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(in-package "ACL2")
(include-book "jvm-model")
(include-book "djvm-model")
(include-book "state-equiv-def")
(include-book "generic")
(local
(in-theory (enable
djvm-check-INVOKE
djvm-check-POP
djvm-check-PUSH
djvm-check-RETURN
djvm-check-IFEQ)))
(defthm state-equiv-implies-pushStack-state-equiv
(implies (state-equiv jvm-s djvm-s)
(state-equiv (pushStack v jvm-s)
(pushStack v djvm-s))))
(defthm state-equiv-implies-call-frame-equiv-equal
(implies (and (state-equiv jvm-s djvm-s)
(consp (g 'call-stack djvm-s)))
(call-frame-equiv (car (g 'call-stack jvm-s))
(car (g 'call-stack djvm-s))))
:hints (("Goal" :in-theory (enable state-equiv))))
(defthm state-equiv-implies-topStack-equal
(implies (state-equiv jvm-s djvm-s)
(equal (topstack jvm-s)
(topstack djvm-s)))
:hints (("Goal" :cases ((consp (g 'call-stack djvm-s)))
:in-theory (disable state-equiv-implies-call-frame-equiv-equal))
("Subgoal 1" :use ((:instance state-equiv-implies-call-frame-equiv-equal)))))
(defthm state-equiv-implies-method-name-equal
(implies (state-equiv jvm-s djvm-s)
(equal (g 'method-name (car (g 'call-stack jvm-s)))
(g 'method-name (car (g 'call-stack djvm-s)))))
:hints (("Goal" :cases ((consp (g 'call-stack djvm-s)))
:in-theory (disable state-equiv-implies-call-frame-equiv-equal))
("Subgoal 1" :use ((:instance
state-equiv-implies-call-frame-equiv-equal)))))
(defthm state-equiv-implies-op-stack-equal
(implies (state-equiv jvm-s djvm-s)
(equal (g 'op-stack (car (g 'call-stack jvm-s)))
(g 'op-stack (car (g 'call-stack djvm-s)))))
:hints (("Goal" :cases ((consp (g 'call-stack djvm-s)))
:in-theory (disable state-equiv-implies-call-frame-equiv-equal))
("Subgoal 1" :use ((:instance
state-equiv-implies-call-frame-equiv-equal)))))
(defthm state-equiv-implies-popStack-state-equiv
(implies (state-equiv jvm-s djvm-s)
(state-equiv (popStack jvm-s)
(popStack djvm-s)))
:hints (("Goal" :use ((:instance state-equiv-implies-op-stack-equal)))))
(defthm state-equiv-implies-set-pc-state-equiv
(implies (state-equiv jvm-s djvm-s)
(state-equiv (set-pc pc jvm-s)
(set-pc pc djvm-s))))
(defthm state-equiv-implies-get-pc-equal
(implies (state-equiv jvm-s djvm-s)
(equal (get-pc jvm-s)
(get-pc djvm-s))))
(defthm state-equiv-implies-push-init-frame
(implies (state-equiv jvm-s djvm-s)
(state-equiv (pushInitFrame
name locals jvm-s)
(pushInitFrame
name locals djvm-s))))
(defthm state-equiv-implies-pop-call-stack
(implies (state-equiv jvm-s djvm-s)
(state-equiv (s 'call-stack
(cdr (g 'call-stack jvm-s))
jvm-s)
(s 'call-stack
(cdr (g 'call-stack djvm-s))
djvm-s))))
(in-theory (disable pushStack popStack set-pc get-pc
state-equiv
pushInitFrame
pushStack))
(defthm state-equiv-implies-popStack-n
(implies (state-equiv jvm-s djvm-s)
(state-equiv (popStack-n jvm-s n)
(popStack-n djvm-s n)))
:hints (("Goal" :do-not '(generalize))))
(defthm call-stack-equiv-implies-consp
(implies (CALL-STACK-EQUIV jvm-cs djvm-cs)
(equal (consp jvm-cs)
(consp djvm-cs))))
(defthm state-equiv-implies-consp-call-stack
(implies (state-equiv jvm-s djvm-s)
(equal (consp (g 'call-stack jvm-s))
(consp (g 'call-stack djvm-s))))
:hints (("Goal" :in-theory (enable state-equiv call-stack-equiv))))
(defthm state-equiv-implies-consp-call-stack-2
(implies (state-equiv jvm-s djvm-s)
(equal (consp (cdr (g 'call-stack jvm-s)))
(consp (cdr (g 'call-stack djvm-s)))))
:hints (("Goal" :in-theory (enable state-equiv call-stack-equiv))))
(defthm class-table-equiv-implies-method-equiv
(implies (and (class-table-equiv jvm-cl djvm-cl)
(bound? name djvm-cl))
(method-equiv (cdr (assoc-equal name jvm-cl))
(cdr (assoc-equal name djvm-cl)))))
(defthm state-equiv-implies-method-code-equal
(implies (and (state-equiv jvm-s djvm-s)
(case-split (bound? name (g 'method-table djvm-s))))
(equal (g 'code (cdr (assoc-equal name (g 'method-table jvm-s))))
(g 'code (cdr (assoc-equal name (g 'method-table djvm-s))))))
:hints (("Goal" :in-theory (e/d (state-equiv)
(class-table-equiv
class-table-equiv-implies-method-equiv))
:use ((:instance class-table-equiv-implies-method-equiv
(jvm-cl (g 'method-table jvm-s))
(djvm-cl (g 'method-table djvm-s)))))))
(defthm state-equiv-implies-nargs-equal
(implies (and (state-equiv jvm-s djvm-s)
(case-split (bound? name (g 'method-table djvm-s))))
(equal (g 'nargs (cdr (assoc-equal name (g 'method-table jvm-s))))
(g 'nargs(cdr (assoc-equal name (g 'method-table djvm-s))))))
:hints (("Goal" :in-theory (e/d (state-equiv)
(class-table-equiv
class-table-equiv-implies-method-equiv))
:use ((:instance class-table-equiv-implies-method-equiv
(jvm-cl (g 'method-table jvm-s))
(djvm-cl (g 'method-table djvm-s)))))))
(defthm if-not-nil-next-inst-then-bound-general
(implies (not (assoc-equal name cl))
(not (car (nth pc (G 'CODE (CDR (ASSOC-EQUAL name cl))))))))
(defthm if-not-nil-next-inst-then-bound-specific
(implies (car (nth (get-pc djvm-s)
(G 'CODE (CDR (ASSOC-EQUAL name (g 'method-table djvm-s))))))
(assoc-equal name (g 'method-table djvm-s)))
:hints (("Goal" :use ((:instance if-not-nil-next-inst-then-bound-general
(pc (get-pc djvm-s))
(cl (g 'method-table djvm-s)))))))
(defthm djvm-check-step-implies-method-bound
(implies (djvm-check-step djvm-s)
(assoc-equal (g 'method-name
(car (g 'call-stack djvm-s)))
(g 'method-table djvm-s))))
(defthm get-pc-noramlize
(equal (G 'PC (CAR (G 'CALL-STACK JVM-S)))
(get-pc jvm-s))
:hints (("Goal" :in-theory (enable get-pc))))
(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)))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable consistent-state))))
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