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|
(in-package "ACL2")
(include-book "bcv-model")
(local (encapsulate ()
;;; wrap around in local encapsulate!!
;----------------------------------------------------------------------
(defthm collect-witness-merged-code-safe-pc-not-out-of-bound
(implies (not (member pc (collect-pc-merged-code merged-code)))
(not (assoc-equal pc (collect-witness-merged-code-safe
merged-code
sig-frame))))
:hints (("Goal" :do-not '(generalize fertilize))))
;----------------------------------------------------------------------
(defun last-but-one (merged-code)
(if (endp merged-code) nil
(if (endp (cdr merged-code)) nil
(if (equal (cadr merged-code) 'END_OF_CODE)
(car merged-code)
(last-but-one (cdr merged-code))))))
;----------------------------------------------------------------------
(defthm last-merged-code-is-inst
(implies (and (merged-code-safe merged-code sig-frame)
(consp (cdr merged-code)))
(inst? (last-but-one merged-code))))
;; above is slow!!
(defthm inst-implies-pc-properly-bounded
(implies (and (wff-code1 code1 pc)
(member inst code1))
(< (g 'pc inst)
(+ pc (len code1)))))
;----------------------------------------------------------------------
(defthm last-pc-equal
(implies (and (merged-code-safe merged-code sig-frame)
(consp (cdr merged-code)))
(equal (car (last (collect-pc-merged-code merged-code)))
(g 'pc (last-but-one merged-code))))
:hints (("Goal" :do-not '(generalize))))
;;; this is slow!!! not disable any thing.
(encapsulate ()
(local (include-book "bcv-if-verified-then-pc-ordered"))
(defthm merged-code-is-safe-implies-ordered
(implies (and (merged-code-safe merged-code init-frame)
(wff-code1 (extract-code merged-code)
(g 'pc (car merged-code))))
(ordered (collect-pc-merged-code merged-code)))))
(defthm ordered-implies-last-biggest
(implies (and (ordered l)
(member pc l))
(<= pc (car (last l))))
:rule-classes :linear)
(defthm member-collect-pc-implies-consp-cdr
(implies (member pc (collect-pc-merged-code merged-code))
(consp (cdr merged-code)))
:rule-classes :forward-chaining)
(defthm last-but-one-is-biggest
(implies (and (merged-code-safe merged-code init-frame)
(wff-code1 (extract-code merged-code)
(g 'pc (car merged-code)))
(member pc (collect-pc-merged-code merged-code)))
(<= pc (g 'pc (last-but-one merged-code))))
:hints (("Goal" :do-not-induct t
:in-theory (disable merged-code-safe
extract-code
last-pc-equal
collect-pc-merged-code)
:use ((:instance last-pc-equal
(sig-frame init-frame)))))
:rule-classes :linear)
;----------------------------------------------------------------------
(defthm inst-implies-member-extract-code
(implies (and (inst? inst)
(equal (car (last merged-code)) 'END_OF_CODE)
(member inst merged-code))
(member inst (extract-code merged-code))))
;; now it is time to prove
(defthm last-but-one-is-a-member
(implies (and (consp (cdr merged-code))
(equal (car (last merged-code)) 'END_OF_CODE))
(member (last-but-one merged-code) merged-code)))
(defthm merged-code-safe-last-merge-code-is-end-of-code
(implies (merged-code-safe merged-code init-frame)
(equal (car (last merged-code)) 'END_OF_CODE))
:rule-classes :forward-chaining)
(defthm member-in-merged-code-implies-pc-less-lemma
(implies (and (merged-code-safe merged-code init-frame)
(wff-code1 (extract-code merged-code)
(g 'pc (car merged-code)))
(consp (cdr merged-code)))
(< (g 'pc (last-but-one merged-code))
(+ (g 'pc (car merged-code))
(len (extract-code merged-code)))))
:hints (("Goal" :in-theory (disable merged-code-safe
wff-code1
extract-code
last-but-one)))
:rule-classes :linear)
(defthm member-in-merged-code-implies-pc-less
(implies (and (merged-code-safe merged-code init-frame)
(wff-code1 (extract-code merged-code)
(g 'pc (car merged-code)))
(member pc (collect-pc-merged-code merged-code)))
(< pc
(+ (g 'pc (car merged-code))
(len (extract-code merged-code)))))
:hints (("Goal" :in-theory (disable merged-code-safe
wff-code1
extract-code
last-but-one)))
:rule-classes :linear)
;----------------------------------------------------------------------
(encapsulate ()
(local (include-book "bcv-succeed-implies-bcv-simple-succeed"))
(defthm extract-code-mergeStackMapAndCode
(implies (and (equal (car (last (mergeStackMapAndCode maps code method-name method-table)))
'END_OF_CODE)
(wff-code1 code pc))
(equal (extract-code (mergeStackMapAndCode maps code method-name method-table))
code))
:hints (("Goal" :in-theory (enable inst?)))))
(encapsulate ()
(local (include-book "bcv-succeed-implies-bcv-simple-succeed"))
(defthm merged-code-car-pc-same-as-code-specific
(implies (merged-code-safe (mergeStackMapAndCode maps code method-name method-table)
(SIG-METHOD-INIT-FRAME METHOD METHOD-TABLE))
(equal (g 'pc (car (mergeStackMapAndCode maps code method-name method-table)))
(g 'pc (car code))))))
(defthm g-pc-is-zero-from-parsecode1
(implies (CONSP (PARSECODE1 pc code))
(equal (g 'pc (car (parsecode1 pc code)))
pc)))
(defthm parsecode1-len-equal
(equal (len (parsecode1 any code))
(len code)))
;; (defthm collect-witness-merged-code-safe-pc-not-out-of-bound
;; (implies (not (member pc (collect-pc-merged-code merged-code)))
;; (not (assoc-equal pc (collect-witness-merged-code-safe
;; merged-code
;; sig-frame))))
;; :hints (("Goal" :do-not '(generalize fertilize))))
(defun wff-merged-code (merged-code)
(if (endp merged-code) t
(if (endp (cdr merged-code)) t
(and (or (inst? (car merged-code))
(stack-map? (car merged-code)))
(wff-merged-code (cdr merged-code))))))
(defthm member-pc-implies-integerp
(implies (and (member pc (collect-pc-merged-code merged-code))
(wff-merged-code merged-code))
(integerp pc))
:hints (("Goal" :do-not '(generalize)))
:rule-classes :forward-chaining)
(defthm make-inst-inst
(implies (inst? inst)
(inst? (make-inst inst)))
:hints (("Goal" :in-theory (enable make-inst inst?))))
(defthm stack-map-make-stack-map
(IMPLIES (STACK-MAP? MAPS1)
(STACK-MAP? (MAKESTACKMAP MAPS1 method-name METHOD-TABLE)))
:hints (("Goal" :in-theory (enable stack-map?))))
(defthm wff-code1-implies-wff-merge-code
(implies (wff-code1 code pc)
(wff-merged-code (append code (list any)))))
(defthm mergeStackMapAndCode-produce-wff-merged-code
(implies (and (wff-code1 code pc)
(wff-maps maps))
(wff-merged-code (mergeStackMapAndCode maps code method-name
method-table)))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable inst? make-inst
stack-map? makestackmap))))
(defthm member-pc-collect-pc-then-integerp-specific
(implies (and (member pc (collect-pc-merged-code
(mergeStackMapAndCode maps code method-name
method-table)))
(wff-maps maps)
(wff-code1 code pcx))
(integerp pc))
:hints (("Goal" :do-not '(generalize)
:use ((:instance member-pc-implies-integerp
(merged-code
(mergeStackMapAndCode maps code method-name
method-table))))))
:rule-classes :forward-chaining)
(encapsulate ()
(local (include-book "bcv-if-pc-small-then-not-bound-in-witness"))
(defthm merged-code-is-safe-implies-not-bound-smaller
(implies (and (merged-code-safe merged-code init-frame)
(WFF-CODE1 (EXTRACT-CODE MERGED-CODE)
(g 'pc (car merged-code)))
(< pc1 (g 'pc (car merged-code))))
(not (assoc-equal pc1 (collect-witness-merged-code-safe
merged-code init-frame))))))
))
;;(i-am-here)
(defthm bcv-method-implies-integerp-if-bound
(implies (and (bcv-method method method-table)
(assoc-equal pc (collect-witness-bcv-method method method-table)))
(integerp pc))
:hints (("Goal" :in-theory (disable merged-code-safe
;;collect-witness-bcv-method
extract-code
sig-method-init-frame
wff-code1)
:cases ((member pc (collect-pc-merged-code
(MERGESTACKMAPANDCODE (G 'STACKMAPS METHOD)
(PARSECODE1 0 (G 'CODE METHOD))
(G 'METHOD-NAME METHOD)
METHOD-TABLE))))))
:rule-classes :forward-chaining)
(defthm bcv-method-implies-not-bound-if-out-of-bound
(implies (and (bcv-method method method-table)
(assoc-equal pc (collect-witness-bcv-method method method-table)))
(< pc (len (g 'code method))))
:hints (("Goal" :in-theory (disable merged-code-safe
;;collect-witness-bcv-method
extract-code
member-in-merged-code-implies-pc-less
sig-method-init-frame
wff-code1)
:use ((:instance
member-in-merged-code-implies-pc-less
(merged-code
(MERGESTACKMAPANDCODE (G 'STACKMAPS METHOD)
(PARSECODE1 0 (G 'CODE METHOD))
(G 'METHOD-NAME METHOD)
METHOD-TABLE))
(init-frame
(SIG-METHOD-INIT-FRAME METHOD METHOD-TABLE)))))))
(defthm bcv-method-implies-not-bound-if-out-of-bound-specific
(implies (and (bcv-method (current-method st) (g 'method-table st))
(assoc-equal pc (collect-witness-bcv-method
(current-method st)
(g 'method-table st))))
(< pc (len (g 'code (current-method st)))))
:hints (("Goal" :in-theory (disable current-method
bcv-method
collect-witness-bcv-method)))
:rule-classes :linear)
(defthm bcv-method-implies-not-bound-if-out-of-bound-2
(implies (and (bcv-method method method-table)
(assoc-equal pc (collect-witness-bcv-method method method-table)))
(<= 0 pc))
:hints (("Goal" :in-theory (disable merged-code-safe
;;collect-witness-bcv-method
extract-code
member-in-merged-code-implies-pc-less
sig-method-init-frame
wff-code1)
:use ((:instance
merged-code-is-safe-implies-not-bound-smaller
(merged-code
(MERGESTACKMAPANDCODE (G 'STACKMAPS METHOD)
(PARSECODE1 0 (G 'CODE METHOD))
(G 'METHOD-NAME METHOD)
METHOD-TABLE))
(init-frame
(SIG-METHOD-INIT-FRAME METHOD METHOD-TABLE)))))))
(defthm bcv-method-implies-not-bound-if-out-of-bound-specific-2
(implies (and (bcv-method (current-method st) (g 'method-table st))
(assoc-equal pc (collect-witness-bcv-method
(current-method st)
(g 'method-table st))))
(<= 0 pc))
:hints (("Goal" :in-theory (disable current-method
bcv-method
collect-witness-bcv-method)))
:rule-classes :forward-chaining)
|
