEXT-INST DJVM-S)
(EXTRACT-SIG-FRAME (CAR (G 'CALL-STACK DJVM-S))
(G 'METHOD-TABLE
DJVM-S))))
:hints (("Goal"
:in-theory (e/d (next-inst)
(pc-in-range bcv-method
sig-frame-compatible
bcv-simple-check-step-pre-bcv-simple-check-step-pre
collect-witness-bcv-method))
:use ((:instance bcv-simple-check-step-pre-bcv-simple-check-step-pre
(frame1 (EXTRACT-SIG-FRAME (CAR (G 'CALL-STACK DJVM-S))
(G 'METHOD-TABLE
DJVM-S)))
(frame2 (cdr (assoc-equal
(g 'pc (car (g 'call-stack djvm-s)))
(collect-witness-bcv-method
(binding (g 'method-name
(car (g 'call-stack djvm-s)))
(g 'method-table djvm-s))
(g 'method-table djvm-s)))))
(inst (next-inst djvm-s)))))))
;;; we need consistent-state to assert pc-in-range!!
;;; currently this assertion is missing. Fri Nov 18 18:54:26 2005
;;;
;;----------------------------------------------------------------------
(defthm djvm-check-succeed-in-consistent-state
(implies (and (CONSISTENT-STATE DJVM-S)
(bcv-verified-method-table (g 'method-table djvm-s)))
(djvm-check-step djvm-s)))
(defthm verified-program-execute-safely-lemma
(implies (and (CONSISTENT-STATE DJVM-S)
(STATE-EQUIV JVM-S DJVM-S)
(BCV-VERIFIED-METHOD-TABLE (G 'METHOD-TABLE DJVM-S)))
(STATE-EQUIV (M-STEP JVM-S)
(DJVM-STEP DJVM-S))))
(defthm verified-program-executes-safely
(implies (and (consistent-state djvm-s)
(state-equiv jvm-s djvm-s)
(bcv-verified-method-table (g 'method-table djvm-s)))
(state-equiv (m-run jvm-s n)
(djvm-run djvm-s n))))
;----------------------------------------------------------------------
;; (i-am-here);; Mon May 22 15:30:10 2006
(defthm method-name-equal-state-equiv
(implies (state-equiv jvm-s djvm-s)
(equal (g 'method-name (topx (g 'call-stack jvm-s)))
(g 'method-name (topx (g 'call-stack djvm-s)))))
:hints (("Goal" :in-theory (enable state-equiv))))
(defthm class-table-equiv-max-stack-equal
(implies (and (class-table-equiv jvm-cl djvm-cl)
(bound? name djvm-cl))
(equal (max-stack (binding name jvm-cl))
(max-stack (binding name djvm-cl)))))
(defthm max-stack-binding-same-name
(implies (and (state-equiv jvm-s djvm-s)
(bound? name (g 'method-table djvm-s)))
(equal (max-stack (binding name (g 'method-table jvm-s)))
(max-stack (binding name (g 'method-table djvm-s)))))
:hints (("Goal" :in-theory (enable state-equiv)
:use ((:instance class-table-equiv-max-stack-equal
(jvm-cl (g 'method-table jvm-s))
(djvm-cl (g 'method-table djvm-s)))))))
(defthm consistent-state-implies-bound-method-name
(implies (and (consistent-state stx)
(equal (g 'method-table stx) stx-cl))
(bound? (g 'method-name (topx (g 'call-stack stx)))
stx-cl))
:hints (("Goal" :in-theory (enable consistent-state))))
(defthm op-stack-equal-state-equiv
(implies (state-equiv jvm-s djvm-s)
(equal (g 'op-stack (topx (g 'call-stack jvm-s)))
(g 'op-stack (topx (g 'call-stack djvm-s)))))
:hints (("Goal" :in-theory (enable state-equiv))))
(local
(defthm all-method-verified1-bcv-verified-method1
(iff (all-method-verified1 mt mtable)
(bcv-verified-method-table1 mt mtable))))
(defthm consistent-state-implies-bcv-verified-method-table
(implies (consistent-state stx)
(bcv-verified-method-table (g 'method-table stx)))
:hints (("Goal" :in-theory (enable consistent-state bcv-verified-method-table)))
:rule-classes :forward-chaining)
(defthm consistent-state-implies-all-method-verified
(implies (consistent-state stx)
(all-method-verified (g 'method-table stx)))
:hints (("Goal" :in-theory (enable consistent-state)))
:rule-classes :forward-chaining)
(encapsulate ()
(local (include-book "djvm-is-safe"))
(defthm verified-program-never-overflow-operand-stack-in-m
(implies (and (consistent-state stx)
(state-equiv st stx))
(<= (len (g 'op-stack (topx (g 'call-stack (m-run st n)))))
(max-stack (binding (g 'method-name
(topx (g 'call-stack (m-run st n))))
(g 'method-table st)))))
:hints (("Goal" :in-theory (disable binding topx max-stack bound?
m-run djvm-run all-method-verified)
:use ((:instance
verified-program-never-overflow-operand-stack-in-djvm
(st stx))
(:instance method-name-equal-state-equiv
(jvm-s (m-run st n))
(djvm-s (djvm-run stx n)))
(:instance verified-program-executes-safely
(jvm-s st)
(djvm-s stx))
(:instance op-stack-equal-state-equiv
(jvm-s (m-run st n))
(djvm-s (djvm-run stx n)))
(:instance max-stack-binding-same-name
(name (g 'method-name
(topx (g 'call-stack (m-run st n)))))
(jvm-s (m-run st n))
(djvm-s (djvm-run stx n))))))))
;----------------------------------------------------------------------
|
