infoflow: IRQMasks arch split

Signed-off-by: Ryan Barry <ryan.barry@unsw.edu.au>
This commit is contained in:
Ryan Barry 2021-09-15 17:09:12 +10:00 committed by Gerwin Klein
parent 5cbe8af843
commit 392845f94c
2 changed files with 425 additions and 359 deletions

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@ -0,0 +1,179 @@
(*
* Copyright 2020, Data61, CSIRO (ABN 41 687 119 230)
*
* SPDX-License-Identifier: GPL-2.0-only
*)
theory ArchIRQMasks_IF
imports IRQMasks_IF
begin
context Arch begin global_naming ARM
named_theorems IRQMasks_IF_assms
declare storeWord_irq_masks_inv[IRQMasks_IF_assms]
lemma resetTimer_irq_masks[IRQMasks_IF_assms, wp]:
"resetTimer \<lbrace>\<lambda>s. P (irq_masks s)\<rbrace>"
by (simp add: resetTimer_def | wp no_irq)+
lemma delete_objects_irq_masks[IRQMasks_IF_assms, wp]:
"delete_objects ptr bits \<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace>"
apply (simp add: delete_objects_def)
apply (wp dmo_wp no_irq_mapM_x no_irq | simp add: freeMemory_def no_irq_storeWord)+
done
crunch irq_masks[wp]: cleanCacheRange_PoU "\<lambda>s. P (irq_masks s)"
(ignore_del: cleanCacheRange_PoU)
crunch irq_masks[IRQMasks_IF_assms, wp]: invoke_untyped "\<lambda>s. P (irq_masks_of_state s)"
(ignore: delete_objects wp: crunch_wps dmo_wp
wp: mapME_x_inv_wp preemption_point_inv
simp: crunch_simps no_irq_clearMemory
mapM_x_def_bak unless_def)
crunch irq_masks[IRQMasks_IF_assms, wp]: finalise_cap "\<lambda>s. P (irq_masks_of_state s)"
(wp: select_wp crunch_wps dmo_wp no_irq
simp: crunch_simps no_irq_setHardwareASID no_irq_invalidateLocalTLB_ASID
no_irq_set_current_pd no_irq_invalidateLocalTLB_VAASID no_irq_cleanByVA_PoU)
crunch irq_masks[IRQMasks_IF_assms, wp]: send_signal "\<lambda>s. P (irq_masks_of_state s)"
(wp: crunch_wps ignore: do_machine_op wp: dmo_wp simp: crunch_simps)
lemma handle_interrupt_irq_masks[IRQMasks_IF_assms]:
notes no_irq[wp del]
shows
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st and K (irq \<le> maxIRQ)\<rbrace>
handle_interrupt irq
\<lbrace>\<lambda>rv s. P (irq_masks_of_state s)\<rbrace>"
apply (rule hoare_gen_asm)
apply (simp add: handle_interrupt_def split del: if_split)
apply (rule hoare_pre)
apply (rule hoare_if)
apply simp
apply (wp dmo_wp
| simp add: ackInterrupt_def maskInterrupt_def when_def split del: if_split
| wpc
| simp add: get_irq_state_def handle_reserved_irq_def
| wp (once) hoare_drop_imp)+
apply (fastforce simp: domain_sep_inv_def)
done
lemma arch_invoke_irq_control_irq_masks[IRQMasks_IF_assms]:
"\<lbrace>domain_sep_inv False st and arch_irq_control_inv_valid invok\<rbrace>
arch_invoke_irq_control invok
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
apply (case_tac invok)
apply (clarsimp simp: arch_irq_control_inv_valid_def domain_sep_inv_def valid_def)
done
crunches handle_vm_fault, handle_hypervisor_fault
for irq_masks[IRQMasks_IF_assms, wp]: "\<lambda>s. P (irq_masks_of_state s)"
(wp: dmo_wp no_irq simp: no_irq_getDFSR no_irq_getFAR no_irq_getIFSR)
lemma dmo_getActiveIRQ_irq_masks[IRQMasks_IF_assms, wp]:
"do_machine_op (getActiveIRQ in_kernel) \<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace>"
apply (rule hoare_pre, rule dmo_wp)
apply (simp add: getActiveIRQ_def | wp | simp add: no_irq_def | clarsimp)+
done
lemma dmo_getActiveIRQ_return_axiom[IRQMasks_IF_assms, wp]:
"\<lbrace>\<top>\<rbrace> do_machine_op (getActiveIRQ in_kernel) \<lbrace>\<lambda>rv s. (\<forall>x. rv = Some x \<longrightarrow> x \<le> maxIRQ)\<rbrace>"
apply (simp add: getActiveIRQ_def)
apply (rule hoare_pre, rule dmo_wp)
apply (insert irq_oracle_max_irq)
apply (wp alternative_wp select_wp dmo_getActiveIRQ_irq_masks)
apply clarsimp
done
crunch irq_masks[IRQMasks_IF_assms, wp]: activate_thread "\<lambda>s. P (irq_masks_of_state s)"
crunch irq_masks[IRQMasks_IF_assms, wp]: schedule "\<lambda>s. P (irq_masks_of_state s)"
(wp: dmo_wp alternative_wp select_wp crunch_wps simp: crunch_simps clearExMonitor_def)
end
global_interpretation IRQMasks_IF_1?: IRQMasks_IF_1
proof goal_cases
interpret Arch .
case 1 show ?case
by (unfold_locales; (fact IRQMasks_IF_assms)?)
qed
context Arch begin global_naming ARM
crunch irq_masks[IRQMasks_IF_assms, wp]: do_reply_transfer "\<lambda>s. P (irq_masks_of_state s)"
(wp: crunch_wps empty_slot_irq_masks simp: crunch_simps unless_def)
crunch irq_masks[IRQMasks_IF_assms, wp]: arch_perform_invocation "\<lambda>s. P (irq_masks_of_state s)"
(wp: dmo_wp crunch_wps no_irq
simp: no_irq_cleanByVA_PoU no_irq_invalidateLocalTLB_ASID no_irq_do_flush)
(* FIXME: remove duplication in this proof -- requires getting the wp automation
to do the right thing with dropping imps in validE goals *)
lemma invoke_tcb_irq_masks[IRQMasks_IF_assms]:
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st and tcb_inv_wf tinv\<rbrace>
invoke_tcb tinv
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
apply (case_tac tinv)
apply((wp restart_irq_masks hoare_vcg_if_lift mapM_x_wp[OF _ subset_refl]
| wpc
| simp split del: if_split add: check_cap_at_def
| clarsimp)+)[3]
defer
apply ((wp | simp )+)[2]
(* NotificationControl *)
apply (rename_tac option)
apply (case_tac option)
apply ((wp | simp)+)[2]
(* just ThreadControl left *)
apply (simp add: split_def cong: option.case_cong)
apply wpsimp+
apply (rule hoare_post_impErr[OF cap_delete_irq_masks[where P=P]])
apply blast
apply blast
apply (wpsimp wp: hoare_vcg_all_lift_R hoare_vcg_const_imp_lift_R
checked_cap_insert_domain_sep_inv)+
apply (rule_tac Q="\<lambda> r s. domain_sep_inv False st s \<and> P (irq_masks_of_state s)"
and E="\<lambda>_ s. P (irq_masks_of_state s)" in hoare_post_impErr)
apply (wp hoare_vcg_conj_liftE1 cap_delete_irq_masks)
apply fastforce
apply blast
apply (wpsimp wp: static_imp_wp hoare_vcg_all_lift checked_cap_insert_domain_sep_inv)+
apply (rule_tac Q="\<lambda> r s. domain_sep_inv False st s \<and> P (irq_masks_of_state s)"
and E="\<lambda>_ s. P (irq_masks_of_state s)" in hoare_post_impErr)
apply (wp hoare_vcg_conj_liftE1 cap_delete_irq_masks)
apply fastforce
apply blast
apply (simp add: option_update_thread_def | wp static_imp_wp hoare_vcg_all_lift | wpc)+
by fastforce+
end
global_interpretation IRQMasks_IF_2?: IRQMasks_IF_2
proof goal_cases
interpret Arch .
case 1 show ?case
by (unfold_locales; (fact IRQMasks_IF_assms)?)
qed
context begin interpretation Arch .
requalify_facts
init_arch_objects_irq_masks
arch_activate_idle_thread_irq_masks
retype_region_irq_masks
end
declare
init_arch_objects_irq_masks[wp]
arch_activate_idle_thread_irq_masks[wp]
retype_region_irq_masks[wp]
end

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@ -8,333 +8,243 @@ theory IRQMasks_IF
imports "Access.ArchDomainSepInv"
begin
context begin interpretation Arch . (*FIXME: arch_split*)
abbreviation irq_masks_of_state :: "det_ext state \<Rightarrow> irq \<Rightarrow> bool" where
"irq_masks_of_state s \<equiv> irq_masks (machine_state s)"
lemma resetTimer_irq_masks[wp]:
"\<lbrace>\<lambda>s. P (irq_masks s)\<rbrace> resetTimer \<lbrace>\<lambda>_ s. P (irq_masks s)\<rbrace>"
apply(simp add: resetTimer_def | wp no_irq)+
done
lemma storeWord_irq_masks[wp]:
"\<lbrace>\<lambda>s. P (irq_masks s)\<rbrace> storeWord x y \<lbrace>\<lambda>_ s. P (irq_masks s)\<rbrace>"
apply(wp del: no_irq | simp add: storeWord_def)+
done
lemma detype_irq_masks[simp]:
"irq_masks (machine_state (detype S s)) = irq_masks_of_state s"
apply(simp add: detype_def)
done
lemma delete_objects_irq_masks[wp]:
"\<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace> delete_objects param_a param_b
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
apply(simp add: delete_objects_def)
apply(wp dmo_wp no_irq_mapM_x no_irq | simp add: freeMemory_def no_irq_storeWord)+
done
crunch irq_masks[wp]: cleanCacheRange_PoU "\<lambda>s. P (irq_masks s)"
(ignore_del: cleanCacheRange_PoU)
crunch irq_masks[wp]: invoke_untyped "\<lambda>s. P (irq_masks_of_state s)"
(ignore: delete_objects wp: crunch_wps dmo_wp
wp: mapME_x_inv_wp preemption_point_inv
simp: crunch_simps no_irq_clearMemory
mapM_x_def_bak unless_def)
by (simp add: detype_def)
crunch irq_masks[wp]: cap_insert "\<lambda>s. P (irq_masks_of_state s)"
(wp: crunch_wps)
lemma invoke_irq_handler_irq_masks:
"\<lbrace>domain_sep_inv False st and (\<lambda>s. (\<exists>ptr'. cte_wp_at ((=) (IRQHandlerCap irq)) ptr' s))\<rbrace>
invoke_irq_handler blah
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
by (clarsimp simp: valid_def domain_sep_inv_def)
lemma empty_slot_irq_masks:
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and K (irq_opt = NullCap)\<rbrace>
empty_slot slot irq_opt
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
apply (rule hoare_gen_asm)
apply (wpsimp simp: empty_slot_def post_cap_deletion_def)
done
lemma spec_strengthen_errE:
"\<lbrakk> s \<turnstile> \<lbrace>P\<rbrace> f \<lbrace>Q\<rbrace>, \<lbrace>E'\<rbrace>; \<And>s r. E' s r \<Longrightarrow> E s r \<rbrakk>
\<Longrightarrow> s \<turnstile> \<lbrace>P\<rbrace> f \<lbrace>Q\<rbrace>, \<lbrace>E\<rbrace>"
by (auto simp: spec_validE_def validE_def valid_def split: sum.splits)
crunch irq_masks[wp]: create_cap "\<lambda>s. P (irq_masks_of_state s)"
crunch irq_masks[wp]: cap_swap_for_delete "\<lambda>s. P (irq_masks_of_state s)"
locale IRQMasks_IF_1 =
fixes state_t :: "'s :: state_ext state"
assumes resetTimer_irq_masks[wp]:
"resetTimer \<lbrace>\<lambda>s. P (irq_masks s)\<rbrace>"
and storeWord_irq_masks[wp]:
"storeWord x y \<lbrace>\<lambda>s. P (irq_masks s)\<rbrace>"
and delete_objects_irq_masks[wp]:
"delete_objects ptr bits \<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace>"
and invoke_untyped_irq_masks[wp]:
"invoke_untyped ui \<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace>"
and finalise_cap_irq_masks[wp]:
"finalise_cap cap final \<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace>"
and send_signal_irq_masks[wp]:
"send_signal ntfnptr badge \<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace>"
and handle_vm_fault_irq_masks[wp]:
"handle_vm_fault t vmft \<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace>"
and handle_hypervisor_fault_irq_masks[wp]:
"handle_hypervisor_fault t hvft \<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace>"
and handle_interrupt_irq_masks:
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False (st :: 's state) and K (irq \<le> maxIRQ)\<rbrace>
handle_interrupt irq
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
and arch_invoke_irq_control_irq_masks:
"\<lbrace>domain_sep_inv False st and arch_irq_control_inv_valid ivk\<rbrace>
arch_invoke_irq_control ivk
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
and dmo_getActiveIRQ_irq_masks[wp]:
"do_machine_op (getActiveIRQ in_kernel) \<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace>"
and dmo_getActiveIRQ_return_axiom[wp]:
"\<lbrace>\<top>\<rbrace>
do_machine_op (getActiveIRQ in_kernel)
\<lbrace>\<lambda>rv s :: det_state. (\<forall>x. rv = Some x \<longrightarrow> x \<le> maxIRQ)\<rbrace>"
and activate_thread_irq_masks[wp]:
"activate_thread \<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace>"
and schedule_irq_masks[wp]:
"schedule \<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace>"
begin
crunch irq_masks[wp]: set_extra_badge "\<lambda>s. P (irq_masks_of_state s)"
(wp: crunch_wps dmo_wp)
crunch irq_masks[wp]: send_ipc "\<lambda>s. P (irq_masks_of_state s)"
(wp: crunch_wps simp: crunch_simps ignore: const_on_failure rule: transfer_caps_loop_pres)
lemma invoke_irq_handler_irq_masks:
shows
"\<lbrace>domain_sep_inv False st and (\<lambda>s. (\<exists>ptr'. cte_wp_at ((=) (IRQHandlerCap irq)) ptr' s))\<rbrace>
invoke_irq_handler blah
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
apply(clarsimp simp: valid_def domain_sep_inv_def)
done
lemma empty_slot_irq_masks:
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and K (irq_opt = NullCap)\<rbrace>
empty_slot slot irq_opt
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
apply(rule hoare_gen_asm)
apply(simp add: empty_slot_def post_cap_deletion_def | wp)+
done
crunch irq_masks[wp]: do_reply_transfer "\<lambda>s. P (irq_masks_of_state s)"
(wp: crunch_wps empty_slot_irq_masks simp: crunch_simps unless_def)
crunch irq_masks[wp]: finalise_cap "\<lambda>s. P (irq_masks_of_state s)"
(wp: select_wp crunch_wps dmo_wp no_irq simp: crunch_simps no_irq_setHardwareASID no_irq_set_current_pd no_irq_invalidateLocalTLB_ASID no_irq_invalidateLocalTLB_VAASID no_irq_cleanByVA_PoU)
crunch irq_masks[wp]: send_signal "\<lambda>s. P (irq_masks_of_state s)"
(wp: crunch_wps ignore: do_machine_op wp: dmo_wp simp: crunch_simps)
lemma handle_interrupt_irq_masks:
notes no_irq[wp del]
shows
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st and K (irq \<le> maxIRQ)\<rbrace>
handle_interrupt irq
\<lbrace>\<lambda>rv s. P (irq_masks_of_state s)\<rbrace>"
apply (rule hoare_gen_asm)
apply(simp add: handle_interrupt_def split del: if_split)
apply (rule hoare_pre)
apply (rule hoare_if)
apply simp
apply( wp dmo_wp
| simp add: ackInterrupt_def maskInterrupt_def when_def split del: if_split
| wpc
| simp add: get_irq_state_def handle_reserved_irq_def
| wp (once) hoare_drop_imp)+
apply (fastforce simp: domain_sep_inv_def)
done
crunch irq_masks[wp]: cap_swap_for_delete "\<lambda>s. P (irq_masks_of_state s)"
(* Clagged from re_del_domain_sep_inv' -- would Dan's annotations be good here? *)
lemma rec_del_irq_masks':
notes drop_spec_valid[wp_split del] drop_spec_validE[wp_split del]
rec_del.simps[simp del]
shows
"s \<turnstile> \<lbrace> (\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st\<rbrace>
(rec_del call)
\<lbrace>\<lambda> a s. (case call of (FinaliseSlotCall x y) \<Rightarrow> y \<or> fst a \<longrightarrow> snd a = NullCap | _ \<Rightarrow> True) \<and> domain_sep_inv False st s \<and> P (irq_masks_of_state s)\<rbrace>,\<lbrace>\<lambda>_. domain_sep_inv False st and (\<lambda>s. P (irq_masks_of_state s))\<rbrace>"
proof (induct s arbitrary: rule: rec_del.induct, simp_all only: rec_del_fails hoare_fail_any)
notes drop_spec_valid[wp_split del] drop_spec_validE[wp_split del] rec_del.simps[simp del]
shows "s \<turnstile> \<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st\<rbrace>
rec_del call
\<lbrace>\<lambda>a s. (case call of (FinaliseSlotCall x y) \<Rightarrow> y \<or> fst a \<longrightarrow> snd a = NullCap
| _ \<Rightarrow> True) \<and>
domain_sep_inv False st s \<and> P (irq_masks_of_state s)\<rbrace>,
\<lbrace>\<lambda>_. domain_sep_inv False st and (\<lambda>s. P (irq_masks_of_state s))\<rbrace>"
proof (induct s arbitrary: rule: rec_del.induct, simp_all only: rec_del_fails hoare_fail_any)
case (1 slot exposed s) show ?case
apply(simp add: split_def rec_del.simps)
apply(wp empty_slot_domain_sep_inv empty_slot_irq_masks drop_spec_validE[OF returnOk_wp] drop_spec_validE[OF liftE_wp] | simp)+
apply(rule spec_strengthen_postE[OF "1.hyps", simplified])
apply (wpsimp wp: empty_slot_domain_sep_inv empty_slot_irq_masks
drop_spec_validE[OF returnOk_wp] drop_spec_validE[OF liftE_wp]
simp: split_def rec_del.simps)
apply (fastforce intro: spec_strengthen_postE[OF "1.hyps", simplified])
done
next
case (2 slot exposed s) show ?case
apply (simp add: rec_del.simps split del: if_split)
apply (rule hoare_pre_spec_validE)
apply (wp drop_spec_validE[OF returnOk_wp] drop_spec_validE[OF liftE_wp] set_cap_domain_sep_inv
| simp add: split_def split del: if_split)+
apply (rule spec_strengthen_postE)
apply (rule "2.hyps"[simplified], fastforce+)
apply (rule drop_spec_validE, (wp preemption_point_inv | simp)+)[1]
apply simp
apply (rule spec_strengthen_postE)
apply (rule "2.hyps"[simplified], fastforce+)
apply (wp finalise_cap_domain_sep_inv_cap get_cap_wp
finalise_cap_returns_NullCap[where irqs=False, simplified]
drop_spec_validE[OF liftE_wp] set_cap_domain_sep_inv
| simp split del: if_split
| wp (once) hoare_drop_imps)+
apply (blast dest: cte_wp_at_domain_sep_inv_cap)
done
next
case (3 ptr bits n slot s) show ?case
apply (simp add: rec_del.simps)
apply (wp drop_spec_validE[OF returnOk_wp] drop_spec_validE[OF liftE_wp])
apply (rule hoare_pre_spec_validE)
apply (wp drop_spec_validE[OF assertE_wp])
apply fastforce
done
next
case (2 slot exposed s) show ?case
apply(simp add: rec_del.simps split del: if_split)
apply(rule hoare_pre_spec_validE)
apply(wp drop_spec_validE[OF returnOk_wp] drop_spec_validE[OF liftE_wp] set_cap_domain_sep_inv
|simp add: split_def split del: if_split)+
apply(rule spec_strengthen_postE)
apply(rule "2.hyps"[simplified], fastforce+)
apply(rule drop_spec_validE, (wp preemption_point_inv | simp)+)[1]
apply simp
apply(rule spec_strengthen_postE)
apply(rule "2.hyps"[simplified], fastforce+)
apply(wp finalise_cap_domain_sep_inv_cap get_cap_wp
finalise_cap_returns_NullCap[where irqs=False, simplified]
drop_spec_validE[OF liftE_wp] set_cap_domain_sep_inv
|simp split del: if_split
|wp (once) hoare_drop_imps)+
apply(blast dest: cte_wp_at_domain_sep_inv_cap)
done
next
case (3 ptr bits n slot s) show ?case
apply(simp add: rec_del.simps)
apply (wp drop_spec_validE[OF returnOk_wp] drop_spec_validE[OF liftE_wp])
apply(rule hoare_pre_spec_validE)
apply (wp drop_spec_validE[OF assertE_wp])
apply(fastforce)
done
next
next
case (4 ptr bits n slot s) show ?case
apply(simp add: rec_del.simps)
apply (wp drop_spec_validE[OF returnOk_wp] drop_spec_validE[OF liftE_wp] set_cap_domain_sep_inv
drop_spec_validE[OF assertE_wp] get_cap_wp | simp)+
apply (simp add: rec_del.simps)
apply (wpsimp wp: drop_spec_validE[OF returnOk_wp] drop_spec_validE[OF liftE_wp]
set_cap_domain_sep_inv drop_spec_validE[OF assertE_wp] get_cap_wp)
apply (rule spec_strengthen_postE[OF "4.hyps", simplified])
apply(simp add: returnOk_def return_def)
apply(clarsimp simp: domain_sep_inv_cap_def)
apply (simp add: returnOk_def return_def)
apply (clarsimp simp: domain_sep_inv_cap_def)
done
qed
lemma spec_strengthen_errE:
"\<lbrakk>s \<turnstile> \<lbrace>P\<rbrace> f \<lbrace>Q\<rbrace>, \<lbrace>E'\<rbrace>; \<And>s r. E' s r \<Longrightarrow> E s r\<rbrakk> \<Longrightarrow> s \<turnstile> \<lbrace>P\<rbrace> f \<lbrace>Q\<rbrace>, \<lbrace>E\<rbrace>"
apply(auto simp: spec_validE_def validE_def valid_def split: sum.splits)
done
qed
lemma rec_del_irq_masks:
"\<lbrace> (\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st\<rbrace>
(rec_del call)
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>,\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
apply(rule use_spec)
apply(rule hoare_pre_spec_validE)
apply(rule spec_strengthen_postE)
apply(rule spec_strengthen_errE[OF rec_del_irq_masks'])
apply auto
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st\<rbrace>
rec_del call
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>, \<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
apply (rule use_spec)
apply (rule hoare_pre_spec_validE)
apply (rule spec_strengthen_postE)
apply (rule spec_strengthen_errE[OF rec_del_irq_masks'])
apply auto
done
lemma cap_delete_irq_masks:
"\<lbrace> (\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st\<rbrace>
cap_delete blah
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st\<rbrace>
cap_delete blah
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>,\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
by (simp add: cap_delete_def) (wpsimp wp: rec_del_irq_masks)
lemma arch_invoke_irq_control_irq_masks:
"\<lbrace>domain_sep_inv False st and arch_irq_control_inv_valid invok\<rbrace>
arch_invoke_irq_control invok
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
apply(case_tac invok)
apply(clarsimp simp: arch_irq_control_inv_valid_def domain_sep_inv_def valid_def)
done
lemma invoke_irq_control_irq_masks:
"\<lbrace>domain_sep_inv False st and irq_control_inv_valid invok\<rbrace>
invoke_irq_control invok
"\<lbrace>domain_sep_inv False (st :: 's state) and irq_control_inv_valid ivk\<rbrace>
invoke_irq_control ivk
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
apply(case_tac invok)
apply(clarsimp simp: irq_control_inv_valid_def domain_sep_inv_def valid_def)
apply (cases ivk)
apply (clarsimp simp: irq_control_inv_valid_def domain_sep_inv_def valid_def)
apply (clarsimp simp: arch_invoke_irq_control_irq_masks)
done
crunch irq_masks[wp]: arch_perform_invocation, bind_notification "\<lambda>s. P (irq_masks_of_state s)"
(wp: dmo_wp crunch_wps no_irq simp: crunch_simps no_irq_cleanByVA_PoU no_irq_invalidateLocalTLB_ASID no_irq_do_flush)
end
crunch irq_masks[wp]: cancel_ipc "\<lambda>s. P (irq_masks_of_state s)"
(wp: select_wp crunch_wps simp: crunch_simps)
crunch irq_masks[wp]: restart, set_mcpriority "\<lambda>s. P (irq_masks_of_state s)"
crunch irq_masks[wp]: bind_notification, unbind_notification "\<lambda>s. P (irq_masks_of_state s)"
(wp: dmo_wp crunch_wps no_irq simp: crunch_simps)
crunch irq_masks[wp]: suspend "\<lambda>s. P (irq_masks_of_state s)"
lemma checked_insert_irq_masks[wp]:
"\<lbrace>\<lambda> s. P (irq_masks_of_state s)\<rbrace>
check_cap_at a b
(check_cap_at c d
(cap_insert e f g))
\<lbrace>\<lambda>r s. P (irq_masks_of_state s)\<rbrace>"
apply(wp | simp add: check_cap_at_def)+
done
(* FIXME: remove duplication in this proof -- requires getting the wp
automation to do the right thing with dropping imps in validE
goals *)
lemma invoke_tcb_irq_masks:
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st and
Tcb_AI.tcb_inv_wf tinv\<rbrace>
invoke_tcb tinv
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
apply(case_tac tinv)
apply((wp restart_irq_masks hoare_vcg_if_lift mapM_x_wp[OF _ subset_refl]
| wpc
| simp split del: if_split add: check_cap_at_def
| clarsimp)+)[3]
defer
apply((wp | simp )+)[2]
(* NotificationControl *)
apply (rename_tac option)
apply (case_tac option)
apply ((wp | simp)+)[2]
(* just ThreadControl left *)
apply (simp add: split_def cong: option.case_cong)
apply (wp hoare_vcg_all_lift_R
hoare_vcg_all_lift hoare_vcg_const_imp_lift_R
checked_cap_insert_domain_sep_inv
cap_delete_deletes
cap_delete_valid_cap cap_delete_cte_at
|wpc
|simp add: emptyable_def tcb_cap_cases_def tcb_cap_valid_def
tcb_at_st_tcb_at
|strengthen use_no_cap_to_obj_asid_strg)+
apply(rule hoare_post_impErr[OF cap_delete_irq_masks[where P=P]])
apply blast
apply blast
apply (wp hoare_vcg_all_lift_R
hoare_vcg_all_lift hoare_vcg_const_imp_lift_R
checked_cap_insert_domain_sep_inv
cap_delete_deletes
cap_delete_valid_cap cap_delete_cte_at
|wpc
|simp add: emptyable_def tcb_cap_cases_def tcb_cap_valid_def
tcb_at_st_tcb_at
|strengthen use_no_cap_to_obj_asid_strg)+
apply(rule_tac Q="\<lambda> r s. domain_sep_inv False st s \<and> P (irq_masks_of_state s)" and E="\<lambda>_ s. P (irq_masks_of_state s)" in hoare_post_impErr)
apply(wp hoare_vcg_conj_liftE1 cap_delete_irq_masks)
apply fastforce
apply blast
apply (wp static_imp_wp hoare_vcg_all_lift_R
hoare_vcg_all_lift hoare_vcg_const_imp_lift_R
checked_cap_insert_domain_sep_inv
cap_delete_deletes
cap_delete_valid_cap cap_delete_cte_at
|wpc
|simp add: emptyable_def tcb_cap_cases_def tcb_cap_valid_def
tcb_at_st_tcb_at
|strengthen use_no_cap_to_obj_asid_strg)+
apply(rule_tac Q="\<lambda> r s. domain_sep_inv False st s \<and> P (irq_masks_of_state s)" and E="\<lambda>_ s. P (irq_masks_of_state s)" in hoare_post_impErr)
apply(wp hoare_vcg_conj_liftE1 cap_delete_irq_masks)
apply fastforce
apply blast
apply(rule hoare_pre)
apply(simp add: option_update_thread_def tcb_cap_cases_def
| wp static_imp_wp hoare_vcg_all_lift
thread_set_emptyable
thread_set_valid_cap
thread_set_cte_at thread_set_no_cap_to_trivial
| wpc)+
by fastforce+
"check_cap_at a b (check_cap_at c d (cap_insert e f g)) \<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace>"
by (wpsimp simp: check_cap_at_def)
crunch irq_masks[wp]: cap_move "\<lambda>s. P (irq_masks_of_state s)"
lemma irq_state_independent_irq_masks:
"irq_state_independent (\<lambda>s. P (irq_masks s))"
apply(clarsimp simp: irq_state_independent_def)
done
lemma preemption_point_irq_masks[wp]:
"\<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace> preemption_point \<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
"preemption_point \<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace>"
by (wp preemption_point_inv, simp+)
crunch irq_masks[wp]: cancel_badged_sends "\<lambda>s. P (irq_masks_of_state s)"
(wp: crunch_wps dmo_wp no_irq hoare_unless_wp
simp: filterM_mapM crunch_simps no_irq_clearMemory
ignore: filterM)
context IRQMasks_IF_1 begin
lemma cap_revoke_irq_masks':
notes drop_spec_valid[wp_split del] drop_spec_validE[wp_split del]
shows
"s \<turnstile> \<lbrace> (\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st\<rbrace>
cap_revoke slot
\<lbrace> \<lambda>_ s. P (irq_masks_of_state s)\<rbrace>, \<lbrace> \<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
proof(induct rule: cap_revoke.induct[where ?a1.0=s])
shows "s \<turnstile> \<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st\<rbrace>
cap_revoke slot
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>, \<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
proof (induct rule: cap_revoke.induct[where ?a1.0=s])
case (1 slot s)
show ?case
apply(subst cap_revoke.simps)
apply(rule hoare_pre_spec_validE)
apply (wp "1.hyps")
apply(wp spec_valid_conj_liftE2 | simp)+
apply(wp drop_spec_validE[OF valid_validE[OF preemption_point_irq_masks]]
drop_spec_validE[OF valid_validE[OF preemption_point_domain_sep_inv]]
cap_delete_domain_sep_inv cap_delete_irq_masks
drop_spec_validE[OF assertE_wp] drop_spec_validE[OF returnOk_wp]
drop_spec_validE[OF liftE_wp] select_wp
drop_spec_validE[OF hoare_vcg_conj_liftE1]
| simp | wp (once) hoare_drop_imps)+
apply fastforce
done
qed
apply (subst cap_revoke.simps)
apply (rule hoare_pre_spec_validE)
apply (wp "1.hyps")
apply (wp spec_valid_conj_liftE2 | simp)+
apply (wp drop_spec_validE[OF valid_validE[OF preemption_point_irq_masks]]
drop_spec_validE[OF valid_validE[OF preemption_point_domain_sep_inv]]
cap_delete_domain_sep_inv cap_delete_irq_masks
drop_spec_validE[OF assertE_wp] drop_spec_validE[OF returnOk_wp]
drop_spec_validE[OF liftE_wp] select_wp
drop_spec_validE[OF hoare_vcg_conj_liftE1]
| simp | wp (once) hoare_drop_imps)+
apply fastforce
done
qed
lemmas cap_revoke_irq_masks = use_spec(2)[OF cap_revoke_irq_masks']
crunch irq_masks[wp]: cancel_badged_sends "\<lambda>s. P (irq_masks_of_state s)"
(wp: crunch_wps dmo_wp no_irq hoare_unless_wp simp: filterM_mapM crunch_simps no_irq_clearMemory no_irq_invalidateLocalTLB_ASID
ignore: filterM)
lemma finalise_slot_irq_masks:
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st\<rbrace> finalise_slot p e \<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
apply(simp add: finalise_slot_def | wp rec_del_irq_masks)+
done
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st\<rbrace>
finalise_slot p e
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
by (simp add: finalise_slot_def | wp rec_del_irq_masks)+
lemma invoke_cnode_irq_masks:
"\<lbrace> (\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st and
valid_cnode_inv ci\<rbrace>
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st and valid_cnode_inv ci\<rbrace>
invoke_cnode ci
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
unfolding invoke_cnode_def
apply(case_tac ci)
apply(wp cap_insert_irq_masks cap_move_irq_masks cap_revoke_irq_masks[where st=st] cap_delete_irq_masks[where st=st] | simp split del: if_split)+
apply(rule hoare_pre)
by(wp hoare_vcg_all_lift | simp | wpc | wp (once) hoare_drop_imps | rule hoare_pre)+
apply (cases ci)
by (wpsimp wp: cap_move_irq_masks cap_insert_irq_masks hoare_vcg_all_lift hoare_drop_imps
cap_revoke_irq_masks[where st=st] cap_delete_irq_masks[where st=st]
split_del: if_split)+
crunch irq_masks[wp]: handle_fault "\<lambda>s. P (irq_masks_of_state s)"
(simp: crunch_simps wp: crunch_wps)
crunch irq_masks[wp]: reply_from_kernel "\<lambda>s. P (irq_masks_of_state s)"
(simp: crunch_simps wp: crunch_wps)
end
fun irq_of_handler_inv where
"irq_of_handler_inv (ACKIrq irq) = irq" |
@ -343,52 +253,62 @@ fun irq_of_handler_inv where
crunch irq_masks[wp]: invoke_domain "\<lambda>s. P (irq_masks_of_state s)"
lemma perform_invocation_irq_masks:
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and (\<lambda>s. (\<forall> blah. oper = InvokeIRQHandler blah \<longrightarrow> (\<exists>ptr'. cte_wp_at ((=) (IRQHandlerCap (irq_of_handler_inv blah))) ptr' s))) and domain_sep_inv False st and valid_invocation oper\<rbrace>
perform_invocation blocking calling oper
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
apply(case_tac oper)
apply(simp | wp invoke_tcb_irq_masks invoke_cnode_irq_masks[where st=st] invoke_irq_control_irq_masks[where st=st] invoke_irq_handler_irq_masks[where st=st])+
apply blast
apply(simp | wp)+
done
crunch irq_masks[wp]: handle_fault "\<lambda>s. P (irq_masks_of_state s)"
(simp: crunch_simps wp: crunch_wps)
crunch irq_masks[wp]: reply_from_kernel "\<lambda>s. P (irq_masks_of_state s)"
(simp: crunch_simps wp: crunch_wps)
lemma decode_invocation_IRQHandlerCap:
"\<lbrace> cte_wp_at ((=) cap) slot \<rbrace>
"\<lbrace>cte_wp_at ((=) cap) slot\<rbrace>
decode_invocation label args cap_index slot cap blah
\<lbrace>\<lambda>rv s.
(\<forall>x. rv = InvokeIRQHandler x \<longrightarrow>
(\<exists>a b. cte_wp_at
((=) (IRQHandlerCap (irq_of_handler_inv x)))
(a, b) s))\<rbrace>,-"
apply(simp add: decode_invocation_def split del: if_split)
apply(rule hoare_pre)
\<lbrace>\<lambda>rv s. \<forall>x. rv = InvokeIRQHandler x
\<longrightarrow> (\<exists>a b. cte_wp_at ((=) (IRQHandlerCap (irq_of_handler_inv x))) (a, b) s)\<rbrace>, -"
apply (simp add: decode_invocation_def split del: if_split)
apply (rule hoare_pre)
apply (wp | wpc | simp add: o_def)+
apply (rule hoare_post_imp_R[where Q'="\<top>\<top>"])
apply wp
apply (clarsimp simp: uncurry_def)
apply(wp | wpc | simp add: decode_irq_handler_invocation_def o_def split del: if_split)+
apply (safe | rule TrueI | simp add: op_equal | rule exI[where x="fst slot"], rule exI[where x="snd slot"])+
apply (wp | wpc | simp add: decode_irq_handler_invocation_def o_def split del: if_split)+
apply (safe | simp add: op_equal | rule exI[where x="fst slot"] exI[where x="snd slot"])+
done
lemma handle_yield_irq_masks_of_state[wp]:
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st and invs\<rbrace>
handle_yield
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
by (wpsimp simp: handle_yield_def)
locale IRQMasks_IF_2 = IRQMasks_IF_1 state_t
for state_t :: "'s :: state_ext state" +
assumes do_reply_transfer_irq_masks[wp]:
"do_reply_transfer sender receiver slot grant \<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace>"
and arch_perform_invocation_irq_masks[wp]:
"arch_perform_invocation i \<lbrace>\<lambda>s. P (irq_masks_of_state s)\<rbrace>"
and invoke_tcb_irq_masks:
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False (st :: 's state) and tcb_inv_wf tinv\<rbrace>
invoke_tcb tinv
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
begin
lemma perform_invocation_irq_masks:
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and
(\<lambda>s. (\<forall>blah. oper = InvokeIRQHandler blah
\<longrightarrow> (\<exists>ptr'. cte_wp_at ((=) (IRQHandlerCap (irq_of_handler_inv blah))) ptr' s))) and
domain_sep_inv False (st :: 's state) and valid_invocation oper\<rbrace>
perform_invocation blocking calling oper
\<lbrace>\<lambda>_ s. P (irq_masks_of_state s)\<rbrace>"
apply (cases oper)
by (wpsimp wp: invoke_tcb_irq_masks invoke_cnode_irq_masks[where st=st]
invoke_irq_control_irq_masks[where st=st]
invoke_irq_handler_irq_masks[where st=st]
| fastforce)+
lemma handle_invocation_irq_masks:
"\<lbrace> (\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st and invs\<rbrace>
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False (st :: 's state) and invs\<rbrace>
handle_invocation calling blocking
\<lbrace> \<lambda> rv s. P (irq_masks_of_state s) \<rbrace>"
\<lbrace>\<lambda>rv s. P (irq_masks_of_state s)\<rbrace>"
apply (simp add: handle_invocation_def ts_Restart_case_helper split_def
liftE_liftM_liftME liftME_def bindE_assoc
split del: if_split)
apply(wp static_imp_wp syscall_valid perform_invocation_irq_masks[where st=st] hoare_vcg_all_lift hoare_vcg_ex_lift decode_invocation_IRQHandlerCap
| simp split del: if_split)+
apply(simp add: invs_valid_objs)
liftE_liftM_liftME liftME_def bindE_assoc)
apply (wp static_imp_wp syscall_valid perform_invocation_irq_masks[where st=st]
hoare_vcg_all_lift hoare_vcg_ex_lift decode_invocation_IRQHandlerCap
| simp add: invs_valid_objs)+
done
crunch irq_masks[wp]: handle_reply "\<lambda>s. P (irq_masks_of_state s)"
@ -396,72 +316,39 @@ crunch irq_masks[wp]: handle_reply "\<lambda>s. P (irq_masks_of_state s)"
crunch irq_masks[wp]: handle_recv "\<lambda>s. P (irq_masks_of_state s)"
(wp: crunch_wps simp: crunch_simps)
crunch irq_masks[wp]: handle_vm_fault, handle_hypervisor_fault "\<lambda>s. P (irq_masks_of_state s)"
(wp: dmo_wp no_irq ignore: getFAR getDFSR getIFSR simp: no_irq_getDFSR no_irq_getFAR no_irq_getIFSR)
lemma dmo_getActiveIRQ_irq_masks[wp]:
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s))\<rbrace>
do_machine_op (getActiveIRQ in_kernel)
\<lbrace>\<lambda>rv s. P (irq_masks_of_state s) \<rbrace>"
apply(rule hoare_pre, rule dmo_wp)
apply(simp add: getActiveIRQ_def | wp | simp add: no_irq_def | clarsimp)+
done
lemma dmo_getActiveIRQ_return_axiom[wp]:
"\<lbrace>\<top>\<rbrace>
do_machine_op (getActiveIRQ in_kernel)
\<lbrace>(\<lambda>rv s. (\<forall>x. rv = Some x \<longrightarrow> x \<le> maxIRQ)) \<rbrace>"
apply (simp add: getActiveIRQ_def)
apply(rule hoare_pre, rule dmo_wp)
apply (insert irq_oracle_max_irq)
apply (wp alternative_wp select_wp dmo_getActiveIRQ_irq_masks)
apply clarsimp
done
lemma handle_yield_irq_masks_of_state[wp]:
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st and invs\<rbrace>
handle_yield
\<lbrace>\<lambda>rv s. P (irq_masks_of_state s)\<rbrace>"
apply (simp add: handle_yield_def)
apply wp
apply simp
done
lemma handle_event_irq_masks:
"\<lbrace> (\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st and invs\<rbrace>
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False (st :: 's state) and invs\<rbrace>
handle_event ev
\<lbrace> \<lambda> rv s. P (irq_masks_of_state s) \<rbrace>"
\<lbrace>\<lambda>rv s. P (irq_masks_of_state s)\<rbrace>"
apply ((case_tac ev, rename_tac syscall, case_tac syscall);
(solves \<open>(simp add: handle_send_def handle_call_def
| wp handle_invocation_irq_masks[where st=st] handle_interrupt_irq_masks[where st=st]
hoare_vcg_all_lift
| wpc
| wp (once) hoare_drop_imps)+\<close>)?)
apply (rule hoare_pre)
(solves \<open>(simp add: handle_send_def handle_call_def
| wp handle_invocation_irq_masks[where st=st]
handle_interrupt_irq_masks[where st=st]
hoare_vcg_all_lift
| wpc
| wp (once) hoare_drop_imps)+\<close>)?)
apply simp
apply (wp handle_interrupt_irq_masks[where st=st] | wpc | simp )+
apply (rule_tac Q="\<lambda>rv s. P (irq_masks_of_state s) \<and> domain_sep_inv False st s
\<and> (\<forall>x. rv = Some x \<longrightarrow> x \<le> maxIRQ)" in hoare_strengthen_post)
apply (wp | clarsimp)+
apply (wp handle_interrupt_irq_masks[where st=st] | wpc | simp)+
apply (rule_tac Q="\<lambda>rv s. P (irq_masks_of_state s) \<and> domain_sep_inv False st s \<and>
(\<forall>x. rv = Some x \<longrightarrow> x \<le> maxIRQ)" in hoare_strengthen_post)
apply wpsimp+
done
crunch irq_masks[wp]: activate_thread "\<lambda>s. P (irq_masks_of_state s)"
crunch irq_masks[wp]: schedule "\<lambda>s. P (irq_masks_of_state s)"
(wp: dmo_wp alternative_wp select_wp crunch_wps simp: crunch_simps clearExMonitor_def)
lemma call_kernel_irq_masks:
"\<lbrace> (\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False st and einvs and (\<lambda>s. ev \<noteq> Interrupt \<longrightarrow> ct_active s)\<rbrace>
"\<lbrace>(\<lambda>s. P (irq_masks_of_state s)) and domain_sep_inv False (st :: 's state) and einvs
and (\<lambda>s. ev \<noteq> Interrupt \<longrightarrow> ct_active s)\<rbrace>
call_kernel ev
\<lbrace> \<lambda> rv s. P (irq_masks_of_state s) \<rbrace>"
apply(simp add: call_kernel_def)
\<lbrace>\<lambda>rv s. P (irq_masks_of_state s)\<rbrace>"
apply (simp add: call_kernel_def)
apply (wp handle_interrupt_irq_masks[where st=st])+
apply (rule_tac Q="\<lambda>rv s. P (irq_masks_of_state s) \<and> domain_sep_inv False st s \<and> (\<forall>x. rv = Some x \<longrightarrow> x \<le> maxIRQ)" in hoare_strengthen_post)
apply (rule_tac Q="\<lambda>rv s. P (irq_masks_of_state s) \<and> domain_sep_inv False st s \<and>
(\<forall>x. rv = Some x \<longrightarrow> x \<le> maxIRQ)" in hoare_strengthen_post)
apply (wp | simp)+
apply(rule_tac Q="\<lambda> x s. P (irq_masks_of_state s) \<and> domain_sep_inv False st s" and F="E" for E in hoare_post_impErr)
apply(rule valid_validE)
apply(wp handle_event_irq_masks[where st=st] valid_validE[OF handle_event_domain_sep_inv] | simp)+
apply (rule_tac Q="\<lambda>x s. P (irq_masks_of_state s) \<and> domain_sep_inv False st s"
and F="E" for E in hoare_post_impErr)
apply (rule valid_validE)
apply (wp handle_event_irq_masks[where st=st] valid_validE[OF handle_event_domain_sep_inv]
| simp)+
done
end