Co2sobj_prop.thy
changeset 40 8557d7872fdb
parent 34 e7f850d1e08e
child 41 db15ef2ee18c
equal deleted inserted replaced
39:13bba99ca090 40:8557d7872fdb
   413 apply (frule is_file_in_current)
   413 apply (frule is_file_in_current)
   414 apply (drule current_file_has_sfile, simp)
   414 apply (drule current_file_has_sfile, simp)
   415 apply (auto simp:cf2sfile_def sectxt_of_pf_def get_parentfs_ctxts'_def split:if_splits option.splits)
   415 apply (auto simp:cf2sfile_def sectxt_of_pf_def get_parentfs_ctxts'_def split:if_splits option.splits)
   416 done
   416 done
   417 
   417 
       
   418 lemma is_file_has_sfile':
       
   419   "\<lbrakk>is_file s f; valid s\<rbrakk> \<Longrightarrow> \<exists> sf. cf2sfile s f = Some sf"
       
   420 by (drule is_file_has_sfile, auto)
       
   421 
   418 lemma is_dir_has_sfile:
   422 lemma is_dir_has_sfile:
   419   "\<lbrakk>is_dir s f; valid s\<rbrakk> \<Longrightarrow> (case f of
   423   "\<lbrakk>is_dir s f; valid s\<rbrakk> \<Longrightarrow> (case f of
   420       [] \<Rightarrow> cf2sfile s f = Some sroot
   424       [] \<Rightarrow> cf2sfile s f = Some sroot
   421     | a # pf \<Rightarrow> (\<exists> sec psec asecs. cf2sfile s f = Some 
   425     | a # pf \<Rightarrow> (\<exists> sec psec asecs. cf2sfile s f = Some 
   422       (if (\<not> deleted (O_dir f) s \<and> is_init_dir f) then Init f else Created,
   426       (if (\<not> deleted (O_dir f) s \<and> is_init_dir f) then Init f else Created,
   424        (sectxt_of_obj s (O_dir pf) = Some psec) \<and> (get_parentfs_ctxts s pf = Some asecs)))"
   428        (sectxt_of_obj s (O_dir pf) = Some psec) \<and> (get_parentfs_ctxts s pf = Some asecs)))"
   425 apply (case_tac f, simp add:sroot_only)
   429 apply (case_tac f, simp add:sroot_only)
   426 apply (frule is_dir_in_current, frule is_dir_not_file)
   430 apply (frule is_dir_in_current, frule is_dir_not_file)
   427 apply (drule current_file_has_sfile, simp)
   431 apply (drule current_file_has_sfile, simp)
   428 apply (auto simp:cf2sfile_def split:if_splits option.splits)
   432 apply (auto simp:cf2sfile_def split:if_splits option.splits)
       
   433 done
       
   434 
       
   435 lemma is_dir_has_sdir':
       
   436   "\<lbrakk>is_dir s f; valid s\<rbrakk> \<Longrightarrow> \<exists> sf. cf2sfile s f = Some sf"
       
   437 apply (case_tac f)
       
   438 apply (rule_tac x = sroot in exI)
       
   439 apply (simp add:sroot_only)
       
   440 apply (drule is_dir_has_sfile, auto)
   429 done
   441 done
   430 
   442 
   431 lemma sroot_set:
   443 lemma sroot_set:
   432   "valid s \<Longrightarrow> \<exists> sec. sroot = (Init [], sec, None, {}) \<and> sectxt_of_obj s (O_dir []) = Some sec"
   444   "valid s \<Longrightarrow> \<exists> sec. sroot = (Init [], sec, None, {}) \<and> sectxt_of_obj s (O_dir []) = Some sec"
   433 apply (frule root_is_dir)
   445 apply (frule root_is_dir)
  1596 by (drule_tac p'= p' in cp2sproc_exit, simp+)
  1608 by (drule_tac p'= p' in cp2sproc_exit, simp+)
  1597 
  1609 
  1598 lemmas cp2sproc_simps = cp2sproc_open cp2sproc_closefd cp2sproc_attach cp2sproc_detach cp2sproc_deleteshm
  1610 lemmas cp2sproc_simps = cp2sproc_open cp2sproc_closefd cp2sproc_attach cp2sproc_detach cp2sproc_deleteshm
  1599   cp2sproc_clone cp2sproc_execve cp2sproc_kill cp2sproc_exit cp2sproc_other 
  1611   cp2sproc_clone cp2sproc_execve cp2sproc_kill cp2sproc_exit cp2sproc_other 
  1600 
  1612 
       
  1613 lemma current_proc_has_sp:
       
  1614   "\<lbrakk>p \<in> current_procs s; valid s\<rbrakk> \<Longrightarrow> \<exists> sp. cp2sproc s p = Some sp"
       
  1615 by (auto simp:cp2sproc_def split:option.splits dest!:current_has_sec')
       
  1616 
       
  1617 lemma current_proc_has_sp':
       
  1618   "\<lbrakk>cp2sproc s p = None; valid s\<rbrakk> \<Longrightarrow> p \<notin> current_procs s"
       
  1619 by (auto dest:current_proc_has_sp)
       
  1620 
       
  1621 
       
  1622 
       
  1623 (* simpset for cf2sfiles *)
       
  1624 
       
  1625 lemma cf2sfiles_open:
       
  1626   "\<lbrakk>valid (Open p f flag fd opt # s); f' \<in> current_files (Open p f flag fd opt # s)\<rbrakk>
       
  1627    \<Longrightarrow> cf2sfiles (Open p f flag fd opt # s) f' = (
       
  1628      if (f' = f \<and> opt \<noteq> None) 
       
  1629      then (case cf2sfile (Open p f flag fd opt # s) f of 
       
  1630              Some sf \<Rightarrow> {sf}  
       
  1631            | _       \<Rightarrow> {} )
       
  1632      else cf2sfiles s f')"
       
  1633 apply (frule vt_grant_os, frule vd_cons)
       
  1634 apply (auto simp:cf2sfiles_def cf2sfile_open_none cf2sfile_simps same_inode_files_open
       
  1635   split:if_splits option.splits dest!:current_file_has_sfile' dest:cf2sfile_open)
       
  1636 apply (rule_tac x = "f'a" in bexI, drule same_inode_files_prop1, simp add:cf2sfile_open_some1, simp)+
       
  1637 done
       
  1638 
       
  1639 lemma cf2sfiles_other:
       
  1640   "\<lbrakk>valid (e # s);
       
  1641     \<forall> p f flag fd opt. e \<noteq> Open p f flag fd opt;
       
  1642     \<forall> p fd. e \<noteq> CloseFd p fd;
       
  1643     \<forall> p f. e \<noteq> UnLink p f;
       
  1644     \<forall> p f f'. e \<noteq> LinkHard p f f'\<rbrakk> \<Longrightarrow> cf2sfiles (e # s) = cf2sfiles s"
       
  1645 apply (frule vt_grant_os, frule vd_cons, rule ext)
       
  1646 apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI)
       
  1647 apply (drule Set.CollectD, erule bexE, rule CollectI)
       
  1648 apply (rule_tac x = f' in bexI, case_tac e)
       
  1649 apply (auto simp:cf2sfiles_def cf2sfile_simps same_inode_files_simps current_files_simps
       
  1650   split:if_splits option.splits dest!:current_file_has_sfile' dest:same_inode_files_prop1 cf2sfile_other')
       
  1651 apply (drule_tac f' = f' in cf2sfile_rmdir)
       
  1652 apply (simp add:current_files_simps same_inode_files_prop1 same_inode_files_prop3 dir_is_empty_def)+
       
  1653 
       
  1654 apply (rule_tac x = f' in bexI, case_tac e)
       
  1655 apply (auto simp:cf2sfiles_def cf2sfile_simps same_inode_files_simps current_files_simps
       
  1656   split:if_splits option.splits dest!:current_file_has_sfile' dest:same_inode_files_prop1 cf2sfile_other')
       
  1657 apply (drule_tac f' = f' in cf2sfile_rmdir)
       
  1658 apply (simp add:current_files_simps same_inode_files_prop1 same_inode_files_prop3 dir_is_empty_def)+
       
  1659 done
       
  1660 
       
  1661 lemma cf2sfile_linkhard1':
       
  1662   "\<lbrakk>valid (LinkHard p oldf f # s); f' \<in> same_inode_files s f''\<rbrakk>
       
  1663    \<Longrightarrow> cf2sfile (LinkHard p oldf f# s) f' = cf2sfile s f'"
       
  1664 apply (drule same_inode_files_prop1)
       
  1665 by (simp add:cf2sfile_linkhard1)
       
  1666 
       
  1667 lemma cf2sfiles_linkhard:
       
  1668   "valid (LinkHard p oldf f # s) \<Longrightarrow> cf2sfiles (LinkHard p oldf f # s) = (\<lambda> f'. 
       
  1669      if (f' = f \<or> f' \<in> same_inode_files s oldf)
       
  1670      then (case (cf2sfile (LinkHard p oldf f # s) f) of
       
  1671              Some sf \<Rightarrow> cf2sfiles s oldf \<union> {sf}
       
  1672            | _       \<Rightarrow> {})
       
  1673      else cf2sfiles s f')"
       
  1674 apply (frule vt_grant_os, frule vd_cons, rule ext)
       
  1675 apply (auto simp:cf2sfiles_def cf2sfile_linkhard1' same_inode_files_linkhard current_files_linkhard 
       
  1676   split:if_splits option.splits dest!:current_file_has_sfile' current_has_sec' dest:same_inode_files_prop1)
       
  1677 done
       
  1678 
       
  1679 lemma cf2sfile_unlink':
       
  1680   "\<lbrakk>valid (UnLink p f # s); f' \<in> same_inode_files (UnLink p f # s) f''\<rbrakk>
       
  1681    \<Longrightarrow> cf2sfile (UnLink p f # s) f' = cf2sfile s f'"
       
  1682 apply (drule same_inode_files_prop1)
       
  1683 by (simp add:cf2sfile_unlink)
       
  1684 
       
  1685 lemma cf2sfiles_unlink:
       
  1686   "\<lbrakk>valid (UnLink p f # s); f' \<in> current_files (UnLink p f # s)\<rbrakk> \<Longrightarrow> cf2sfiles (UnLink p f # s) f' = ( 
       
  1687      if (f' \<in> same_inode_files s f \<and> proc_fd_of_file s f = {} \<and> 
       
  1688          (\<forall> f'' \<in> same_inode_files s f. f'' \<noteq> f \<longrightarrow> cf2sfile s f'' \<noteq> cf2sfile s f)) then 
       
  1689         (case (cf2sfile s f) of 
       
  1690            Some sf \<Rightarrow> cf2sfiles s f' - {sf}
       
  1691          | _       \<Rightarrow> {})
       
  1692      else cf2sfiles s f')"
       
  1693 apply (frule vt_grant_os, frule vd_cons, simp add:current_files_simps split:if_splits)
       
  1694 apply (rule conjI, clarify, frule is_file_has_sfile', simp, erule exE, simp)
       
  1695 apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
       
  1696 apply (erule bexE, frule_tac f' = f' in same_inode_files_unlink)
       
  1697 apply (simp add:current_files_unlink, simp, erule conjE)
       
  1698 apply (erule_tac x = f'a in ballE, frule_tac f' = "f'a" in cf2sfile_unlink)
       
  1699 apply (simp add:current_files_unlink same_inode_files_prop1, simp)
       
  1700 apply (rule_tac x = f'a in bexI, simp, simp)
       
  1701 apply (drule_tac f = f and f' = f' and f'' = f'a in same_inode_files_prop4, simp+)
       
  1702 apply (erule conjE|erule exE|erule bexE)+
       
  1703 apply (case_tac "f'a = f", simp)
       
  1704 apply (frule_tac f' = f' in same_inode_files_unlink, simp add:current_files_unlink)
       
  1705 apply (frule_tac f' = f'a in cf2sfile_unlink, simp add:current_files_unlink same_inode_files_prop1)
       
  1706 apply (rule_tac x = f'a in bexI, simp, simp)
       
  1707 
       
  1708 apply (rule impI)+
       
  1709 apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
       
  1710 apply (erule bexE, frule_tac f' = f' in same_inode_files_unlink)
       
  1711 apply (simp add:current_files_unlink, simp, (erule conjE)+)
       
  1712 apply (rule_tac x = f'a in bexI, frule_tac f' = "f'a" in cf2sfile_unlink)
       
  1713 apply (simp add:current_files_unlink same_inode_files_prop1, simp, simp)
       
  1714 apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_unlink)
       
  1715 apply (simp add:current_files_unlink, simp)
       
  1716 apply (case_tac "f'a = f", simp)
       
  1717 apply (frule_tac f = f' and f' = f in same_inode_files_prop5, simp)
       
  1718 apply (erule bexE, erule conjE)
       
  1719 apply (rule_tac x = f'' in bexI)
       
  1720 apply (drule_tac f' = f'' in cf2sfile_unlink, simp add:current_files_unlink same_inode_files_prop1)
       
  1721 apply (simp, simp, erule same_inode_files_prop4, simp)
       
  1722 apply (rule_tac x = f'a in bexI)
       
  1723 apply (drule_tac f' = f'a in cf2sfile_unlink, simp add:current_files_unlink same_inode_files_prop1)
       
  1724 apply (simp, simp)
       
  1725 
       
  1726 
       
  1727 apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
       
  1728 apply (erule bexE, frule_tac f' = f' in same_inode_files_unlink)
       
  1729 apply (simp add:current_files_unlink, simp)
       
  1730 apply (rule_tac x = f'a in bexI)
       
  1731 apply (frule_tac f' = f'a in cf2sfile_unlink)
       
  1732 apply (simp add:same_inode_files_prop1 current_files_unlink, simp, simp)
       
  1733 apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_unlink)
       
  1734 apply (simp add:current_files_unlink, simp)
       
  1735 apply (rule_tac x = f'a in bexI)
       
  1736 apply (frule_tac f' = f'a in cf2sfile_unlink)
       
  1737 apply (simp add:same_inode_files_prop1 current_files_unlink, simp, simp)
       
  1738 done
       
  1739 
       
  1740 lemma cf2sfiles_closefd:
       
  1741   "\<lbrakk>valid (CloseFd p fd # s); f' \<in> current_files (CloseFd p fd # s)\<rbrakk> \<Longrightarrow> cf2sfiles (CloseFd p fd # s) f' = (
       
  1742      case (file_of_proc_fd s p fd) of
       
  1743        Some f \<Rightarrow> if (f' \<in> same_inode_files s f \<and> proc_fd_of_file s f = {(p, fd)} \<and> f \<in> files_hung_by_del s \<and> 
       
  1744                     (\<forall> f'' \<in> same_inode_files s f. f'' \<noteq> f \<longrightarrow> cf2sfile s f'' \<noteq> cf2sfile s f)) 
       
  1745                  then (case (cf2sfile s f) of 
       
  1746                          Some sf \<Rightarrow> cf2sfiles s f' - {sf}
       
  1747                        | _       \<Rightarrow> {})
       
  1748                  else cf2sfiles s f'
       
  1749      | _       \<Rightarrow> cf2sfiles s f')"
       
  1750 
       
  1751 apply (frule vt_grant_os, frule vd_cons, case_tac "file_of_proc_fd s p fd")
       
  1752 apply (simp_all add:current_files_simps split:if_splits)
       
  1753 
       
  1754 apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
       
  1755 apply (erule bexE, frule_tac f' = f' in same_inode_files_closefd)
       
  1756 apply (simp add:current_files_closefd, simp)
       
  1757 apply (rule_tac x = f'a in bexI)
       
  1758 apply (frule_tac f = f'a in cf2sfile_closefd)
       
  1759 apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
       
  1760 apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_closefd)
       
  1761 apply (simp add:current_files_closefd, simp)
       
  1762 apply (rule_tac x = f'a in bexI)
       
  1763 apply (frule_tac f = f'a in cf2sfile_closefd)
       
  1764 apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
       
  1765 
       
  1766 apply (rule conjI, clarify, frule file_of_pfd_is_file, simp)
       
  1767 apply (frule is_file_has_sfile', simp, erule exE, simp)
       
  1768 apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
       
  1769 apply (erule bexE, frule_tac f' = f' in same_inode_files_closefd)
       
  1770 apply (simp add:current_files_closefd, simp, erule conjE)
       
  1771 apply (erule_tac x = f'a in ballE, frule_tac f = "f'a" in cf2sfile_closefd)
       
  1772 apply (simp add:current_files_closefd same_inode_files_prop1, simp)
       
  1773 apply (rule_tac x = f'a in bexI, simp, simp)
       
  1774 apply (drule_tac f = a and f' = f' and f'' = f'a in same_inode_files_prop4, simp+)
       
  1775 apply (erule conjE|erule exE|erule bexE)+
       
  1776 apply (case_tac "f'a = a", simp)
       
  1777 apply (frule_tac f' = f' in same_inode_files_closefd, simp add:current_files_closefd, simp)
       
  1778 apply (frule_tac f = f'a in cf2sfile_closefd, simp add:current_files_closefd same_inode_files_prop1)
       
  1779 apply (rule_tac x = f'a in bexI, simp, simp)
       
  1780 
       
  1781 apply (rule impI)+
       
  1782 apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
       
  1783 apply (erule bexE, frule_tac f' = f' in same_inode_files_closefd)
       
  1784 apply (simp add:current_files_closefd, simp, (erule conjE)+)
       
  1785 apply (rule_tac x = f'a in bexI, frule_tac f = f'a in cf2sfile_closefd)
       
  1786 apply (simp add:current_files_closefd same_inode_files_prop1, simp, simp)
       
  1787 apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_closefd)
       
  1788 apply (simp add:current_files_closefd, simp)
       
  1789 apply (case_tac "f'a = a", simp)
       
  1790 apply (frule_tac f = f' and f' = a in same_inode_files_prop5, simp)
       
  1791 apply (erule bexE, erule conjE)
       
  1792 apply (rule_tac x = f'' in bexI)
       
  1793 apply (drule_tac f = f'' in cf2sfile_closefd, simp add:current_files_closefd same_inode_files_prop1)
       
  1794 apply (simp, simp, erule same_inode_files_prop4, simp)
       
  1795 apply (rule_tac x = f'a in bexI)
       
  1796 apply (drule_tac f = f'a in cf2sfile_closefd, simp add:current_files_closefd same_inode_files_prop1)
       
  1797 apply (simp, simp)
       
  1798 
       
  1799 apply (rule conjI, clarify)
       
  1800 
       
  1801 apply (rule impI)
       
  1802 apply (case_tac "a \<in> files_hung_by_del s", simp_all)
       
  1803 apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
       
  1804 apply (erule bexE, frule_tac f' = f' in same_inode_files_closefd)
       
  1805 apply (simp add:current_files_closefd, simp)
       
  1806 apply (rule_tac x = f'a in bexI)
       
  1807 apply (frule_tac f = f'a in cf2sfile_closefd)
       
  1808 apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
       
  1809 apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_closefd)
       
  1810 apply (simp add:current_files_closefd, simp)
       
  1811 apply (rule_tac x = f'a in bexI)
       
  1812 apply (frule_tac f = f'a in cf2sfile_closefd)
       
  1813 apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
       
  1814 apply (simp add:cf2sfiles_def, rule set_eqI, rule iffI, drule CollectD)
       
  1815 apply (erule bexE, frule_tac f' = f' in same_inode_files_closefd)
       
  1816 apply (simp add:current_files_closefd, simp)
       
  1817 apply (rule_tac x = f'a in bexI)
       
  1818 apply (frule_tac f = f'a in cf2sfile_closefd)
       
  1819 apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
       
  1820 apply (drule CollectD, erule bexE, frule_tac f' = f' in same_inode_files_closefd)
       
  1821 apply (simp add:current_files_closefd, simp)
       
  1822 apply (rule_tac x = f'a in bexI)
       
  1823 apply (frule_tac f = f'a in cf2sfile_closefd)
       
  1824 apply (simp add:same_inode_files_prop1 current_files_closefd, simp, simp)
       
  1825 done
       
  1826 
       
  1827 lemmas cf2sfiles_simps = cf2sfiles_open cf2sfiles_linkhard cf2sfiles_other
       
  1828   cf2sfiles_unlink cf2sfiles_closefd
       
  1829   
       
  1830 
       
  1831 (* simpset for co2sobj *)
       
  1832 
       
  1833 lemma co2sobj_execve:
       
  1834   "\<lbrakk>valid (Execve p f fds # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Execve p f fds # s) obj = (
       
  1835       if (obj = O_proc p)
       
  1836       then (case (cp2sproc (Execve p f fds # s) p) of
       
  1837               Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> Tainted s \<or> O_file f \<in> Tainted s))
       
  1838             | _       \<Rightarrow> None) 
       
  1839       else co2sobj s obj )"
       
  1840 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  1841 apply (simp_all add:current_files_simps cf2sfiles_other ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  1842 apply (case_tac "cp2sproc (Execve p f fds # s) p")
       
  1843 apply (drule current_proc_has_sp', simp, simp)
       
  1844 apply (simp (no_asm_simp) add:cp2sproc_execve tainted_eq_Tainted split:option.splits)
       
  1845 apply (frule_tac s = s in is_dir_has_sdir', simp, erule exE, simp)
       
  1846 apply (frule_tac ff = list in cf2sfile_other', simp_all)
       
  1847 apply (simp add:is_dir_in_current)
       
  1848 done
       
  1849 
       
  1850 lemma co2sobj_clone:
       
  1851   "\<lbrakk>valid (Clone p p' fds shms # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Clone p p' fds shms # s) obj = (
       
  1852       if (obj = O_proc p')
       
  1853       then (case (cp2sproc (Clone p p' fds shms # s) p') of
       
  1854               Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> Tainted s))
       
  1855             | _       \<Rightarrow> None)
       
  1856       else co2sobj s obj )"
       
  1857 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  1858 apply (simp_all add:current_files_simps cf2sfiles_other ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  1859 apply (case_tac "cp2sproc (Clone p p' fds shms # s) p'")
       
  1860 apply (drule current_proc_has_sp', simp, simp)
       
  1861 apply ((erule conjE)+, frule_tac p = p in current_proc_has_sec, simp, erule exE, simp)
       
  1862 apply (rule conjI, rule impI, simp)
       
  1863 apply (simp (no_asm_simp) add:cp2sproc_clone tainted_eq_Tainted split:option.splits)
       
  1864 
       
  1865 apply (frule_tac s = s in is_dir_has_sdir', simp, erule exE, simp)
       
  1866 apply (frule_tac ff = list in cf2sfile_other', simp_all)
       
  1867 apply (simp add:is_dir_in_current)
       
  1868 done
       
  1869 
       
  1870 lemma co2sobj_ptrace:
       
  1871   "\<lbrakk>valid (Ptrace p p' # s); alive s obj\<rbrakk>\<Longrightarrow> co2sobj (Ptrace p p' # s) obj = (
       
  1872      case obj of
       
  1873        O_proc p'' \<Rightarrow> if (info_flow_shm s p' p'') 
       
  1874                      then (case (cp2sproc s p'') of 
       
  1875                              Some sp \<Rightarrow> Some (S_proc sp (O_proc p'' \<in> Tainted s \<or> O_proc p \<in> Tainted s))
       
  1876                            | _       \<Rightarrow> None)
       
  1877                      else if (info_flow_shm s p p'')
       
  1878                           then (case (cp2sproc s p'') of 
       
  1879                                   Some sp \<Rightarrow> Some (S_proc sp (O_proc p'' \<in> Tainted s \<or> O_proc p' \<in> Tainted s))
       
  1880                                 | _       \<Rightarrow> None)
       
  1881                           else co2sobj s (O_proc p'')
       
  1882     | _          \<Rightarrow> co2sobj s obj)"
       
  1883 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  1884 apply (simp_all add:current_files_simps ch2sshm_other cq2smsgq_other cf2sfiles_other tainted_eq_Tainted)
       
  1885 
       
  1886 apply (auto simp:cp2sproc_other tainted_eq_Tainted split:option.splits
       
  1887   dest!:current_proc_has_sec' current_proc_has_sp' intro:info_flow_shm_Tainted)[1]
       
  1888 
       
  1889 apply (frule_tac s = s in is_dir_has_sdir', simp, erule exE, simp)
       
  1890 apply (frule_tac ff = list in cf2sfile_other', simp_all)
       
  1891 apply (simp add:is_dir_in_current)
       
  1892 done
       
  1893 
       
  1894 lemma co2sobj_open:
       
  1895   "\<lbrakk>valid (Open p f flag fd opt # s); alive (Open p f flag fd opt # s) obj\<rbrakk> 
       
  1896    \<Longrightarrow> co2sobj (Open p f flag fd opt # s) obj = (case obj of 
       
  1897      O_file f' \<Rightarrow> if (f' = f \<and> opt \<noteq> None)
       
  1898                   then (case (cf2sfile (Open p f flag fd opt # s) f) of
       
  1899                           Some sf \<Rightarrow> Some (S_file {sf} (O_proc p \<in> Tainted s))
       
  1900                         | _       \<Rightarrow> None)
       
  1901                   else co2sobj s (O_file f')
       
  1902    | O_proc p' \<Rightarrow> if (p' = p) 
       
  1903                   then (case (cp2sproc (Open p f flag fd opt # s) p) of
       
  1904                           Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> Tainted s))
       
  1905                         | _       \<Rightarrow> None)
       
  1906                   else co2sobj s (O_proc p')
       
  1907    | _         \<Rightarrow> co2sobj s obj )"
       
  1908 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  1909 apply (auto simp:cp2sproc_simps tainted_eq_Tainted split:option.splits
       
  1910            dest!:current_proc_has_sp' intro:info_flow_shm_Tainted)[1]
       
  1911 
       
  1912 apply (simp split:if_splits t_object.splits)
       
  1913 apply (rule conjI, rule impI, erule conjE, erule exE, simp, (erule exE|erule conjE)+)
       
  1914 apply (case_tac "cf2sfile (Open p f flag fd (Some y) # s) f")
       
  1915 apply (drule current_file_has_sfile', simp, simp add:current_files_simps, simp)
       
  1916 apply (frule_tac f' = f in cf2sfiles_open, simp add:current_files_simps)
       
  1917 apply (simp add:tainted_eq_Tainted)
       
  1918 apply (rule impI, rule notI, drule Tainted_in_current, simp, simp add:is_file_in_current)
       
  1919 apply (rule impI, simp add:tainted_eq_Tainted cf2sfiles_open is_file_in_current split:option.splits)
       
  1920 
       
  1921 apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  1922 
       
  1923 apply (frule is_dir_in_current)
       
  1924 apply (frule_tac f' = list in cf2sfile_open)
       
  1925 apply (simp add:current_files_simps split:option.splits)
       
  1926 apply (simp split:if_splits option.splits)
       
  1927 done
       
  1928 
       
  1929 lemma co2sobj_readfile:
       
  1930   "\<lbrakk>valid (ReadFile p fd # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (ReadFile p fd # s) obj = (
       
  1931      case obj of
       
  1932        O_proc p' \<Rightarrow> (case (file_of_proc_fd s p fd) of
       
  1933                        Some f \<Rightarrow> (if (info_flow_shm s p p' \<and> O_file f \<in> Tainted s)
       
  1934                                   then (case (cp2sproc s p') of
       
  1935                                           Some sp \<Rightarrow> Some (S_proc sp True)
       
  1936                                         | _       \<Rightarrow> None)
       
  1937                                   else co2sobj s obj)
       
  1938                     | _       \<Rightarrow> None)
       
  1939      | _         \<Rightarrow> co2sobj s obj)"
       
  1940 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  1941 apply (auto simp:cp2sproc_simps tainted_eq_Tainted split:option.splits
       
  1942            dest!:current_proc_has_sp' intro:info_flow_shm_Tainted)[1]
       
  1943 apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  1944 
       
  1945 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' 
       
  1946              simp:current_files_simps cf2sfiles_simps cf2sfile_simps 
       
  1947              dest:is_file_in_current is_dir_in_current)
       
  1948 done
       
  1949 
       
  1950 lemma co2sobj_writefile:
       
  1951   "\<lbrakk>valid (WriteFile p fd # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (WriteFile p fd # s) obj = (
       
  1952      case obj of
       
  1953        O_file f' \<Rightarrow> (case (file_of_proc_fd s p fd) of
       
  1954                        Some f \<Rightarrow> (if (f \<in> same_inode_files s f') 
       
  1955                                   then Some (S_file (cf2sfiles s f') 
       
  1956                                                     (O_file f' \<in> Tainted s \<or> O_proc p \<in> Tainted s))
       
  1957                                   else co2sobj s obj)
       
  1958                     | _       \<Rightarrow> None)
       
  1959      | _         \<Rightarrow> co2sobj s obj)"
       
  1960 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  1961 apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  1962 
       
  1963 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
       
  1964              simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
       
  1965                   same_inode_files_prop6
       
  1966              dest:is_file_in_current is_dir_in_current)
       
  1967 
       
  1968 (* should delete has_same_inode !?!?*)
       
  1969 by (auto simp:same_inode_files_def is_file_def has_same_inode_def split:if_splits option.splits)
       
  1970 
       
  1971 lemma co2sobj_closefd:
       
  1972   "\<lbrakk>valid (CloseFd p fd # s); alive (CloseFd p fd # s) obj\<rbrakk> \<Longrightarrow> co2sobj (CloseFd p fd # s) obj = (
       
  1973       case obj of 
       
  1974         O_file f' \<Rightarrow> (case (file_of_proc_fd s p fd) of 
       
  1975                         Some f \<Rightarrow> (if (f' \<in> same_inode_files s f \<and> proc_fd_of_file s f = {(p, fd)} \<and>
       
  1976                                        f \<in> files_hung_by_del s \<and> (\<forall> f'' \<in> same_inode_files s f. 
       
  1977                                        f'' \<noteq> f \<longrightarrow> cf2sfile s f'' \<noteq> cf2sfile s f))
       
  1978                                    then (case (cf2sfile s f, co2sobj s (O_file f')) of
       
  1979                                            (Some sf, Some (S_file sfs b)) \<Rightarrow> Some (S_file (sfs - {sf}) b)
       
  1980                                          | _                              \<Rightarrow> None)
       
  1981                                    else co2sobj s obj)
       
  1982                      | _       \<Rightarrow> co2sobj s obj)
       
  1983       | O_proc p' \<Rightarrow> (if (p = p') 
       
  1984                       then (case (cp2sproc (CloseFd p fd # s) p) of
       
  1985                               Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> Tainted s))
       
  1986                             | _       \<Rightarrow> None)
       
  1987                       else co2sobj s obj)
       
  1988       | _         \<Rightarrow> co2sobj s obj) "
       
  1989 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  1990 apply (simp_all add:current_files_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  1991 apply (auto simp:cp2sproc_simps tainted_eq_Tainted split:option.splits if_splits
       
  1992            dest!:current_proc_has_sp' intro:info_flow_shm_Tainted)[1]
       
  1993 
       
  1994 apply (frule is_file_in_current)
       
  1995 apply (case_tac "file_of_proc_fd s p fd")
       
  1996 apply (simp add:tainted_eq_Tainted)
       
  1997 apply (drule_tac f' = list in cf2sfiles_closefd, simp add:current_files_closefd, simp)
       
  1998 apply (frule_tac f' = list in cf2sfiles_closefd, simp)
       
  1999 apply (simp add:is_file_simps current_files_simps)
       
  2000 apply (auto simp add:tainted_eq_Tainted cf2sfile_closefd split:if_splits option.splits
       
  2001   dest!:current_file_has_sfile' dest:hung_file_in_current)[1]
       
  2002 
       
  2003 apply (simp add:is_dir_simps, frule is_dir_in_current)
       
  2004 apply (frule_tac f = list in cf2sfile_closefd)
       
  2005 apply (clarsimp simp:current_files_closefd split:option.splits)
       
  2006 apply (drule file_of_pfd_is_file', simp+)
       
  2007 done
       
  2008 
       
  2009 lemma co2sobj_unlink:
       
  2010   "\<lbrakk>valid (UnLink p f # s); alive (UnLink p f # s) obj\<rbrakk> \<Longrightarrow> co2sobj (UnLink p f # s) obj = (
       
  2011       case obj of
       
  2012         O_file f' \<Rightarrow> if (f' \<in> same_inode_files s f \<and> proc_fd_of_file s f = {} \<and> 
       
  2013                         (\<forall> f'' \<in> same_inode_files s f. f'' \<noteq> f \<longrightarrow> cf2sfile s f'' \<noteq> cf2sfile s f))
       
  2014                      then (case (cf2sfile s f, co2sobj s (O_file f')) of
       
  2015                              (Some sf, Some (S_file sfs b)) \<Rightarrow> Some (S_file (sfs - {sf}) b)
       
  2016                            | _                              \<Rightarrow> None)
       
  2017                      else co2sobj s obj
       
  2018       | _         \<Rightarrow> co2sobj s obj)"
       
  2019 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  2020 apply (simp_all add:current_files_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  2021 apply (auto simp:cp2sproc_simps tainted_eq_Tainted split:option.splits if_splits
       
  2022            dest!:current_proc_has_sp' intro:info_flow_shm_Tainted)[1]
       
  2023 apply (frule is_file_in_current)
       
  2024 apply (frule_tac f' = list in cf2sfile_unlink, simp)
       
  2025 apply (frule_tac f' = list in cf2sfiles_unlink, simp)
       
  2026 apply (simp add:is_file_simps current_files_simps)
       
  2027 apply (auto simp add:tainted_eq_Tainted is_file_in_current split:if_splits option.splits
       
  2028   dest!:current_file_has_sfile')[1]
       
  2029 
       
  2030 apply (simp add:is_dir_simps, frule is_dir_in_current)
       
  2031 apply (frule_tac f' = list in cf2sfile_unlink)
       
  2032 apply (clarsimp simp:current_files_unlink split:option.splits)
       
  2033 apply (drule file_dir_conflict, simp+)
       
  2034 done
       
  2035 
       
  2036 lemma co2sobj_rmdir:
       
  2037   "\<lbrakk>valid (Rmdir p f # s); alive (Rmdir p f # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Rmdir p f # s) obj = co2sobj s obj"
       
  2038 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  2039 apply (simp_all add:current_files_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  2040 apply (auto simp:cp2sproc_simps tainted_eq_Tainted split:option.splits if_splits
       
  2041            dest!:current_proc_has_sp' intro:info_flow_shm_Tainted)[1]
       
  2042 apply (simp add:is_file_simps dir_is_empty_def)
       
  2043 apply (case_tac "f = list", drule file_dir_conflict, simp, simp)
       
  2044 apply (simp add:cf2sfiles_other)
       
  2045 apply (auto simp:cf2sfile_simps dest:is_dir_in_current)
       
  2046 done
       
  2047 
       
  2048 lemma co2sobj_mkdir:
       
  2049   "\<lbrakk>valid (Mkdir p f i # s); alive (Mkdir p f i # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Mkdir p f i # s) obj = (
       
  2050       if (obj = O_dir f) 
       
  2051       then (case (cf2sfile (Mkdir p f i # s) f) of 
       
  2052               Some sf \<Rightarrow> Some (S_dir sf)
       
  2053             | _       \<Rightarrow> None)
       
  2054       else co2sobj s obj)"
       
  2055 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  2056 apply (simp_all add:current_files_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  2057 apply (auto simp:cp2sproc_simps tainted_eq_Tainted split:option.splits if_splits
       
  2058            dest!:current_proc_has_sp' intro:info_flow_shm_Tainted)[1]
       
  2059 apply (frule_tac cf2sfiles_other, simp+)
       
  2060 apply (frule is_dir_in_current, rule impI, simp add:current_files_mkdir)
       
  2061 apply (frule current_file_has_sfile, simp, erule exE, simp)
       
  2062 apply (drule cf2sfile_mkdir1, simp+)
       
  2063 done
       
  2064 
       
  2065 lemma same_inodes_Tainted:
       
  2066   "\<lbrakk>f \<in> same_inode_files s f'; valid s\<rbrakk> \<Longrightarrow> (O_file f \<in> Tainted s) = (O_file f' \<in> Tainted s)"
       
  2067 apply (frule same_inode_files_prop8, frule same_inode_files_prop7)
       
  2068 apply (auto intro:has_same_inode_Tainted)
       
  2069 done
       
  2070 
       
  2071 lemma co2sobj_linkhard:
       
  2072   "\<lbrakk>valid (LinkHard p oldf f # s); alive (LinkHard p oldf f # s) obj\<rbrakk> 
       
  2073    \<Longrightarrow> co2sobj (LinkHard p oldf f # s) obj = (
       
  2074     case obj of
       
  2075       O_file f' \<Rightarrow> if (f' = f \<or> f' \<in> same_inode_files s oldf)
       
  2076                    then (case (cf2sfile (LinkHard p oldf f # s) f) of
       
  2077                            Some sf \<Rightarrow> Some (S_file (cf2sfiles s oldf \<union> {sf}) (O_file oldf \<in> Tainted s))
       
  2078                          | _       \<Rightarrow> None)
       
  2079                    else co2sobj s obj
       
  2080     | _         \<Rightarrow> co2sobj s obj)"
       
  2081 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  2082 apply (simp_all add:current_files_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  2083 apply (auto simp:cp2sproc_simps tainted_eq_Tainted split:option.splits if_splits
       
  2084            dest!:current_proc_has_sp' intro:info_flow_shm_Tainted)[1]
       
  2085 apply (frule_tac cf2sfiles_linkhard, simp+)
       
  2086 apply (frule_tac f' = f in cf2sfile_linkhard, simp add:current_files_linkhard)
       
  2087 apply (auto simp:is_file_simps sectxt_of_obj_simps current_files_simps is_file_in_current same_inodes_Tainted
       
  2088   split:option.splits if_splits dest:Tainted_in_current 
       
  2089   dest!:current_has_sec' current_file_has_sfile')[1]
       
  2090 
       
  2091 apply (frule is_dir_in_current, simp add:current_files_linkhard is_dir_simps is_dir_in_current)
       
  2092 apply (frule is_dir_in_current)
       
  2093 apply (frule current_file_has_sfile, simp)
       
  2094 apply (drule cf2sfile_linkhard1, simp+)
       
  2095 done
       
  2096 
       
  2097 lemma co2sobj_truncate:
       
  2098   "\<lbrakk>valid (Truncate p f len # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Truncate p f len # s) obj = (
       
  2099       case obj of
       
  2100         O_file f' \<Rightarrow> if (f' \<in> same_inode_files s f \<and> len > 0)
       
  2101                      then Some (S_file (cf2sfiles s f') (O_file f' \<in> Tainted s \<or> O_proc p \<in> Tainted s))
       
  2102                      else co2sobj s obj
       
  2103       | _         \<Rightarrow> co2sobj s obj)"
       
  2104 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  2105 apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  2106 
       
  2107 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
       
  2108              simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
       
  2109                   same_inode_files_prop6
       
  2110              dest:is_file_in_current is_dir_in_current)
       
  2111 
       
  2112 (* should delete has_same_inode !?!?*)
       
  2113 by (auto simp:same_inode_files_def is_file_def has_same_inode_def split:if_splits option.splits)
       
  2114 
       
  2115 lemma co2sobj_kill:
       
  2116   "\<lbrakk>valid (Kill p p' # s); alive (Kill p p' # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Kill p p' # s) obj = co2sobj s obj"
       
  2117 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  2118 apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  2119 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
       
  2120              simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
       
  2121                   same_inode_files_prop6
       
  2122              dest:is_file_in_current is_dir_in_current)
       
  2123 done
       
  2124 
       
  2125 lemma co2sobj_exit:
       
  2126   "\<lbrakk>valid (Exit p # s); alive (Exit p # s) obj\<rbrakk> \<Longrightarrow> co2sobj (Exit p # s) obj = co2sobj s obj"
       
  2127 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  2128 apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  2129 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
       
  2130              simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
       
  2131                   same_inode_files_prop6
       
  2132              dest:is_file_in_current is_dir_in_current)
       
  2133 done
       
  2134 
       
  2135 lemma co2sobj_createmsgq:
       
  2136   "\<lbrakk>valid (CreateMsgq p q # s); alive (CreateMsgq p q # s) obj\<rbrakk> \<Longrightarrow> co2sobj (CreateMsgq p q # s) obj = (
       
  2137       case obj of
       
  2138         O_msgq q' \<Rightarrow> if (q' = q) then (case (cq2smsgq (CreateMsgq p q # s) q) of
       
  2139                                          Some sq \<Rightarrow> Some (S_msgq sq)
       
  2140                                        | _       \<Rightarrow> None)
       
  2141                      else co2sobj s obj
       
  2142       | _        \<Rightarrow> co2sobj s obj)"
       
  2143 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  2144 apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  2145 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
       
  2146              simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
       
  2147                   same_inode_files_prop6
       
  2148              dest!:current_has_smsgq'
       
  2149              dest:is_file_in_current is_dir_in_current cq2smsg_createmsgq)
       
  2150 done
       
  2151 
       
  2152 lemma co2sobj_sendmsg:
       
  2153   "\<lbrakk>valid (SendMsg p q m # s); alive (SendMsg p q m # s) obj\<rbrakk> \<Longrightarrow> co2sobj (SendMsg p q m # s) obj = (
       
  2154       case obj of
       
  2155         O_msgq q' \<Rightarrow> if (q' = q) then (case (cq2smsgq (SendMsg p q m # s) q) of
       
  2156                                          Some sq \<Rightarrow> Some (S_msgq sq)
       
  2157                                        | _       \<Rightarrow> None)
       
  2158                      else co2sobj s obj
       
  2159       | _        \<Rightarrow> co2sobj s obj)"
       
  2160 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  2161 apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  2162 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
       
  2163              simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
       
  2164                   same_inode_files_prop6
       
  2165              dest!:current_has_smsgq'
       
  2166              dest:is_file_in_current is_dir_in_current cq2smsg_sendmsg)
       
  2167 done
       
  2168 
       
  2169 lemma co2sobj_recvmsg:
       
  2170   "\<lbrakk>valid (RecvMsg p q m # s); alive (RecvMsg p q m # s) obj\<rbrakk> \<Longrightarrow> co2sobj (RecvMsg p q m # s) obj = (
       
  2171       case obj of
       
  2172         O_msgq q' \<Rightarrow> if (q' = q) then (case (cq2smsgq (RecvMsg p q m # s) q) of
       
  2173                                          Some sq \<Rightarrow> Some (S_msgq sq)
       
  2174                                        | _       \<Rightarrow> None)
       
  2175                      else co2sobj s obj
       
  2176       | O_proc p' \<Rightarrow> if (info_flow_shm s p p' \<and> O_msg q m \<in> Tainted s)
       
  2177                      then (case (cp2sproc s p') of
       
  2178                              Some sp \<Rightarrow> Some (S_proc sp True)
       
  2179                            | _       \<Rightarrow> None)
       
  2180                      else co2sobj s obj
       
  2181       | _         \<Rightarrow> co2sobj s obj)"
       
  2182 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  2183 apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  2184 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
       
  2185              simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
       
  2186                   same_inode_files_prop6
       
  2187              dest!:current_has_smsgq'
       
  2188              dest:is_file_in_current is_dir_in_current cq2smsg_recvmsg)
       
  2189 done
       
  2190 
       
  2191 lemma co2sobj_removemsgq:
       
  2192   "\<lbrakk>valid (RemoveMsgq p q # s); alive (RemoveMsgq p q # s) obj\<rbrakk> 
       
  2193    \<Longrightarrow> co2sobj (RemoveMsgq p q # s) obj = co2sobj s obj"
       
  2194 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  2195 apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  2196 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
       
  2197              simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
       
  2198                   same_inode_files_prop6
       
  2199              dest!:current_has_smsgq'
       
  2200              dest:is_file_in_current is_dir_in_current cq2smsg_removemsgq)
       
  2201 done
       
  2202 
       
  2203 lemma co2sobj_createshm:
       
  2204   "\<lbrakk>valid (CreateShM p h # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (CreateShM p h # s) obj = co2sobj s obj"
       
  2205 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  2206 apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  2207 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
       
  2208              simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
       
  2209                   same_inode_files_prop6 ch2sshm_simps
       
  2210              dest!:current_shm_has_sh'
       
  2211              dest:is_file_in_current is_dir_in_current)
       
  2212 done
       
  2213 
       
  2214 lemma co2sobj_detach:
       
  2215   "\<lbrakk>valid (Detach p h # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Detach p h # s) obj = (
       
  2216       case obj of
       
  2217         O_proc p' \<Rightarrow> if (p' = p) then (case (cp2sproc (Detach p h # s) p) of
       
  2218                                          Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> Tainted s))
       
  2219                                        | _       \<Rightarrow> None)
       
  2220                      else co2sobj s obj
       
  2221       | _         \<Rightarrow> co2sobj s obj)"
       
  2222 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  2223 apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  2224 
       
  2225 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
       
  2226              simp:current_files_simps cf2sfiles_simps cf2sfile_simps cp2sproc_simps tainted_eq_Tainted
       
  2227                   same_inode_files_prop6 ch2sshm_simps
       
  2228              dest!:current_shm_has_sh'
       
  2229              dest:is_file_in_current is_dir_in_current)
       
  2230 done
       
  2231 
       
  2232 lemma co2sobj_deleteshm:
       
  2233   "\<lbrakk>valid (DeleteShM p h # s); alive (DeleteShM p h # s) obj\<rbrakk> \<Longrightarrow> co2sobj (DeleteShM p h # s) obj = (
       
  2234       case obj of
       
  2235         O_proc p' \<Rightarrow> (case (cp2sproc (DeleteShM p h # s) p') of
       
  2236                         Some sp \<Rightarrow> Some (S_proc sp (O_proc p' \<in> Tainted s))
       
  2237                       | _       \<Rightarrow> None)
       
  2238       | _         \<Rightarrow> co2sobj s obj)"
       
  2239 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  2240 apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  2241 
       
  2242 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' current_proc_has_sp'
       
  2243              simp:current_files_simps cf2sfiles_simps cf2sfile_simps tainted_eq_Tainted
       
  2244                   same_inode_files_prop6 ch2sshm_simps
       
  2245              dest!:current_shm_has_sh' 
       
  2246              dest:is_file_in_current is_dir_in_current)
       
  2247 done
       
  2248 
       
  2249 lemma co2sobj_attach:
       
  2250   "\<lbrakk>valid (Attach p h flag # s); alive s obj\<rbrakk> \<Longrightarrow> co2sobj (Attach p h flag # s) obj = (
       
  2251       case obj of
       
  2252         O_proc p' \<Rightarrow> if (p' = p)
       
  2253                      then (case (cp2sproc (Attach p h flag # s) p) of
       
  2254                              Some sp \<Rightarrow> Some (S_proc sp (O_proc p \<in> Tainted s \<or> 
       
  2255               (\<exists> p'. O_proc p' \<in> Tainted s \<and> (p', SHM_RDWR) \<in> procs_of_shm s h)))
       
  2256                            | _       \<Rightarrow> None)
       
  2257                      else if (\<exists> flag'. (p', flag') \<in> procs_of_shm s h)
       
  2258                           then (case (cp2sproc s p') of 
       
  2259                                   Some sp \<Rightarrow> Some (S_proc sp (O_proc p' \<in> Tainted s \<or>
       
  2260               (O_proc p \<in> Tainted s \<and> flag = SHM_RDWR)))
       
  2261                                 | _       \<Rightarrow> None)
       
  2262                           else co2sobj s obj
       
  2263       | _         \<Rightarrow> co2sobj s obj)"
       
  2264 apply (frule vt_grant_os, frule vd_cons, case_tac obj)
       
  2265 apply (simp_all add:current_files_simps is_dir_simps ch2sshm_other cq2smsgq_other tainted_eq_Tainted)
       
  2266 
       
  2267 apply (rule conjI|rule impI|erule exE)+
       
  2268 apply (simp split:option.splits)
       
  2269 apply (rule impI, frule current_proc_has_sp, simp)
       
  2270 apply ((erule exE)+, auto simp:cp2sproc_attach tainted_eq_Tainted)[1]
       
  2271 apply (rule impI|rule conjI)+
       
  2272 apply (subgoal_tac "p \<in> current_procs (Attach p h flag # s)")
       
  2273 apply (drule_tac p = p in current_proc_has_sp, simp, erule exE)
       
  2274 apply (auto simp:tainted_eq_Tainted)[1]
       
  2275 apply (simp, rule impI)
       
  2276 apply (subgoal_tac "nat \<in> current_procs (Attach p h flag # s)")
       
  2277 apply (drule_tac p = nat in current_proc_has_sp, simp, erule exE)
       
  2278 apply (drule_tac p = nat in current_proc_has_sp, simp, erule exE)
       
  2279 apply (auto simp:cp2sproc_attach tainted_eq_Tainted)[1]
       
  2280 apply simp
       
  2281 
       
  2282 apply (auto split:if_splits option.splits dest!:current_file_has_sfile' 
       
  2283              simp:current_files_simps cf2sfiles_simps cf2sfile_simps tainted_eq_Tainted
       
  2284                   same_inode_files_prop6 
       
  2285              dest:is_file_in_current is_dir_in_current)
       
  2286 done
       
  2287 
       
  2288 
       
  2289 lemma co2sobj_other:
       
  2290   "\<lbrakk>valid (e # s); alive (e # s) obj; 
       
  2291     \<forall> p f fds. e \<noteq> Execve p f fds;
       
  2292     \<forall> p p' fds shms. e \<noteq> Clone p p' fds shms;
       
  2293     \<forall> p p'. e \<noteq> Ptrace p p';
       
  2294     \<forall> p f flags fd opt. e \<noteq> Open p f flags fd opt;
       
  2295     \<forall> p fd. e \<noteq> ReadFile p fd;
       
  2296     \<forall> p fd. e \<noteq> WriteFile p fd;
       
  2297     \<forall> p fd. e \<noteq> CloseFd p fd;
       
  2298     \<forall> p f. e \<noteq> UnLink p f;
       
  2299     \<forall> p f. e \<noteq> Rmdir p f;
       
  2300     \<forall> p f i. e \<noteq> Mkdir p f i;
       
  2301     \<forall> p f f'. e \<noteq> LinkHard p f f';
       
  2302     \<forall> p f len. e \<noteq> Truncate p f len;
       
  2303     \<forall> p q. e \<noteq> CreateMsgq p q;
       
  2304     \<forall> p q m. e \<noteq> SendMsg p q m;
       
  2305     \<forall> p q m. e \<noteq> RecvMsg p q m;
       
  2306     \<forall> p q. e \<noteq> RemoveMsgq p q;
       
  2307     \<forall> p h. e \<noteq> CreateShM p h;
       
  2308     \<forall> p h flag. e \<noteq> Attach p h flag;
       
  2309     \<forall> p h. e \<noteq> Detach p h;
       
  2310     \<forall> p h. e \<noteq> DeleteShM p h
       
  2311    \<rbrakk> \<Longrightarrow> co2sobj (e # s) obj = co2sobj s obj"
       
  2312 apply (frule vt_grant, case_tac e)
       
  2313 apply (auto intro:co2sobj_kill co2sobj_exit)
       
  2314 done
       
  2315 
       
  2316 lemmas co2sobj_simps = co2sobj_execve co2sobj_clone co2sobj_ptrace co2sobj_open co2sobj_readfile
       
  2317   co2sobj_writefile co2sobj_closefd co2sobj_unlink co2sobj_rmdir co2sobj_mkdir co2sobj_linkhard
       
  2318   co2sobj_truncate co2sobj_kill co2sobj_exit co2sobj_createmsgq co2sobj_sendmsg co2sobj_recvmsg
       
  2319   co2sobj_removemsgq co2sobj_attach co2sobj_detach co2sobj_createshm co2sobj_deleteshm
       
  2320 
  1601 end
  2321 end
  1602 
  2322 
  1603 (*<*)
  2323 (*<*)
  1604 end
  2324 end
  1605 (*>*)
  2325 (*>*)