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    • Atc-symbolic-execution-rules

    Atc-exec-expr-when-asg-indir-rule-generation

    Code to generate the rules for executing assignments to integers by pointer.

    Definitions and Theorems

    Function: atc-exec-expr-when-asg-indir-rules-gen

    (defun atc-exec-expr-when-asg-indir-rules-gen (type)
     (declare (xargs :guard (typep type)))
     (declare (xargs :guard (type-nonchar-integerp type)))
     (let ((__function__ 'atc-exec-expr-when-asg-indir-rules-gen))
      (declare (ignorable __function__))
      (b*
       ((fixtype (integer-type-to-fixtype type))
        (pred (pack fixtype 'p))
        (constructor (pack 'type- fixtype))
        (type-of-value-when-pred (pack 'type-of-value-when- pred))
        (not-pred-of-value-pointer (pack 'not- pred '-of-value-pointer))
        (value-kind-when-pred (pack 'value-kind-when- pred))
        (writer (pack fixtype '-write))
        (name (pack 'exec-expr-when-asg-indir-when-
                    pred))
        (name-mod-proofs (pack name '-for-modular-proofs))
        (formula
         (cons
          'implies
          (cons
           (cons
            'and
            (cons
             '(syntaxp (quotep expr))
             (cons
              '(equal (expr-kind expr) :binary)
              (cons
               '(equal (binop-kind (expr-binary->op expr))
                       :asg)
               (cons
                '(equal left (expr-binary->arg1 expr))
                (cons
                 '(equal right (expr-binary->arg2 expr))
                 (cons
                  '(equal (expr-kind left) :unary)
                  (cons
                   '(equal (unop-kind (expr-unary->op left))
                           :indir)
                   (cons
                    '(equal arg (expr-unary->arg left))
                    (cons
                     '(equal (expr-kind arg) :ident)
                     (cons
                      '(equal var (expr-ident->get arg))
                      (cons
                       '(expr-purep right)
                       (cons
                        '(integerp limit)
                        (cons
                         '(>= limit
                              (1+ (max 2 (expr-pure-limit right))))
                         (cons
                          '(equal ptr (read-var var compst))
                          (cons
                           '(valuep ptr)
                           (cons
                            '(value-case ptr :pointer)
                            (cons
                             '(value-pointer-validp ptr)
                             (cons
                              (cons
                               'equal
                               (cons
                                   '(value-pointer->reftype ptr)
                                   (cons (cons constructor 'nil) 'nil)))
                              (cons
                               '(equal
                                     eval (exec-expr-pure right compst))
                               (cons
                                '(expr-valuep eval)
                                (cons
                                 '(equal
                                      eval1 (apconvert-expr-value eval))
                                 (cons
                                  '(expr-valuep eval1)
                                  (cons
                                   '(equal
                                         val (expr-value->value eval1))
                                   (cons
                                    (cons pred '(val))
                                    '((equal
                                       oldval
                                       (read-object
                                         (value-pointer->designator ptr)
                                         compst))
                                      (valuep oldval)
                                      (not (equal (value-kind oldval)
                                                  :array))
                                      (equal
                                       compst1
                                       (write-object
                                         (value-pointer->designator ptr)
                                         val compst))
                                      (compustatep
                                       compst1)))))))))))))))))))))))))))
           '((equal (exec-expr expr compst fenv limit)
                    (mv (expr-value val nil) compst1))))))
        (formula-mod-proofs
         (cons
          'implies
          (cons
           (cons
            'and
            (cons
             '(syntaxp (quotep expr))
             (cons
              '(equal (expr-kind expr) :binary)
              (cons
               '(equal (binop-kind (expr-binary->op expr))
                       :asg)
               (cons
                '(equal left (expr-binary->arg1 expr))
                (cons
                 '(equal right (expr-binary->arg2 expr))
                 (cons
                  '(equal (expr-kind left) :unary)
                  (cons
                   '(equal (unop-kind (expr-unary->op left))
                           :indir)
                   (cons
                    '(equal arg (expr-unary->arg left))
                    (cons
                     '(equal (expr-kind arg) :ident)
                     (cons
                      '(equal var (expr-ident->get arg))
                      (cons
                       '(expr-purep right)
                       (cons
                        '(integerp limit)
                        (cons
                         '(>= limit
                              (1+ (max 2 (expr-pure-limit right))))
                         (cons
                          '(equal ptr (read-var var compst))
                          (cons
                           '(valuep ptr)
                           (cons
                            '(value-case ptr :pointer)
                            (cons
                             '(value-pointer-validp ptr)
                             (cons
                              (cons
                               'equal
                               (cons
                                   '(value-pointer->reftype ptr)
                                   (cons (cons constructor 'nil) 'nil)))
                              (cons
                               '(equal
                                     eval (exec-expr-pure right compst))
                               (cons
                                '(expr-valuep eval)
                                (cons
                                 '(equal
                                      eval1 (apconvert-expr-value eval))
                                 (cons
                                  '(expr-valuep eval1)
                                  (cons
                                   '(equal
                                         val (expr-value->value eval1))
                                   (cons
                                    (cons pred '(val))
                                    (cons
                                     '(equal
                                       oldval
                                       (read-object
                                         (value-pointer->designator ptr)
                                         compst))
                                     (cons
                                      '(valuep oldval)
                                      (cons
                                       '(not (equal (value-kind oldval)
                                                    :array))
                                       (cons
                                        (cons
                                         'equal
                                         (cons
                                          'compst1
                                          (cons
                                           (cons
                                            'write-object
                                            (cons
                                              '(value-pointer->designator
                                                    ptr)
                                              (cons (cons writer '(val))
                                                    '(compst))))
                                           'nil)))
                                        '((compustatep
                                           compst1)))))))))))))))))))))))))))))))
           '((equal (exec-expr expr compst fenv limit)
                    (mv (expr-value val nil) compst1))))))
        (events
         (cons
          (cons
           'defruled
           (cons
            name
            (cons
             formula
             (cons
              ':expand
              (cons
               '((exec-expr expr compst fenv limit)
                 (exec-expr (expr-binary->arg1 expr)
                            compst fenv (1- limit)))
               (cons
                ':enable
                (cons
                 (cons
                  'exec-expr-to-exec-expr-pure-when-expr-pure-limit
                  (cons
                   'max
                   (cons
                    'nfix
                    (cons
                     'exec-expr
                     (cons
                      'exec-unary
                      (cons
                       'exec-indir
                       (cons
                        'exec-ident
                        (cons
                         'apconvert-expr-value-when-not-value-array-alt
                         (cons
                          'value-kind-when-scharp
                          (cons
                           'read-object-of-objdesign-of-var-to-read-var
                           (cons
                            type-of-value-when-pred
                            (cons
                             not-pred-of-value-pointer
                             (cons
                                  value-kind-when-pred
                                  '(expr-purep binop-purep))))))))))))))
                 (cons
                  ':disable
                  (cons
                   '(equal-of-error equal-of-expr-value)
                   (cons
                    ':prep-lemmas
                    (cons
                     (cons
                      (cons
                       'defrule
                       (cons
                        'lemma
                        (cons
                         (cons
                          'implies
                          (cons
                           (cons
                            'and
                            (cons
                             '(expr-valuep (apconvert-expr-value eval))
                             (cons
                              (cons
                                   pred
                                   '((expr-value->value
                                          (apconvert-expr-value eval))))
                              'nil)))
                           (cons (cons pred '((expr-value->value eval)))
                                 'nil)))
                         '(:enable apconvert-expr-value))))
                      'nil)
                     'nil)))))))))))
          (cons
           (cons
            'defruled
            (cons
               name-mod-proofs
               (cons formula-mod-proofs
                     (cons ':use
                           (cons name
                                 (cons ':enable (cons writer 'nil)))))))
           'nil))))
       (mv name events))))

    Theorem: symbolp-of-atc-exec-expr-when-asg-indir-rules-gen.name

    (defthm symbolp-of-atc-exec-expr-when-asg-indir-rules-gen.name
      (b* (((mv ?name ?events)
            (atc-exec-expr-when-asg-indir-rules-gen type)))
        (symbolp name))
      :rule-classes :rewrite)

    Theorem: pseudo-event-form-listp-of-atc-exec-expr-when-asg-indir-rules-gen.events

    (defthm
     pseudo-event-form-listp-of-atc-exec-expr-when-asg-indir-rules-gen.events
     (b* (((mv ?name ?events)
           (atc-exec-expr-when-asg-indir-rules-gen type)))
       (pseudo-event-form-listp events))
     :rule-classes :rewrite)

    Function: atc-exec-expr-when-asg-indir-rules-gen-loop

    (defun atc-exec-expr-when-asg-indir-rules-gen-loop (types)
     (declare (xargs :guard (type-listp types)))
     (declare (xargs :guard (type-nonchar-integer-listp types)))
     (let ((__function__ 'atc-exec-expr-when-asg-indir-rules-gen-loop))
       (declare (ignorable __function__))
       (b* (((when (endp types)) (mv nil nil))
            ((mv name events)
             (atc-exec-expr-when-asg-indir-rules-gen (car types)))
            ((mv more-names more-events)
             (atc-exec-expr-when-asg-indir-rules-gen-loop (cdr types))))
         (mv (cons name more-names)
             (append events more-events)))))

    Theorem: symbol-listp-of-atc-exec-expr-when-asg-indir-rules-gen-loop.names

    (defthm
      symbol-listp-of-atc-exec-expr-when-asg-indir-rules-gen-loop.names
      (b* (((mv ?names ?events)
            (atc-exec-expr-when-asg-indir-rules-gen-loop types)))
        (symbol-listp names))
      :rule-classes :rewrite)

    Theorem: pseudo-event-form-listp-of-atc-exec-expr-when-asg-indir-rules-gen-loop.events

    (defthm
     pseudo-event-form-listp-of-atc-exec-expr-when-asg-indir-rules-gen-loop.events
     (b* (((mv ?names ?events)
           (atc-exec-expr-when-asg-indir-rules-gen-loop types)))
       (pseudo-event-form-listp events))
     :rule-classes :rewrite)

    Function: atc-exec-expr-when-asg-indir-rules-gen-all

    (defun atc-exec-expr-when-asg-indir-rules-gen-all nil
     (declare (xargs :guard t))
     (let ((__function__ 'atc-exec-expr-when-asg-indir-rules-gen-all))
      (declare (ignorable __function__))
      (b* (((mv names events)
            (atc-exec-expr-when-asg-indir-rules-gen-loop
                 *nonchar-integer-types*)))
       (cons
        'progn
        (cons
         (cons
          'defsection
          (cons
           'atc-exec-expr-when-asg-indir-rules
           (cons
            ':short
            (cons
             '"Rules for executing assignment expressions
                     to integers by pointer."
             (append
              events
              (cons
               (cons
                'defval
                (cons '*atc-exec-expr-when-asg-indir-rules*
                      (cons (cons 'quote
                                  (cons (append names
                                                '((:e expr-kind)
                                                  (:e binop-kind)
                                                  (:e expr-binary->op)
                                                  (:e expr-binary->arg1)
                                                  (:e expr-binary->arg2)
                                                  (:e unop-kind)
                                                  (:e expr-unary->op)
                                                  (:e expr-unary->arg)
                                                  (:e expr-ident->get)))
                                        'nil))
                            'nil)))
               'nil))))))
         'nil)))))

    Theorem: pseudo-event-formp-of-atc-exec-expr-when-asg-indir-rules-gen-all

    (defthm
       pseudo-event-formp-of-atc-exec-expr-when-asg-indir-rules-gen-all
      (b* ((event (atc-exec-expr-when-asg-indir-rules-gen-all)))
        (pseudo-event-formp event))
      :rule-classes :rewrite)