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|
(in-package "ACL2")
(include-book "bcv-model")
(include-book "bcv-simple-model")
(include-book "generic")
;; (local (include-book "bcv-find-correct-witness-bcv-check-pre"))
(encapsulate ()
(local
(defthm get-is-stack-map-sig-frame-pop-n
(equal (g 'is-stack-map (sig-frame-pop-n n sig-frame))
(g 'is-stack-map sig-frame))))
(local
(defthm get-is-inst-sig-frame-pop-n
(equal (g 'is-inst (sig-frame-pop-n n sig-frame))
(g 'is-inst sig-frame))))
(local
(defthm get-pc-sig-frame-pop-n
(equal (g 'pc (sig-frame-pop-n n sig-frame))
(g 'pc sig-frame))))
(defthm bcv-execute-step-produce-stack-map-or-aftergoto
(implies (and (stack-map? stack-map)
(bcv-check-step-pre inst stack-map)
(not (stack-map? (bcv-execute-step inst stack-map))))
(equal (bcv-execute-step inst stack-map) 'aftergoto))))
;----------------------------------------------------------------------
;; Subgoal *1/9.12'4'
;; (IMPLIES
;; (AND
;; (CONSP MERGED-CODE2)
;; (NOT (EQUAL INIT-FRAME 'AFTERGOTO))
;; (NOT (STACK-MAP? MERGED-CODE1))
;; (INST? MERGED-CODE1)
;; (EQUAL (G 'PC INIT-FRAME)
;; (G 'PC MERGED-CODE1))
;; (BCV-CHECK-STEP-PRE MERGED-CODE1 INIT-FRAME)
;; (SIG-FRAME-COMPATIBLE
;; STACK-MAP
;; (CDR (ASSOC-EQUAL (G 'PC INIT-FRAME)
;; (COLLECT-WITNESS-MERGED-CODE-SAFE
;; MERGED-CODE2
;; (BCV-EXECUTE-STEP MERGED-CODE1 INIT-FRAME)))))
;; (MERGED-CODE-SAFE MERGED-CODE2
;; (BCV-EXECUTE-STEP MERGED-CODE1 INIT-FRAME))
;; (WFF-CODE1 (EXTRACT-CODE MERGED-CODE2)
;; (+ 1 (G 'PC INIT-FRAME)))
;; (MEMBER STACK-MAP MERGED-CODE2)
;; (STACK-MAP? INIT-FRAME)
;; (STACK-MAP? STACK-MAP)
;; (EQUAL (G 'PC STACK-MAP)
;; (G 'PC INIT-FRAME)))
;; (SIG-FRAME-COMPATIBLE STACK-MAP INIT-FRAME)).
;; we want to prove that sig-frame-compatible
;; (SIG-FRAME-COMPATIBLE
;; STACK-MAP
;; (CDR (ASSOC-EQUAL (G 'PC INIT-FRAME)
;; (COLLECT-WITNESS-MERGED-CODE-SAFE
;; MERGED-CODE2
;; (BCV-EXECUTE-STEP MERGED-CODE1
;; INIT-FRAME)))))
;;
;; is impossible when
;;
;; (WFF-CODE1 (EXTRACT-CODE MERGED-CODE2)
;; (+ 1 (G 'PC INIT-FRAME)))
(defthm stack-map-implies-not-sig-frame-compatible
(implies (stack-map? x)
(not (sig-frame-compatible x nil))))
(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))))))
(encapsulate ()
(local (include-book "bcv-if-verified-then-pc-ordered"))
(local (defthm merged-code-safe-implies-pc-less-than
(implies (and (WFF-CODE1 (EXTRACT-CODE MERGED-CODE)
(+ 1 pc))
(consp (extract-code merged-code))
(merged-code-safe merged-code sig-frame))
(< pc
(g 'pc (car merged-code))))
:rule-classes :linear))
(defthm merged-code-safe-implies-pc-less-than-rewrite
(implies (and (WFF-CODE1 (EXTRACT-CODE MERGED-CODE)
(+ 1 pc))
(consp (extract-code merged-code))
(merged-code-safe merged-code sig-frame))
(< pc
(g 'pc (car merged-code))))))
;----------------------------------------------------------------------
(encapsulate ()
(local (include-book "bcv-find-correct-witness-bcv-check-pre"))
(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))
(defthm sig-frame-compatible-reflexive
(SIG-FRAME-COMPATIBLE STACK-MAP STACK-MAP))
(defthm sig-frame-compatible-pc-equal-f
(implies (SIG-FRAME-COMPATIBLE init-frame stack-map)
(equal (g 'pc init-frame)
(g 'pc stack-map)))
:rule-classes :forward-chaining)
(defthm sig-frame-compatible-transitive
(implies (and (sig-frame-compatible frame1 frame2)
(SIG-FRAME-COMPATIBLE frame2 frame3))
(sig-frame-compatible frame1 frame3)))
(defthm merged-code-safe-implies-merged-code-pc-is-pc
(implies (and (merged-code-safe merged-code init-frame)
(stack-map? init-frame))
(equal (g 'pc (car merged-code))
(g 'pc init-frame)))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable sig-frame-compatible inst? stack-map?
bcv-check-step-pre
bcv-execute-step))))
(defthm collect-witness-merged-code-safe-not-consp-if-not-extract-code
(implies (not (consp (extract-code merged-code)))
(not (consp (collect-witness-merged-code-safe merged-code init-frame)))))
(defthm first-stack-map-frame-is-compatible-with-the-last-frame-for-a-same-pc
(IMPLIES (and (merged-code-safe merged-code stack-map)
(stack-map? stack-map)
(equal (g 'pc stack-map) pc))
(SIG-FRAME-COMPATIBLE
stack-map
(CDR (ASSOC-EQUAL
pc
(COLLECT-WITNESS-MERGED-CODE-SAFE MERGED-CODE stack-map)))))
:hints (("Goal" :do-not '(generalize)
:in-theory (disable sig-frame-compatible inst? stack-map?
bcv-check-step-pre
bcv-execute-step))))
;; (i-am-here) ;; Mon Nov 14 16:34:29 2005
(defthm |Subgoal *1/9.12'4'|
(IMPLIES
(AND
(CONSP MERGED-CODE2)
(NOT (EQUAL INIT-FRAME 'AFTERGOTO))
(INST? MERGED-CODE1)
(BCV-CHECK-STEP-PRE MERGED-CODE1 INIT-FRAME)
(SIG-FRAME-COMPATIBLE
STACK-MAP
(CDR (ASSOC-EQUAL (G 'PC INIT-FRAME)
(COLLECT-WITNESS-MERGED-CODE-SAFE
MERGED-CODE2
(BCV-EXECUTE-STEP MERGED-CODE1 INIT-FRAME)))))
(EQUAL (G 'PC INIT-FRAME)
(G 'PC MERGED-CODE1))
(MERGED-CODE-SAFE MERGED-CODE2
(BCV-EXECUTE-STEP MERGED-CODE1 INIT-FRAME))
(WFF-CODE1 (EXTRACT-CODE MERGED-CODE2)
(+ 1 (G 'PC INIT-FRAME)))
(MEMBER STACK-MAP MERGED-CODE2)
(STACK-MAP? INIT-FRAME)
(STACK-MAP? STACK-MAP)
(EQUAL (G 'PC STACK-MAP)
(G 'PC INIT-FRAME)))
(SIG-FRAME-COMPATIBLE STACK-MAP INIT-FRAME))
:hints (("Goal" :do-not '(generalize fertilize)
:in-theory (disable sig-frame-compatible inst? stack-map?
;; assoc-equal
wff-code1
bcv-check-step-pre
extract-code
bcv-execute-step)
:cases ((consp (extract-code merged-code2)))
:do-not-induct t)))
(defthm verified-implies-partial-sig-vector-compatible-with-full-vector-lemma
(implies (and (merged-code-safe merged-code init-frame)
(consp (cdr merged-code))
(wff-code1 (extract-code merged-code)
(g 'pc (car merged-code)))
(member stack-map merged-code)
(or (stack-map? init-frame)
(equal init-frame 'aftergoto))
(stack-map? stack-map)
(equal (g 'pc stack-map) pc))
(sig-frame-compatible
stack-map
(cdr (assoc-equal pc (collect-witness-merged-code-safe
merged-code init-frame)))))
:hints (("Goal" :do-not '(generalize fertilize)
:in-theory (disable sig-frame-compatible inst? stack-map?
;; wff-code1
;; assoc-equal
bcv-check-step-pre
;;extract-code
bcv-execute-step))))
|
