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DomainSepInv.thy
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(*
* Copyright 2020, Data61, CSIRO (ABN 41 687 119 230)
*
* SPDX-License-Identifier: GPL-2.0-only
*)
theory DomainSepInv
imports
"ArchIpc_AC" (* for transfer_caps_loop_pres_dest lec_valid_cap' set_simple_ko_get_tcb thread_set_tcb_fault_update_valid_mdb *)
"Lib.WPBang"
begin
text \<open>
We define and prove an invariant that is necessary to achieve domain
separation on seL4. In its strongest form, we require that all IRQs, other than
those for the timer, are inactive, and that no IRQControl or
IRQHandler caps are present (to prevent any inactive IRQs from becoming
active in the future).
It always requires that there are no domain caps.
\<close>
text \<open>
When @{term irqs} is @{term False} we require that non-timer IRQs are off permanently.
\<close>
definition domain_sep_inv :: "bool \<Rightarrow> 'a :: state_ext state \<Rightarrow> 'b :: state_ext state \<Rightarrow> bool" where
"domain_sep_inv irqs st s \<equiv>
(\<forall>slot. \<not> cte_wp_at ((=) DomainCap) slot s) \<and>
(irqs \<or> (\<forall>irq slot. \<not> cte_wp_at ((=) IRQControlCap) slot s
\<and> \<not> cte_wp_at ((=) (IRQHandlerCap irq)) slot s
\<and> interrupt_states s irq \<noteq> IRQSignal
\<and> interrupt_states s irq \<noteq> IRQReserved
\<and> interrupt_states s = interrupt_states st))"
definition domain_sep_inv_cap where
"domain_sep_inv_cap irqs cap \<equiv> case cap of
IRQControlCap \<Rightarrow> irqs
| IRQHandlerCap irq \<Rightarrow> irqs
| DomainCap \<Rightarrow> False
| _ \<Rightarrow> True"
lemma cte_wp_at_not_domain_sep_inv_cap:
"cte_wp_at (not domain_sep_inv_cap irqs) slot s \<longleftrightarrow>
((irqs \<longrightarrow> False) \<and>
(\<not> irqs \<longrightarrow> (cte_wp_at ((=) IRQControlCap) slot s \<or>
(\<exists> irq. cte_wp_at ((=) (IRQHandlerCap irq)) slot s)))) \<or>
cte_wp_at ((=) DomainCap) slot s"
apply (rule iffI)
apply (drule cte_wp_at_norm)
apply clarsimp
apply (case_tac c, simp_all add: domain_sep_inv_cap_def pred_neg_def)
apply (auto elim: cte_wp_at_weakenE split: if_splits)
done
lemma domain_sep_inv_def2:
"domain_sep_inv irqs st s =
((\<forall>slot. \<not> cte_wp_at ((=) DomainCap) slot s) \<and>
(irqs \<or> (\<forall>irq slot. \<not> cte_wp_at ((=) IRQControlCap) slot s
\<and> \<not> cte_wp_at ((=) (IRQHandlerCap irq)) slot s)) \<and>
(irqs \<or> (\<forall>irq. interrupt_states s irq \<noteq> IRQSignal
\<and> interrupt_states s irq \<noteq> IRQReserved
\<and> interrupt_states s = interrupt_states st)))"
by (fastforce simp: domain_sep_inv_def)
lemma domain_sep_inv_wp:
assumes nctrl:
"\<And>slot. \<lbrace>(\<lambda>s. \<not> cte_wp_at (not domain_sep_inv_cap irqs) slot s) and P\<rbrace>
f
\<lbrace>\<lambda>_ s. \<not> cte_wp_at (not domain_sep_inv_cap irqs) slot s\<rbrace>"
assumes irq_pres:
"\<And>P. \<not> irqs \<Longrightarrow> \<lbrace>(\<lambda>s. P (interrupt_states s)) and R\<rbrace>
f
\<lbrace>\<lambda>_ s. P (interrupt_states s)\<rbrace>"
shows
"\<lbrace>domain_sep_inv irqs st and P and (\<lambda>s. irqs \<or> R s)\<rbrace>
f
\<lbrace>\<lambda>_. domain_sep_inv irqs st\<rbrace>"
apply (clarsimp simp: domain_sep_inv_def2 valid_def)
apply (subst conj_assoc[symmetric])
apply (rule conjI)
apply (rule conjI)
apply (intro allI)
apply (erule use_valid[OF _ hoare_strengthen_post[OF nctrl]])
apply (fastforce simp: cte_wp_at_not_domain_sep_inv_cap)
apply (fastforce simp: cte_wp_at_not_domain_sep_inv_cap)
apply (fastforce elim!: use_valid[OF _ hoare_strengthen_post[OF nctrl]]
simp: cte_wp_at_not_domain_sep_inv_cap)
apply (case_tac "irqs")
apply blast
apply (rule disjI2)
apply simp
apply (intro allI conjI)
apply (erule_tac P1="\<lambda>x. x irq \<noteq> IRQSignal" in use_valid[OF _ irq_pres], assumption)
apply blast
apply (erule use_valid[OF _ irq_pres], assumption)
apply blast
apply (erule use_valid[OF _ irq_pres], assumption)
apply blast
done
lemma domain_sep_inv_triv:
assumes cte_pres: "\<And>P slot. \<lbrace>\<lambda>s. \<not> cte_wp_at P slot s\<rbrace> f \<lbrace>\<lambda>_ s. \<not> cte_wp_at P slot s\<rbrace>"
assumes irq_pres: "\<And>P. \<lbrace>\<lambda>s. P (interrupt_states s)\<rbrace> f \<lbrace>\<lambda>_ s. P (interrupt_states s)\<rbrace>"
shows "\<lbrace>domain_sep_inv irqs st\<rbrace> f \<lbrace>\<lambda>_. domain_sep_inv irqs st\<rbrace>"
apply (rule domain_sep_inv_wp[where P="\<top>" and R="\<top>", simplified])
apply (rule cte_pres, rule irq_pres)
done
lemma domain_sep_inv_arch_state_update[simp]:
"domain_sep_inv irqs st (s\<lparr>arch_state := blah\<rparr>) = domain_sep_inv irqs st s"
by (simp add: domain_sep_inv_def)
lemma domain_sep_inv_machine_state_update[simp]:
"domain_sep_inv irqs st (s\<lparr>machine_state := X\<rparr>) = domain_sep_inv irqs st s"
by (simp add: domain_sep_inv_def)
lemma detype_interrupts_states[simp]:
"interrupt_states (detype S s) = interrupt_states s"
by (simp add: detype_def)
lemma detype_domain_sep_inv[simp]:
"domain_sep_inv irqs st s \<longrightarrow> domain_sep_inv irqs st (detype S s)"
by (fastforce simp: domain_sep_inv_def)
lemma domain_sep_inv_detype_lift:
"\<lbrace>P\<rbrace> f \<lbrace>\<lambda>rv. domain_sep_inv irqs st\<rbrace> \<Longrightarrow>
\<lbrace>P\<rbrace> f \<lbrace>\<lambda>rv s. domain_sep_inv irqs st (detype S s)\<rbrace>"
by (strengthen detype_domain_sep_inv, assumption)
crunch domain_sep_inv[wp]: set_extra_badge "domain_sep_inv irqs st"
(* FIXME: following 3 lemmas clagged from FinalCaps *)
lemma set_cap_neg_cte_wp_at_other_helper':
"\<lbrakk> oslot \<noteq> slot; ko_at (TCB x) (fst oslot) s;
tcb_cap_cases (snd oslot) = Some (ogetF, osetF, orestr);
kheap (s\<lparr>kheap := kheap s(fst oslot \<mapsto> TCB (osetF (\<lambda> x. cap) x))\<rparr>) (fst slot) = Some (TCB tcb);
tcb_cap_cases (snd slot) = Some (getF, setF, restr); P (getF tcb) \<rbrakk>
\<Longrightarrow> cte_wp_at P slot s"
apply (case_tac "fst oslot = fst slot")
apply (rule cte_wp_at_tcbI)
apply (fastforce split: if_splits simp: obj_at_def)
apply assumption
apply (fastforce split: if_splits simp: tcb_cap_cases_def dest: prod_eqI)
apply (rule cte_wp_at_tcbI)
apply (fastforce split: if_splits simp: obj_at_def)
apply assumption
apply assumption
done
lemma set_cap_neg_cte_wp_at_other_helper:
"\<lbrakk> \<not> cte_wp_at P slot s; oslot \<noteq> slot; ko_at (TCB x) (fst oslot) s;
tcb_cap_cases (snd oslot) = Some (getF, setF, restr) \<rbrakk>
\<Longrightarrow> \<not> cte_wp_at P slot (s\<lparr>kheap := kheap s(fst oslot \<mapsto> TCB (setF (\<lambda> x. cap) x))\<rparr>)"
apply (rule notI)
apply (erule cte_wp_atE)
apply (fastforce elim: notE intro: cte_wp_at_cteI split: if_splits)
apply (fastforce elim: notE intro: set_cap_neg_cte_wp_at_other_helper')
done
lemma set_cap_neg_cte_wp_at_other:
"oslot \<noteq> slot \<Longrightarrow> set_cap cap oslot \<lbrace>\<lambda>s. \<not> cte_wp_at P slot s\<rbrace>"
unfolding set_cap_def
apply (wp set_object_wp get_object_wp | wpc | simp add: split_def)+
apply (intro allI impI conjI)
apply (rule notI)
apply (erule cte_wp_atE)
apply (fastforce split: if_splits dest: prod_eqI elim: notE intro: cte_wp_at_cteI simp: obj_at_def)
apply (fastforce split: if_splits elim: notE intro: cte_wp_at_tcbI)
apply (auto dest: set_cap_neg_cte_wp_at_other_helper)
done
lemma set_cap_neg_cte_wp_at:
"\<lbrace>\<lambda>s. \<not> cte_wp_at P slot s \<and> \<not> P capa\<rbrace>
set_cap capa slota
\<lbrace>\<lambda>_ s. \<not> cte_wp_at P slot s\<rbrace>"
apply (case_tac "slot = slota")
apply simp
apply (simp add: set_cap_def set_object_def)
apply (rule hoare_pre)
apply (wp get_object_wp | wpc)+
apply (fastforce elim: cte_wp_atE intro: cte_wp_at_cteI cte_wp_at_tcbI)
apply (rule hoare_pre)
apply (rule set_cap_neg_cte_wp_at_other, simp+)
done
lemma domain_sep_inv_cap_IRQControlCap:
"\<lbrakk> domain_sep_inv_cap irqs cap; \<not> irqs \<rbrakk> \<Longrightarrow> cap \<noteq> IRQControlCap"
by (auto simp: domain_sep_inv_cap_def)
lemma domain_sep_inv_cap_IRQHandlerCap:
"\<lbrakk> domain_sep_inv_cap irqs cap; \<not> irqs \<rbrakk> \<Longrightarrow> cap \<noteq> IRQHandlerCap irq"
by (auto simp: domain_sep_inv_cap_def)
lemma set_cap_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and K (domain_sep_inv_cap irqs cap)\<rbrace>
set_cap cap slot
\<lbrace>\<lambda>_. domain_sep_inv irqs st\<rbrace>"
apply (rule hoare_gen_asm)
apply (rule hoare_pre)
apply (rule domain_sep_inv_wp)
apply (wp set_cap_neg_cte_wp_at | simp add: pred_neg_def | blast)+
done
lemma cte_wp_at_domain_sep_inv_cap:
"\<lbrakk> domain_sep_inv irqs st s; cte_wp_at ((=) cap) slot s \<rbrakk>
\<Longrightarrow> domain_sep_inv_cap irqs cap"
apply (case_tac slot)
apply (auto simp: domain_sep_inv_def domain_sep_inv_cap_def split: cap.splits)
done
lemma weak_derived_irq_handler:
"weak_derived (IRQHandlerCap irq) cap \<Longrightarrow> cap = (IRQHandlerCap irq)"
by (auto simp: weak_derived_def copy_of_def same_object_as_def split: cap.splits if_splits)
(* FIXME: move to CSpace_AI *)
lemma weak_derived_DomainCap:
"weak_derived c' c \<Longrightarrow> (c' = DomainCap) = (c = DomainCap)"
apply (clarsimp simp: weak_derived_def)
apply (erule disjE)
apply (clarsimp simp: copy_of_def split: if_split_asm)
apply (auto simp: is_cap_simps same_object_as_def
split: cap.splits)[1]
apply simp
done
lemma cte_wp_at_weak_derived_domain_sep_inv_cap:
"\<lbrakk> domain_sep_inv irqs st s; cte_wp_at (weak_derived cap) slot s \<rbrakk>
\<Longrightarrow> domain_sep_inv_cap irqs cap"
apply (cases slot)
apply (force simp: domain_sep_inv_def domain_sep_inv_cap_def
split: cap.splits
dest: cte_wp_at_norm weak_derived_irq_handler weak_derived_DomainCap)
done
lemma is_derived_IRQHandlerCap:
"is_derived m src (IRQHandlerCap irq) cap \<Longrightarrow> (cap = IRQHandlerCap irq)"
apply (clarsimp simp: is_derived_def)
apply (case_tac cap, simp_all add: is_cap_simps cap_master_cap_def)
done
(* FIXME: move to CSpace_AI *)
lemma DomainCap_is_derived:
"is_derived m src DomainCap cap \<Longrightarrow> cap = DomainCap"
by (auto simp: is_derived_def is_reply_cap_def is_master_reply_cap_def cap_master_cap_def
split: cap.splits)
lemma cte_wp_at_is_derived_domain_sep_inv_cap:
"\<lbrakk> domain_sep_inv irqs st s; cte_wp_at (is_derived (cdt s) slot cap) slot s \<rbrakk>
\<Longrightarrow> domain_sep_inv_cap irqs cap"
apply (cases slot)
apply (fastforce simp: domain_sep_inv_def domain_sep_inv_cap_def
split: cap.splits
dest: cte_wp_at_norm DomainCap_is_derived is_derived_IRQHandlerCap)
done
lemma domain_sep_inv_exst_update[simp]:
"domain_sep_inv irqs st (trans_state f s) = domain_sep_inv irqs st s"
by (simp add: domain_sep_inv_def)
lemma domain_sep_inv_is_original_cap_update[simp]:
"domain_sep_inv irqs st (s\<lparr>is_original_cap := X\<rparr>) = domain_sep_inv irqs st s"
by (simp add: domain_sep_inv_def)
lemma domain_sep_inv_cdt_update[simp]:
"domain_sep_inv irqs st (s\<lparr>cdt := X\<rparr>) = domain_sep_inv irqs st s"
by (simp add: domain_sep_inv_def)
crunch domain_sep_inv[wp]: update_cdt "domain_sep_inv irqs st"
lemma set_untyped_cap_as_full_domain_sep_inv[wp]:
"set_untyped_cap_as_full a b c \<lbrace>domain_sep_inv irqs st\<rbrace>"
apply (clarsimp simp: set_untyped_cap_as_full_def)
apply (rule hoare_pre)
apply (rule set_cap_domain_sep_inv)
apply (case_tac a, simp_all add: domain_sep_inv_cap_def)
done
lemma cap_insert_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and (\<lambda>s. cte_wp_at (is_derived (cdt s) slot cap) slot s)\<rbrace>
cap_insert cap slot dest_slot
\<lbrace>\<lambda>_. domain_sep_inv irqs st \<rbrace>"
apply (simp add: cap_insert_def)
apply (wpsimp wp: set_cap_domain_sep_inv get_cap_wp set_original_wp dxo_wp_weak)
apply (blast dest: cte_wp_at_is_derived_domain_sep_inv_cap)
done
lemma domain_sep_inv_cap_NullCap[simp]:
"domain_sep_inv_cap irqs NullCap"
by (simp add: domain_sep_inv_cap_def)
lemma cap_move_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and (\<lambda>s. cte_wp_at (weak_derived cap) slot s)\<rbrace>
cap_move cap slot dest_slot
\<lbrace>\<lambda>_. domain_sep_inv irqs st \<rbrace>"
apply (simp add: cap_move_def)
apply (wpsimp wp: set_cap_domain_sep_inv get_cap_wp set_original_wp dxo_wp_weak)
apply (blast dest: cte_wp_at_weak_derived_domain_sep_inv_cap)
done
lemma set_irq_state_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and (\<lambda>s. stt = interrupt_states s irq)\<rbrace>
set_irq_state stt irq
\<lbrace>\<lambda>_. domain_sep_inv irqs st\<rbrace>"
apply (simp add: set_irq_state_def)
apply (wp | simp add: do_machine_op_def | wpc)+
done
locale DomainSepInv_1 =
fixes state_ext_t :: "'state_ext :: state_ext itself"
assumes arch_finalise_cap_domain_sep_inv[wp]:
"arch_finalise_cap c x \<lbrace>\<lambda>s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)\<rbrace>"
and arch_post_cap_deletion_domain_sep_inv[wp]:
"arch_post_cap_deletion acap \<lbrace>\<lambda>s :: det_ext state. domain_sep_inv irqs st s\<rbrace>"
and init_arch_objects_domain_sep_inv[wp]:
"init_arch_objects typ ptr n sz refs \<lbrace>\<lambda>s :: det_ext state. domain_sep_inv irqs st s\<rbrace>"
and prepare_thread_delete_domain_sep_inv[wp]:
"prepare_thread_delete t \<lbrace>\<lambda>s :: det_ext state. domain_sep_inv irqs st s\<rbrace>"
and arch_finalise_cap_rv:
"\<lbrace>\<lambda>_. P (NullCap,NullCap)\<rbrace> arch_finalise_cap c x \<lbrace>\<lambda>rv s :: det_ext state. P rv\<rbrace>"
begin
lemma deleted_irq_handler_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and K irqs\<rbrace>
deleted_irq_handler irq
\<lbrace>\<lambda>_ s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)\<rbrace>"
apply (rule hoare_gen_asm)
apply (simp add: deleted_irq_handler_def set_irq_state_def)
apply wp
apply (simp add: domain_sep_inv_def)
done
lemma empty_slot_domain_sep_inv:
"\<lbrace>\<lambda>s. domain_sep_inv irqs st s \<and> (\<not> irqs \<longrightarrow> b = NullCap)\<rbrace>
empty_slot a b
\<lbrace>\<lambda>_ s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)\<rbrace>"
unfolding empty_slot_def post_cap_deletion_def
by (wpsimp wp: get_cap_wp set_cap_domain_sep_inv set_original_wp dxo_wp_weak
static_imp_wp deleted_irq_handler_domain_sep_inv)
end
lemma set_simple_ko_neg_cte_wp_at[wp]:
"set_simple_ko f a b \<lbrace>\<lambda>s. \<not> cte_wp_at P slot s\<rbrace>"
apply (simp add: set_simple_ko_def)
apply (wp set_object_wp_strong get_object_wp
| simp add: partial_inv_def a_type_def split: kernel_object.splits)+
apply (case_tac "a = fst slot")
apply (clarsimp split: kernel_object.splits)
apply (fastforce elim: cte_wp_atE simp: obj_at_def)
apply (fastforce elim: cte_wp_atE intro: cte_wp_at_cteI cte_wp_at_tcbI)
done
crunch domain_sep_inv[wp]: set_simple_ko "domain_sep_inv irqs st"
(wp: domain_sep_inv_triv)
lemma set_thread_state_neg_cte_wp_at[wp]:
"set_thread_state a b \<lbrace>\<lambda>s. \<not> cte_wp_at P slot s\<rbrace>"
apply (simp add: set_thread_state_def)
apply (wp set_object_wp get_object_wp dxo_wp_weak| simp)+
apply (case_tac "a = fst slot")
apply (clarsimp split: kernel_object.splits)
apply (erule notE)
apply (erule cte_wp_atE)
apply (fastforce simp: obj_at_def)
apply (drule get_tcb_SomeD)
apply (rule cte_wp_at_tcbI)
apply simp
apply assumption
apply (fastforce simp: tcb_cap_cases_def split: if_splits)
apply (fastforce elim: cte_wp_atE intro: cte_wp_at_cteI cte_wp_at_tcbI)
done
lemma set_bound_notification_neg_cte_wp_at[wp]:
"set_bound_notification a b \<lbrace>\<lambda>s. \<not> cte_wp_at P slot s\<rbrace>"
apply (simp add: set_bound_notification_def)
apply (wp set_object_wp get_object_wp dxo_wp_weak| simp)+
apply (case_tac "a = fst slot")
apply (clarsimp split: kernel_object.splits)
apply (erule notE)
apply (erule cte_wp_atE)
apply (fastforce simp: obj_at_def)
apply (drule get_tcb_SomeD)
apply (rule cte_wp_at_tcbI)
apply simp
apply assumption
apply (fastforce simp: tcb_cap_cases_def split: if_splits)
apply (fastforce elim: cte_wp_atE intro: cte_wp_at_cteI cte_wp_at_tcbI)
done
crunch domain_sep_inv[wp]: set_thread_state, set_bound_notification, get_bound_notification "domain_sep_inv irqs st"
(wp: domain_sep_inv_triv)
lemma thread_set_tcb_fault_update_neg_cte_wp_at[wp]:
"thread_set (tcb_fault_update blah) t \<lbrace>\<lambda>s. \<not> cte_wp_at P slot s\<rbrace>"
apply (simp add: thread_set_def)
apply (wp set_object_wp get_object_wp | simp)+
apply (case_tac "t = fst slot")
apply (clarsimp split: kernel_object.splits)
apply (erule notE)
apply (erule cte_wp_atE)
apply (fastforce simp: obj_at_def)
apply (drule get_tcb_SomeD)
apply (rule cte_wp_at_tcbI)
apply simp
apply assumption
apply (fastforce simp: tcb_cap_cases_def split: if_splits)
apply (fastforce elim: cte_wp_atE intro: cte_wp_at_cteI cte_wp_at_tcbI)
done
lemma thread_set_tcb_fault_update_domain_sep_inv[wp]:
"thread_set (tcb_fault_update blah) t \<lbrace>domain_sep_inv irqs st\<rbrace>"
by (wp domain_sep_inv_triv)
crunch domain_sep_inv[wp]: as_user "domain_sep_inv irqs st"
(wp: domain_sep_inv_triv)
lemma get_cap_domain_sep_inv_cap:
"\<lbrace>domain_sep_inv irqs st\<rbrace> get_cap cap \<lbrace>\<lambda>rv s. domain_sep_inv_cap irqs rv\<rbrace>"
by (wpsimp wp: get_cap_wp simp: cte_wp_at_domain_sep_inv_cap)
crunch domain_sep_inv[wp]: cap_swap_for_delete "domain_sep_inv irqs st"
(wp: get_cap_domain_sep_inv_cap dxo_wp_weak simp: crunch_simps ignore: cap_swap_ext)
lemma preemption_point_domain_sep_inv[wp]:
"preemption_point \<lbrace>domain_sep_inv irqs st\<rbrace>"
by (wp preemption_point_inv | simp)+
context DomainSepInv_1 begin
crunches cap_delete_one
for domain_sep_inv[wp]: "\<lambda>s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)"
(wp: mapM_x_wp' hoare_unless_wp dxo_wp_weak simp: crunch_simps)
lemma reply_cancel_ipc_domain_sep_inv[wp]:
"\<lbrace>domain_sep_inv irqs st\<rbrace>
reply_cancel_ipc t
\<lbrace>\<lambda>_ s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)\<rbrace>"
apply (simp add: reply_cancel_ipc_def)
apply (wp select_wp)
apply (rule hoare_strengthen_post[OF thread_set_tcb_fault_update_domain_sep_inv])
apply auto
done
crunches finalise_cap
for domain_sep_inv[wp]: "\<lambda>s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)"
(wp: dxo_wp_weak)
lemma finalise_cap_domain_sep_inv_cap:
"\<lbrace>\<lambda>s. domain_sep_inv_cap irqs cap\<rbrace>
finalise_cap cap b
\<lbrace>\<lambda>rv s :: det_ext state. domain_sep_inv_cap irqs (fst rv)\<rbrace>"
including no_pre
apply (case_tac cap)
apply (wp | simp add: o_def split del: if_split split: cap.splits
| fastforce split: if_splits simp: domain_sep_inv_cap_def)+
apply (rule hoare_pre, wp, fastforce)
apply (rule hoare_pre, simp, wp, fastforce simp: domain_sep_inv_cap_def)
apply (wpc | wp arch_finalise_cap_rv | simp)+
done
lemma finalise_cap_returns_NullCap:
"\<lbrace>\<lambda>s. domain_sep_inv_cap irqs cap\<rbrace>
finalise_cap cap b
\<lbrace>\<lambda>rv s :: det_ext state. \<not> irqs \<longrightarrow> snd rv = NullCap\<rbrace>"
apply (case_tac cap)
by (wpsimp wp: arch_finalise_cap_rv simp: o_def domain_sep_inv_cap_def split_del: if_split)+
lemma rec_del_domain_sep_inv':
notes drop_spec_valid[wp_split del] drop_spec_validE[wp_split del]
rec_del.simps[simp del]
shows
"s \<turnstile> \<lbrace>domain_sep_inv irqs st\<rbrace>
rec_del call
\<lbrace>\<lambda>rv s. (case call of (FinaliseSlotCall x y) \<Rightarrow> (y \<or> fst rv) \<longrightarrow> \<not> irqs \<longrightarrow> snd rv = NullCap
| _ \<Rightarrow> True) \<and>
domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)\<rbrace>,
\<lbrace>\<lambda>_. domain_sep_inv irqs st\<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 (wpsimp wp: empty_slot_domain_sep_inv
drop_spec_validE[OF returnOk_wp]
drop_spec_validE[OF liftE_wp])
apply (rule spec_strengthen_postE[OF "1.hyps"])
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", fastforce+)
apply (rule drop_spec_validE, (wp preemption_point_inv| simp)+)[1]
apply simp
apply (rule spec_strengthen_postE)
apply (rule "2.hyps", fastforce+)
apply (wp finalise_cap_domain_sep_inv_cap get_cap_wp
finalise_cap_returns_NullCap
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 (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 (rule spec_strengthen_postE[OF "4.hyps"])
apply (simp add: returnOk_def return_def)
apply (clarsimp simp: domain_sep_inv_cap_def)
done
qed
lemma rec_del_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st\<rbrace>
rec_del call
\<lbrace>\<lambda>_ s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)\<rbrace>"
apply (rule validE_valid)
apply (rule use_spec)
apply (rule spec_strengthen_postE[OF rec_del_domain_sep_inv'])
by fastforce
crunches cap_delete
for domain_sep_inv[wp]: "\<lambda>s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)"
lemma cap_revoke_domain_sep_inv':
notes drop_spec_valid[wp_split del] drop_spec_validE[wp_split del]
shows
"s \<turnstile> \<lbrace> domain_sep_inv irqs st\<rbrace>
cap_revoke slot
\<lbrace> \<lambda>_ s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)\<rbrace>, \<lbrace> \<lambda>_. domain_sep_inv irqs st\<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_domain_sep_inv]]
drop_spec_validE[OF valid_validE[OF cap_delete_domain_sep_inv]]
drop_spec_validE[OF assertE_wp] drop_spec_validE[OF returnOk_wp]
drop_spec_validE[OF liftE_wp] select_wp
| simp | wp (once) hoare_drop_imps)+
done
qed
lemmas cap_revoke_domain_sep_inv[wp] = use_spec(2)[OF cap_revoke_domain_sep_inv']
end
lemma cap_move_cte_wp_at_other:
"\<lbrace>cte_wp_at P slot and K (slot \<noteq> dest_slot \<and> slot \<noteq> src_slot)\<rbrace>
cap_move cap src_slot dest_slot
\<lbrace>\<lambda>_. cte_wp_at P slot\<rbrace>"
unfolding cap_move_def
by (wpsimp wp: set_cdt_cte_wp_at set_cap_cte_wp_at' dxo_wp_weak static_imp_wp set_original_wp)
lemma cte_wp_at_weak_derived_ReplyCap:
"cte_wp_at ((=) (ReplyCap x False R)) slot s
\<Longrightarrow> cte_wp_at (weak_derived (ReplyCap x False R)) slot s"
apply (erule cte_wp_atE)
apply (rule cte_wp_at_cteI)
apply assumption
apply assumption
apply assumption
apply simp
apply (rule cte_wp_at_tcbI)
apply auto
done
lemma thread_set_tcb_registers_caps_merge_default_tcb_neg_cte_wp_at[wp]:
"thread_set (tcb_registers_caps_merge default_tcb) word \<lbrace>\<lambda>s. \<not> cte_wp_at P slot s\<rbrace>"
unfolding thread_set_def
apply (wp set_object_wp | simp)+
apply (case_tac "word = fst slot")
apply (clarsimp split: kernel_object.splits)
apply (erule notE)
apply (erule cte_wp_atE)
apply (fastforce simp: obj_at_def)
apply (drule get_tcb_SomeD)
apply (rule cte_wp_at_tcbI)
apply simp
apply assumption
apply (clarsimp simp: tcb_cap_cases_def tcb_registers_caps_merge_def split: if_splits)
apply (fastforce elim: cte_wp_atE intro: cte_wp_at_cteI cte_wp_at_tcbI)
done
lemma thread_set_tcb_registers_caps_merge_default_tcb_domain_sep_inv[wp]:
"thread_set (tcb_registers_caps_merge default_tcb) word \<lbrace>domain_sep_inv irqs st\<rbrace>"
by (wp domain_sep_inv_triv)
lemma cancel_badged_sends_domain_sep_inv[wp]:
"cancel_badged_sends epptr badge \<lbrace>domain_sep_inv irqs st\<rbrace>"
apply (simp add: cancel_badged_sends_def)
apply (wpsimp wp: dxo_wp_weak mapM_wp | simp add: filterM_mapM | wp (once) hoare_drop_imps)+
done
lemma create_cap_domain_sep_inv[wp]:
"create_cap tp sz p dev slot \<lbrace>domain_sep_inv irqs st\<rbrace>"
apply (simp add: create_cap_def)
apply (rule hoare_pre)
apply (wp set_cap_domain_sep_inv dxo_wp_weak | wpc | simp)+
apply clarsimp
apply (case_tac tp, simp_all add: domain_sep_inv_cap_def)
done
lemma retype_region_neg_cte_wp_at_not_domain_sep_inv_cap:
"retype_region base n sz ty dev \<lbrace>\<lambda>s. \<not> cte_wp_at (not domain_sep_inv_cap irqs) slot s\<rbrace>"
apply (rule hoare_pre)
apply (simp only: retype_region_def retype_addrs_def foldr_upd_app_if fun_app_def K_bind_def)
apply (wp dxo_wp_weak | simp)+
apply clarsimp
apply (case_tac "fst slot \<in> (\<lambda>p. ptr_add base (p * 2 ^ obj_bits_api ty sz)) ` {0..<n}")
apply clarsimp
apply (erule cte_wp_atE)
apply (clarsimp simp: default_object_def empty_cnode_def
split: apiobject_type.splits if_splits)
apply (clarsimp simp: default_object_def default_tcb_def tcb_cap_cases_def
split: apiobject_type.splits if_splits)
apply (fastforce elim: cte_wp_atE intro: cte_wp_at_tcbI cte_wp_at_cteI)
done
lemma retype_region_domain_sep_inv[wp]:
"retype_region base n sz tp dev \<lbrace>domain_sep_inv irqs st\<rbrace>"
apply (rule domain_sep_inv_wp[where P="\<top>" and R="\<top>", simplified])
apply (rule retype_region_neg_cte_wp_at_not_domain_sep_inv_cap)
apply wp
done
lemma domain_sep_inv_cap_UntypedCap[simp]:
"domain_sep_inv_cap irqs (UntypedCap dev base sz n)"
by (simp add: domain_sep_inv_cap_def)
crunch domain_sep_inv[wp]: delete_objects "domain_sep_inv irqs st"
(wp: domain_sep_inv_detype_lift)
context DomainSepInv_1 begin
crunches finalise_slot, invoke_untyped, send_signal
for domain_sep_inv[wp]: "\<lambda>s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)"
(wp: crunch_wps mapME_x_inv_wp simp: crunch_simps mapM_x_def_bak)
lemma invoke_cnode_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and valid_cnode_inv ci\<rbrace>
invoke_cnode ci
\<lbrace>\<lambda>_ s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)\<rbrace>"
unfolding invoke_cnode_def
apply (case_tac ci)
apply (wp cap_insert_domain_sep_inv cap_move_domain_sep_inv | simp split del: if_split)+
apply (rule hoare_pre)
apply (wpsimp wp: cap_move_domain_sep_inv cap_move_cte_wp_at_other get_cap_wp,
blast dest: cte_wp_at_weak_derived_domain_sep_inv_cap)+
apply (wpsimp wp: cap_move_domain_sep_inv get_cap_wp)
apply (fastforce dest: cte_wp_at_weak_derived_ReplyCap)
apply (wp | simp | wpc | rule hoare_pre)+
done
end
lemma perform_page_invocation_domain_sep_inv_get_cap_helper:
"\<lbrace>\<top>\<rbrace> get_cap blah \<lbrace>\<lambda>rv s. domain_sep_inv_cap irqs (ArchObjectCap (F rv))\<rbrace>"
apply (simp add: domain_sep_inv_cap_def)
apply (rule wp_post_taut)
done
lemma set_object_tcb_context_update_neg_cte_wp_at:
"\<lbrace>\<lambda>s. \<not> cte_wp_at P slot s \<and> obj_at ((=) (TCB tcb)) ptr s\<rbrace>
set_object ptr (TCB (tcb\<lparr>tcb_arch := arch_tcb_context_set X (arch_tcb tcb)\<rparr>))
\<lbrace>\<lambda>_ s. \<not> cte_wp_at P slot s\<rbrace>"
apply (wp set_object_wp)
apply clarsimp
apply (case_tac "ptr = fst slot")
apply (erule cte_wp_atE)
apply (fastforce simp: obj_at_def)
apply (erule notE)
apply (clarsimp simp: obj_at_def)
apply (rule cte_wp_at_tcbI)
apply simp
apply (fastforce)
apply (fastforce simp: tcb_cap_cases_def split: if_splits)
apply (fastforce elim: cte_wp_atE intro: cte_wp_at_cteI cte_wp_at_tcbI)
done
lemma set_object_tcb_arch_update_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and obj_at ((=) (TCB tcb)) ptr\<rbrace>
set_object ptr (TCB (tcb\<lparr>tcb_arch := arch\<rparr>))
\<lbrace>\<lambda>_. domain_sep_inv irqs st\<rbrace>"
apply (wp set_object_wp)
apply (simp add: domain_sep_inv_def fun_upd_def cte_wp_at_caps_of_state)
apply (fastforce simp: caps_of_state_after_update obj_at_def tcb_cap_cases_def)
done
lemma dxo_domain_sep_inv[wp]:
"do_extended_op eop \<lbrace>domain_sep_inv irqs st\<rbrace>"
by (simp | wp dxo_wp_weak)+
crunch domain_sep_inv[wp]: copy_mrs, set_message_info, set_mrs "domain_sep_inv irqs st"
(wp: crunch_wps set_object_tcb_arch_update_domain_sep_inv simp: crunch_simps ignore: set_object)
lemma cap_insert_domain_sep_inv':
"\<lbrace>domain_sep_inv irqs st and K (domain_sep_inv_cap irqs cap)\<rbrace>
cap_insert cap slot dest_slot
\<lbrace>\<lambda>_. domain_sep_inv irqs st\<rbrace>"
apply (simp add: cap_insert_def)
apply (wp set_cap_domain_sep_inv get_cap_wp dxo_wp_weak | simp split del: if_split)+
done
lemma domain_sep_inv_cap_max_free_index_update[simp]:
"domain_sep_inv_cap irqs (max_free_index_update cap) =
domain_sep_inv_cap irqs cap"
by (simp add: max_free_index_def free_index_update_def split: cap.splits)
lemma domain_sep_inv_cap_ArchObjectCap[simp]:
"domain_sep_inv_cap irqs (ArchObjectCap arch_cap)"
by (simp add: domain_sep_inv_cap_def)
locale DomainSepInv_2 = DomainSepInv_1 state_ext_t
for state_ext_t :: "'state_ext :: state_ext itself" +
assumes arch_switch_to_thread_domain_sep_inv[wp]:
"arch_switch_to_thread t \<lbrace>\<lambda>s :: det_ext state. domain_sep_inv irqs (st :: 'state_ext state) s\<rbrace>"
and arch_switch_to_idle_thread_domain_sep_inv[wp]:
"arch_switch_to_idle_thread \<lbrace>\<lambda>s :: det_ext state. domain_sep_inv irqs st s\<rbrace>"
and arch_activate_idle_thread_domain_sep_inv[wp]:
"arch_activate_idle_thread t \<lbrace>\<lambda>s :: det_ext state. domain_sep_inv irqs st s\<rbrace>"
and arch_mask_irq_signal_domain_sep_inv[wp]:
"arch_mask_irq_signal irq \<lbrace>\<lambda>s :: det_ext state. domain_sep_inv irqs st s\<rbrace>"
and arch_derive_cap_domain_sep_inv[wp]:
"\<lbrace>\<top>\<rbrace> arch_derive_cap acap \<lbrace>\<lambda>rv s :: det_ext state. domain_sep_inv_cap irqs rv\<rbrace>,-"
and arch_post_modify_registers_domain_sep_inv[wp]:
"arch_post_modify_registers cur x31 \<lbrace>\<lambda>s :: det_ext state. domain_sep_inv irqs st s\<rbrace>"
and arch_perform_invocation_domain_sep_inv[wp]:
"\<lbrace>domain_sep_inv irqs st and valid_arch_inv ai\<rbrace>
arch_perform_invocation ai
\<lbrace>\<lambda>_ s :: det_ext state. domain_sep_inv irqs st s\<rbrace>"
and arch_invoke_irq_handler_domain_sep_inv[wp]:
"arch_invoke_irq_handler ihi \<lbrace>\<lambda>s :: det_ext state. domain_sep_inv irqs st s\<rbrace>"
and arch_invoke_irq_control_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and arch_irq_control_inv_valid ivk\<rbrace>
arch_invoke_irq_control ivk
\<lbrace>\<lambda>_ s :: det_ext state. domain_sep_inv irqs st s\<rbrace>"
and handle_arch_fault_reply_domain_sep_inv[wp]:
"handle_arch_fault_reply vmf thread x y \<lbrace>\<lambda>s :: det_ext state. domain_sep_inv irqs st s\<rbrace>"
and handle_hypervisor_fault_domain_sep_inv[wp]:
"handle_hypervisor_fault t hf_t \<lbrace>\<lambda>s :: det_ext state. domain_sep_inv irqs st s\<rbrace>"
and handle_vm_fault_domain_sep_inv[wp]:
"handle_vm_fault t vmf_t \<lbrace>\<lambda>s :: det_ext state. domain_sep_inv irqs st s\<rbrace>"
and handle_reserved_irq_domain_sep_inv[wp]:
"handle_reserved_irq irq \<lbrace>\<lambda>s :: det_ext state. domain_sep_inv irqs st s\<rbrace>"
begin
(* when i is AckIRQ the preconditions here contradict each other, which
is why this lemma is true *)
lemma invoke_irq_handler_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and irq_handler_inv_valid i\<rbrace>
invoke_irq_handler i
\<lbrace>\<lambda>_ s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)\<rbrace>"
apply (case_tac i)
apply (wp cap_insert_domain_sep_inv' | simp)+
apply (rename_tac irq cap cslot_ptr s)
apply (case_tac cap, simp_all add: domain_sep_inv_cap_def)[1]
apply (wp | clarsimp)+
done
(* similarly, the preconditions here tend to contradict one another *)
lemma invoke_control_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and irq_control_inv_valid i\<rbrace>
invoke_irq_control i
\<lbrace>\<lambda>_ s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)\<rbrace>"
including no_pre
apply (case_tac i)
apply (case_tac irqs)
apply (wp cap_insert_domain_sep_inv' | simp )+
apply (simp add: set_irq_state_def, wp, simp)
apply (fastforce simp: domain_sep_inv_def domain_sep_inv_cap_def)
apply (fastforce simp: valid_def domain_sep_inv_def)
apply simp
apply (wp arch_invoke_irq_control_domain_sep_inv)
done
lemma derive_cap_domain_sep_inv_cap:
"\<lbrace>\<lambda>s. domain_sep_inv_cap irqs cap\<rbrace>
derive_cap slot cap
\<lbrace>\<lambda>rv s :: det_ext state. domain_sep_inv_cap irqs rv\<rbrace>,-"
apply (simp add: derive_cap_def)
apply (rule hoare_pre)
apply (wp | wpc | simp add: )+
apply auto
done
end
crunch domain_sep_inv[wp]: receive_signal, complete_signal "domain_sep_inv irqs st"
lemma domain_sep_inv_cap_ReplyCap[simp]:
"domain_sep_inv_cap irqs (ReplyCap param_a param_b param_c)"
by (simp add: domain_sep_inv_cap_def)
lemma setup_caller_cap_domain_sep_inv[wp]:
"\<lbrace>domain_sep_inv irqs st\<rbrace>
setup_caller_cap a b c
\<lbrace>\<lambda>_. domain_sep_inv irqs st\<rbrace>"
apply (simp add: setup_caller_cap_def split del:if_split)
apply (wp cap_insert_domain_sep_inv' | simp)+
done
lemma transfer_caps_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and valid_objs and valid_mdb
and (\<lambda> s. (\<forall>x\<in>set caps.
s \<turnstile> fst x) \<and>
(\<forall>x\<in>set caps.
cte_wp_at
(\<lambda>cp. fst x \<noteq> NullCap \<longrightarrow>
cp = fst x)
(snd x) s \<and>
real_cte_at (snd x) s))\<rbrace>
transfer_caps mi caps endpoint receiver receive_buffer
\<lbrace>\<lambda>_. domain_sep_inv irqs st\<rbrace>"
unfolding transfer_caps_def
apply (wpsimp wp: transfer_caps_loop_pres_dest cap_insert_domain_sep_inv
hoare_vcg_all_lift hoare_vcg_imp_lift)
apply (fastforce elim: cte_wp_at_weakenE)
done
context DomainSepInv_2 begin
lemma do_normal_transfer_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and valid_objs and valid_mdb\<rbrace>
do_normal_transfer sender send_buffer ep badge grant receiver recv_buffer
\<lbrace>\<lambda>_ s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)\<rbrace>"
unfolding do_normal_transfer_def
by (wp transfer_caps_domain_sep_inv hoare_vcg_ball_lift lec_valid_cap' | simp)+
crunches do_fault_transfer
for domain_sep_inv[wp]: "\<lambda>s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)"
lemma do_ipc_transfer_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and valid_objs and valid_mdb\<rbrace>
do_ipc_transfer sender ep badge grant receiver
\<lbrace>\<lambda>_ s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)\<rbrace>"
unfolding do_ipc_transfer_def
apply (wp do_normal_transfer_domain_sep_inv hoare_vcg_all_lift | wpc | wp (once) hoare_drop_imps)+
apply clarsimp
done
lemma send_ipc_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and valid_objs and valid_mdb and
sym_refs \<circ> state_refs_of\<rbrace>
send_ipc block call badge can_grant can_grant_reply thread epptr
\<lbrace>\<lambda>_ s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)\<rbrace>"
unfolding send_ipc_def
apply (wp setup_caller_cap_domain_sep_inv hoare_vcg_if_lift | wpc | simp split del:if_split)+
apply (rule_tac Q="\<lambda> r s. domain_sep_inv irqs st s" in hoare_strengthen_post)
apply (wp do_ipc_transfer_domain_sep_inv dxo_wp_weak | wpc | simp)+
apply (wp (once) hoare_drop_imps)
apply (wp get_simple_ko_wp)+
apply clarsimp
apply (fastforce simp: valid_objs_def valid_obj_def obj_at_def ep_q_refs_of_def
a_type_def ep_redux_simps neq_Nil_conv valid_ep_def
elim: ep_queued_st_tcb_at split: list.splits)
done
lemma receive_ipc_base_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and valid_objs and valid_mdb and
sym_refs \<circ> state_refs_of and ko_at (Endpoint ep) epptr \<rbrace>
receive_ipc_base aag receiver ep epptr rights is_blocking
\<lbrace>\<lambda>_ s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)\<rbrace>"
apply (clarsimp cong: endpoint.case_cong thread_get_def get_thread_state_def)
apply (wp setup_caller_cap_domain_sep_inv dxo_wp_weak | wpc | simp split del: if_split)+
apply (rule_tac Q="\<lambda> r s. domain_sep_inv irqs st s" in hoare_strengthen_post)
apply (wp do_ipc_transfer_domain_sep_inv hoare_vcg_all_lift | wpc | simp)+
apply (wpsimp wp: hoare_vcg_imp_lift[OF set_simple_ko_get_tcb, unfolded disj_not1]
hoare_vcg_all_lift get_simple_ko_wp
simp: a_type_def do_nbrecv_failed_transfer_def)+
apply (fastforce simp: valid_objs_def valid_obj_def obj_at_def
ep_redux_simps neq_Nil_conv valid_ep_def
split: list.splits)
done
lemma receive_ipc_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and valid_objs and valid_mdb and sym_refs \<circ> state_refs_of\<rbrace>
receive_ipc receiver cap is_blocking
\<lbrace>\<lambda>_ s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)\<rbrace>"
unfolding receive_ipc_def
apply (simp add: receive_ipc_def split: cap.splits, clarsimp)
apply (rule hoare_seq_ext[OF _ get_simple_ko_sp])
apply (rule hoare_seq_ext[OF _ gbn_sp])
apply (case_tac ntfnptr, simp)
apply (wp receive_ipc_base_domain_sep_inv get_simple_ko_wp | simp split: if_split option.splits)+
done
lemma send_fault_ipc_domain_sep_inv:
"\<lbrace>domain_sep_inv irqs st and valid_objs and sym_refs \<circ> state_refs_of
and valid_mdb and K (valid_fault fault)\<rbrace>
send_fault_ipc thread fault
\<lbrace>\<lambda>_ s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)\<rbrace>"
unfolding send_fault_ipc_def
apply (rule hoare_gen_asm)+
apply (wp send_ipc_domain_sep_inv thread_set_valid_objs thread_set_tcb_fault_update_valid_mdb
thread_set_refs_trivial thread_set_obj_at_impossible hoare_vcg_ex_lift
| wpc | simp add: Let_def split_def lookup_cap_def valid_tcb_fault_update)+
apply (wpe get_cap_inv[where P="domain_sep_inv irqs st and valid_objs and valid_mdb
and sym_refs o state_refs_of"])
apply (wp | simp)+
done
crunches do_reply_transfer, handle_fault, reply_from_kernel, restart
for domain_sep_inv[wp]: "\<lambda>s. domain_sep_inv irqs (st :: 'state_ext state) (s :: det_ext state)"
(wp: handle_arch_fault_reply_domain_sep_inv dxo_wp_weak crunch_wps ignore: thread_set)
end
crunch domain_sep_inv[wp]: setup_reply_master "domain_sep_inv irqs st"
(wp: crunch_wps simp: crunch_simps)
lemma thread_set_tcb_ipc_buffer_update_neg_cte_wp_at[wp]:
"thread_set (tcb_ipc_buffer_update f) t \<lbrace>\<lambda>s. \<not> cte_wp_at P slot s\<rbrace>"
unfolding thread_set_def
apply (wp set_object_wp | simp)+
apply (case_tac "t = fst slot")
apply (clarsimp split: kernel_object.splits)
apply (erule notE)
apply (erule cte_wp_atE)
apply (fastforce simp: obj_at_def)
apply (drule get_tcb_SomeD)
apply (rule cte_wp_at_tcbI)
apply simp
apply assumption
apply (fastforce simp: tcb_cap_cases_def split: if_splits)
apply (fastforce elim: cte_wp_atE intro: cte_wp_at_cteI cte_wp_at_tcbI)
done
lemma thread_set_tcb_ipc_buffer_update_domain_sep_inv[wp]:
"thread_set (tcb_ipc_buffer_update f) t \<lbrace>domain_sep_inv irqs st\<rbrace>"
by (rule domain_sep_inv_triv; wp)
lemma thread_set_tcb_fault_handler_update_neg_cte_wp_at[wp]:
"thread_set (tcb_fault_handler_update f) t \<lbrace>\<lambda>s. \<not> cte_wp_at P slot s\<rbrace>"
unfolding thread_set_def
apply (wp set_object_wp | simp)+
apply (case_tac "t = fst slot")
apply (clarsimp split: kernel_object.splits)
apply (erule notE)
apply (erule cte_wp_atE)
apply (fastforce simp: obj_at_def)
apply (drule get_tcb_SomeD)
apply (rule cte_wp_at_tcbI)
apply simp
apply assumption
apply (fastforce simp: tcb_cap_cases_def split: if_splits)
apply (fastforce elim: cte_wp_atE intro: cte_wp_at_cteI cte_wp_at_tcbI)
done
lemma thread_set_tcb_fault_handler_update_domain_sep_inv[wp]:
"thread_set (tcb_fault_handler_update f) t \<lbrace>domain_sep_inv irqs st\<rbrace>"
by (rule domain_sep_inv_triv; wp)
lemma thread_set_tcb_tcb_mcpriority_update_neg_cte_wp_at[wp]:
"thread_set (tcb_mcpriority_update f) t \<lbrace>\<lambda>s. \<not> cte_wp_at P slot s\<rbrace>"
unfolding thread_set_def
apply (wp set_object_wp | simp)+
apply (case_tac "t = fst slot")
apply (clarsimp split: kernel_object.splits)
apply (erule notE)
apply (erule cte_wp_atE)
apply (fastforce simp: obj_at_def)
apply (drule get_tcb_SomeD)
apply (rule cte_wp_at_tcbI)
apply simp
apply assumption
apply (fastforce simp: tcb_cap_cases_def split: if_splits)
apply (fastforce elim: cte_wp_atE intro: cte_wp_at_cteI cte_wp_at_tcbI)
done
lemma thread_set_tcb_tcp_mcpriority_update_domain_sep_inv[wp]:
"thread_set (tcb_mcpriority_update f) t \<lbrace>domain_sep_inv irqs st\<rbrace>"
by (rule domain_sep_inv_triv; wp)
lemma same_object_as_domain_sep_inv_cap:
"\<lbrakk> same_object_as a cap; domain_sep_inv_cap irqs cap \<rbrakk>
\<Longrightarrow> domain_sep_inv_cap irqs a"