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|
(in-package "BCV")
(include-book "typechecker")
(include-book "typechecker-ext")
(include-book "typechecker-simple")
(include-book "bcv-base")
(defthm extract-frame-pc-subset-extract-pc
(implies (member pc (extract-frame-pc
(collect-sig-frame-vector env mergedcode stackmap)))
(member pc (extract-pc (extract-code mergedcode))))
:hints (("Goal" :in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
jvm::inst-size
next-pc
sig-do-inst
isstackmap
makestackmap
allinstructions
isEnd
mapFrame
getMap
mapOffset
frameIsAssignable
isInstruction
isStackMap))))
;;;
;;; need a good library of is-suffix and is-subsequence
;;;
;; (defthm ordered-implies-ordered2
;; (iff (ordered l)
;; (ordered2 l)))
(defthm subsetp-extract-code-l
(subsetp (extract-code l) l))
(defthm member-x-member-extract-pc
(implies (and (member x (extract-pc l1))
(subsetp l1 l2)
(wff-merged-code-weak l2))
(member x (extract-pc l2))))
(defthm subsetp-cdr-subsetp
(implies (subsetp l1 l2)
(subsetp (cdr l1) l2)))
(defthm member-x-mermber-extract-pc
(implies (and (member x l)
(isInstruction x)
(wff-merged-code-weak l))
(member (instrOffset x) (extract-pc l)))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable isInstruction isStackMap
isEnd instrOffset
mapOffset))))
(defthm member-x-mermber-extract-pc-2
(implies (and (member x l)
(isStackMap x)
(wff-merged-code-weak l))
(member (mapOffset (getMap x)) (extract-pc l)))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable isInstruction isStackMap
isEnd instrOffset
getMap
mapOffset))))
(defthm subsetp-subsetp-extract-pc
(implies (and (subsetp l1 l2)
(wff-merged-code-weak l2))
(subsetp (extract-pc l1) (extract-pc l2)))
:hints (("Goal" :in-theory (disable isInstruction isStackMap
isEnd instrOffset getMap
mapOffset)
:do-not '(generalize))))
(defthm all-no-less-than-subsetp
(implies (and (all-no-less-than x s2)
(subsetp s1 s2))
(all-no-less-than x s1)))
(defthm all-no-less-than-all-no-less-than
(implies (and (all-no-less-than y l)
(< x y))
(all-no-less-than x l)))
(defthm pc-wff-mergedcode1-all-no-less
(implies (pc-wff-mergedcode1 pc mergedcode)
(all-no-less-than pc (extract-pc mergedcode)))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable isInstruction isStackMap
isEnd getMap instrOffset
mapOffset
jvm::inst-size))))
;; above not necessary!!
(defthm pc-wff-mergedcode1-ordered-pc
(implies (pc-wff-mergedcode1 pc mergedcode)
(ordered (extract-pc mergedcode)))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable isInstruction isStackMap
isEnd getMap instrOffset
mapOffset
jvm::inst-size))))
;; (skip-proofs
;; (defthm pc-wff-mergedcode1-ordered-pc-2
;; (implies (pc-wff-mergedcode1 pc mergedcode)
;; (ordered2 (extract-pc mergedcode)))
;; :hints (("Goal" :in-theory (disable isInstruction isStackMap
;; isEnd
;; jvm::inst-size)))
;; :rule-classes :forward-chaining))
;; (defthm ordered-ordered-extract-code
;; (implies (ordered2 (extract-pc l))
;; (ordered2 (extract-pc (extract-code l))))
;; :hints (("Goal" :in-theory (disable isInstruction isStackMap
;; instrOffset)
;; :do-not '(generalize))))
(defthm all-strictly-less-if-less-than-first-orderred
(implies (and (ordered l)
(< pc (car l)))
(all-strictly-less-than pc l)))
(defthm pc-wff-mergedcode1-isInstruction-then-next-pc-is-greater-lemma
(implies (and (pc-wff-mergedcode1 pc mergedcode)
(consp mergedcode)
(isInstruction (car mergedcode)))
(all-strictly-less-than pc (extract-pc (cdr mergedcode))))
:hints (("Goal" :do-not '(generalize)
:do-not-induct t
:use ((:instance all-strictly-less-if-less-than-first-orderred
(l (extract-pc (cdr mergedcode)))))
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
;;ordered-implies-ordered2
all-strictly-less-if-less-than-first-orderred
pc-wff-mergedcode1-ordered-pc
jvm::inst-size
next-pc
sig-do-inst
isstackmap
makestackmap
allinstructions
isEnd
mapFrame
getMap
mapOffset
frameIsAssignable
isInstruction
isStackMap))
("Subgoal 2" :use ((:instance pc-wff-mergedcode1-ordered-pc
(pc (+ (JVM::INST-SIZE (car MERGEDCODE))
(INSTROFFSET (car MERGEDCODE))))
(mergedcode (cdr mergedcode)))))
("Subgoal 1" :expand (PC-WFF-MERGEDCODE1 (+ (JVM::INST-SIZE MERGEDCODE1)
(INSTROFFSET MERGEDCODE1))
MERGEDCODE2))))
(defthm all-strictly-less-than-subsetp
(implies (and (all-strictly-less-than x s2)
(subsetp s1 s2))
(all-strictly-less-than x s1)))
(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)))))
:hints (("Goal" :do-not '(generalize)
:do-not-induct t
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
;;ordered-implies-ordered2
all-strictly-less-if-less-than-first-orderred
pc-wff-mergedcode1-ordered-pc
jvm::inst-size
next-pc
sig-do-inst
isstackmap
makestackmap
allinstructions
isEnd
mapFrame
getMap
mapOffset
frameIsAssignable
isInstruction
isStackMap)
:use ((:instance all-strictly-less-than-subsetp
(s2 (extract-pc (cdr mergedcode)))
(s1 (extract-pc (extract-code (cdr mergedcode))))
(x pc))))))
(defthm pc-wff-mergedcode1-isInstruction-then-next-pc-is-greater-specific
(implies (and (PC-WFF-MERGEDCODE1 (+ (JVM::INST-SIZE MERGEDCODE1)
(INSTROFFSET MERGEDCODE1))
MERGEDCODE2)
(<= 1 (JVM::INST-SIZE MERGEDCODE1))
(isInstruction mergedcode1))
(all-strictly-less-than (instroffset mergedcode1)
(extract-pc (extract-code mergedcode2))))
:hints (("Goal" :do-not '(generalize)
:do-not-induct t
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
;;ordered-implies-ordered2
all-strictly-less-if-less-than-first-orderred
pc-wff-mergedcode1-ordered-pc
jvm::inst-size
next-pc
sig-do-inst
isstackmap
makestackmap
allinstructions
isEnd
mapFrame
getMap
mapOffset
frameIsAssignable
isInstruction
isStackMap)
:use ((:instance
pc-wff-mergedcode1-isInstruction-then-next-pc-is-greater
(pc (instrOffset mergedcode1))
(mergedcode (cons mergedcode1
mergedcode2)))))))
(defthm subset-cons
(implies (subsetp x l)
(subsetp x (cons y l))))
(defthm subsetp-extract-frame-pc-subset-pc
(subsetp (extract-frame-pc (collect-sig-frame-vector env mergedcode frame))
(extract-pc (extract-code 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))))
;;; no need to go through these troubles!!!
(defthm all-strictly-less-than-subsetp-specific
(implies (all-strictly-less-than x (extract-pc (extract-code mergedcode)))
(all-strictly-less-than x (extract-frame-pc
(collect-sig-frame-vector env mergedcode
init-frame))))
:hints (("Goal" :in-theory (disable extract-frame-pc extract-pc extract-code
all-strictly-less-than collect-sig-frame-vector))))
(defthm pc-wff-mergedcode1-pc-wff-merged-code1
(implies (and (PC-WFF-MERGEDCODE1 pc MERGEDCODE2)
(case-split (not (isEnd (car mergedcode2)))))
(pc-wff-mergedcode1 (next-pc mergedcode2) mergedcode2))
:hints (("Goal" :in-theory (disable isInstruction instrOffset
isStackMap mapOffset
jvm::inst-size
isEnd)
:do-not '(generalize))))
(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))))
: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)
:induct (collect-sig-frame-vector env mergedcode init-frame))))
|
