| (* |
| * Licensed to the Apache Software Foundation (ASF) under one |
| * or more contributor license agreements. See the NOTICE file |
| * distributed with this work for additional information |
| * regarding copyright ownership. The ASF licenses this file |
| * to you under the Apache License, Version 2.0 (the |
| * "License"); you may not use this file except in compliance |
| * with the License. You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, |
| * software distributed under the License is distributed on an |
| * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY |
| * KIND, either express or implied. See the License for the |
| * specific language governing permissions and limitations |
| * under the License. |
| *) |
| |
| theory I_FMT_MSA |
| imports Main "../FMT_MSA" I_ResrcAttr |
| begin |
| |
| datatype SubjAttrConf = nosubjattrconf | |
| is_subjattrconf:subjattr_conf SubjAttrConf SubjAttr |
| |
| definition subjattr_subjid::"SubjAttr\<Rightarrow>ResrcId" where |
| "subjattr_subjid sattr\<equiv>presrc_id(subj_resrcattr sattr)" |
| |
| primrec find_subjid::"SubjAttrConf\<Rightarrow>SubjAttr\<Rightarrow>bool" where |
| "find_subjid nosubjattrconf sattr=False" |
| | "find_subjid (subjattr_conf conf sattrx) sattr= |
| (if subjattr_subjid sattrx=subjattr_subjid sattr |
| then |
| True |
| else find_subjid conf sattr)" |
| |
| primrec delete_subjattr::"SubjAttrConf\<Rightarrow>SubjAttr\<Rightarrow>SubjAttrConf" where |
| "delete_subjattr nosubjattrconf sattr=nosubjattrconf" |
| | "delete_subjattr (subjattr_conf conf sattrx) sattr= |
| (if subjattr_subjid sattrx=subjattr_subjid sattr |
| then |
| delete_subjattr conf sattr |
| else if subjattr_subjid sattrx\<noteq>subjattr_subjid sattr |
| then |
| subjattr_conf(delete_subjattr conf sattr) sattrx |
| else subjattr_conf conf sattrx)" |
| |
| primrec get_subjattr::"SubjAttrConf\<Rightarrow>ResrcId\<Rightarrow>SubjAttr" where |
| "get_subjattr nosubjattrconf rid=nosubjattr" |
| | "get_subjattr (subjattr_conf conf sattr) rid= |
| (if subjattr_subjid sattr=rid |
| then |
| sattr |
| else if subjattr_subjid sattr\<noteq>rid |
| then |
| get_subjattr conf rid |
| else nosubjattr)" |
| |
| primrec subjattrconf_uniq::"SubjAttrConf\<Rightarrow>bool" where |
| "subjattrconf_uniq nosubjattrconf=False" |
| | "subjattrconf_uniq (subjattr_conf conf sattr)= |
| (if subjattr_subjid sattr\<noteq>noresrcid\<and> |
| conf=nosubjattrconf |
| then |
| True |
| else if subjattr_subjid sattr\<noteq>noresrcid\<and> |
| (\<not>find_subjid conf sattr)\<and> |
| subjattrconf_uniq conf |
| then |
| True |
| else False)" |
| |
| primrec valid_subjattrconf::"SubjAttrConf\<Rightarrow>bool" where |
| "valid_subjattrconf nosubjattrconf=False" |
| |"valid_subjattrconf (subjattr_conf conf sattr)= |
| (if conf=nosubjattrconf\<and> |
| sattr\<noteq>nosubjattr\<and> |
| info_type(subj_resrcattr sattr)=Func |
| then |
| True |
| else if conf\<noteq>nosubjattrconf\<and> |
| sattr\<noteq>nosubjattr\<and> |
| info_type(subj_resrcattr sattr)=Func\<and> |
| (\<not>find_subjid conf sattr)\<and> |
| subjattrconf_uniq conf |
| then |
| True |
| else False)" |
| |
| interpretation SubjAttrConf : SubjAttrConf nousrid valid_usrid noresrcid valid_resrcid noinfoid |
| valid_infoid InSgx OutSgx is_insgx Device Normal |
| is_normal Data Func is_data noresrcattr resrc_attr |
| presrc_id info_id trust_level presrc_type |
| info_type nousrattr usr_attr usrattr_id |
| nousrattrconf usrattr_conf is_usrattrconf find_usrid |
| delete_usrattr get_usrattr valid_usrattrconf nosubjattr |
| subj_attr subj_callerattr |
| subj_participants subj_resrcattr nosubjattrconf |
| subjattr_conf is_subjattrconf subjattr_subjid |
| find_subjid delete_subjattr get_subjattr |
| subjattrconf_uniq valid_subjattrconf |
| proof |
| show "\<not> is_subjattrconf nosubjattrconf" by auto |
| next |
| fix conf |
| fix attr |
| show "is_subjattrconf (subjattr_conf conf attr)" by auto |
| next |
| fix x |
| show "x = nosubjattrconf \<or> |
| (\<exists>conf attr. x = subjattr_conf conf attr)" |
| proof (cases x) |
| assume "x = nosubjattrconf" |
| from this show " x = nosubjattrconf \<or> (\<exists>conf attr. x = subjattr_conf conf attr)" by auto |
| next |
| fix x21 |
| fix x22 |
| assume "x = subjattr_conf x21 x22" |
| from this show "x = nosubjattrconf \<or> |
| (\<exists>conf attr. x = subjattr_conf conf attr)" by auto |
| qed |
| next |
| show "subjattr_subjid nosubjattr = noresrcid" |
| by (auto simp add:subjattr_subjid_def nosubjattr_def noresrcattr_def) |
| next |
| fix attr |
| show "\<not> find_subjid nosubjattrconf attr" by auto |
| next |
| fix attrx |
| fix attr |
| fix conf |
| show "subjattr_subjid attrx = subjattr_subjid attr \<Longrightarrow> |
| find_subjid (subjattr_conf conf attrx) attr" |
| by auto |
| next |
| fix conf |
| fix attrx |
| fix attr |
| show "find_subjid conf attr \<Longrightarrow> |
| find_subjid (subjattr_conf conf attrx) attr" by auto |
| next |
| fix conf |
| fix attrx |
| fix attr |
| show "\<not> find_subjid conf attr \<and> |
| subjattr_subjid attrx \<noteq> subjattr_subjid attr \<Longrightarrow> |
| \<not> find_subjid (subjattr_conf conf attrx) attr" by auto |
| next |
| fix attr |
| show "delete_subjattr nosubjattrconf attr = nosubjattrconf" by auto |
| next |
| fix attrx |
| fix attr |
| fix conf |
| show "subjattr_subjid attrx = subjattr_subjid attr \<Longrightarrow> |
| delete_subjattr (subjattr_conf conf attrx) attr = |
| delete_subjattr conf attr" by auto |
| next |
| fix attrx |
| fix attr |
| fix conf |
| show "subjattr_subjid attrx \<noteq> subjattr_subjid attr \<Longrightarrow> |
| delete_subjattr (subjattr_conf conf attrx) attr = |
| subjattr_conf (delete_subjattr conf attr) attrx" by auto |
| next |
| fix elem |
| show "get_subjattr nosubjattrconf elem = nosubjattr" by auto |
| next |
| fix attr |
| fix elem |
| fix conf |
| show "subjattr_subjid attr = elem \<Longrightarrow> |
| get_subjattr (subjattr_conf conf attr) elem = attr" by auto |
| next |
| fix attr |
| fix elem |
| fix conf |
| show "get_subjattr conf elem = nosubjattr \<and> |
| subjattr_subjid attr \<noteq> elem \<Longrightarrow> |
| get_subjattr (subjattr_conf conf attr) elem = nosubjattr" by auto |
| next |
| fix elem |
| fix attr |
| fix conf |
| show "get_subjattr conf elem \<noteq> nosubjattr \<and> |
| subjattr_subjid attr \<noteq> elem \<Longrightarrow> |
| get_subjattr (subjattr_conf conf attr) elem = |
| get_subjattr conf elem" by auto |
| next |
| show "\<not> subjattrconf_uniq nosubjattrconf" by auto |
| next |
| fix conf |
| fix attr |
| show "subjattr_subjid attr \<noteq> noresrcid \<and> conf = nosubjattrconf \<Longrightarrow> |
| subjattrconf_uniq (subjattr_conf conf attr)" by auto |
| next |
| fix conf |
| fix attr |
| show "subjattrconf_uniq conf \<and> |
| \<not> find_subjid conf attr \<and> subjattr_subjid attr \<noteq> noresrcid \<Longrightarrow> |
| subjattrconf_uniq (subjattr_conf conf attr)" by auto |
| next |
| fix conf |
| fix attr |
| show "subjattr_subjid attr = noresrcid \<Longrightarrow> |
| \<not> subjattrconf_uniq (subjattr_conf conf attr)" by auto |
| next |
| fix conf |
| fix attr |
| show "conf \<noteq> nosubjattrconf \<and> \<not> subjattrconf_uniq conf \<Longrightarrow> |
| \<not> subjattrconf_uniq (subjattr_conf conf attr)" by auto |
| next |
| fix conf |
| fix attr |
| show "conf \<noteq> nosubjattrconf \<and> find_subjid conf attr \<Longrightarrow> |
| \<not> subjattrconf_uniq (subjattr_conf conf attr)" by auto |
| next |
| show "\<And>P conf. |
| P nosubjattrconf \<Longrightarrow> |
| (\<And>conf1 attr1. P conf1 \<Longrightarrow> P (subjattr_conf conf1 attr1)) \<Longrightarrow> |
| P conf" |
| proof (erule SubjAttrConf.induct) |
| show "\<And>P conf x1 x2. |
| (\<And>conf1 attr1. P conf1 \<Longrightarrow> P (subjattr_conf conf1 attr1)) \<Longrightarrow> |
| P x1 \<Longrightarrow> P (subjattr_conf x1 x2)" by auto |
| qed |
| next |
| fix sattr |
| show "subjattr_subjid sattr = presrc_id (subj_resrcattr sattr)" |
| by (auto simp:subjattr_subjid_def) |
| next |
| show "\<not> valid_subjattrconf nosubjattrconf" by auto |
| next |
| fix conf |
| fix sattr |
| show "conf = nosubjattrconf \<and> |
| sattr \<noteq> nosubjattr \<and> |
| info_type (subj_resrcattr sattr) = InfoType.Func \<Longrightarrow> |
| valid_subjattrconf (subjattr_conf conf sattr)" by auto |
| next |
| fix conf |
| fix sattr |
| show "conf = nosubjattrconf \<and> |
| sattr = nosubjattr \<and> |
| info_type (subj_resrcattr sattr) = InfoType.Func \<Longrightarrow> |
| \<not> valid_subjattrconf (subjattr_conf conf sattr)" by auto |
| next |
| fix conf |
| fix sattr |
| show "conf = nosubjattrconf \<and> |
| sattr \<noteq> nosubjattr \<and> |
| info_type (subj_resrcattr sattr) \<noteq> InfoType.Func \<Longrightarrow> |
| \<not> valid_subjattrconf (subjattr_conf conf sattr)" by auto |
| next |
| fix conf |
| fix sattr |
| show "conf \<noteq> nosubjattrconf \<and> |
| sattr \<noteq> nosubjattr \<and> |
| info_type (subj_resrcattr sattr) = InfoType.Func \<and> |
| \<not> find_subjid conf sattr \<and> subjattrconf_uniq conf \<Longrightarrow> |
| valid_subjattrconf (subjattr_conf conf sattr)" by auto |
| next |
| fix conf |
| fix sattr |
| show "conf \<noteq> nosubjattrconf \<and> sattr = nosubjattr \<Longrightarrow> |
| \<not> valid_subjattrconf (subjattr_conf conf sattr)" by auto |
| next |
| fix conf |
| fix sattr |
| show "conf \<noteq> nosubjattrconf \<and> |
| sattr \<noteq> nosubjattr \<and> |
| info_type (subj_resrcattr sattr) \<noteq> InfoType.Func \<and> |
| \<not> find_subjid conf sattr \<and> subjattrconf_uniq conf \<Longrightarrow> |
| \<not> valid_subjattrconf (subjattr_conf conf sattr)" by auto |
| next |
| fix conf |
| fix sattr |
| show "conf \<noteq> nosubjattrconf \<and> |
| sattr \<noteq> nosubjattr \<and> |
| info_type (subj_resrcattr sattr) = InfoType.Func \<and> |
| find_subjid conf sattr \<and> subjattrconf_uniq conf \<Longrightarrow> |
| \<not> valid_subjattrconf (subjattr_conf conf sattr)" by auto |
| next |
| fix conf |
| fix sattr |
| show "conf \<noteq> nosubjattrconf \<and> |
| sattr \<noteq> nosubjattr \<and> |
| info_type (subj_resrcattr sattr) = InfoType.Func \<and> |
| \<not> find_subjid conf sattr \<and> \<not> subjattrconf_uniq conf \<Longrightarrow> |
| \<not> valid_subjattrconf (subjattr_conf conf sattr)" by auto |
| qed |
| |
| datatype ObjAttrConf = noobjattrconf | |
| is_objattrconf:objattr_conf ObjAttrConf ObjAttr |
| |
| definition objattr_objid::"ObjAttr\<Rightarrow>ResrcId" where |
| "objattr_objid oattr\<equiv>presrc_id(obj_resrcattr oattr)" |
| |
| primrec find_objid::"ObjAttrConf\<Rightarrow>ObjAttr\<Rightarrow>bool" where |
| "find_objid noobjattrconf oattr=False" |
| | "find_objid (objattr_conf conf oattrx) oattr= |
| (if objattr_objid oattrx=objattr_objid oattr |
| then |
| True |
| else find_objid conf oattr)" |
| |
| primrec delete_objattr::"ObjAttrConf\<Rightarrow>ObjAttr\<Rightarrow>ObjAttrConf" where |
| "delete_objattr noobjattrconf oattr=noobjattrconf" |
| | "delete_objattr (objattr_conf conf oattrx) oattr= |
| (if objattr_objid oattrx=objattr_objid oattr |
| then |
| delete_objattr conf oattr |
| else if objattr_objid oattrx\<noteq>objattr_objid oattr |
| then |
| objattr_conf(delete_objattr conf oattr) oattrx |
| else objattr_conf conf oattrx)" |
| |
| primrec get_objattr::"ObjAttrConf\<Rightarrow>ResrcId\<Rightarrow>ObjAttr" where |
| "get_objattr noobjattrconf rid=noobjattr" |
| | "get_objattr (objattr_conf conf oattr) rid= |
| (if objattr_objid oattr=rid |
| then |
| oattr |
| else if objattr_objid oattr\<noteq>rid |
| then |
| get_objattr conf rid |
| else noobjattr)" |
| |
| primrec valid_objattrconf::"ObjAttrConf\<Rightarrow>bool" where |
| "valid_objattrconf noobjattrconf=False" |
| | "valid_objattrconf (objattr_conf conf oattr)= |
| (if objattr_objid oattr\<noteq>noresrcid\<and> |
| conf=noobjattrconf |
| then |
| True |
| else if objattr_objid oattr\<noteq>noresrcid\<and> |
| (\<not>find_objid conf oattr)\<and> |
| valid_objattrconf conf |
| then |
| True |
| else False)" |
| |
| interpretation ObjAttrConf : ObjAttrConf noresrcid valid_resrcid noinfoid valid_infoid InSgx |
| OutSgx is_insgx Device Normal is_normal Data Func is_data |
| noresrcattr resrc_attr presrc_id info_id trust_level |
| presrc_type info_type nousrid valid_usrid nousrattr |
| usr_attr usrattr_id nousrattrconf usrattr_conf |
| is_usrattrconf find_usrid delete_usrattr get_usrattr |
| valid_usrattrconf noobjattr obj_attr |
| obj_owners obj_resrcattr noobjattrconf objattr_conf |
| is_objattrconf objattr_objid find_objid delete_objattr |
| get_objattr valid_objattrconf |
| proof |
| show "\<not> is_objattrconf noobjattrconf" by auto |
| next |
| fix conf |
| fix attr |
| show "is_objattrconf (objattr_conf conf attr)" by auto |
| next |
| fix x |
| show "x = noobjattrconf \<or> |
| (\<exists>conf attr. x = objattr_conf conf attr)" |
| proof (cases x) |
| assume "x = noobjattrconf" |
| from this show "x = noobjattrconf \<or> (\<exists>conf attr. x = objattr_conf conf attr)" by auto |
| next |
| fix x21 |
| fix x22 |
| assume "x = objattr_conf x21 x22" |
| from this show "x = noobjattrconf \<or> |
| (\<exists>conf attr. x = objattr_conf conf attr)" by auto |
| qed |
| next |
| show "objattr_objid noobjattr = noresrcid" |
| by (auto simp:objattr_objid_def noobjattr_def noresrcattr_def) |
| next |
| fix attr |
| show "\<not> find_objid noobjattrconf attr" by auto |
| next |
| fix conf |
| fix attrx |
| fix attr |
| show "objattr_objid attrx = objattr_objid attr \<Longrightarrow> |
| find_objid (objattr_conf conf attrx) attr" by auto |
| next |
| fix conf |
| fix attrx |
| fix attr |
| show "find_objid conf attr \<Longrightarrow> find_objid (objattr_conf conf attrx) attr" by auto |
| next |
| fix conf |
| fix attrx |
| fix attr |
| show "\<not> find_objid conf attr \<and> |
| objattr_objid attrx \<noteq> objattr_objid attr \<Longrightarrow> |
| \<not> find_objid (objattr_conf conf attrx) attr" by auto |
| next |
| fix attr |
| show "delete_objattr noobjattrconf attr = noobjattrconf" by auto |
| next |
| fix attrx |
| fix attr |
| fix conf |
| show "objattr_objid attrx = objattr_objid attr \<Longrightarrow> |
| delete_objattr (objattr_conf conf attrx) attr = |
| delete_objattr conf attr" by auto |
| next |
| fix attrx |
| fix attr |
| fix conf |
| show "objattr_objid attrx \<noteq> objattr_objid attr \<Longrightarrow> |
| delete_objattr (objattr_conf conf attrx) attr = |
| objattr_conf (delete_objattr conf attr) attrx" by auto |
| next |
| fix elem |
| show "get_objattr noobjattrconf elem = noobjattr" by auto |
| next |
| fix attr |
| fix elem |
| fix conf |
| show "objattr_objid attr = elem \<Longrightarrow> |
| get_objattr (objattr_conf conf attr) elem = attr" by auto |
| next |
| fix attr |
| fix elem |
| fix conf |
| show "get_objattr conf elem = noobjattr \<and> objattr_objid attr \<noteq> elem \<Longrightarrow> |
| get_objattr (objattr_conf conf attr) elem = noobjattr" by auto |
| next |
| fix elem |
| fix attr |
| fix conf |
| show "get_objattr conf elem \<noteq> noobjattr \<and> objattr_objid attr \<noteq> elem \<Longrightarrow> |
| get_objattr (objattr_conf conf attr) elem = get_objattr conf elem" by auto |
| next |
| show "\<not> valid_objattrconf noobjattrconf" by auto |
| next |
| fix conf |
| fix attr |
| show "objattr_objid attr \<noteq> noresrcid \<and> conf = noobjattrconf \<Longrightarrow> |
| valid_objattrconf (objattr_conf conf attr)" by auto |
| next |
| fix conf |
| fix attr |
| show "valid_objattrconf conf \<and> |
| \<not> find_objid conf attr \<and> objattr_objid attr \<noteq> noresrcid \<Longrightarrow> |
| valid_objattrconf (objattr_conf conf attr)" by auto |
| next |
| fix conf |
| fix attr |
| show "objattr_objid attr = noresrcid \<Longrightarrow> |
| \<not> valid_objattrconf (objattr_conf conf attr)" by auto |
| next |
| fix conf |
| fix attr |
| show "conf \<noteq> noobjattrconf \<and> \<not> valid_objattrconf conf \<Longrightarrow> |
| \<not> valid_objattrconf (objattr_conf conf attr)" by auto |
| next |
| fix conf |
| fix attr |
| show "conf \<noteq> noobjattrconf \<and> find_objid conf attr \<Longrightarrow> |
| \<not> valid_objattrconf (objattr_conf conf attr)" by auto |
| next |
| show "\<And>P conf. |
| P noobjattrconf \<Longrightarrow> |
| (\<And>conf1 attr1. P conf1 \<Longrightarrow> P (objattr_conf conf1 attr1)) \<Longrightarrow> |
| P conf" |
| proof (erule ObjAttrConf.induct) |
| show "\<And>P conf x1 x2. |
| (\<And>conf1 attr1. P conf1 \<Longrightarrow> P (objattr_conf conf1 attr1)) \<Longrightarrow> |
| P x1 \<Longrightarrow> P (objattr_conf x1 x2)" by auto |
| qed |
| next |
| fix oattr |
| show "objattr_objid oattr = presrc_id (obj_resrcattr oattr)" |
| by (auto simp:objattr_objid_def) |
| qed |
| |
| end |
