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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-isAssignable-transitive"))
(defthm isAssignable-Transitive
(implies (and (good-bcv-type t1 icl)
(good-bcv-type t2 icl)
(good-bcv-type t3 icl)
(equal (classtableEnvironment env) scl)
(good-icl icl)
(good-scl scl)
(icl-scl-compatible icl scl)
(isAssignable t1 t2 env)
(isAssignable t2 t3 env))
(isAssignable t1 t3 env))
:hints (("Goal" :in-theory (e/d () (isjavaassignable good-scl jvm::primitive-type?))
:do-not '(generalize fertilize)))))
;; ;;;
;; ;;; transitive!!! ;;; problem with domain!!
;; ;;;
;;(include-book "bcv-good-env-encapsulate")
; Matt K. mod: Avoid raw Lisp error in tau; see similar disable in
; BCV/bcv-isAssignable-transitive.lisp.
(local (in-theory (disable (:e tau-system))))
(defthm typelist-assignable-transitive
(implies (and (good-env env)
(good-typelist l1 env)
(good-typelist l2 env)
(good-typelist l3 env)
(typelistassignable l1 l2 env)
(typelistassignable l2 l3 env))
(TYPELISTASSIGNABLE l1 l3 ENV))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable isAssignable
good-bcv-type
classtableEnvironment
icl-scl-compatible
good-icl good-scl))
("Subgoal *1/9" :use ((:instance isAssignable-Transitive
(icl (icl-witness env))
(scl (classtableEnvironment env))
(t1 (car l1))
(t2 (car l2))
(t3 (car l3)))))))
(defthm frameIsAssignable-transitive
(implies (and (frameIsAssignable frame1 frame2 env)
(frameIsAssignable frame2 frame3 env)
(good-env env)
(good-frame frame1 env)
(good-frame frame2 env)
(good-frame frame3 env))
(frameIsAssignable frame1 frame3 env)))
(encapsulate ()
(local (include-book "bcv-searchStackFrame-reduce-support"))
(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))))))
(defthm typelist-assignable-reflexive
(TYPELISTASSIGNABLE x x ENV))
(defthm frameisassignable-reflexive
(FRAMEISASSIGNABLE frame frame env))
(defun never-after-goto (frames)
(if (endp frames) t
(and (not (equal (mapFrame (getMap (car frames))) 'aftergoto))
(never-after-goto (cdr frames)))))
(defthm all-good-frames-extract-frames
(implies (and (all-good-frames (extract-frames mergedcode) env)
(consp mergedcode)
(wff-mergedcode-instr mergedcode)
(wff-merged-code-weak mergedcode)
(isStackMap (car mergedcode)))
(good-frame (next-stackframe mergedcode) env))
:hints (("Goal" :in-theory (disable isEnd isInstruction
mapFrame getMap
isStackMap
good-frame))))
(defthm frameIsAssignable-Transitive-specific-x
(implies (and (FRAMEISASSIGNABLE (MAPFRAME (GETMAP MERGEDCODE3))
(NEXT-STACKFRAME MERGEDCODE4)
ENV)
(FRAMEISASSIGNABLE (MAPFRAME (GETMAP MERGEDCODE1))
(MAPFRAME (GETMAP MERGEDCODE3))
ENV)
(GOOD-FRAME (MAPFRAME (GETMAP MERGEDCODE1))
ENV)
(GOOD-FRAME (MAPFRAME (GETMAP MERGEDCODE3))
ENV)
(consp mergedcode4)
(wff-merged-code-weak mergedcode4)
(wff-mergedcode-instr mergedcode4)
(ALL-GOOD-FRAMES (EXTRACT-FRAMES MERGEDCODE4)
ENV)
(good-env env)
(isStackMap (car mergedcode4)))
(FRAMEISASSIGNABLE (MAPFRAME (GETMAP MERGEDCODE1))
(NEXT-STACKFRAME MERGEDCODE4)
ENV))
:hints (("Goal" :in-theory (disable frameisassignable
good-frame
mapframe
getmap
isStackMap)
:do-not-induct t
:use ((:instance frameisassignable-transitive
(frame1 (MAPFRAME (GETMAP MERGEDCODE1)))
(frame2 (MAPFRAME (GETMAP MERGEDCODE3)))
(frame3 (next-stackframe mergedcode4)))))))
(defthm mergedcodeIsTypeSafe-implies-stackmap-assignable-lemma
(implies (and (mergedcodeIsTypeSafe env mergedcode init-frame)
(isStackMap (car mergedcode))
(never-after-goto (extract-frames mergedcode))
(wff-merged-code-weak mergedcode)
(wff-mergedcode-instr mergedcode)
(all-good-frames (extract-frames mergedcode) env)
(good-env env))
(frameisassignable (mapFrame (getMap (car mergedcode)))
(next-stackframe mergedcode) env))
: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
good-frame
frameIsAssignable
isInstruction
isStackMap))))
(defthm pc-wff-mergedcode1-never-aftergoto-x
(implies (pc-wff-mergedcode1 pc mergedcode)
(never-after-goto (extract-frames mergedcode)))
:rule-classes :forward-chaining
:hints (("Goal" :in-theory (disable isInstruction isEnd isStackMap
jvm::inst-size))))
(defthm pc-wff-mergedcode1-pc-implies-pc-next-pc
(implies (and (pc-wff-mergedcode1 pc mergedcode)
(not (isEnd (car mergedcode))))
(pc-wff-mergedcode1 (next-pc mergedcode)
mergedcode))
:rule-classes :forward-chaining
:hints (("Goal" :in-theory (disable isInstruction isEnd isStackMap
jvm::inst-size))))
(defthm pc-wff-mergedcode1-pc-implies-pc-next-pc-specific
(implies (and (pc-wff-mergedcode1 pc mergedcode)
(member stackmap mergedcode)
(isStackMap stackmap))
(pc-wff-mergedcode1 (next-pc mergedcode)
mergedcode))
:rule-classes :forward-chaining
:hints (("Goal" :in-theory (disable isInstruction isEnd isStackMap
jvm::inst-size))))
(defthm mergedcodeIsTypesafe-implies-stackmap-more-specific
(implies (and (mergedcodeIsTypesafe env mergedcode init-frame)
(pc-wff-mergedcode1 (next-pc mergedcode) mergedcode)
(member stackmap mergedcode)
(isStackmap stackmap)
(all-good-frames (extract-frames mergedcode) env)
(good-env env))
(frameisassignable (mapFrame (getMap stackmap))
(next-stackframe (suffix stackmap mergedcode))
env))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable instructionIsTypeSafe
instructionSatisfiesHandlers
instrOffset
jvm::inst-size
good-frame
sig-do-inst
isstackmap
makestackmap
allinstructions
isEnd
mapFrame
getMap
mapOffset
frameIsAssignable
isInstruction
isStackMap))))
;;;
;;; appears that lemma are not necessary!! once we manage to prove
;;;
;;; mergedcodeIsTypeSafe-implies-stackmap-assignable-lemma
;;;
;;;
;; (encapsulate ()
;; (local (include-book "bcv-searchStackFrame-reduce-support"))
;; (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))))))
(defthm mergedcodeIsTypesafe-implies-stackmap-searchStackFrame
(implies (and (mergedcodeIsTypesafe env mergedcode init-frame)
(member stackmap mergedcode)
(pc-wff-mergedcode1 pc mergedcode)
(member stackmap mergedcode)
(isStackmap stackmap)
(all-good-frames (extract-frames mergedcode) env)
(good-env env))
(frameisassignable (mapFrame (getMap stackmap))
(searchStackFrame
(mapOffset (getMap stackmap))
(stack-map-wrap
(collect-sig-frame-vector env mergedcode
init-frame)))
env))
:hints (("Goal" :in-theory (disable searchStackFrame
mapOffset getMap
mapFrame
next-pc
mergedcodeIsTypesafe
pc-wff-mergedcode1
collect-sig-frame-vector
jvm::inst-size
isStackmap good-frame
frameisassignable)
:restrict ((collect-sig-frame-vector-collect-last-frame
((pc pc)))
(mergedcodeIsTypesafe-implies-stackmap-more-specific
((init-frame init-frame))))
:do-not-induct t)))
(defthm member-good-frames
(implies (and (member x frames)
(all-good-frames frames env))
(good-frame (mapFrame (getMap x)) env))
:hints (("Goal" :in-theory (disable good-frame)))
:rule-classes :forward-chaining)
(defthm member-good-frames-b
(implies (and (member x frames)
(all-good-frames frames env))
(good-frame (mapFrame (getMap x)) env))
:hints (("Goal" :in-theory (disable good-frame))))
(defthm isStackmap-member-extract-frames
(implies (and (isStackmap frame)
(member frame mergedcode)
(wff-merged-code-weak mergedcode))
(member frame (extract-frames mergedcode))))
(defthm isStackmap-good-frame-specific
(implies (and (member x (allinstructions env))
(pc-wff-mergedcode1 0 (allinstructions env))
(isStackmap x)
(all-good-frames (extract-frames (allinstructions env)) env))
(good-frame (mapFrame (getMap x)) env))
:hints (("Goal" :in-theory (disable good-frame mapFrame getMap
isStackmap allinstructions)
:restrict ((member-good-frames-b
((frames (extract-frames (allinstructions env)))))))))
(defthm frameIsAssignable-transitive-specific
(implies (and (FRAMEISASSIGNABLE
(CAR
(SIG-DO-INST
MERGEDCODE1 ENV
(SEARCHSTACKFRAME
(INSTROFFSET MERGEDCODE1)
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV (ALLINSTRUCTIONS ENV)
INIT-FRAME)))))
(MAPFRAME (GETMAP MERGEDCODE3))
ENV)
(isStackMap mergedcode3)
(equal (mapOffset (getMap mergedcode3)) npc)
(member mergedcode3 (allinstructions env))
(pc-wff-mergedcode1 0 (allinstructions env))
(mergedcodeIsTypesafe env (allinstructions env) init-frame)
(GOOD-FRAME
(SEARCHSTACKFRAME
(MAPOFFSET (GETMAP MERGEDCODE3))
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV (ALLINSTRUCTIONS ENV)
INIT-FRAME)))
ENV)
(good-frame (SEARCHSTACKFRAME
(INSTROFFSET MERGEDCODE1)
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV (ALLINSTRUCTIONS ENV)
INIT-FRAME)))
env)
(all-good-frames (extract-frames (allinstructions env)) env)
(good-env env))
(FRAMEISASSIGNABLE
(CAR
(SIG-DO-INST
MERGEDCODE1 ENV
(SEARCHSTACKFRAME
(INSTROFFSET MERGEDCODE1)
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV (ALLINSTRUCTIONS ENV)
INIT-FRAME)))))
(SEARCHSTACKFRAME
npc
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV (ALLINSTRUCTIONS ENV)
INIT-FRAME)))
env))
:hints (("Goal" :restrict ((frameisassignable-transitive
((frame2 (MAPFRAME (GETMAP MERGEDCODE3)))
(frame1 (CAR
(SIG-DO-INST
MERGEDCODE1 ENV
(SEARCHSTACKFRAME
(INSTROFFSET MERGEDCODE1)
(STACK-MAP-WRAP (COLLECT-SIG-FRAME-VECTOR ENV (ALLINSTRUCTIONS ENV)
INIT-FRAME))))))))
(mergedcodeIsTypesafe-implies-stackmap-searchStackFrame
((init-frame init-frame)
(pc 0))))
:do-not-induct t
:in-theory (disable instructionIsTypeSafe
collect-sig-frame-vector-collect-last-frame
instructionSatisfiesHandlers
pc-wff-mergedcode1
good-frame
mergedcodeIsTypesafe
mergedcodeIsTypesafe-implies-stackmap-more-specific
instrOffset
sig-do-inst
allinstructions
isEnd
mapFrame
getMap mapOffset
frameIsAssignable
isInstruction
isStackMap))))
|
