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|
(in-package "ACL2")
(include-book "djvm-model")
(include-book "generic")
(include-book "consistent-state")
(include-book "consistent-state-properties")
(local (include-book "consistent-state-step"))
(local (in-theory (disable consistent-state)))
(local
(defthm bcv-simple-check-step-pre-PUSH
(implies (and (equal (op-code inst) 'PUSH)
(bcv-simple-check-step-pre inst
(extract-sig-frame
(topx (g 'call-stack st))
(g 'method-table st))))
(<= (+ 1 (len (g 'op-stack (car (g 'call-stack st)))))
(g 'max-stack (car (g 'call-stack st)))))
:hints (("Goal" :in-theory (enable bcv-simple-check-step-pre)))))
(local
(defthm bcv-simple-check-step-pre-PUSH-specific
(implies (and (equal (op-code (next-inst st)) 'PUSH)
(bcv-simple-check-step-pre (next-inst st)
(extract-sig-frame
(topx (g 'call-stack st))
(g 'method-table st))))
(<= (+ 1 (len (g 'op-stack (car (g 'call-stack st)))))
(g 'max-stack (car (g 'call-stack st)))))
:hints (("Goal" :in-theory (enable bcv-simple-check-step-pre)))))
;;(i-am-here) ;; Thu Oct 20 16:52:57 2005
;; should be easy if we add the assertion that pc is integerp in
;; consistent-frame
(local
(defthm consistent-state-op-code-push-implies-pc-in-range
(implies (and (consistent-state st)
(equal (op-code (next-inst st)) 'PUSH))
(pc-in-range st))))
(local (in-theory (disable next-inst bcv-simple-check-step-pre
extract-sig-frame pc-in-range
collect-witness-bcv-method
bcv-method
op-code consistent-state
sig-frame-compatible
current-method)))
(local
(defthm bcv-simple-execute-step-inst-push-fact-1
(implies (equal (op-code inst) 'PUSH)
(equal (g 'pc (car (bcv-simple-execute-step inst pre)))
(+ 1 (g 'pc pre))))))
(local
(defthm bcv-simple-execute-step-inst-push-fact-2
(implies (equal (op-code inst) 'PUSH)
(member (car (bcv-simple-execute-step inst pre))
(bcv-simple-execute-step inst pre)))))
;; (local
;; (defthm consistent-state-implies-all-next-state-safe-PUSH
;; (implies (and (consistent-state st)
;; (equal (op-code (next-inst st)) 'PUSH))
;; (all-next-state-safe (bcv-simple-execute-step (next-inst st)
;; (cdr (assoc-equal
;; (g 'pc (car (g
;; 'call-stack st)))
;; (g 'sig-vector
;; (current-method
;; st)))))
;; (g 'sig-vector
;; (current-method st))))
;; :hints (("Goal" :in-theory (disable bcv-simple-execute-step next-inst
;; all-next-state-safe)))))
(local
(defthm |Subgoal 5|
(IMPLIES
(AND (CONSISTENT-STATE ST)
(EQUAL (op-code (NEXT-INST ST)) 'PUSH))
(EQUAL
(G 'PC
(CDR (ASSOC-EQUAL (+ 1 (g 'pc (car (g 'call-stack st))))
(collect-witness-bcv-method (current-method st)
(g 'method-table st)))))
(+ 1 (g 'pc (car (g 'call-stack st))))))
:hints (("Goal"
:in-theory (e/d () (bcv-simple-execute-step))
:use ((:instance all-next-state-safe-implies-pc-equal
(x (car (bcv-simple-execute-step (next-inst st)
(cdr (assoc-equal
(g 'pc
(car
(g 'call-stack
st)))
(collect-witness-bcv-method (current-method st)
(g 'method-table st)))))))
(l (bcv-simple-execute-step
(next-inst st)
(cdr (assoc-equal
(g 'pc
(car
(g 'call-stack
st)))
(collect-witness-bcv-method (current-method st)
(g 'method-table st))))))
(sig-vector (collect-witness-bcv-method (current-method st)
(g 'method-table st)))))))))
;; this is true, because:
;;
;; 1. we know bcv-simple-execute-step for push produce a frame of (+ pc 1)
;; 2. we know consistent-state, we know sig-frame-compatible pc with
;; registered sig-frame
;; 3. from 2, we know (pc sig-frame) equal (pc st)
;; 4. we know bcv-simple-inst at pc.
;; 5. we know next-state's pc is (pc sig-frame) + 1
;;
;; We could add an extra assertion about the consistent-state.
;; so that we can show that (g 'pc (binding pc vector)) == pc
;;
;; but it is not necessary!
;;
;; the decision is that we need to do |Subgoal 2| in any case!!
;;
(local
(defthm bcv-simple-execute-step-inst-push-fact-3
(implies (equal (op-code inst) 'PUSH)
(equal (g 'max-stack (car (bcv-simple-execute-step inst pre)))
(g 'max-stack pre)))))
(local
(defthm |Subgoal 4|
(IMPLIES
(AND (CONSISTENT-STATE ST)
(EQUAL (op-code (NEXT-INST ST)) 'PUSH))
(EQUAL
(G 'MAX-STACK
(CDR (ASSOC-EQUAL (+ 1 (G 'PC (CAR (G 'CALL-STACK ST))))
(collect-witness-bcv-method (current-method st)
(g 'method-table st)))))
(G 'MAX-STACK (CAR (G 'CALL-STACK ST)))))
:hints (("Goal"
:in-theory (e/d () (bcv-simple-execute-step))
:use ((:instance all-next-state-safe-implies-max-stack-equal
(x (car (bcv-simple-execute-step (next-inst st)
(cdr (assoc-equal
(g 'pc
(car
(g 'call-stack
st)))
(collect-witness-bcv-method (current-method st)
(g 'method-table st)))))))
(l (bcv-simple-execute-step
(next-inst st)
(cdr (assoc-equal
(g 'pc
(car
(g 'call-stack
st)))
(collect-witness-bcv-method (current-method st)
(g 'method-table st))))))
(sig-vector (collect-witness-bcv-method (current-method st)
(g 'method-table st)))))))))
;; 1. We know consistent-state, we know sig-frame-compatible pc with registered
;; sig-frame
;;
;; 2. we know bcv-simple-execute-step does not change max-stack for push.
;;
;; 3. we know (max-stack sig-frame) is equal to (max-stack st) ...
;;
;; 4. we know ....
;;
(local
(defthm bcv-simple-execute-step-inst-push-fact-4
(implies (equal (op-code inst) 'PUSH)
(equal (g 'method-table (car (bcv-simple-execute-step inst pre)))
(g 'method-table pre)))))
(local
(defthm |Subgoal 3|
(IMPLIES
(AND (CONSISTENT-STATE ST)
(EQUAL (op-code (NEXT-INST ST)) 'PUSH))
(EQUAL
(G 'method-table
(CDR (ASSOC-EQUAL (+ 1 (G 'PC (CAR (G 'CALL-STACK ST))))
(collect-witness-bcv-method
(current-method st)
(g 'method-table st)))))
(G 'method-table st)))
:hints (("Goal"
:in-theory (e/d () (bcv-simple-execute-step
consistent-state-sig-frame-compatible))
:use ((:instance consistent-state-sig-frame-compatible)
(:instance all-next-state-safe-implies-method-table-equal
(x (car (bcv-simple-execute-step (next-inst st)
(cdr (assoc-equal
(g 'pc
(car
(g 'call-stack
st)))
(collect-witness-bcv-method (current-method st)
(g 'method-table st)))))))
(l (bcv-simple-execute-step
(next-inst st)
(cdr (assoc-equal
(g 'pc
(car
(g 'call-stack
st)))
(collect-witness-bcv-method (current-method st)
(g 'method-table st))))))
(sig-vector (collect-witness-bcv-method (current-method st)
(g 'method-table st)))))))))
(local
(defthm bcv-simple-execute-step-inst-push-fact-5
(implies (equal (op-code inst) 'PUSH)
(equal (g 'op-stack (car (bcv-simple-execute-step inst pre)))
(+ 1 (g 'op-stack pre))))))
(local
(defthm |Subgoal 2|
(implies (AND (CONSISTENT-STATE ST)
(EQUAL (op-code (NEXT-INST ST)) 'PUSH))
(EQUAL
(G 'OP-STACK
(CDR (ASSOC-EQUAL (+ 1 (G 'PC (CAR (G 'CALL-STACK ST))))
(collect-witness-bcv-method (current-method st)
(g 'method-table st)))))
(+ 1
(LEN (G 'OP-STACK (CAR (G 'CALL-STACK ST)))))))
:hints (("Goal"
:in-theory (e/d () (bcv-simple-execute-step
consistent-state-sig-frame-compatible))
:use ((:instance consistent-state-sig-frame-compatible)
(:instance all-next-state-safe-implies-opstack-equal
(x (car (bcv-simple-execute-step (next-inst st)
(cdr (assoc-equal
(g 'pc
(car
(g 'call-stack
st)))
(collect-witness-bcv-method (current-method st)
(g 'method-table st)))))))
(l (bcv-simple-execute-step
(next-inst st)
(cdr (assoc-equal
(g 'pc
(car
(g 'call-stack
st)))
(collect-witness-bcv-method (current-method st)
(g 'method-table st))))))
(sig-vector (collect-witness-bcv-method (current-method st)
(g 'method-table st)))))))))
(local
(defthm bcv-simple-execute-step-inst-method-name-fact
(implies (equal (op-code inst) 'PUSH)
(equal (g 'method-name (car (bcv-simple-execute-step inst pre)))
(g 'method-name pre)))))
(local
(defthm |Subgoal 1|
(implies (AND (CONSISTENT-STATE ST)
(EQUAL (op-code (NEXT-INST ST)) 'PUSH))
(EQUAL
(G 'method-name
(CDR (ASSOC-EQUAL (+ 1 (G 'PC (CAR (G 'CALL-STACK ST))))
(collect-witness-bcv-method
(current-method st)
(g 'method-table st)))))
(G 'method-name
(CAR (G 'CALL-STACK ST)))))
:hints (("Goal"
:in-theory (e/d () (bcv-simple-execute-step
consistent-state-sig-frame-compatible))
:use ((:instance consistent-state-sig-frame-compatible)
(:instance all-next-state-safe-implies-method-name-equal
(x (car (bcv-simple-execute-step (next-inst st)
(cdr (assoc-equal
(g 'pc
(car
(g 'call-stack
st)))
(collect-witness-bcv-method (current-method st)
(g 'method-table st)))))))
(l (bcv-simple-execute-step
(next-inst st)
(cdr (assoc-equal
(g 'pc
(car
(g 'call-stack
st)))
(collect-witness-bcv-method (current-method st)
(g 'method-table st))))))
(sig-vector (collect-witness-bcv-method (current-method st)
(g 'method-table st)))))))))
(local
(defthm current-method-normalize
(equal (CDR (ASSOC-EQUAL (G 'METHOD-NAME
(CAR (G 'CALL-STACK ST)))
(G 'METHOD-TABLE ST)))
(current-method st))
:hints (("Goal" :in-theory (enable current-method)))))
;;(i-am-here) ;; Thu Oct 20 17:14:34 2005
;;(local (include-book "arithmetic/top-with-meta" :dir :system))
(local
(defthm consistent-state-preserved-by-PUSH-lemma
(implies (and (consistent-state st)
(equal (next-inst st) inst)
(equal (op-code inst) 'PUSH)
(djvm-check-PUSH inst st))
(consistent-state-step
(djvm-execute-PUSH inst st)))
:hints (("Goal" :in-theory (enable sig-frame-compatible pc-in-range)))))
(local (in-theory (disable djvm-execute-PUSH djvm-check-PUSH
consistent-state-step)))
(local
(defthm consistent-state-step-implies-consistent-state-djvm-execute-PUSH
(implies (consistent-state-step (djvm-execute-PUSH inst st))
(consistent-state (djvm-execute-PUSH inst st)))
:hints (("Goal" :use ((:instance
consistent-state-step-implies-implies-consistent-state
(s (djvm-execute-PUSH inst st))))))))
;--- EXPORT ----
(defthm consistent-state-preserved-by-DJVM-PUSH
(implies (and (consistent-state st)
(equal (next-inst st) inst)
(equal (op-code inst) 'PUSH)
(djvm-check-PUSH inst st))
(consistent-state
(djvm-execute-PUSH inst st))))
|
