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(in-package "BCV")
(include-book "typechecker")
(include-book "typechecker-ext")
(include-book "typechecker-simple")
(include-book "bcv-base")
;----------------------------------------------------------------------
(encapsulate ()
(local (include-book "bcv-collected-frames-are-strictly-ordered"))
(defthm pc-wff-mergedcode1-isInstruction-then-next-pc-is-greater
(implies (and (pc-wff-mergedcode1 pc mergedcode)
(consp mergedcode)
(isInstruction (car mergedcode)))
(all-strictly-less-than (instroffset (car mergedcode))
(extract-pc (extract-code (cdr mergedcode)))))))
(defthm pc-wff-mergedcode1-strictly-ordered-extract-pc-extract-code
(implies (pc-wff-mergedcode1 pc mergedcode)
(strictly-ordered (extract-pc (extract-code mergedcode))))
:hints (("Goal" :in-theory (disable isInstruction
isstackmap
jvm::inst-size
mapOffset getMap
instroffset
isEnd))))
;----------------------------------------------------------------------
;----------------------------------------------------------------------
(defthm strictly-ordered-next-inst
(implies (and (strictly-ordered (extract-pc (extract-code mergedcode)))
(wff-merged-code-weak mergedcode)
(member inst mergedcode)
(isInstruction inst)
(isInstruction (next-inst inst mergedcode)))
(< (instroffset inst)
(instroffset (next-inst inst mergedcode))))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable isInstruction
isstackmap
jvm::inst-size
mapOffset
getMap
instroffset
isEnd))))
;;;
;;; well this is proved by induction!!!
;;;
;;; although we usually don't want to prove such things using induction
;;; directly!!
;;;
;; :use ((:instance member-suffix-then-strictly-greater
;; (x (instroffset inst))
;; (y (instroffset (next-inst inst mergedcode)))
;; (l (extract-pc (extract-code mergedcode))))
;; (:instance
;; member-code-isInstruction-implies-member-extract-pc-general
;; (inst (next-inst inst mergedcode))
;; (pc-list (cdr (suffix (instroffset inst)
;; (extract-pc (extract-code
;; mergedcode)))))
;; (mergedcode (cdr (suffix inst mergedcode))))
;; (:instance member-inst-implies-consp
;; (inst (next-inst inst mergedcode))
;; (mergedcode (cdr (suffix inst mergedcode)))))
;; :do-not-induct t)))
;----------------------------------------------------------------------
;; (defthm pc-wff-mergedcode1-implies-wff-merged-code-weak
;; (implies (pc-wff-mergedcode1 pc mergedcode)
;; (wff-merged-code-weak mergedcode))
;; :rule-classes :forward-chaining
;; :hints (("Goal" :do-not '(generalize)
;; :in-theory (disable isInstruction
;; isstackmap
;; jvm::inst-size
;; mapOffset
;; getMap
;; instroffset
;; isEnd))))
;;; in bcv-base.lisp
;;
(defthm next-inst-never-occur-before
(implies (and (member inst mergedcode)
(pc-wff-mergedcode1 pc mergedcode)
(isInstruction (next-inst inst mergedcode))
(isInstruction inst))
(< (instroffset inst)
(instroffset (next-inst inst mergedcode))))
:rule-classes :linear
:hints (("Goal" :do-not '(generalize)
:in-theory (disable isInstruction
isstackmap
jvm::inst-size
mapOffset
getMap
instroffset
isEnd))))
(defthm member-inst-pc-no-less-than
(implies (and (member inst mergedcode)
(pc-wff-mergedcode1 pc mergedcode)
(isInstruction inst))
(<= pc (instroffset inst)))
:rule-classes :linear
:hints (("Goal" :do-not '(generalize)
:in-theory (disable isInstruction
isstackmap
jvm::inst-size
mapOffset
getMap
instroffset
isEnd))))
(defthm member-inst-pc-no-less-than-specific
(implies (and (member inst mergedcode)
(pc-wff-mergedcode1 pc mergedcode)
(isInstruction inst)
(isInstruction (next-inst inst mergedcode)))
(< pc (instroffset (next-inst inst mergedcode))))
:rule-classes :linear
:hints (("Goal" :in-theory (disable instroffset isInstruction
pc-wff-mergedcode1
next-inst member))))
;----------------------------------------------------------------------
;; (defthm member-del-x-member
;; (implies (and (member x l)
;; (member y l)
;; (not (equal x y)))
;; (member x (del y l))))
;; (defthm strictly-ordered-list-del-member
;; (implies (strictly-ordered l)
;; (not (member x (del x l)))))
;; (defthm member-member-pc
;; (implies (and (member inst mergedcode)
;; (wff-merged-code-weak mergedcode)
;; (isInstruction inst))
;; (member (instroffset inst)
;; (extract-pc (extract-code mergedcode)))))
;; (defthm extract-pc-del-is-del-extract-pc
;; (implies (and ;; (strictly-ordered (extract-pc (extract-code mergedcode)))
;; (unique
;; (member inst mergedcode)
;; (isInstruction inst))
;; (equal (extract-pc (extract-code (del inst mergedcode)))
;; (del (instroffset inst) (extract-pc (extract-code
;; mergedcode)))))
;; :hints (("Goal" :do-not '(generalize)
;; :in-theory (disable isInstruction
;; isstackmap
;; jvm::inst-size
;; mapOffset
;; getMap
;; instroffset
;; isEnd))))
(defthm strictly-ordered-next-inst-specific
(implies (and (equal (instroffset inst2)
(instroffset inst1))
(member inst1 mergedcode)
(member inst2 mergedcode)
(strictly-ordered (extract-pc (extract-code mergedcode)))
(wff-merged-code-weak mergedcode)
(isInstruction inst1)
(isInstruction inst2))
(equal inst2 inst1))
:rule-classes :forward-chaining
:hints (("Goal" :do-not '(generalize fertilize)
:in-theory (disable isInstruction
isstackmap
jvm::inst-size
mapOffset
getMap
instroffset
isEnd))))
(defthm pc-wff-mergedcode1-all-greater-than
(implies (and (pc-wff-mergedcode1 pc mergedcode)
(member inst mergedcode)
(isInstruction inst))
(<= pc (instroffset inst)))
:rule-classes :linear
:hints (("Goal" :do-not '(generalize fertilize)
:in-theory (disable isInstruction
isstackmap
jvm::inst-size
mapOffset
getMap
instroffset
isEnd))))
(defthm not-pc-wff-mergecode1-if-member
(implies (and (< 0 x)
(member inst mergedcode2)
(isInstruction inst))
(not (PC-WFF-MERGEDCODE1 (+ x
(INSTROFFSET INST))
MERGEDCODE2)))
:hints (("Goal" :do-not '(generalize fertilize)
:do-not-induct t
:use ((:instance pc-wff-mergedcode1-all-greater-than
(pc (+ x (instroffset inst)))
(mergedcode mergedcode2)))
:in-theory (disable isInstruction
isstackmap
jvm::inst-size
mapOffset
getMap
instroffset
isEnd))))
;----------------------------------------------------------------------
;----------------------------------------------------------------------
(defthm mergecodeIsTypeSafe-implies-collect-sig-vector-compatible-1
(implies (and (mergedcodeIsTypeSafe env mergecode stackframe)
(member inst mergecode)
(isInstruction inst)
(isInstruction (next-inst inst mergecode))
(pc-wff-mergedcode1 (next-pc mergecode) mergecode))
(equal (car (sig-do-inst inst
env
(searchStackFrame (instroffset inst)
(stack-map-wrap
(collect-sig-frame-vector
env mergecode
stackframe)))))
(searchStackFrame (instroffset (next-inst inst mergecode))
(stack-map-wrap (collect-sig-frame-vector
env mergecode
stackframe)))))
:hints (("Goal" :do-not '(generalize fertilize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
jvm::inst-size
sig-do-inst
isstackmap
makestackmap
allinstructions
isEnd
mapFrame
getMap
mapOffset
frameIsAssignable
isInstruction
isStackMap))))
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