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|
(in-package "BCV")
(include-book "typechecker")
(include-book "typechecker-ext")
(include-book "typechecker-simple")
(include-book "bcv-base")
(defthm is-suffix-then-is-suffix-suffix
(implies (and (is-suffix mergedcode all-merged-code)
(consp mergedcode))
(is-suffix mergedcode (suffix (car mergedcode) all-merged-code))))
;; (defun prefix (mergedcode1 mergedcode)
;; (if (equal mergedcode mergedcode1) nil
;; (if (endp mergedcode) "impossible"
;; (cons (car mergedcode)
;; (prefix mergedcode1 (cdr mergedcode))))))
(defun all-stack-frame (frames)
(if (endp frames) t
(and (isStackMap (car frames))
(all-stack-frame (cdr frames)))))
(defthm next-stackframe-append-stack-frames-in-front
(implies (and (isStackMap frame)
(isStackMap (car any)))
(equal (next-stackframe (cons frame any))
(next-stackframe any)))
:hints (("Goal" :in-theory (disable isInstruction
isStackMap
isEnd))))
(defun induct-append (frames any)
(if (endp frames) (list frames any)
(induct-append (cdr frames)
(cons (car frames) any))))
(defthm next-stackframe-append-stack-frames-in-front-2
(implies (and (all-stack-frame frames)
(isStackMap (car any)))
(equal (next-stackframe (append frames any))
(next-stackframe any)))
:hints (("Goal" :in-theory (disable isInstruction
isStackMap
next-stackframe
isEnd)
:do-not '(generalize fertilize)
:induct (induct-append frames any))))
(defthm suffix-is-append-prefix
(implies (is-suffix mergedcode1 mergedcode)
(equal (append (prefix mergedcode1 mergedcode)
mergedcode1)
mergedcode)))
;----------------------------------------------------------------------
;; (defthm member-instruction
;; (implies (and (member instr prefix)
;; (wff-stack-map-offset-2 (append prefix mergedcode))
;; (wff-merged-code-weak (append prefix mergedcode))
;; (ordered (extract-pc (append prefix mergedcode))))
;; (< (next-pc (car prefix))
;; (next-pc mergedcode)))
;; :hints (("Goal" :in-theory (disable isInstruction isStackMap
;; isEnd mapOffset instrOffset))))
(defun all-less-than (x l)
(if (endp l) t
(and (<= (car l) x)
(all-less-than x (car l)))))
(defun wff-merged-code-weak-2 (l)
(if (endp l) t
(and (or (isStackMap (car l))
(isInstruction (car l)))
(wff-merged-code-weak-2 (cdr l)))))
(defthm wff-stack-map-offset-2-implies-strictly-less-than
(implies (and (wff-stack-map-offset-2 mergedcode)
(wff-merged-code-weak-2 mergedcode)
(member inst mergedcode)
(isInstruction inst)
(consp (cdr (suffix inst mergedcode))))
(< (instrOffset inst)
(next-pc (cdr (suffix inst mergedcode))))))
(defthm wff-stack-map-offset-2-wff-stack-map-offset
(implies (wff-stack-map-offset-2 (append prefix (cons x any)))
(wff-stack-map-offset-2 (append prefix (list x))))
:hints (("Goal" :in-theory (disable isEnd isInstruction isStackMap
instrOffset
mapOffset next-pc)
:do-not '(generalize))))
(defthm wff-merged-code-weak-implies-wff-merged-code-weak-2
(implies (and (wff-merged-code-weak (append prefix (cons x any)))
(isStackMap x))
(wff-merged-code-weak-2 (append prefix (list x))))
:hints (("Goal" :in-theory (disable isEnd isInstruction isStackMap
instrOffset
mapOffset next-pc)
:do-not '(generalize))))
(defthm ordered-implies-no-less-than
(implies (and (member x l)
(ordered l))
(<= x (car (last l)))))
(defthm extract-pc-apppend
(implies (wff-merged-code-weak-2 (append prefix mergedcode))
(equal (extract-pc (append prefix mergedcode))
(append (extract-pc prefix) (extract-pc mergedcode)))))
(defthm car-last-append
(equal (car (last (append l (list x))))
x))
(defthm member-inst-member
(implies (and (member inst prefix)
(consp mergedcode))
(member (car (cdr (suffix inst (append prefix mergedcode))))
(append prefix mergedcode))))
(defthm member-pc-member
(implies (and (member inst mergedcode)
(wff-merged-code-weak-2 mergedcode)
(isInstruction inst))
(member (instrOffset inst) (extract-pc mergedcode)))
:hints (("Goal" :in-theory (disable isInstruction isStackMap
mapOffset
isEnd instrOffset))))
(defthm member-next-pc-member
(implies (and (member (car l) (append l1 l2))
(wff-merged-code-weak-2 (append l1 l2)))
(member (next-pc l)
(append (extract-pc l1)
(extract-pc l2)))))
(defthm ordered-append-nil
(equal (ordered (append l nil))
(ordered l)))
(defthm isStackMap-consp
(implies (ISSTACKMAP MERGEDCODE1)
(consp mergedcode1))
:rule-classes :forward-chaining)
(defthm ordered-append-1
(implies (ORDERED (append l1 l2))
(ordered l1))
:rule-classes :forward-chaining)
(defthm ordered-append-1-specific
(implies (ordered (extract-pc (append prefix (cons x l))))
(ordered (extract-pc (append prefix (list x)))))
:hints (("Goal" :in-theory (disable isEnd isInstruction isStackMap
instrOffset
mapOffset next-pc)
:do-not '(generalize)))
:rule-classes :forward-chaining)
(defthm ordered-append-1-specific-further
(implies (and (wff-merged-code-weak-2 (append prefix (list x)))
(isStackMap x))
(equal (extract-pc (append prefix (list x)))
(append (extract-pc prefix) (list (mapOffset (getMap x)))))))
(defthm member-inst-prefix
(implies (member inst prefix)
(CONSP (CDR (SUFFIX INST
(APPEND PREFIX (LIST MERGEDCODE1)))))))
(defthm member-inst-member-append
(implies (member inst prefix)
(MEMBER INST
(APPEND PREFIX (LIST MERGEDCODE1)))))
(defthm wff-stack-map-offset-member-then-last-pc-larger
(implies (and (ordered (extract-pc (append prefix mergedcode)))
(wff-stack-map-offset-2 (append prefix mergedcode))
(wff-merged-code-weak (append prefix mergedcode))
(isInstruction inst)
(consp mergedcode)
(isStackMap (car mergedcode))
(member inst prefix))
(< (instrOffset inst)
(mapOffset (getMap (car mergedcode)))))
:hints (("Goal" :in-theory (disable isEnd isInstruction isStackMap
instrOffset getMap
mapOffset next-pc)
:use ((:instance wff-stack-map-offset-2-implies-strictly-less-than
(mergedcode (append prefix (list (car
mergedcode)))))
(:instance ordered-implies-no-less-than
(x (NEXT-PC (CDR (SUFFIX INST
(APPEND PREFIX (LIST (car MERGEDCODE)))))))
(l (extract-pc (append prefix (list (car
mergedcode))))))
(:instance member-inst-member
(mergedcode (append prefix (list (car
mergedcode)))))
(:instance member-next-pc-member
(l (cdr (suffix inst (append prefix (list (car
mergedcode))))))
(l1 prefix)
(l2 (list (car mergedcode))))
(:instance wff-merged-code-weak-implies-wff-merged-code-weak-2
(x (car mergedcode))
(any (cdr mergedcode)))
(:instance ordered-append-1-specific
(x (car mergedcode))
(l (cdr mergedcode))))
:do-not-induct t))
:rule-classes :linear)
;; stupid!! Fri Dec 30 20:56:18 2005
;----------------------------------------------------------------------
(defthm extract-pc-is-consp
(implies (and (WFF-MERGED-CODE-WEAK (APPEND PREFIX MERGEDCODE))
(isStackMap (car mergedcode)))
(CONSP (EXTRACT-PC (APPEND PREFIX MERGEDCODE)))))
(defthm extract-pc-ordered-fact
(implies (and (ORDERED (EXTRACT-PC (APPEND PREFIX mergedcode)))
(wff-merged-code-weak (append prefix mergedcode))
(isStackMap (car mergedcode)))
(<= (car (extract-pc (append prefix mergedcode)))
(mapOffset (getMap (car mergedcode)))))
:hints (("Goal" :in-theory (disable isEnd isInstruction isStackMap
instrOffset getMap
mapOffset)))
:rule-classes :forward-chaining)
(defthm wff-merged-code-weak-never-end
(implies (and (wff-merged-code-weak (append prefix mergedcode))
(isStackMap (car mergedcode)))
(not (isEnd (car (append prefix mergedcode)))))
:hints (("Goal" :in-theory (disable isEnd isInstruction isStackMap
instrOffset getMap
mapOffset))))
;----------------------------------------------------------------------
(defthm wff-stack-map-offset-2-implies-all-frames-lemma
(implies (and (wff-stack-map-offset-2 (append prefix mergedcode))
(wff-merged-code-weak (append prefix mergedcode))
(isStackMap (car mergedcode))
(ordered (extract-pc (append prefix mergedcode)))
(equal (next-pc prefix)
(mapOffset (getMap (car mergedcode)))))
(all-stack-frame prefix))
:hints (("Goal" :in-theory (disable isEnd isInstruction isStackMap
instrOffset getMap
mapOffset)
:do-not '(generalize fertilize))))
;----------------------------------------------------------------------
(defthm car-prefix-is-car
(implies (and (is-suffix mergedcode1 mergedcode)
(not (equal mergedcode1 mergedcode))
(consp mergedcode))
(equal (car (prefix mergedcode1 mergedcode))
(car mergedcode))))
;; (NEXT-PC (PREFIX MERGEDCODE1 MERGEDCODE))
(defthm wff-stack-map-offset-2-implies-all-frames
(implies (and (wff-stack-map-offset-2 mergedcode)
(wff-merged-code-weak mergedcode)
(ordered (extract-pc mergedcode))
(is-suffix mergedcode1 mergedcode)
(isStackMap (car mergedcode1))
(isStackMap (car mergedcode))
(equal (mapOffset (getMap (car mergedcode)))
(mapOffset (getMap (car mergedcode1)))))
(all-stack-frame (prefix mergedcode1 mergedcode)))
:hints (("Goal" :in-theory (disable isEnd isInstruction isStackMap
instrOffset getMap
mapOffset)
:do-not-induct t
:cases ((equal mergedcode1 mergedcode)))
("Subgoal 2" :use ((:instance wff-stack-map-offset-2-implies-all-frames-lemma
(prefix (prefix mergedcode1 mergedcode))
(mergedcode mergedcode1))))))
;----------------------------------------------------------------------
;; (defthm next-stackframe-append-stack-frames-in-front-2
;; (implies (and (all-stack-frame frames)
;; (isStackMap (car any)))
;; (equal (next-stackframe (append frames any))
;; (next-stackframe any)))
;; :hints (("Goal" :in-theory (disable isInstruction
;; isStackMap
;; next-stackframe
;; isEnd)
;; :do-not '(generalize fertilize)
;; :induct (induct-append frames any))))
(defthm is-suffix-suffix
(implies (member x l)
(IS-SUFFIX (SUFFIX x l) l)))
(defthm car-suffix-is-car
(implies (member x all-merged-code)
(equal (car (SUFFIX x ALL-MERGED-CODE))
x)))
(defthm wff-stack-map-offset-2-suffix
(implies (and (wff-stack-map-offset-2 all-merged-code)
(member x all-merged-code))
(WFF-STACK-MAP-OFFSET-2 (SUFFIX x ALL-MERGED-CODE))))
(defthm wff-merged-code-weak-suffix
(implies (and (wff-merged-code-weak all-merged-code)
(member x all-merged-code)
(not (isEnd x)))
(WFF-MERGED-CODE-WEAK (SUFFIX x ALL-MERGED-CODE))))
(defthm ordered-suffix
(implies (and (ordered (extract-pc all-merged-code))
(member x all-merged-code)
(wff-merged-code-weak all-merged-code))
(ORDERED (EXTRACT-PC (SUFFIX x ALL-MERGED-CODE))))
:hints (("Goal" :in-theory (disable isEnd isInstruction isStackMap
instrOffset getMap
mapOffset))))
(defthm is-suffix-suffix-2
(implies (and (is-suffix mergedcode all-merged-code)
(consp mergedcode))
(IS-SUFFIX MERGEDCODE (SUFFIX (CAR MERGEDCODE) ALL-MERGED-CODE))))
(defthm isStackMap-consp-x
(implies (isStackMap (car mergedcode))
(consp mergedcode))
:rule-classes :forward-chaining)
(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)))
:hints (("Goal" :in-theory (disable isInstruction
isStackMap
isEnd
next-stackframe
mapOffset
mapFrame
instrOffset
getMap)
:do-not-induct t
:do-not '(generalize fertilize)
:use ((:instance next-stackframe-append-stack-frames-in-front-2
(frames (prefix mergedcode
(suffix (car mergedcode)
all-merged-code)))
(any mergedcode))))))
;----------------------------------------------------------------------
|
