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|
(in-package "ACL2")
(include-book "jvm-model")
;------------------------------------------------------------
;
; The BCV for the Small Machine
;
;------------------------------------------------------------
(defun stack-map? (map)
(and (equal (g 'is-stack-map map) t)
(equal (g 'is-inst map) nil)
(integerp (g 'pc map))))
(defun inst? (inst)
(and (equal (g 'is-inst inst) t)
(equal (g 'is-stack-map inst) nil)
(integerp (g 'pc inst))))
(defun wff-code1 (code pc)
(if (endp code)
(equal code nil)
(and (and (inst? (car code))
(equal (g 'pc (car code)) pc)
(not (stack-map? (car code))))
(wff-code1 (cdr code) (+ 1 pc)))))
(defun wff-code (code)
(and (consp code)
(wff-code1 code 0)))
(defun wff-maps (maps)
(if (endp maps) (equal maps nil)
(and (stack-map? (car maps))
(wff-maps (cdr maps)))))
(defun bcv-op-code (inst)
(op-code (g 'inst inst)))
(defun bcv-arg (inst)
(arg (g 'inst inst)))
;----------------------------------------------------------------------
(defun max-stack (sig-frame)
(g 'max-stack sig-frame))
(defun bcv-check-PUSH (inst sig-frame)
(declare (ignore inst))
(<= (+ 1 (g 'op-stack sig-frame))
(max-stack sig-frame)))
(defun advance-pc (sig-frame)
(s 'pc
(+ 1 (g 'pc sig-frame))
sig-frame))
(defun sig-frame-push-value (v sig-frame)
(declare (ignore v))
(s 'op-stack
(+ 1 (g 'op-stack sig-frame))
sig-frame))
(defun bcv-execute-PUSH (inst sig-frame)
(advance-pc
(sig-frame-push-value (bcv-arg inst)
sig-frame)))
(defun bcv-check-POP (inst sig-frame)
(declare (ignore inst))
(<= 1 (g 'op-stack sig-frame)))
(defun sig-frame-pop-value (sig-frame)
(if (zp (g 'op-stack sig-frame))
sig-frame
(s 'op-stack
(- (g 'op-stack sig-frame) 1)
sig-frame)))
(defun bcv-execute-POP (inst sig-frame)
(declare (ignore inst))
(advance-pc
(sig-frame-pop-value sig-frame)))
;;; The only important thing we care (in this example) is the size of the
;;; operand stack.
;;;
;;; Our BCV examine a program, method by method.
;;;
;;; We will show that verified program will never violate the operand stack
;;; size limit.
(defun sig-local-compatible (slocals glocals)
(declare (ignore slocals glocals))
;; temp implementation
t)
(defun sig-opstack-compatible (sframe gframe)
(equal (g 'op-stack sframe)
(g 'op-stack gframe)))
(defun sig-frame-compatible (sframe gframe)
(and (equal (g 'pc sframe)
(g 'pc gframe))
(equal (g 'max-stack sframe)
(g 'max-stack gframe))
(equal (g 'method-name sframe)
(g 'method-name gframe))
(equal (g 'method-table sframe)
(g 'method-table gframe))
(sig-opstack-compatible sframe gframe)
(sig-local-compatible (g 'locals sframe)
(g 'locals gframe))))
(defun targetIsSafe (pc sig-frame partial-sig-vector)
(and (bound? pc partial-sig-vector)
(stack-map? (binding pc partial-sig-vector))
(sig-frame-compatible
sig-frame
(binding pc partial-sig-vector))))
;; (i-am-here) ;; Fri Oct 28 21:01:16 2005
(defun extract-partial-sig-vector (maps)
(if (endp maps) nil
(cons (cons (g 'pc (car maps))
(car maps))
(extract-partial-sig-vector (cdr maps)))))
;; (defun bcv-check-IFEQ (inst sig-frame)
;; (and (<= 1 (g 'op-stack sig-frame))
;; (targetIsSafe
;; (arg inst)
;; (sig-frame-pop-value sig-frame)
;; (extract-partial-sig-vector
;; (g 'stackmaps
;; (binding (g 'method-name sig-frame)
;; (g 'method-table sig-frame)))))))
;; ;; (extract-sig-vector (g 'stackmaps sig-frame)))
(defun update-maps-with-method-table (maps method-name method-table)
(if (endp maps) maps
(cons (s 'method-name method-name (s 'method-table method-table
(s 'max-stack
(g 'max-stack
(binding method-name
method-table))
(car maps))))
(update-maps-with-method-table (cdr maps) method-name method-table))))
(defun bcv-check-IFEQ (inst sig-frame)
(and (<= 1 (g 'op-stack sig-frame))
(targetIsSafe
(bcv-arg inst)
(s 'pc (bcv-arg inst)
(sig-frame-pop-value sig-frame))
(extract-partial-sig-vector
(update-maps-with-method-table
(g 'stackmaps
(binding (g 'method-name sig-frame)
(g 'method-table sig-frame)))
(g 'method-name sig-frame)
(g 'method-table sig-frame))))))
;; (extract-sig-vector (g 'stackmaps sig-frame)))
(defun bcv-execute-IFEQ (inst sig-frame)
(declare (ignore inst))
(advance-pc (sig-frame-pop-value sig-frame)))
;; note IFEQ has two possible return state!
(defun bcv-check-INVOKE (inst sig-frame)
(let* ((method-name (bcv-arg inst))
(method-table (g 'method-table sig-frame))
(method (binding method-name method-table))
(nargs (g 'nargs method)))
(and (bound? method-name method-table)
(<= 0 (g 'max-stack (binding method-name method-table)))
(integerp nargs)
(<= 0 nargs)
(<= nargs (g 'op-stack sig-frame))
(<= (+ 1 (- (g 'op-stack sig-frame)
nargs))
(max-stack sig-frame)))))
;;; Note:
;;; make sure it has enough space for arguments
;;; make sure the return value will not overflow the stack!!
;;;
;;; values are always of size 1!! (in JVM it could be size two)
(defun sig-frame-pop-n (n sig-frame)
(if (zp n)
sig-frame
(sig-frame-pop-n (- n 1)
(sig-frame-pop-value sig-frame))))
(defun bcv-execute-INVOKE (inst sig-frame)
(let* ((method-name (bcv-arg inst))
(method-table (g 'method-table sig-frame))
(method (binding method-name method-table))
(nargs (g 'nargs method))
(ret (g 'ret method)))
(advance-pc
(sig-frame-push-value ret
(sig-frame-pop-n nargs sig-frame)))))
(defun bcv-check-HALT (inst sig-frame)
(declare (ignore inst sig-frame))
t)
(defun bcv-execute-HALT (inst sig-frame)
(declare (ignore inst sig-frame))
'aftergoto)
;;;
;;; the specially handling of this make the proof
;;; a lot complicated!!
;;;
;;; Mon Nov 7 13:32:14 2005
(defun bcv-check-RETURN (inst sig-frame)
(declare (ignore inst))
(<= 1 (g 'op-stack sig-frame)))
(defun bcv-execute-RETURN (inst sig-frame)
(declare (ignore inst sig-frame))
'aftergoto)
(defun bcv-check-step-pre (inst sig-frame)
(let* ((opcode (bcv-op-code inst)))
(cond ((equal opcode 'INVOKE)
(bcv-check-INVOKE inst sig-frame))
((equal opcode 'PUSH)
(bcv-check-PUSH inst sig-frame))
((equal opcode 'IFEQ)
(bcv-check-IFEQ inst sig-frame))
((equal opcode 'HALT)
(bcv-check-HALT inst sig-frame))
((equal opcode 'POP)
(bcv-check-POP inst sig-frame))
((equal opcode 'RETURN)
(bcv-check-RETURN inst sig-frame))
(t nil))))
(defun bcv-execute-step (inst sig-frame)
(let* ((opcode (bcv-op-code inst)))
(cond ((equal opcode 'INVOKE)
(bcv-execute-INVOKE inst sig-frame))
((equal opcode 'PUSH)
(bcv-execute-PUSH inst sig-frame))
((equal opcode 'IFEQ)
(bcv-execute-IFEQ inst sig-frame))
((equal opcode 'HALT)
(bcv-execute-HALT inst sig-frame))
((equal opcode 'POP)
(bcv-execute-POP inst sig-frame))
((equal opcode 'RETURN)
(bcv-execute-RETURN inst sig-frame))
(t nil))))
;;
;; invariant of the following function.
;; if sig-vector contains a frame at (g 'pc (sig-frame))
;; then the next instruction must be at position (pc ..)
;;
;; if all instruction is covered, then verification succeed!
;;
;; ;;
;; ;; (defun bcv-method1 (code sig-vector sig-frame)
;; ;; (mylet ((pc (g 'pc sig-frame)))
;; ;;
;;
;; The actual BCV is first to merge code with signature state
;;
;; then run through the code once.
;;
;; We will need to formalize that code is in fact consecutive.
;;
;;(i-am-here) ;; Mon Oct 31 20:07:11 2005
(defun mapOffset (map)
(g 'pc map))
(defun instrOffset (inst)
(g 'pc inst))
(defun makeStackMap (map method-name method-table)
(s 'is-stack-map t
(s 'is-inst nil
(s 'method-name method-name
(s 'method-table method-table
(s 'max-stack
(g 'max-stack
(binding method-name method-table))
map))))))
(defun make-inst (inst)
(s 'is-inst t
(s 'is-stack-map nil inst)))
(defun mergeStackMapAndCode (maps ParsedCode method-name method-table)
(if (endp maps)
(append ParsedCode (list 'END_OF_CODE))
(if (endp ParsedCode)
nil
(let ((mpc (mapOffset (car maps)))
(pc (instrOffset (car ParsedCode))))
(if (equal mpc pc)
(cons (makeStackMap (car maps) method-name method-table)
(cons (make-inst (car ParsedCode))
(mergeStackMapAndCode (cdr maps)
(cdr ParsedCode)
method-name
method-table)))
(if (< pc mpc)
(cons (make-inst (car ParsedCode))
(mergeStackMapAndCode maps (cdr ParsedCode)
method-name
method-table))
nil))))))
(defun merged-code-safe (mergedcode sig-frame)
(if (endp mergedcode) nil
(if (endp (cdr mergedcode))
(and (equal (car mergedcode) 'END_OF_CODE)
(equal sig-frame 'aftergoto))
(if (equal sig-frame 'aftergoto)
(and (stack-map? (car mergedcode))
(equal (g 'pc (car mergedcode))
(g 'pc (cadr mergedcode)))
(merged-code-safe (cdr mergedcode)
(car mergedcode)))
(cond ((stack-map? (car mergedcode))
(and (sig-frame-compatible sig-frame (car mergedcode))
(merged-code-safe (cdr mergedcode)
(car mergedcode))))
((inst? (car mergedcode))
(and (equal (g 'pc sig-frame)
(g 'pc (car mergedcode)))
(bcv-check-step-pre (car mergedcode) sig-frame)
(merged-code-safe
(cdr mergedcode)
(bcv-execute-step (car mergedcode) sig-frame))))
(t nil))))))
(defun sig-init-locals (method)
;; tmp, we only deal with number of values on the operand stack!
(declare (ignore method))
nil)
(defun sig-method-init-frame (method method-table)
(s 'is-stack-map t
(s 'is-inst nil
(s 'method-table method-table
;; note these method in method-table does
;; not have sig-vector
(s 'method-name ;; these could be merged into one
(g 'method-name method) ;; structure called "env"!!
(s 'max-stack ;; we will then to prove that "env"
(g 'max-stack method) ;; does not change.
(s 'pc 0 ;; instead of proving a lot of similiar things!!
(s 'op-stack 0
(s 'locals
(sig-init-locals method) nil)))))))))
;; (defun extract-sig-vector (mergedcode)
;; (if (endp mergedcode) nil
;; (if (stack-map? (car mergedcode))
;; (cons (cons (g 'pc (car mergedcode))
;; (car mergedcode))
;; (extract-sig-vector (cdr mergedcode)))
;; (extract-sig-vector (cdr mergedcode)))))
;; (i-am-here) ;; Tue Nov 8 13:39:26 2005
(defun parsecode1 (pc code)
(if (endp code) code
(cons (make-inst (s 'pc pc
(s 'inst (car code) nil)))
(parsecode1 (+ 1 pc) (cdr code)))))
(defun parsecode (code)
(parsecode1 0 code))
(defun bcv-method (method method-table)
(let* ((code (g 'code method))
(maps (g 'stackmaps method)))
(and (wff-code (parsecode code))
(wff-maps maps)
(merged-code-safe
(mergeStackMapAndCode
maps (parsecode code) (g 'method-name method) method-table)
(sig-method-init-frame method
method-table)))))
;----------------------------------------------------------------------
(defun extract-sig-locals (frame)
(declare (ignore frame))
nil)
(defun extract-sig-frame (frame method-table)
(s 'method-table method-table
(s 'max-stack
(g 'max-stack frame)
(s 'method-name
(g 'method-name frame)
(s 'pc (g 'pc frame)
(s 'op-stack (len (g 'op-stack frame))
(s 'locals
(extract-sig-locals frame) nil)))))))
;----------------------------------------------------------------------
(defun bcv-verified-method-table1 (method-table1 method-table)
(if (endp method-table1) t
(and (bcv-method (cdr (car method-table1)) method-table)
(bcv-verified-method-table1 (cdr method-table1) method-table))))
(defun bcv-verified-method-table (method-table)
(bcv-verified-method-table1 method-table method-table))
;----------------------------------------------------------------------
;; (defun merged-code-safe (mergedcode sig-frame)
;; (if (endp mergedcode) nil
;; (if (endp (cdr mergedcode))
;; (and (equal (car mergedcode) 'END_OF_CODE)
;; (equal sig-frame 'aftergoto))
;; (if (equal sig-frame 'aftergoto)
;; (and (stack-map? (car mergedcode))
;; (equal (g 'pc (car mergedcode))
;; (+ 1 (g 'pc (cadr mergedcode)))) ;; bug!!
;; (merged-code-safe (cdr mergedcode)
;; (car mergedcode)))
;; ;; error detected when we attend to reason about
;; ;; HALT ..
;; (cond ((stack-map? (car mergedcode))
;; (and (sig-frame-compatible sig-frame (car mergedcode))
;; (equal (g 'pc sig-frame)
;; (g 'pc (cdr mergedcode))) ;; bug!!
;; (merged-code-safe (cdr mergedcode)
;; (car mergedcode))))
;; ((inst? (car mergedcode))
;; (and (equal (g 'pc sig-frame)
;; (g 'pc (car mergedcode)))
;; (bcv-check-step-pre (car mergedcode) sig-frame)
;; (merged-code-safe
;; (cdr mergedcode)
;; (bcv-execute-step (car mergedcode) sig-frame))))
;; (t nil))))))
;; wrong one!!
;;
;; (defun collect-witness-merged-code-safe (mergedcode sig-frame)
;; (if (endp mergedcode) nil
;; (if (endp (cdr mergedcode)) nil
;; (if (equal sig-frame 'aftergoto)
;; (and (stack-map? (car mergedcode))
;; (equal (g 'pc (car mergedcode))
;; (+ 1 (g 'pc sig-frame))) ;; bug !!!
;; (collect-witness-merged-code-safe
;; (cdr mergedcode) (car mergedcode)))
;; (cond ((stack-map? (car mergedcode))
;; (and (sig-frame-compatible sig-frame (car mergedcode))
;; (not (endp (cdr mergedcode)))
;; (equal (g 'pc (cdr mergedcode)) ;; bug!!!
;; (g 'pc sig-frame))
;; (collect-witness-merged-code-safe
;; (cdr mergedcode) (car mergedcode))))
;; ((inst? (car mergedcode))
;; (and (equal (g 'pc sig-frame)
;; (g 'pc (car mergedcode)))
;; (bcv-check-step-pre (car mergedcode) sig-frame)
;; (cons (cons (g 'pc sig-frame)
;; sig-frame)
;; (collect-witness-merged-code-safe
;; (cdr mergedcode)
;; (bcv-execute-step (car mergedcode)
;; sig-frame)))))
;; (t nil))))))
;;
;;
;; (defun merged-code-safe (mergedcode sig-frame)
;; (if (endp mergedcode) nil
;; (if (endp (cdr mergedcode))
;; (and (equal (car mergedcode) 'END_OF_CODE)
;; (equal sig-frame 'aftergoto))
;; (if (equal sig-frame 'aftergoto)
;; (and (stack-map? (car mergedcode))
;; (equal (g 'pc (car mergedcode))
;; (g 'pc (cadr mergedcode)))
;; (merged-code-safe (cdr mergedcode)
;; (car mergedcode)))
;; (cond ((stack-map? (car mergedcode))
;; (and (sig-frame-compatible sig-frame (car mergedcode))
;; (merged-code-safe (cdr mergedcode)
;; (car mergedcode))))
;; ((inst? (car mergedcode))
;; (and (equal (g 'pc sig-frame)
;; (g 'pc (car mergedcode)))
;; (bcv-check-step-pre (car mergedcode) sig-frame)
;; (merged-code-safe
;; (cdr mergedcode)
;; (bcv-execute-step (car mergedcode) sig-frame))))
;; (t nil))))))
(defun collect-witness-merged-code-safe (mergedcode sig-frame)
(if (endp mergedcode) nil
(if (endp (cdr mergedcode)) nil
(if (equal sig-frame 'aftergoto)
(and (stack-map? (car mergedcode))
(equal (g 'pc (car mergedcode))
(g 'pc (cadr mergedcode)))
(collect-witness-merged-code-safe
(cdr mergedcode) (car mergedcode)))
(cond ((stack-map? (car mergedcode))
(and (sig-frame-compatible sig-frame (car mergedcode))
(merged-code-safe (cdr mergedcode)
(car mergedcode))
(collect-witness-merged-code-safe
(cdr mergedcode) (car mergedcode))))
((inst? (car mergedcode))
(and (equal (g 'pc sig-frame)
(g 'pc (car mergedcode)))
(bcv-check-step-pre (car mergedcode) sig-frame)
(merged-code-safe
(cdr mergedcode)
(bcv-execute-step (car mergedcode) sig-frame))
(cons (cons (g 'pc sig-frame)
sig-frame)
(collect-witness-merged-code-safe
(cdr mergedcode)
(bcv-execute-step (car mergedcode)
sig-frame)))))
(t nil))))))
(defun collect-witness-bcv-method (method method-table)
(collect-witness-merged-code-safe
(mergeStackMapAndCode
(g 'stackmaps method)
(parsecode (g 'code method))
(g 'method-name method)
method-table)
(SIG-METHOD-INIT-FRAME METHOD METHOD-TABLE)))
;----------------------------------------------------------------------
(defun extract-maps (merged-code)
(if (endp merged-code) nil
(if (endp (cdr merged-code)) nil
(if (stack-map? (car merged-code))
(cons (car merged-code)
(extract-maps (cdr merged-code)))
(extract-maps (cdr merged-code))))))
(defun extract-code (merged-code)
(if (endp merged-code) nil
(if (endp (cdr merged-code)) nil
(if (inst? (car merged-code))
(cons (car merged-code)
(extract-code (cdr merged-code)))
(extract-code (cdr merged-code))))))
;----------------------------------------------------------------------
(defun partial-sig-vector-compatible1 (partial1 partial full)
(if (endp partial1) t
(and (sig-frame-compatible (binding (caar partial1)
partial)
(binding (caar partial1) full))
(partial-sig-vector-compatible1 (cdr partial1) partial full))))
(defun partial-sig-vector-compatible (partial full)
(partial-sig-vector-compatible1 partial partial full))
;----------------------------------------------------------------------
(defun wff-maps-consistent (maps init-frame)
(if (endp maps) t
(and (equal (g 'method-name (car maps))
(g 'method-name init-frame))
(equal (g 'method-table (car maps))
(g 'method-table init-frame))
(wff-maps-consistent (cdr maps) init-frame))))
;----------------------------------------------------------------------
(defun collect-pc-merged-code (merged-code)
(if (endp merged-code) nil
(if (endp (cdr merged-code))
nil
(cons (g 'pc (car merged-code))
(collect-pc-merged-code (cdr merged-code))))))
(defun ordered (pc-list)
(if (endp pc-list)
t
(if (endp (cdr pc-list))
t
(and (<= (car pc-list)
(cadr pc-list))
(ordered (cdr pc-list))))))
;----------------------------------------------------------------------
(defun collect-keys-from-witness (sig-vector)
(if (endp sig-vector) nil
(cons (car (car sig-vector))
(collect-keys-from-witness (cdr sig-vector)))))
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