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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 consistent-state-op-code-IFEQ-implies-pc-in-range
(implies (and (consistent-state st)
(equal (op-code (next-inst st)) 'IFEQ))
(pc-in-range st))
:hints (("Goal" :in-theory (enable next-inst)))))
(local (in-theory (disable next-inst bcv-simple-check-step-pre
extract-sig-frame pc-in-range
op-code consistent-state
bcv-method collect-witness-bcv-method
sig-frame-compatible
current-method)))
(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)))))
;; (defthm consistent-state-len-opstack-in-limit-specific
;; (implies (consistent-state st)
;; (<= (len (cdr (g 'op-stack (car (g 'call-stack st)))))
;; (g 'max-stack (car (g 'call-stack st)))))
;; :hints (("Goal" :use consistent-state-len-opstack-in-limit)))
(local
(defthm bcv-simple-execute-step-inst-IFEQ-fact-1
(implies (equal (op-code inst) 'IFEQ)
(equal (g 'pc (cadr (bcv-simple-execute-step inst pre)))
(cadr inst)))))
(local
(defthm bcv-simple-execute-step-inst-IFEQ-fact-1-2
(implies (equal (op-code inst) 'IFEQ)
(equal (g 'pc (car (bcv-simple-execute-step inst pre)))
(+ 1 (g 'pc pre))))))
(defthm IFEQ-produce-consp
(implies (equal (op-code inst) 'IFEQ)
(CONSP (bcv-simple-execute-step inst any-frame))))
(defthm IFEQ-produce-consp-2
(implies (equal (op-code inst) 'IFEQ)
(bcv-simple-execute-step inst any-frame)))
(defthm IFEQ-produce-consp-3
(implies (equal (op-code inst) 'IFEQ)
(CONSP (cdr (bcv-simple-execute-step inst any-frame)))))
(defthm IFEQ-produce-consp-4
(implies (and (case-split (cadr inst))
(equal (op-code inst) 'IFEQ))
(cadr (bcv-simple-execute-step inst any-frame))))
(defthm member-cadr
(implies (consp (cdr l))
(member (cadr l) l)))
(local
(defthm |Subgoal 5|
(IMPLIES
(AND (CONSISTENT-STATE ST)
(EQUAL (op-code (NEXT-INST ST)) 'IFEQ)
(equal (car (g 'op-stack (car (g 'call-stack st)))) 0))
(EQUAL
(G 'PC
(CDR (ASSOC-EQUAL (cadr (next-inst st))
(collect-witness-bcv-method
(current-method st)
(g 'method-table st)))))
(cadr (next-inst st))))
:hints (("Goal"
:in-theory (e/d () (bcv-simple-execute-step))
:use ((:instance all-next-state-safe-implies-pc-equal
(x (cadr (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-IFEQ-fact-2
(implies (equal (op-code inst) 'IFEQ)
(equal (g 'max-stack (car (bcv-simple-execute-step inst pre)))
(g 'max-stack pre)))))
(local
(defthm bcv-simple-execute-step-inst-IFEQ-fact-3
(implies (equal (op-code inst) 'IFEQ)
(equal (g 'max-stack (cadr (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)) 'IFEQ)
(equal (car (g 'op-stack (car (g 'call-stack st)))) 0))
(EQUAL
(G 'MAX-STACK
(CDR (ASSOC-EQUAL (cadr (next-inst 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 (cadr (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-IFEQ-fact-4
(implies (equal (op-code inst) 'IFEQ)
(equal (g 'method-table (car (bcv-simple-execute-step inst pre)))
(g 'method-table pre))))
)
(local
(defthm bcv-simple-execute-step-inst-IFEQ-fact-5
(implies (equal (op-code inst) 'IFEQ)
(equal (g 'method-table (cadr (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)) 'IFEQ))
(EQUAL
(G 'method-table
(CDR (ASSOC-EQUAL (cadr (next-inst 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 (cadr (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-IFEQ-fact-6
(implies (equal (op-code inst) 'IFEQ)
(equal (g 'op-stack (car (bcv-simple-execute-step inst pre)))
(g 'op-stack (sig-frame-pop-value pre))))))
(local
(defthm bcv-simple-execute-step-inst-IFEQ-fact-7
(implies (equal (op-code inst) 'IFEQ)
(equal (g 'op-stack (cadr (bcv-simple-execute-step inst pre)))
(g 'op-stack (sig-frame-pop-value pre))))))
(local
(defthm bcv-simple-check-step-pre-IFEQ
(implies (and (equal (op-code inst) 'IFEQ)
(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))))))
:hints (("Goal" :in-theory (enable bcv-simple-check-step-pre)))))
(local
(defthm bcv-simple-check-step-pre-IFEQ-specific
(implies (and (equal (op-code (next-inst st)) 'IFEQ)
(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))))))
:hints (("Goal" :in-theory (enable bcv-simple-check-step-pre)))
:rule-classes :linear))
(local
(defthm |Subgoal 2|
(implies (AND (CONSISTENT-STATE ST)
(EQUAL (op-code (NEXT-INST ST)) 'IFEQ))
(EQUAL
(G 'OP-STACK
(CDR (ASSOC-EQUAL (cadr (next-inst 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 (cadr (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 |Subgoal 5-2|
(IMPLIES
(AND (CONSISTENT-STATE ST)
(EQUAL (op-code (NEXT-INST ST)) 'IFEQ)
(not (equal (car (g 'op-stack (car (g 'call-stack st)))) 0)))
(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)))))))))
(local
(defthm |Subgoal 4-2|
(IMPLIES
(AND (CONSISTENT-STATE ST)
(EQUAL (op-code (NEXT-INST ST)) 'IFEQ)
(not (equal (car (g 'op-stack (car (g 'call-stack st)))) 0)))
(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)))))))))
(local
(defthm |Subgoal 3-2|
(IMPLIES
(AND (CONSISTENT-STATE ST)
(EQUAL (op-code (NEXT-INST ST)) 'IFEQ))
(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 |Subgoal 2-2|
(implies (AND (CONSISTENT-STATE ST)
(EQUAL (op-code (NEXT-INST ST)) 'IFEQ))
(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)))))))))
;;(i-am-here)
(local
(defthm bcv-simple-execute-step-inst-method-name-fact-1
(implies (equal (op-code inst) 'IFEQ)
(equal (g 'method-name (car (bcv-simple-execute-step inst pre)))
(g 'method-name pre)))))
(local
(defthm bcv-simple-execute-step-inst-method-name-fact-2
(implies (equal (op-code inst) 'IFEQ)
(equal (g 'method-name (cadr (bcv-simple-execute-step inst pre)))
(g 'method-name pre)))))
(local
(defthm |Subgoal 1-1|
(implies (AND (CONSISTENT-STATE ST)
(EQUAL (op-code (NEXT-INST ST)) 'IFEQ))
(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 |Subgoal 1-2|
(IMPLIES
(AND (CONSISTENT-STATE ST)
(EQUAL (op-code (NEXT-INST ST)) 'IFEQ))
(EQUAL
(G 'method-name
(CDR (ASSOC-EQUAL (cadr (next-inst 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 (cadr (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-check-step-pre-IFEQ-specific
;; (implies (and (equal (op-code (next-inst st)) 'IFEQ)
;; (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))))))
;; :hints (("Goal" :in-theory (enable bcv-simple-check-step-pre)))
;; :rule-classes :linear))
(local
(defthm len-consp
(implies (< 0 (len l))
(consp l))))
;;(i-am-here) ;; Sun Nov 20 21:00:45 2005
(local
(defthm consistent-state-preserved-by-IFEQ-lemma
(implies (and (consistent-state st)
(equal (next-inst st) inst)
(equal (op-code inst) 'IFEQ)
(djvm-check-IFEQ inst st))
(consistent-state-step
(djvm-execute-IFEQ inst st)))
:hints (("Goal" :in-theory (enable sig-frame-compatible pc-in-range)))))
;----------------------------------------------------------------------
(local (in-theory (disable djvm-execute-IFEQ consistent-state-step)))
(local
(defthm consistent-state-step-implies-consistent-state-djvm-execute-IFEQ
(implies (consistent-state-step (djvm-execute-IFEQ inst st))
(consistent-state (djvm-execute-IFEQ inst st)))
:hints (("Goal" :use ((:instance
consistent-state-step-implies-implies-consistent-state
(s (djvm-execute-IFEQ inst st))))))))
(defthm consistent-state-preserved-by-DJVM-IFEQ
(implies (and (consistent-state st)
(equal (next-inst st) inst)
(equal (op-code inst) 'IFEQ)
(djvm-check-IFEQ inst st))
(consistent-state
(djvm-execute-IFEQ inst st))))
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