lh-l4v/proof/infoflow/PasUpdates.thy

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(*
* Copyright 2014, NICTA
*
* This software may be distributed and modified according to the terms of
* the GNU General Public License version 2. Note that NO WARRANTY is provided.
* See "LICENSE_GPLv2.txt" for details.
*
* @TAG(NICTA_GPL)
*)
theory PasUpdates
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imports
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"Arch_IF"
"FinalCaps"
"../invariant-abstract/EmptyFail_AI"
begin
context begin interpretation Arch . (*FIXME: arch_split*)
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crunch idle_thread[wp]: preemption_point "\<lambda>s::det_state. P (idle_thread s)"
(wp: OR_choiceE_weak_wp crunch_wps simp: crunch_simps ignore: do_extended_op OR_choiceE)
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crunch idle_thread[wp]: cap_swap_for_delete,finalise_cap,cap_move,cap_swap,cap_delete,cancel_badged_sends "\<lambda>s::det_state. P (idle_thread s)" (wp: syscall_valid crunch_wps rec_del_preservation cap_revoke_preservation modify_wp dxo_wp_weak simp: crunch_simps check_cap_at_def filterM_mapM unless_def ignore: without_preemption filterM rec_del check_cap_at cap_revoke)
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crunch idle_thread[wp]: handle_event "\<lambda>s::det_state. P (idle_thread s)" (wp: syscall_valid crunch_wps rec_del_preservation cap_revoke_preservation dxo_wp_weak simp: crunch_simps check_cap_at_def filterM_mapM unless_def ignore: without_preemption filterM rec_del check_cap_at cap_revoke resetTimer ackInterrupt getFAR getDFSR getIFSR getActiveIRQ)
abbreviation (input) domain_fields where "domain_fields P s \<equiv> P (domain_time s) (domain_index s) (domain_list s)"
lemma preemption_point_domain_fields[wp]:
"\<lbrace>domain_fields P\<rbrace> preemption_point \<lbrace>\<lambda>_. domain_fields P\<rbrace>"
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by (simp add: preemption_point_def
| wp OR_choiceE_weak_wp modify_wp
| wpc
| simp add: reset_work_units_def update_work_units_def)+
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crunch domain_fields[wp]: retype_region_ext,create_cap_ext,cap_insert_ext,ethread_set,cap_move_ext,empty_slot_ext,cap_swap_ext,set_thread_state_ext,tcb_sched_action,reschedule_required,cap_swap_for_delete,finalise_cap,cap_move,cap_swap,cap_delete,cancel_badged_sends,cap_insert "domain_fields P" (wp: syscall_valid select_wp crunch_wps rec_del_preservation cap_revoke_preservation modify_wp simp: crunch_simps check_cap_at_def filterM_mapM unless_def ignore: without_preemption filterM rec_del check_cap_at cap_revoke)
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lemma cap_revoke_domain_fields[wp]:"\<lbrace>domain_fields P\<rbrace> cap_revoke a \<lbrace>\<lambda>_. domain_fields P\<rbrace>"
by (rule cap_revoke_preservation2; wp)
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lemma invoke_cnode_domain_fields[wp]: "\<lbrace>domain_fields P\<rbrace> invoke_cnode a \<lbrace>\<lambda>_. domain_fields P\<rbrace>"
unfolding invoke_cnode_def
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by (wpsimp simp: without_preemption_def crunch_simps
wp: get_cap_wp hoare_vcg_all_lift hoare_vcg_imp_lift
| rule conjI)+
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crunch domain_fields[wp]:
set_domain,set_priority,set_extra_badge,
possible_switch_to,handle_send,handle_recv,handle_reply
"domain_fields P"
(wp: syscall_valid crunch_wps rec_del_preservation cap_revoke_preservation
transfer_caps_loop_pres mapME_x_inv_wp
simp: crunch_simps check_cap_at_def filterM_mapM unless_def detype_def detype_ext_def mapM_x_defsym ignore: without_preemption filterM rec_del check_cap_at cap_revoke resetTimer ackInterrupt getFAR getDFSR getIFSR getActiveIRQ const_on_failure freeMemory)
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lemma invoke_cnode_cur_domain[wp]: "\<lbrace>\<lambda>s. P (cur_domain s)\<rbrace> invoke_cnode a \<lbrace>\<lambda>r s. P (cur_domain s)\<rbrace>"
apply (simp add: invoke_cnode_def)
apply (rule hoare_pre)
apply (wp | wpc | clarsimp | intro impI conjI | wp_once crunch_wps hoare_vcg_all_lift )+
done
crunch cur_domain[wp]: handle_event "\<lambda>s. P (cur_domain s)" (wp: syscall_valid select_wp crunch_wps check_cap_inv cap_revoke_preservation simp: crunch_simps filterM_mapM unless_def ignore: without_preemption check_cap_at filterM getActiveIRQ resetTimer ackInterrupt const_on_failure getFAR getDFSR getIFSR)
definition pas_wellformed_noninterference where
"pas_wellformed_noninterference aag \<equiv>
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(\<forall>x\<in>range (pasObjectAbs aag) - {SilcLabel}.
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pas_wellformed (aag\<lparr> pasSubject := x \<rparr>)) \<and>
(\<forall>x. pas_wellformed (aag\<lparr> pasSubject := pasDomainAbs aag x \<rparr>) \<and> pasDomainAbs aag x \<noteq> SilcLabel)"
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lemma pas_wellformed_noninterference_silc[intro!]:
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"pas_wellformed_noninterference aag \<Longrightarrow> pasDomainAbs aag x \<noteq> SilcLabel"
apply (simp add: pas_wellformed_noninterference_def)
done
lemma pasObjectAbs_pasSubject_update:
"pasObjectAbs (aag\<lparr> pasSubject := x \<rparr>) = pasObjectAbs aag"
apply simp
done
lemma pasASIDAbs_pasSubject_update:
"pasASIDAbs (aag\<lparr> pasSubject := x \<rparr>) = pasASIDAbs aag"
apply simp
done
lemma pasIRQAbs_pasSubject_update:
"pasIRQAbs (aag\<lparr> pasSubject := x \<rparr>) = pasIRQAbs aag"
apply simp
done
lemma state_asids_to_policy_pasSubject_update:
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"state_asids_to_policy_aux (aag\<lparr> pasSubject := x \<rparr>) caps asid vrefs =
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state_asids_to_policy_aux aag caps asid vrefs"
apply(rule equalityI)
apply(clarify)
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apply(erule state_asids_to_policy_aux.cases
|simp
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|fastforce intro: state_asids_to_policy_aux.intros)+
apply(clarify)
apply(erule state_asids_to_policy_aux.cases)
apply(simp,
subst pasObjectAbs_pasSubject_update[symmetric],
subst pasASIDAbs_pasSubject_update[symmetric],
rule state_asids_to_policy_aux.intros, assumption+)+
done
lemma state_irqs_to_policy_pasSubject_update:
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"state_irqs_to_policy_aux (aag\<lparr> pasSubject := x \<rparr>) caps =
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state_irqs_to_policy_aux aag caps"
apply(rule equalityI)
apply(clarify)
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apply(erule state_irqs_to_policy_aux.cases, simp,
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blast intro: state_irqs_to_policy_aux.intros)
apply(clarify)
apply(erule state_irqs_to_policy_aux.cases)
apply(simp)
apply(subst pasObjectAbs_pasSubject_update[symmetric])
apply(subst pasIRQAbs_pasSubject_update[symmetric])
apply(rule state_irqs_to_policy_aux.intros)
apply assumption+
done
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lemma irq_map_wellformed_pasSubject_update:
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"irq_map_wellformed_aux (aag\<lparr> pasSubject := x \<rparr>) irqn =
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irq_map_wellformed_aux aag irqn"
apply(clarsimp simp: irq_map_wellformed_aux_def)
done
lemma tcb_domain_map_wellformed_pasSubject_update:
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"tcb_domain_map_wellformed_aux (aag\<lparr> pasSubject := x \<rparr>) irqn =
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tcb_domain_map_wellformed_aux aag irqn"
apply(clarsimp simp: tcb_domain_map_wellformed_aux_def)
done
lemma pas_refined_pasSubject_update':
"\<lbrakk>pas_refined aag s; pas_wellformed (aag\<lparr> pasSubject := x \<rparr>)\<rbrakk> \<Longrightarrow>
pas_refined (aag\<lparr> pasSubject := x \<rparr>) s"
apply(subst pas_refined_def)
apply(safe del: subsetI)
apply (simp add: irq_map_wellformed_pasSubject_update pas_refined_def)
apply (simp add: tcb_domain_map_wellformed_pasSubject_update pas_refined_def)
apply (clarsimp simp: pas_refined_def)
apply(fastforce intro: pas_refined_asid_mem simp: state_asids_to_policy_pasSubject_update)
apply(fastforce simp: pas_refined_def state_irqs_to_policy_pasSubject_update)
done
lemma pas_wellformed_pasSubject_update:
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"\<lbrakk>pas_wellformed_noninterference aag\<rbrakk> \<Longrightarrow>
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pas_wellformed (aag\<lparr>pasSubject := pasDomainAbs aag x\<rparr>)"
by (auto simp: pas_wellformed_noninterference_def)
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lemmas pas_refined_pasSubject_update = pas_refined_pasSubject_update'[OF _ pas_wellformed_pasSubject_update]
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lemma guarded_pas_domain_pasSubject_update[simp]:
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"guarded_pas_domain (aag\<lparr>pasSubject := x\<rparr>) s = guarded_pas_domain aag s"
apply (simp add: guarded_pas_domain_def)
done
lemma silc_inv_pasSubject_update':
"\<lbrakk>silc_inv aag st s; x \<noteq> SilcLabel\<rbrakk> \<Longrightarrow> silc_inv (aag\<lparr>pasSubject := x\<rparr>) st s"
apply(auto simp: silc_inv_def silc_dom_equiv_def equiv_for_def intra_label_cap_def cap_points_to_label_def)
done
lemma silc_inv_pasSubject_update:
"\<lbrakk>silc_inv aag st s; pas_wellformed_noninterference aag\<rbrakk> \<Longrightarrow> silc_inv (aag\<lparr>pasSubject := pasDomainAbs aag x\<rparr>) st s"
apply (clarsimp intro!: silc_inv_pasSubject_update')
done
lemma prop_of_pasMayActivate_update_idemp:
"\<lbrakk>P aag; pasMayActivate aag = v\<rbrakk> \<Longrightarrow> P (aag\<lparr> pasMayActivate := v \<rparr>)"
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by (hypsubst, auto)
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lemma pasObjectAbs_pasMayActivate_update:
"pasObjectAbs (aag\<lparr> pasMayActivate := x \<rparr>) = pasObjectAbs aag"
apply simp
done
lemma pasASIDAbs_pasMayActivate_update:
"pasASIDAbs (aag\<lparr> pasMayActivate := x \<rparr>) = pasASIDAbs aag"
apply simp
done
lemma pasIRQAbs_pasMayActivate_update:
"pasIRQAbs (aag\<lparr> pasMayActivate := x \<rparr>) = pasIRQAbs aag"
apply simp
done
lemma state_asids_to_policy_pasMayActivate_update:
"state_asids_to_policy (aag\<lparr> pasMayActivate := x \<rparr>) s =
state_asids_to_policy aag s"
apply(rule equalityI)
apply(clarify)
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apply(erule state_asids_to_policy_aux.cases
|simp
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|fastforce intro: state_asids_to_policy_aux.intros)+
apply(clarify)
apply(erule state_asids_to_policy_aux.cases)
apply(simp,
subst pasObjectAbs_pasMayActivate_update[symmetric],
subst pasASIDAbs_pasMayActivate_update[symmetric],
rule state_asids_to_policy_aux.intros, assumption+)+
done
lemma state_irqs_to_policy_pasMayActivate_update:
"state_irqs_to_policy (aag\<lparr> pasMayActivate := x \<rparr>) s =
state_irqs_to_policy aag s"
apply(rule equalityI)
apply(clarify)
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apply(erule state_irqs_to_policy_aux.cases
|simp
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|fastforce intro: state_irqs_to_policy_aux.intros)+
apply(clarify)
apply(erule state_irqs_to_policy_aux.cases)
apply(simp,
subst pasObjectAbs_pasMayActivate_update[symmetric],
subst pasIRQAbs_pasMayActivate_update[symmetric],
rule state_irqs_to_policy_aux.intros, assumption+)+
done
lemma pas_refined_pasMayActivate_update:
"pas_refined aag s \<Longrightarrow>
pas_refined (aag\<lparr> pasMayActivate := x \<rparr>) s"
apply(simp add: pas_refined_def)
apply(clarsimp simp: irq_map_wellformed_aux_def state_asids_to_policy_pasMayActivate_update state_irqs_to_policy_pasMayActivate_update tcb_domain_map_wellformed_aux_def)
done
lemma prop_of_pasMayEditReadyQueues_update_idemp:
"\<lbrakk>P aag; pasMayEditReadyQueues aag = v\<rbrakk> \<Longrightarrow> P (aag\<lparr> pasMayEditReadyQueues := v \<rparr>)"
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by clarsimp
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lemma pasObjectAbs_pasMayEditReadyQueues_update:
"pasObjectAbs (aag\<lparr> pasMayEditReadyQueues := x \<rparr>) = pasObjectAbs aag"
apply simp
done
lemma pasASIDAbs_pasMayEditReadyQueues_update:
"pasASIDAbs (aag\<lparr> pasMayEditReadyQueues := x \<rparr>) = pasASIDAbs aag"
apply simp
done
lemma pasIRQAbs_pasMayEditReadyQueues_update:
"pasIRQAbs (aag\<lparr> pasMayEditReadyQueues := x \<rparr>) = pasIRQAbs aag"
apply simp
done
lemma state_asids_to_policy_pasMayEditReadyQueues_update:
"state_asids_to_policy (aag\<lparr> pasMayEditReadyQueues := x \<rparr>) s =
state_asids_to_policy aag s"
apply(rule equalityI)
apply(clarify)
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apply(erule state_asids_to_policy_aux.cases
|simp
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|fastforce intro: state_asids_to_policy_aux.intros)+
apply(clarify)
apply(erule state_asids_to_policy_aux.cases)
apply(simp,
subst pasObjectAbs_pasMayEditReadyQueues_update[symmetric],
subst pasASIDAbs_pasMayEditReadyQueues_update[symmetric],
rule state_asids_to_policy_aux.intros, assumption+)+
done
lemma state_irqs_to_policy_pasMayEditReadyQueues_update:
"state_irqs_to_policy (aag\<lparr> pasMayEditReadyQueues := x \<rparr>) s =
state_irqs_to_policy aag s"
apply(rule equalityI)
apply(clarify)
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apply(erule state_irqs_to_policy_aux.cases
|simp
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|fastforce intro: state_irqs_to_policy_aux.intros)+
apply(clarify)
apply(erule state_irqs_to_policy_aux.cases)
apply(simp,
subst pasObjectAbs_pasMayEditReadyQueues_update[symmetric],
subst pasIRQAbs_pasMayEditReadyQueues_update[symmetric],
rule state_irqs_to_policy_aux.intros, assumption+)+
done
lemma pas_refined_pasMayEditReadyQueues_update:
"pas_refined aag s \<Longrightarrow>
pas_refined (aag\<lparr> pasMayEditReadyQueues := x \<rparr>) s"
apply(simp add: pas_refined_def)
apply(clarsimp simp: irq_map_wellformed_aux_def state_asids_to_policy_pasMayEditReadyQueues_update state_irqs_to_policy_pasMayEditReadyQueues_update tcb_domain_map_wellformed_aux_def)
done
end
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end