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|
(in-package "BCV")
(include-book "typechecker")
(include-book "typechecker-ext")
(include-book "typechecker-simple")
(include-book "bcv-base")
;----------------------------------------------------------------------
(defthm mergedcodeIsTypesafe-implies-all-good-frames
(implies (and (mergedcodeIsTypesafe env mergedcode init-frame)
(all-good-frames (extract-frames mergedcode) env)
(good-frame init-frame env)
(good-env env))
(all-good-frames (stack-map-wrap
(collect-sig-frame-vector env mergedcode
init-frame))
env))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
sig-do-inst
allinstructions
isEnd
good-frame
mapFrame
getMap mapOffset
frameIsAssignable
isInstruction
isStackMap))))
(defun offset-found (pc l)
(if (endp l) nil
(or (equal (mapOffset (getMap (car l))) pc)
(offset-found pc (cdr l)))))
(defun all-stack-frames (l)
(if (endp l) t
(and (isstackmapframe (car l))
(all-stack-frames (cdr l)))))
(defthm all-stack-frame-stack-map-wrap
(all-stack-frames (stack-map-wrap l)))
(defthm all-good-frames-found-then-good
(implies (and (all-good-frames l env)
(all-stack-frames l)
(offset-found pc l))
(good-frame (searchstackframe pc l) env))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable good-frame
isStackMap
mapOffset
mapFrame
getMap))))
(defthm mergedcodeIsTypesafe-offset-found
(implies (and (mergedcodeIsTypesafe env mergedcode init-frame)
(member inst mergedcode)
(isInstruction inst))
(offset-found (instrOffset inst)
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV mergedcode
INIT-FRAME))))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
sig-do-inst
allinstructions
isEnd
good-frame
mapFrame
getMap mapOffset
frameIsAssignable
isInstruction
isStackMap))))
(defthm good-frame-searchStackMap
(implies (and (mergedcodeIsTypesafe env mergedcode init-frame)
(member inst mergedcode)
(isInstruction inst)
(all-good-frames (extract-frames mergedcode) env)
(good-frame init-frame env)
(good-env env))
(good-frame (searchstackframe (instrOffset inst)
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV mergedcode
INIT-FRAME)))
env))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
sig-do-inst
allinstructions
isEnd
good-frame
mapFrame
getMap mapOffset
frameIsAssignable
isInstruction
isStackMap))))
(local
(defthm is-suffix-wff-merged-code-instr-2
(implies (and (wff-mergedcode-instr mergedcode)
(isStackMap (car mergedcode)))
(isInstruction (car (forward-to-next-inst mergedcode))))))
(local
(defthm is-suffix-wff-merged-code-instr-wff-merged-code-instr
(implies (and (is-suffix mergedcode1 mergedcode2)
(wff-mergedcode-instr mergedcode2))
(wff-mergedcode-instr mergedcode1))
:rule-classes :forward-chaining))
(local
(defthm is-suffix-suffix
(implies (member frame mergedcode)
(is-suffix (suffix frame mergedcode) mergedcode))))
(local
(defthm equal-car-suffix-is-frame
(implies (member frame mergedcode)
(equal (car (suffix frame mergedcode))
frame))))
(defthm frame-pc-is-equal-some-pc
(implies (and (wff-mergedcode-instr mergedcode)
(member frame mergedcode)
(isStackMap frame))
(isInstruction
(car (forward-to-next-inst (suffix frame mergedcode)))))
:hints (("Goal" :in-theory (disable suffix
isInstruction
wff-mergedcode-instr isStackMap)
:use ((:instance
is-suffix-wff-merged-code-instr-wff-merged-code-instr
(mergedcode1 (suffix frame mergedcode))
(mergedcode2 mergedcode))))))
(local
(defthm is-suffix-wff-stack-map-offset
(implies (and (wff-stack-map-offset mergedcode)
(wff-mergedcode-instr mergedcode)
(isStackMap (car mergedcode)))
(equal (mapOffset (getMap (car mergedcode)))
(instrOffset (car (forward-to-next-inst mergedcode)))))))
(local
(defthm is-suffix-wff-stack-map-offset-wff-stack-map-offset
(implies (and (is-suffix mergedcode1 mergedcode2)
(wff-stack-map-offset mergedcode2))
(wff-stack-map-offset mergedcode1))
:rule-classes :forward-chaining))
(defthm frame-pc-is-equal-some-pc-2
(implies (and (wff-stack-map-offset mergedcode)
(wff-mergedcode-instr mergedcode)
(member frame mergedcode)
(isStackMap frame))
(equal (mapOffset (getMap frame))
(instrOffset (car (forward-to-next-inst (suffix frame mergedcode))))))
:hints (("Goal" :in-theory (disable suffix
isEnd
forward-to-next-inst
wff-mergedcode-instr
is-suffix-wff-stack-map-offset
wff-stack-map-offset
isStackMap
isInstruction
mapOffset
getMap)
:use ((:instance
is-suffix-wff-merged-code-instr-wff-merged-code-instr
(mergedcode1 (suffix frame mergedcode))
(mergedcode2 mergedcode))
(:instance
is-suffix-wff-stack-map-offset-wff-stack-map-offset
(mergedcode1 (suffix frame mergedcode))
(mergedcode2 mergedcode))
(:instance
is-suffix-wff-stack-map-offset
(mergedcode (suffix frame mergedcode)))))))
(local
(defthm is-suffix-wff-merged-code-instr-3
(implies (and (wff-mergedcode-instr mergedcode)
(isStackMap (car mergedcode)))
(member (car (forward-to-next-inst mergedcode))
mergedcode))))
(local
(defthm member-suffix-member-all
(implies (member inst (suffix x mergedcode))
(member inst mergedcode))))
(defthm frame-pc-is-equal-some-pc-3
(implies (and (wff-mergedcode-instr mergedcode)
(member frame mergedcode)
(isStackMap frame))
(member (car (forward-to-next-inst (suffix frame mergedcode)))
mergedcode))
:hints (("Goal" :in-theory (disable suffix
isEnd
forward-to-next-inst
wff-mergedcode-instr
is-suffix-wff-stack-map-offset
wff-stack-map-offset
isStackMap
isInstruction
mapOffset
getMap)
:use ((:instance
is-suffix-wff-merged-code-instr-wff-merged-code-instr
(mergedcode1 (suffix frame mergedcode))
(mergedcode2 mergedcode))
(:instance
member-suffix-member-all
(inst (car (forward-to-next-inst (suffix frame mergedcode))))
(x frame))))))
(defthm mergedcodeIsTypesafe-offset-found-2
(implies (and (mergedcodeIsTypesafe env mergedcode init-frame)
(wff-mergedcode-instr mergedcode)
(wff-stack-map-offset mergedcode)
(member frame mergedcode)
(isStackMap frame))
(offset-found (mapOffset (getMap frame))
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV mergedcode
INIT-FRAME))))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
sig-do-inst
allinstructions
isEnd
jvm::inst-size
good-frame
mapFrame
getMap mapOffset
frameIsAssignable
isInstruction
isStackMap))))
(defthm good-frame-searchStackMap-2
(implies (and (mergedcodeIsTypesafe env mergedcode init-frame)
(all-good-frames (extract-frames mergedcode) env)
(member frame mergedcode)
(isStackMap frame)
(wff-mergedcode-instr mergedcode)
(wff-stack-map-offset mergedcode)
(good-frame init-frame env)
(good-env env))
(good-frame (searchstackframe (mapOffset (getMap frame))
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV mergedcode
INIT-FRAME)))
env))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
sig-do-inst
allinstructions
isEnd
jvm::inst-size
good-frame
mapFrame
getMap mapOffset
frameIsAssignable
isInstruction
isStackMap)
:do-not-induct t
:use ((:instance good-frame-searchStackMap
(inst (car (forward-to-next-inst (suffix frame
mergedcode)))))))))
|
