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|
(in-package "ACL2")
(include-book "consistent-state")
(include-book "bcv-simple-model")
(include-book "bcv-model")
(defthm consistent-call-stack1-top-frame-pc-modication-no-change
(implies (consistent-call-stack1 call-stack top-frame method-table)
(consistent-call-stack1 call-stack (s 'pc anypc top-frame)
method-table)))
(defthm consistent-call-stack1-top-frame-opstack-modication-no-change
(implies (consistent-call-stack1 call-stack top-frame method-table)
(consistent-call-stack1 call-stack (s 'op-stack anyopstack top-frame)
method-table)))
(defthm consistent-state-consistent-call-stack1
(implies (CONSISTENT-STATE ST)
(CONSISTENT-CALL-STACK1 (CDR (G 'CALL-STACK ST))
(car (g 'call-stack st))
(g 'method-table st)))
:hints (("Goal" :in-theory (enable consistent-state))))
(defthm consistent-state-consistent-call-stack1-f
(implies (CONSISTENT-STATE ST)
(CONSISTENT-CALL-STACK1 (CDR (G 'CALL-STACK ST))
(car (g 'call-stack st))
(g 'method-table st)))
:hints (("Goal" :in-theory (enable consistent-state)))
:rule-classes :forward-chaining)
;----------------------------------------------------------------------
(encapsulate ()
(local (include-book "bcv-succeed-implies-bcv-simple-succeed"))
(defthm bcv-succeed-implies-bcv-simple-succeed
(implies (and (bcv-method method method-table)
(equal method (binding (g 'method-name method)
method-table))
(bcv-verified-method-table method-table))
(bcv-simple-method
(s 'sig-vector
(collect-witness-bcv-method
method method-table)
method)
method-table))))
(defthm bcv-verified-method-table1-is-all-method-verified1-normalize
(equal (BCV-VERIFIED-METHOD-TABLE1 method-table1 method-table)
(all-method-verified1 method-table1 method-table)))
(defthm bcv-verified-method-table-is-all-method-verified-normalize
(equal (BCV-VERIFIED-METHOD-TABLE method-table)
(all-method-verified method-table)))
(defthm consistent-state-implies-current-method-verified
(implies (and (consistent-state st)
(equal (g 'method-table st) method-table))
(bcv-simple-method (s 'sig-vector (collect-witness-bcv-method
(current-method st) method-table)
(current-method st))
method-table))
:hints (("Goal" :in-theory (disable bcv-simple-method bcv-method
collect-witness-bcv-method))))
;----------------------------------------------------------------------
(local (include-book "bcv-simple-method-properties"))
(local (in-theory (disable bcv-simple-check-step-pre extract-sig-frame
current-method next-inst consistent-state)))
(local (include-book "generic"))
(local
(defthm consistent-state-consistent-callee-frame
(implies (consistent-state st)
(consistent-callee-frame
(car (g 'call-stack st))
(g 'method-table st)))
:hints (("Goal" :in-theory (e/d (consistent-state)
(consistent-callee-frame))))))
(local
(defthm current-method-normalize
(equal (CDR (ASSOC-EQUAL (G 'METHOD-NAME
(CAR (G 'CALL-STACK ST)))
(G 'METHOD-TABLE ST)))
(current-method st))
:hints (("Goal" :in-theory (enable current-method)))))
(defthm consistent-state-sig-frame-compatible
(implies (consistent-state st)
(sig-frame-compatible
(extract-sig-frame
(car (g 'call-stack st))
(g 'method-table st))
(cdr (assoc-equal (g 'pc (car (g 'call-stack st)))
(collect-witness-bcv-method
(current-method st)
(g 'method-table st))))))
:hints (("Goal" :in-theory (e/d () (sig-frame-compatible
consistent-state-consistent-callee-frame))
:use ((:instance consistent-state-consistent-callee-frame)))))
(local (in-theory (disable sig-frame-compatible collect-witness-bcv-method)))
;; (i-am-here) ;; Wed Nov 2 22:43:41 2005
(defthm consistent-state-bcv-simple-check-step-pre-if-pc-in-range
(implies (and (consistent-state st)
(pc-in-range st))
(bcv-simple-check-step-pre
(next-inst st)
(extract-sig-frame
(car (g 'call-stack st))
(g 'method-table st))))
:hints (("Goal" :in-theory (e/d (next-inst)
(bcv-simple-check-step-pre
bcv-simple-check-step-pre-if-sig-frame-compatible
bcv-simple-execute-step))
:use ((:instance
bcv-simple-method-implies-next-inst-verified
;; from bcv-simple-method-properties.lisp
(pc (g 'pc (car (g 'call-stack st))))
(method (s 'sig-vector (collect-witness-bcv-method
(current-method st)
(g 'method-table st))
(current-method st)))
(method-table (g 'method-table st)))
(:instance bcv-simple-check-step-pre-if-sig-frame-compatible
(sframe (extract-sig-frame
(car (g 'call-stack st))
(g 'method-table st)))
(gframe (cdr (assoc-equal (g 'pc (car (g 'call-stack st)))
(collect-witness-bcv-method
(current-method st)
(g 'method-table st)))))
(inst (next-inst st)))))))
;;; because from consistent-state we know bcv-simple-method
;;; from consistent-state we know extract-sig-frame from st
;;; is more specific than recorded
;;; sig-frame
;;; from (bcv-simple-method (current-method st)) we know
;;; bcv-simple-check-step-pre inst on recorded (more general) sig-frame!!
;;; we proved that bcv-simple-check-step-pre succeed on more specific frame
(defthm consistent-state-all-next-state-safe-if-pc-in-range
(implies (and (consistent-state st)
(pc-in-range st))
(all-next-state-safe
(bcv-simple-execute-step (next-inst st)
(extract-sig-frame
(car (g 'call-stack st))
(g 'method-table st)))
(collect-witness-bcv-method (current-method st)
(g 'method-table st))))
:hints (("Goal" :in-theory (e/d (next-inst)
(all-next-state-safe
collect-witness-bcv-method
bcv-simple-method-implies-next-inst-verified
bcv-check-step-post-if-sig-frame-compatible
bcv-simple-execute-step))
:use ((:instance
bcv-simple-method-implies-next-inst-verified
(pc (g 'pc (car (g 'call-stack st))))
(method (s 'sig-vector
(collect-witness-bcv-method (current-method st)
(g 'method-table st))
(current-method st)))
(method-table (g 'method-table st)))
(:instance bcv-check-step-post-if-sig-frame-compatible
(sframe (extract-sig-frame
(car (g 'call-stack st))
(g 'method-table st)))
(gframe (cdr (assoc-equal (g 'pc (car (g 'call-stack st)))
(collect-witness-bcv-method (current-method st)
(g 'method-table st)))))
(inst (next-inst st))
(vector (collect-witness-bcv-method
(current-method st)
(g 'method-table st))))))))
(defthm consistent-state-all-next-state-safe-if-pc-in-range-weak
(implies (and (consistent-state st)
(pc-in-range st))
(all-next-state-safe
(bcv-simple-execute-step (next-inst st)
(cdr (assoc-equal
(g 'pc (car (g 'call-stack st)))
(collect-witness-bcv-method
(current-method st)
(g 'method-table st)))))
(collect-witness-bcv-method (current-method st)
(g 'method-table st))))
:hints (("Goal" :in-theory (e/d (next-inst)
(all-next-state-safe
bcv-simple-method-implies-next-inst-verified
bcv-check-step-post-if-sig-frame-compatible
bcv-simple-execute-step))
:use ((:instance
bcv-simple-method-implies-next-inst-verified
(pc (g 'pc (car (g 'call-stack st))))
(method (s 'sig-vector
(collect-witness-bcv-method (current-method st)
(g 'method-table st))
(current-method st)))
(method-table (g 'method-table st)))))))
;; notes: this kind of rule does not fire too easily!!
;; because we have rewrite rules that rewrite (g 'method-table st) into ....
;;
;; Let's see how it works!! Sun Nov 20 18:07:53 2005
(defthm consistent-state-max-stack-equal
(IMPLIES (CONSISTENT-STATE ST)
(EQUAL (G 'MAX-STACK
(current-method st))
(G 'MAX-STACK (CAR (G 'CALL-STACK ST)))))
:hints (("Goal" :in-theory (enable consistent-state current-method))))
;----------------------------------------------------------------------
(local
(defthm sig-frame-compatible-equal-pc
(implies (sig-frame-compatible frame1 frame2)
(equal (g 'pc frame2)
(g 'pc frame1)))
:hints (("Goal" :in-theory (enable sig-frame-compatible)))))
(defthm consistent-state-implies-sig-frame-pc-is-pc
(implies (consistent-state st)
(equal (g 'pc
(cdr (assoc-equal (g 'pc (car (g 'call-stack st)))
(collect-witness-bcv-method
(current-method st)
(g 'method-table st)))))
(g 'pc (car (g 'call-stack st)))))
:hints (("Goal"
:use ((:instance
consistent-state-sig-frame-compatible)
(:instance sig-frame-compatible-equal-pc
(frame1 (extract-sig-frame (car (g 'call-stack st))
(g 'method-table st)))
(frame2 (cdr (assoc-equal (g 'pc (car (g 'call-stack st)))
(collect-witness-bcv-method
(current-method st)
(g 'method-table st))))))))))
;----------------------------------------------------------------------
(defthm all-next-state-safe-implies-sig-frame-compatible
(implies (and (all-next-state-safe l sig-vector)
(member x l))
(sig-frame-compatible x
(cdr (assoc-equal
(g 'pc x) sig-vector)))))
(defthm all-next-state-safe-implies-pc-equal
(implies (and (all-next-state-safe l sig-vector)
(member x l))
(equal (g 'pc (cdr (assoc-equal (g 'pc x) sig-vector)))
(g 'pc x)))
:hints (("Goal" :use ((:instance sig-frame-compatible-equal-pc
(frame1 x)
(frame2 (cdr (assoc-equal (g 'pc x) sig-vector))))))))
;----------------------------------------------------------------------
(local
(defthm sig-frame-compatible-equal-max-stack
(implies (sig-frame-compatible frame1 frame2)
(equal (g 'max-stack frame2)
(g 'max-stack frame1)))
:hints (("Goal" :in-theory (enable sig-frame-compatible)))))
(defthm consistent-state-implies-sig-frame-max-stack-is-max-stack
(implies (consistent-state st)
(equal (g 'max-stack
(cdr (assoc-equal (g 'pc (car (g 'call-stack st)))
(collect-witness-bcv-method
(current-method st)
(g 'method-table st)))))
(g 'max-stack (car (g 'call-stack st)))))
:hints (("Goal"
:use ((:instance
consistent-state-sig-frame-compatible)
(:instance sig-frame-compatible-equal-max-stack
(frame1 (extract-sig-frame (car (g 'call-stack st))
(g 'method-table st)))
(frame2 (cdr (assoc-equal (g 'pc (car (g 'call-stack st)))
(collect-witness-bcv-method (current-method st)
(g 'method-table st))))))))))
(defthm all-next-state-safe-implies-max-stack-equal
(implies (and (all-next-state-safe l sig-vector)
(member x l))
(equal (g 'max-stack (cdr (assoc-equal (g 'pc x) sig-vector)))
(g 'max-stack x)))
:hints (("Goal" :use ((:instance sig-frame-compatible-equal-max-stack
(frame1 x)
(frame2 (cdr (assoc-equal (g 'pc x)
sig-vector))))))))
;----------------------------------------------------------------------
(local
(defthm sig-frame-compatible-equal-method-table
(implies (sig-frame-compatible frame1 frame2)
(equal (g 'method-table frame2)
(g 'method-table frame1)))
:hints (("Goal" :in-theory (enable sig-frame-compatible)))))
(defthm all-next-state-safe-implies-method-table-equal
(implies (and (all-next-state-safe l sig-vector)
(member x l))
(equal (g 'method-table (cdr (assoc-equal (g 'pc x) sig-vector)))
(g 'method-table x)))
:hints (("Goal" :use ((:instance sig-frame-compatible-equal-method-table
(frame1 x)
(frame2 (cdr (assoc-equal (g 'pc x) sig-vector))))))))
;;(i-am-here) ;; Thu Oct 20 16:26:26 2005
(local
(defthm sig-frame-compatible-extract-sig-frame-general
(implies (sig-frame-compatible
(extract-sig-frame any-frame method-table)
frame)
(equal (g 'method-table frame)
method-table))))
(defthm sig-frame-compatible-extract-sig-frame
(implies (sig-frame-compatible
(extract-sig-frame any-frame method-table)
(cdr (assoc-equal pc vector)))
(equal (g 'method-table (cdr (assoc-equal pc vector)))
method-table)))
;;; this is a bad rewrite rule
;----------------------------------------------------------------------
(local
(defthm sig-frame-compatible-equal-op-stack
(implies (sig-frame-compatible frame1 frame2)
(equal (g 'op-stack frame2)
(g 'op-stack frame1)))
:hints (("Goal" :in-theory (enable sig-frame-compatible)))))
(defthm all-next-state-safe-implies-opstack-equal
(implies (and (all-next-state-safe l sig-vector)
(member x l))
(equal (g 'op-stack (cdr (assoc-equal (g 'pc x) sig-vector)))
(g 'op-stack x)))
:hints (("Goal" :use ((:instance sig-frame-compatible-equal-op-stack
(frame1 x)
(frame2 (cdr (assoc-equal (g 'pc x) sig-vector))))))))
;;(i-am-here) ;; Thu Oct 20 16:26:26 2005
(local
(defthm sig-frame-compatible-extract-sig-frame-general-opstack
(implies (sig-frame-compatible
(extract-sig-frame any-frame method-table)
frame)
(equal (g 'op-stack frame)
(len (g 'op-stack any-frame))))))
(defthm sig-frame-compatible-extract-sig-frame-opstack
(implies (sig-frame-compatible
(extract-sig-frame any-frame method-table)
(cdr (assoc-equal pc vector)))
(equal (g 'op-stack (cdr (assoc-equal pc vector)))
(len (g 'op-stack any-frame)))))
;----------------------------------------------------------------------
(local
(defthm sig-frame-compatible-equal-method-name
(implies (sig-frame-compatible frame1 frame2)
(equal (g 'method-name frame2)
(g 'method-name frame1)))
:hints (("Goal" :in-theory (enable sig-frame-compatible)))))
(defthm all-next-state-safe-implies-method-name-equal
(implies (and (all-next-state-safe l sig-vector)
(member x l))
(equal (g 'method-name (cdr (assoc-equal (g 'pc x) sig-vector)))
(g 'method-name x)))
:hints (("Goal" :use ((:instance sig-frame-compatible-equal-method-name
(frame1 x)
(frame2 (cdr (assoc-equal (g 'pc x) sig-vector))))))))
;----------------------------------------------------------------------
(local
(defthm sig-frame-compatible-extract-sig-frame-general-method-name
(implies (sig-frame-compatible
(extract-sig-frame any-frame method-table)
frame)
(equal (g 'method-name frame)
(g 'method-name any-frame)))))
(defthm sig-frame-compatible-extract-sig-frame-method-name
(implies (sig-frame-compatible
(extract-sig-frame any-frame method-table)
(cdr (assoc-equal pc vector)))
(equal (g 'method-name (cdr (assoc-equal pc vector)))
(g 'method-name any-frame))))
;----------------------------------------------------------------------
;;(i-am-here) ;; Thu Nov 3 23:55:53 2005
(local
(defthm sig-frame-compatible-extract-sig-frame-general-method-name-2
(implies (sig-frame-compatible
(sig-frame-push-value any any-frame)
frame)
(equal (g 'method-name frame)
(g 'method-name any-frame)))
:hints (("Goal" :in-theory (enable sig-frame-compatible)))))
(defthm sig-frame-compatible-extract-sig-frame-method-name-2
(implies (sig-frame-compatible
(sig-frame-push-value any any-frame)
(cdr (assoc-equal pc vector)))
(equal (g 'method-name (cdr (assoc-equal pc vector)))
(g 'method-name any-frame)))
:hints (("Goal" :in-theory (disable sig-frame-push-value))))
;----------------------------------------------------------------------
;----------------------------------------------------------------------
(defthm cdr-g-call-stack-popStack-n
(equal (cdr (g 'call-stack (popstack-n st n)))
(cdr (g 'call-stack st))))
(defthm consistent-call-stack1-top-frame-opstack-popStack-n-no-change
(implies (consistent-call-stack1 call-stack (car (g 'call-stack st)) method-table)
(consistent-call-stack1 call-stack (car (g 'call-stack
(popstack-n st n)))
method-table)))
;----------------------------------------------------------------------
;;(i-am-here);; Fri Oct 21 13:13:08 2005
(defthm consistent-state-len-opstack-in-limit
(implies (consistent-state st)
(<= (len (g 'op-stack (car (g 'call-stack st))))
(g 'max-stack (car (g 'call-stack st)))))
:hints (("Goal" :in-theory (enable consistent-state)))
:rule-classes :linear)
;----------------------------------------------------------------------
(defthm consistent-state-len-opstack-in-limit-specific
(implies (consistent-state st)
(<= (len (cdr (g 'op-stack (car (g 'call-stack st)))))
(g 'max-stack (car (g 'call-stack st)))))
:hints (("Goal" :use consistent-state-len-opstack-in-limit)))
;----------------------------------------------------------------------
;;(i-am-here) ;; Thu Nov 3 22:39:51 2005
(defthm consistent-state-implies-method-name-equal
(IMPLIES (CONSISTENT-STATE ST)
(EQUAL (G 'METHOD-NAME (CURRENT-METHOD ST))
(G 'METHOD-NAME
(CAR (G 'CALL-STACK ST)))))
:hints (("Goal" :in-theory (enable consistent-state))))
;----------------------------------------------------------------------
(defthm consistent-state-implies-name-equal-2
(IMPLIES (AND (CONSISTENT-STATE ST)
(CONSP (CDR (G 'CALL-STACK ST))))
(EQUAL (G 'METHOD-NAME
(CDR (ASSOC-EQUAL (G 'METHOD-NAME
(CADR (G 'CALL-STACK ST)))
(G 'METHOD-TABLE ST))))
(G 'METHOD-NAME
(CADR (G 'CALL-STACK ST)))))
:hints (("Goal" :in-theory (enable consistent-state))))
;----------------------------------------------------------------------
;;; (i-am-here) ;; Sun Nov 20 20:04:39 2005
(defthm consistent-state-bcv-method-current-method
(implies (consistent-state st)
(bcv-method (current-method st) (g 'method-table st)))
:hints (("Goal" :in-theory (e/d (consistent-state current-method)
(bcv-method))))
:rule-classes :forward-chaining)
;----------------------------------------------------------------------
;;(i-am-here) ;; Sun Nov 20 22:17:37 2005
(defthm wff-method-table-implies-g-method-name-normalize
(implies (and (wff-method-table method-table)
(assoc-equal name method-table))
(equal (g 'method-name (cdr (assoc-equal name method-table)))
name)))
(defthm consistent-state-implies-wff-method-table
(implies (consistent-state djvm-s)
(wff-method-table (g 'method-table djvm-s)))
:hints (("Goal" :in-theory (enable consistent-state))))
;----------------------------------------------------------------------
(defthm consistent-state-implies-pc-in-range-f
(implies (consistent-state st)
(pc-in-range st))
:hints (("Goal" :in-theory (e/d (consistent-state) (pc-in-range))))
:rule-classes :forward-chaining)
;----------------------------------------------------------------------
;;(i-am-here) ;; Mon Nov 21 02:05:40 2005
;; (local (include-book "bcv-simple-method-properties"))
(encapsulate ()
(local
(encapsulate ()
(local (include-book "bcv-simple-method-properties"))
(defthm bcv-simple-method-implies-next-inst-verified
(implies (and (bcv-simple-method method method-table)
(integerp pc)
(<= 0 pc)
(< pc (len (g 'code method))))
(bcv-simple-inst pc
(nth pc (g 'code method))
(g 'sig-vector method))))))
(defthm consistent-state-implies-bcv-simple-inst
(implies (consistent-state st)
(bcv-simple-inst (g 'pc (car (g 'call-stack st)))
(next-inst st)
(collect-witness-bcv-method
(current-method st)
(g 'method-table st))))
:hints (("Goal" :in-theory (e/d (consistent-state
next-inst
pc-in-range)
(bcv-simple-inst
bcv-simple-method
bcv-method
consistent-call-stack
collect-witness-bcv-method))
:use ((:instance bcv-simple-method-implies-next-inst-verified
(method (s 'sig-vector (collect-witness-bcv-method
(current-method st)
(g 'method-table st))
(current-method st)))
(pc (g 'pc (car (g 'call-stack st))))
(method-table (g 'method-table st))))))))
;----------------------------------------------------------------------
(defthm consistent-state-implies-integerp-pc
(implies (consistent-state st)
(integerp (g 'pc (car (g 'call-stack st)))))
:hints (("Goal" :in-theory (enable consistent-state pc-in-range))))
(defthm consistent-state-implies-greater-than-zero
(implies (consistent-state st)
(<= 0 (g 'pc (car (g 'call-stack st)))))
:hints (("Goal" :in-theory (enable consistent-state pc-in-range)))
:rule-classes :linear)
(defthm consistent-state-implies-less-than-len
(implies (consistent-state st)
(< (g 'pc (car (g 'call-stack st)))
(len (g 'code (current-method st)))))
:hints (("Goal" :in-theory (enable consistent-state pc-in-range)))
:rule-classes :linear)
;----------------------------------------------------------------------
(defthm consistent-state-bcv-method-current-method-b
(implies (consistent-state st)
(bcv-method (current-method st)
(g 'method-table st))))
;----------------------------------------------------------------------
(defthm current-method-normalize-x
(equal (CDR (ASSOC-EQUAL (G 'METHOD-NAME
(CAR (G 'CALL-STACK DJVM-S)))
(G 'METHOD-TABLE DJVM-S)))
(current-method djvm-s))
:hints (("Goal" :in-theory (enable current-method))))
;----------------------------------------------------------------------
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