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|
(in-package "ACL2")
(include-book "bcv-model")
(include-book "bcv-simple-model")
(include-book "generic")
;----------------------------------------------------------------------
;; This is not as straightforward as we would like to think:
;;; Because
;;;;; It is not obvious (to us and computer)
;;;;;
;;;;; if one has an instruction that instruction is a member of merged code
;;;;; then, there is we did a bcv-check-step-pre on it at some point
;;;;; during execution.
;;;;;
;;;;; It is not obvious that the stack map recorded into
;;;;; collect-witness-merged-code-safe will not be "masked" by a later stack
;;;;; map declared for the same pc!
;;;;;
;; (defthm merge-code-safe-implies-bcv-check-step-pre-lemma
;; (implies (and (merged-code-safe merged-code sig-frame)
;; (member inst merged-code)
;; (wff-code1 (extract-code merged-code)
;; (g 'pc (car merged-code)))
;; (inst? inst)
;; (equal pc (g 'pc inst))
;; (bound? pc (collect-witness-merged-code-safe
;; merged-code sig-frame)))
;; (bcv-check-step-pre inst
;; (cdr (assoc-equal pc
;; (collect-witness-merged-code-safe
;; merged-code sig-frame)))))
;; :hints (("Goal" :in-theory (e/d (merged-code-safe
;; collect-witness-merged-code-safe)
;; (bcv-check-step-pre inst?
;; sig-frame-compatible
;; stack-map?
;; bcv-execute-step))
;; :do-not '(generalize fertilize)
;; :induct (merged-code-safe merged-code sig-frame))))
(local
(encapsulate ()
(local
(defthm wff-code1-implies-not-member-lemma
(implies (and (wff-code1 code pc)
(< (g 'pc inst) pc))
(not (member inst code)))))
(defthm wff-code1-implies-not-member-lemma-specific
(implies (and (wff-code1 (extract-code merged-code) (+ 1 (g 'pc inst)))
(inst? inst))
(not (member inst (extract-code merged-code))))
:hints (("Goal" :use ((:instance wff-code1-implies-not-member-lemma
(code (extract-code merged-code))
(pc (+ 1 (g 'pc inst)))))
:in-theory (disable wff-code1-implies-not-member-lemma))))))
(local
(defthm inst-not-member-code-not-member-mergedcode-instance
(implies (and (not (member inst (extract-code merged-code)))
(equal (car (last merged-code)) 'END_OF_CODE)
(inst? inst))
(not (member inst merged-code)))))
(local
(defthm merged-code-safe-implies-end-with-end-of-code
(implies (merged-code-safe mergedcode init-frame)
(equal (car (last mergedcode))
'END_OF_CODE))
:hints (("Goal" :in-theory (enable merged-code-safe)))))
(local
(defthm |Subgoal *1/9.7|
(IMPLIES
(AND (MERGED-CODE-SAFE MERGED-CODE sig-frame)
(inst? inst)
(WFF-CODE1 (EXTRACT-CODE MERGED-CODE)
(+ 1 (G 'PC INST))))
(not (MEMBER INST MERGED-CODE)))
:hints (("Goal" :do-not-induct t))))
(defthm merged-code-safe-implies-extract-code-pc-is-same
(implies (and (merged-code-safe merged-code sig-frame)
(stack-map? (car merged-code)))
(equal (g 'pc (car (extract-code merged-code)))
(g 'pc (car merged-code)))))
(defthm merged-code-safe-implies-extract-code-pc-is-same-strong
(implies (merged-code-safe merged-code sig-frame)
(equal (g 'pc (car (extract-code merged-code)))
(g 'pc (car merged-code)))))
;; (local
;; (defthm wff-code1-implies-car-pc
;; (implies (and (wff-code1 code pc)
;; (consp code))
;; (equal (g 'pc (car code)) pc))))
(local
(defthm wff-code1-uniqueness
(IMPLIES
(AND (WFF-CODE1 (EXTRACT-CODE MERGED-CODE4) any)
(MERGED-CODE-SAFE MERGED-CODE4 MERGED-CODE3))
(wff-code1 (extract-code merged-code4)
(g 'pc (car merged-code4))))
:rule-classes :forward-chaining))
;----------------------------------------------------------------------
;
; EXport
(defthm merge-code-safe-implies-bcv-check-step-pre-lemma
(implies (and (merged-code-safe merged-code sig-frame)
(member inst merged-code)
(wff-code1 (extract-code merged-code)
(g 'pc (car merged-code)))
(inst? inst)
(equal pc (g 'pc inst)))
(bcv-check-step-pre inst
(cdr (assoc-equal pc
(collect-witness-merged-code-safe
merged-code sig-frame)))))
:hints (("Goal" :in-theory (e/d (merged-code-safe
collect-witness-merged-code-safe)
(bcv-check-step-pre inst?
sig-frame-compatible
stack-map?
bcv-execute-step))
:do-not '(generalize fertilize)
:induct (merged-code-safe merged-code sig-frame))))
;----------------------------------------------------------------------
(defthm member-extract-code-member-merged-code
(implies (member inst (extract-code merged-code))
(member inst merged-code))
:rule-classes :forward-chaining)
(defthm member-extract-code-implies-inst
(implies (member inst (extract-code merged-code))
(inst? inst))
:rule-classes :forward-chaining)
;----------------------------------------------------------------------
(defthm merge-code-safe-implies-bcv-check-step-pre
(implies (and (merged-code-safe merged-code sig-frame)
(equal (g 'pc sig-frame) 0)
(wff-code (extract-code merged-code))
(member inst (extract-code merged-code))
(equal pc (g 'pc inst)))
(bcv-check-step-pre inst
(cdr (assoc-equal pc
(collect-witness-merged-code-safe
merged-code sig-frame)))))
:hints (("Goal" :in-theory (disable inst? bcv-check-step-pre)
:do-not-induct t)))
;----------------------------------------------------------------------
(defthm wff-code1-uniqueness
(IMPLIES
(AND (WFF-CODE1 (EXTRACT-CODE MERGED-CODE4) any)
(MERGED-CODE-SAFE MERGED-CODE4 MERGED-CODE3))
(wff-code1 (extract-code merged-code4)
(g 'pc (car merged-code4))))
:rule-classes :forward-chaining)
|
