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(in-package "BCV")
(include-book "typechecker")
(include-book "typechecker-ext")
(include-book "typechecker-simple")
(include-book "bcv-base")
;----------------------------------------------------------------------
(defthm collect-sig-frame-vector-is-suffix
(implies (and (is-suffix mergedcode1 mergedcode)
(mergedcodeistypesafe env mergedcode init-frame))
(is-suffix (collect-sig-frame-vector env mergedcode1
(collect-sig-frame-at-mergecode1
env
mergedcode1
mergedcode
init-frame))
(collect-sig-frame-vector env mergedcode init-frame)))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
jvm::inst-size
next-pc
sig-do-inst
isstackmap
makestackmap
allinstructions
isEnd
mapFrame
getMap
mapOffset
frameIsAssignable
isInstruction
isStackMap))))
;----------------------------------------------------------------------
;;;
;;; Thu Dec 29 22:29:44 2005
;;;
(encapsulate ()
(local (include-book "bcv-collected-frames-are-strictly-ordered"))
(defthm collect-sig-frame-vector-return-ordered-list
(implies (pc-wff-mergedcode1 (next-pc mergedcode) mergedcode)
(strictly-ordered (extract-frame-pc
(collect-sig-frame-vector env
mergedcode init-frame))))))
;----------------------------------------------------------------------
;----------------------------------------------------------------------
(defthm sig-do-inst-reduce-to-collect-sig-frame-at-mergecode1
(implies (and (mergedcodeistypesafe env mergedcode init-frame)
(isInstruction (car mergedcode)))
(equal (car (sig-do-inst (car mergedcode) env init-frame))
(collect-sig-frame-at-mergecode1 env (cdr mergedcode)
mergedcode
init-frame)))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
jvm::inst-size
next-pc
sig-do-inst
isstackmap
makestackmap
allinstructions
isEnd
mapFrame
getMap
mapOffset
frameIsAssignable
isInstruction
isStackMap))))
(local (in-theory (disable collect-sig-frame-at-mergecode1)))
;----------------------------------------------------------------------
(encapsulate ()
(local (include-book "bcv-searchStackFrame-only-suffix-matters"))
(defthm searchStackFrame-reduce
(implies (and (is-suffix stack-maps1 stack-maps)
(consp stack-maps1)
(strictly-ordered (extract-frame-pc stack-maps))
(<= (mapOffset (car stack-maps1)) pc))
(equal (searchStackFrame pc (stack-map-wrap stack-maps1))
(searchStackFrame pc (stack-map-wrap stack-maps))))))
;----------------------------------------------------------------------
;; (i-am-here)
(encapsulate ()
(local (include-book "bcv-collect-sig-frame-vector-misc"))
(defthm mergedcodeistypesafe-implies-not-end-consp
(implies (and (mergedcodeistypesafe env mergedcode init-frame)
(consp mergedcode)
(pc-wff-mergedcode1 pc mergedcode)
(not (isEnd (car mergedcode))))
(consp (collect-sig-frame-vector env mergedcode init-frame))))
(defthm mergedcodeistypesafe-mergedcodeistype-safe
(implies (and (mergedcodeistypesafe env mergedcode init-frame)
(consp mergedcode1)
(is-suffix mergedcode1 mergedcode))
(mergedcodeistypesafe env mergedcode1
(collect-sig-frame-at-mergecode1
env mergedcode1 mergedcode init-frame))))
(defthm mapOffset-is-next-pc
(implies (and (mergedcodeistypesafe env mergedcode init-frame)
(pc-wff-mergedcode1 (next-pc mergedcode) mergedcode))
(equal (mapOffset (car (collect-sig-frame-vector env mergedcode
init-frame)))
(next-pc mergedcode))))
(defthm pc-wff-mergedcode1-pc-wff-mergedcode-pc-suffix
(implies (and (pc-wff-mergedcode1 (next-pc mergedcode) mergedcode)
(is-suffix mergedcode1 mergedcode)
(consp mergedcode1)
(not (isEnd (car mergedcode1))))
(pc-wff-mergedcode1 (next-pc mergedcode1) mergedcode1))
:rule-classes :forward-chaining))
(defthm searchStackFrame-reduce-specific
(implies (and (is-suffix mergedcode1 mergedcode)
(consp mergedcode1)
(pc-wff-mergedcode1 (next-pc mergedcode) mergedcode)
(not (isEnd (car mergedcode1)))
(mergedcodeistypesafe env mergedcode init-frame)
(<= (next-pc mergedcode1) pc))
(equal (searchStackFrame pc (stack-map-wrap
(collect-sig-frame-vector
env mergedcode1
(collect-sig-frame-at-mergecode1
env mergedcode1 mergedcode init-frame))))
(searchStackFrame pc (stack-map-wrap
(collect-sig-frame-vector
env mergedcode init-frame)))))
:hints (("Goal" :in-theory (disable collect-sig-frame-vector
mapOffset instrOffset next-pc
mergedcodeistypesafe
searchStackFrame-reduce
isstackmapframe isstackmap isInstruction isEnd
collect-sig-frame-at-mergecode1
InstructionIsTypeSafe
sig-do-inst
jvm::inst-size
is-suffix)
:do-not-induct t
:use ((:instance searchStackFrame-reduce
(stack-maps (collect-sig-frame-vector
env mergedcode init-frame))
(stack-maps1 (collect-sig-frame-vector
env mergedcode1
(collect-sig-frame-at-mergecode1
env mergedcode1 mergedcode
init-frame))))))))
;----------------------------------------------------------------------
;; (i-am-here) ;;Sat Dec 31 02:02:14 2005
(defthm member-frame-ordered
(implies (and (ordered (extract-pc mergedcode))
(wff-merged-code-weak mergedcode)
(isStackMap frame)
(member frame (cdr mergedcode)))
(<= (next-pc mergedcode)
(mapOffset (getMap frame))))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable
mapOffset instrOffset
isstackmapframe isstackmap isInstruction isEnd
jvm::inst-size))))
;;;; Fri Dec 30 15:00:58 2005
;;;;; Fri Dec 30 17:54:07 2005
;; (defun wff-stack-map-offset (mergecode)
;; (if (endp mergecode) t
;; (if (isStackMap (car mergecode))
;; (and (not (endp (cdr mergecode)))
;; (equal (next-pc (cdr mergecode))
;; (mapoffset (getMap (car mergecode))))
;; (wff-stack-map-offset (cdr mergecode)))
;; (wff-stack-map-offset (cdr mergecode)))))
(defthm collect-sig-frame-vector-reduce
(implies (and (isInstruction (car mergedcode4))
(mergedcodeIsTypeSafe env mergedcode4 frame))
(equal
(car (COLLECT-SIG-FRAME-VECTOR ENV MERGEDCODE4 frame))
(list (instrOffset (car mergedcode4))
frame)))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
jvm::inst-size
next-pc
sig-do-inst
isstackmap
makestackmap
allinstructions
isEnd
mapFrame
getMap
mapOffset
frameIsAssignable
isInstruction
isStackMap))))
(defthm searchstackframe-reduce-2
(implies (and (isInstruction (car mergedcode4))
(mergedcodeIsTypeSafe env mergedcode4 frame)
(equal (next-pc mergedcode4) pc))
(equal
(searchstackframe pc
(stack-map-wrap (COLLECT-SIG-FRAME-VECTOR ENV MERGEDCODE4 frame)))
frame))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
jvm::inst-size
next-pc
sig-do-inst
isstackmap
makestackmap
allinstructions
isEnd
mapFrame
getMap
mapOffset
frameIsAssignable
isInstruction
isStackMap))))
(defthm collect-sig-frame-vector-reduce-2
(implies (and (isStackMap (car mergedcode4))
(wff-mergedcode-instr mergedcode4)
(wff-stack-map-offset mergedcode4)
(mergedcodeIsTypeSafe env mergedcode4 frame))
(equal
(car (COLLECT-SIG-FRAME-VECTOR ENV MERGEDCODE4 frame))
(list (mapOffset (getMap (car mergedcode4)))
(next-stackframe mergedcode4))))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
jvm::inst-size
next-pc
sig-do-inst
isstackmap
makestackmap
allinstructions
isEnd
mapFrame
getMap
mapOffset
frameIsAssignable
isInstruction
isStackMap))))
(defthm searchstackframe-reduce-3
(implies (and (isStackMap (car mergedcode4))
(wff-mergedcode-instr mergedcode4)
(wff-stack-map-offset mergedcode4)
(mergedcodeIsTypeSafe env mergedcode4 frame)
(equal (next-pc mergedcode4) pc))
(equal
(searchstackframe pc
(stack-map-wrap (COLLECT-SIG-FRAME-VECTOR ENV MERGEDCODE4 frame)))
(next-stackframe mergedcode4)))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
jvm::inst-size
next-pc
sig-do-inst
isstackmap
makestackmap
allinstructions
isEnd
mapFrame
getMap
mapOffset
frameIsAssignable
isInstruction
isStackMap))))
(defthm searchstackframe-reduce-4
(implies (and (not (isInstruction (car mergedcode4)))
(wff-mergedcode-instr mergedcode4)
(extract-code mergedcode4)
(wff-stack-map-offset mergedcode4)
(wff-merged-code-weak mergedcode4)
(mergedcodeIsTypeSafe env mergedcode4 frame)
(equal (next-pc mergedcode4) pc))
(equal
(searchstackframe pc
(stack-map-wrap (COLLECT-SIG-FRAME-VECTOR ENV MERGEDCODE4 frame)))
(next-stackframe mergedcode4)))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
jvm::inst-size
next-pc
sig-do-inst
isstackmap
makestackmap
allinstructions
isEnd
mapFrame
getMap
mapOffset
frameIsAssignable
isInstruction
isStackMap))))
(defthm wff-mergedcode-offset-tr-implies-consp-extract-pc
(implies (and (MEMBER FRAME MERGEDCODE2)
(wff-stack-map-offset mergedcode2)
(wff-merged-code-weak mergedcode2)
(ISSTACKMAP FRAME))
(CONSP (EXTRACT-PC MERGEDCODE2)))
:hints (("Goal" :in-theory (disable isstackmap
isInstruction
mapOffset
instrOffset
isEnd))))
;; (skip-proofs
;; (defthm wff-stack-map-offset-2-implies-not-equal-frame
;; (implies (and (wff-stack-map-offset-2 mergedcode)
;; (member frame (cdr mergedcode))
;; (isInstruction (car mergedcode))
;; (ordered (extract-pc mergedcode))
;; (consp mergedcode)
;; (consp (cdr mergedcode))
;; (not (isEnd (cadr mergedcode))))
;; (not (equal (instrOffset (car mergedcode))
;; (mapOffset frame))))
;; :rule-classes :forward-chaining))
(defthm ordered-implies-less-not-equal
(implies (and (< pc (car (extract-pc mergedcode)))
(ordered (extract-pc mergedcode))
(isstackmap frame)
(wff-merged-code-weak mergedcode)
(member frame mergedcode)
(< pc (car (extract-pc mergedcode))))
(< pc (mapOffset (getMap frame))))
:hints (("Goal" :in-theory (disable mapOffset
getMap
isEnd
instrOffset
isInstruction
isstackmap)))
:rule-classes :forward-chaining)
;; (skip-proofs
;; (defthm member-frame-ordered
;; (implies (and (ordered (extract-pc mergedcode))
;; (isStackMap frame)
;; (member frame (cdr mergedcode)))
;; (<= (next-pc mergedcode)
;; (mapOffset (getMap frame))))))
(defthm collect-sig-frame-vector-collect-last-frame-lemma
(implies (and (isStackMap frame)
(member frame mergedcode)
(ordered (extract-pc mergedcode))
(wff-stack-map-offset mergedcode)
(wff-stack-map-offset-2 mergedcode)
(wff-merged-code-weak mergedcode)
(wff-mergedcode-instr mergedcode)
(mergedcodeistypesafe env mergedcode init-frame))
(equal (searchStackFrame (mapOffset (getMap frame))
(stack-map-wrap (collect-sig-frame-vector
env mergedcode
init-frame)))
(next-stackframe (suffix frame mergedcode))))
:hints (("Goal" :do-not '(generalize fertilize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
jvm::inst-size
next-pc
sig-do-inst
isstackmap
makestackmap
allinstructions
isEnd
mapFrame
getMap
mapOffset
frameIsAssignable
isInstruction
isStackMap))))
;;;
;;; if we query the collected vector, we get the next stackframe right before
;;; the next instruction
;;;
(defthm pc-wff-mergedcode1-implies-wff-stack-map-offset
(implies (pc-wff-mergedcode1 pc mergedcode)
(wff-stack-map-offset mergedcode))
:hints (("Goal" :in-theory (disable isInstruction isStackMap
isEnd
jvm::inst-size)))
:rule-classes :forward-chaining)
(defthm pc-wff-mergedcode1-implies-wff-merged-code-instr
(implies (pc-wff-mergedcode1 pc mergedcode)
(wff-mergedcode-instr mergedcode))
:hints (("Goal" :in-theory (disable isInstruction isStackMap
isEnd
jvm::inst-size)))
:rule-classes :forward-chaining)
(defthm pc-wff-mergedcode1-implies-ordered-extract-pc
(implies (pc-wff-mergedcode1 pc mergedcode)
(ordered (extract-pc mergedcode)))
:hints (("Goal" :in-theory (disable isInstruction isStackMap
isEnd
jvm::inst-size)
:do-not '(generalize)))
:rule-classes :forward-chaining)
(defthm pc-wff-mergedcode1-implies-wff-stack-map-offset-2
(implies (pc-wff-mergedcode1 pc mergedcode)
(wff-stack-map-offset-2 mergedcode))
:hints (("Goal" :in-theory (disable isInstruction isStackMap
isEnd
jvm::inst-size)
:do-not '(generalize)))
:rule-classes :forward-chaining)
(defthm collect-sig-frame-vector-collect-last-frame
(implies (and (isStackMap frame)
(member frame mergedcode)
(pc-wff-mergedcode1 pc mergedcode)
(mergedcodeistypesafe env mergedcode init-frame))
(equal (searchStackFrame (mapOffset (getMap frame))
(stack-map-wrap (collect-sig-frame-vector
env mergedcode
init-frame)))
(next-stackframe (suffix frame mergedcode))))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
jvm::inst-size
next-pc
sig-do-inst
isstackmap
makestackmap
allinstructions
isEnd
mapFrame
getMap
mapOffset
frameIsAssignable
isInstruction
isStackMap))))
;----------------------------------------------------------------------
;----------------------------------------------------------------------
(encapsulate ()
(local (include-book "bcv-next-stackframe-equal-suffix-suffix"))
(defthm is-suffix-then-suffix-is
(implies (and (is-suffix mergedcode all-merged-code)
(ordered (extract-pc all-merged-code))
(wff-stack-map-offset-2 all-merged-code)
(wff-merged-code-weak all-merged-code)
(member (car mergedcode) all-merged-code)
(isStackMap (car mergedcode)))
(equal (next-stackframe (suffix (car mergedcode) all-merged-code))
(next-stackframe mergedcode)))))
;; Thu Dec 29 17:57:49 2005
;;
;; complication if there is duplicated entries in mergedcode
;;
(defthm is-suffix-not-nil-member
(implies (and (is-suffix mergedcode all-merged-code)
(consp mergedcode))
(member (CAR MERGEDCODE)
ALL-MERGED-CODE))
:rule-classes :forward-chaining)
(defthm isStackMap-car-consp
(implies (isStackMap (car mergedcode))
(consp mergedcode))
:rule-classes :forward-chaining)
(encapsulate ()
(local (include-book "bcv-pc-wff-mergedcode1"))
(defthm is-suffix-pc-wff-mergecode1
(implies (and (is-suffix mergedcode1 mergedcode)
(consp mergedcode1)
(not (isEnd (car mergedcode1)))
(pc-wff-mergedcode1 pc mergedcode))
(pc-wff-mergedcode1 (next-pc mergedcode1)
mergedcode1))
:rule-classes :forward-chaining)
(defthm pc-wff-mergedcode1-isStackMap-consp-remaining
(implies (and (pc-wff-mergedcode1 pc mergedcode)
(isStackMap (car mergedcode)))
(consp (cdr mergedcode)))
:rule-classes :forward-chaining))
;; (i-am-here) ;; Sun Jan 1 20:22:02 2006
(defthm pc-wff-mergedcode1-isStackMap-consp-remaining-specific
(implies
(AND (ISSTACKMAP MERGEDCODE1)
(IS-SUFFIX (CONS MERGEDCODE1 MERGEDCODE2)
ALL-MERGED-CODE)
(PC-WFF-MERGEDCODE1 PC ALL-MERGED-CODE))
(consp mergedcode2))
:hints (("Goal" :use ((:instance
pc-wff-mergedcode1-isStackMap-consp-remaining
(mergedcode (cons mergedcode1 mergedcode2))
(pc (next-pc (cons mergedcode1 mergedcode2))))
(:instance
is-suffix-pc-wff-mergecode1
(mergedcode1 (cons mergedcode1 mergedcode2))
(mergedcode all-merged-code)))
:in-theory (disable isstackmap pc-wff-mergedcode1
isEnd isInstruction
is-suffix-pc-wff-mergecode1
pc-wff-mergedcode1-isStackMap-consp-remaining
is-suffix)))
:rule-classes :forward-chaining)
(defthm pc-wff-mergedcode1-mapOffset-equal-forward-to-next-inst
(implies (and (pc-wff-mergedcode1 pc mergedcode)
(isstackmap (car mergedcode)))
(equal (instrOffset (car (forward-to-next-inst mergedcode)))
(mapOffset (getMap (car mergedcode)))))
:hints (("Goal" :in-theory (disable isInstruction instrOffset mapOffset
isstackmap isend))))
(defthm searchStackFrame-is-if-stack-map
(implies (and (isStackMap (car mergedcode))
(equal (forward-to-next-inst mergedcode)
(forward-to-next-inst x))
(is-suffix mergedcode all-merged-code)
(PC-WFF-MERGEDCODE1 PC ALL-MERGED-CODE)
(mergedcodeistypesafe env all-merged-code init-frame))
(EQUAL
(SEARCHSTACKFRAME
(INSTROFFSET (CAR (FORWARD-TO-NEXT-INST x)))
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV all-merged-code
INIT-FRAME)))
(NEXT-STACKFRAME mergedcode)))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
sig-do-inst
allinstructions
isEnd
jvm::inst-size
mapFrame
getMap mapOffset
frameIsAssignable
isInstruction
isStackMap)
:use ((:instance collect-sig-frame-vector-collect-last-frame
(frame (car mergedcode))
(mergedcode all-merged-code))))))
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