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Ipc_IF.thy
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(*
* Copyright 2022, Proofcraft Pty Ltd
* Copyright 2020, Data61, CSIRO (ABN 41 687 119 230)
*
* SPDX-License-Identifier: GPL-2.0-only
*)
theory Ipc_IF
imports ArchFinalise_IF
begin
section "reads_respects"
subsection "Notifications"
definition ipc_buffer_has_read_auth :: "'a PAS \<Rightarrow> 'a \<Rightarrow> obj_ref option \<Rightarrow> bool" where
"ipc_buffer_has_read_auth aag l \<equiv>
case_option True
(\<lambda>buf'. is_aligned buf' msg_align_bits \<and>
(\<forall>x \<in> ptr_range buf' msg_align_bits. (l,Read,pasObjectAbs aag x) \<in> (pasPolicy aag)))"
abbreviation aag_can_read_or_affect where
"aag_can_read_or_affect aag l x \<equiv>
aag_can_read aag x \<or> aag_can_affect aag l x"
lemma get_cap_reads_respects:
"reads_respects aag l (K (aag_can_read aag (fst slot) \<or> aag_can_affect aag l (fst slot))) (get_cap slot)"
apply (simp add: get_cap_def split_def)
apply (wp get_object_reads_respects | wpc | simp)+
done
lemma set_thread_state_ext_runnable_equiv_but_for_labels:
"\<lbrace>equiv_but_for_labels aag L st and K (pasObjectAbs aag thread \<in> L) and st_tcb_at runnable thread\<rbrace>
set_thread_state_ext thread
\<lbrace>\<lambda>_. equiv_but_for_labels aag L st\<rbrace>"
apply (simp add: set_thread_state_ext_def)
apply (wp gts_wp | rule hoare_pre_cont)+
apply (force simp: st_tcb_at_def obj_at_def)
done
definition all_to_which_has_auth where
"all_to_which_has_auth aag auth source \<equiv> {t. (source,auth,t) \<in> pasPolicy aag}"
definition all_with_auth_to where
"all_with_auth_to aag auth target \<equiv> {x. (x, auth, target) \<in> pasPolicy aag}"
lemma valid_ntfn_WaitingNtfn_tl:
"\<lbrakk> ntfn_obj ntfn = (WaitingNtfn list); valid_ntfn ntfn s;
tl list \<noteq> []; ntfn' = ntfn\<lparr>ntfn_obj := (WaitingNtfn (tl list))\<rparr> \<rbrakk>
\<Longrightarrow> valid_ntfn ntfn' s"
apply (case_tac list, simp_all)
apply (rename_tac a lista)
apply (case_tac lista, simp_all)
apply (clarsimp simp: valid_ntfn_def split: option.splits)
done
lemma tcb_sched_action_equiv_but_for_labels:
"\<lbrace>equiv_but_for_labels aag L st and K (pasObjectAbs aag thread \<in> L) and pas_refined aag\<rbrace>
tcb_sched_action action thread
\<lbrace>\<lambda>_. equiv_but_for_labels aag L st\<rbrace>"
apply (simp add: tcb_sched_action_def, wp)
apply (clarsimp simp: etcb_at_def equiv_but_for_labels_def split: option.splits)
apply (rule states_equiv_forI)
apply (fastforce intro!: equiv_forI elim!: states_equiv_forE dest: equiv_forD[where f=kheap])
apply (simp add: states_equiv_for_def)
apply (fastforce elim: states_equiv_forE intro: equiv_forI dest: equiv_forD[where f=cdt])
apply (fastforce elim: states_equiv_forE intro: equiv_forI dest: equiv_forD[where f=ekheap])
apply (fastforce elim: states_equiv_forE intro: equiv_forI dest: equiv_forD[where f=cdt_list])
apply (fastforce elim: states_equiv_forE intro: equiv_forI dest: equiv_forD[where f=is_original_cap])
apply (fastforce elim: states_equiv_forE intro: equiv_forI dest: equiv_forD[where f=interrupt_states])
apply (fastforce elim: states_equiv_forE intro: equiv_forI dest: equiv_forD[where f=interrupt_irq_node])
apply (fastforce simp: equiv_asids_def elim: states_equiv_forE)
apply (clarsimp simp: pas_refined_def tcb_domain_map_wellformed_aux_def split: option.splits)
apply (rule equiv_forI)
apply (erule_tac x="(thread, tcb_domain (the (ekheap s thread)))" in ballE)
apply (fastforce elim: states_equiv_forE intro: equiv_forI dest: equiv_forD[where f=ready_queues])
apply (force intro: domtcbs)
done
lemma possible_switch_to_equiv_but_for_labels:
"\<lbrace>equiv_but_for_labels aag L st and (\<lambda>s. etcb_at (\<lambda>etcb. tcb_domain etcb \<noteq> cur_domain s) target s)
and K (pasObjectAbs aag target \<in> L) and pas_refined aag\<rbrace>
possible_switch_to target
\<lbrace>\<lambda>_. equiv_but_for_labels aag L st\<rbrace>"
apply (simp add: possible_switch_to_def)
apply (wp tcb_sched_action_equiv_but_for_labels)
(* possible_switch_to does not modify scheduler action if target is in different domain *)
apply (rule hoare_pre_cont)
apply (wp tcb_sched_action_equiv_but_for_labels)
apply (rule hoare_pre_cont)
apply (wp tcb_sched_action_equiv_but_for_labels)+
apply (clarsimp simp: etcb_at_def split: option.splits)
done
crunch set_thread_state_ext, set_thread_state, set_simple_ko
for etcb_at_cdom[wp]: "\<lambda>s. etcb_at (P (cur_domain s)) t s"
(wp: crunch_wps)
locale Ipc_IF_1 =
fixes aag :: "'a subject_label PAS"
assumes lookup_ipc_buffer_reads_respects:
"reads_respects aag l (K (aag_can_read aag thread \<or> aag_can_affect aag l thread))
(lookup_ipc_buffer is_receiver thread)"
and as_user_equiv_but_for_labels:
"\<lbrace>equiv_but_for_labels aag L st and K (pasObjectAbs aag thread \<in> L)\<rbrace>
as_user thread (f :: unit user_monad)
\<lbrace>\<lambda>_. equiv_but_for_labels aag L st\<rbrace>"
and storeWord_equiv_but_for_labels:
"\<lbrace>\<lambda>ms. equiv_but_for_labels aag L st (s\<lparr>machine_state := ms\<rparr>) \<and>
for_each_byte_of_word (\<lambda>x. pasObjectAbs aag x \<in> L) p\<rbrace>
storeWord p v
\<lbrace>\<lambda>_ ms. equiv_but_for_labels aag L st (s\<lparr>machine_state := ms\<rparr>)\<rbrace>"
and set_thread_state_runnable_equiv_but_for_labels:
"runnable tst
\<Longrightarrow> \<lbrace>equiv_but_for_labels aag L st and K (pasObjectAbs aag thread \<in> L)\<rbrace>
set_thread_state thread tst
\<lbrace>\<lambda>_. equiv_but_for_labels aag L st\<rbrace>"
and set_endpoint_equiv_but_for_labels:
"\<lbrace>equiv_but_for_labels aag L st and K (pasObjectAbs aag epptr \<in> L)\<rbrace>
set_endpoint epptr ep
\<lbrace>\<lambda>_. equiv_but_for_labels aag L st\<rbrace>"
and lookup_ipc_buffer_has_read_auth:
"\<lbrace>pas_refined aag and valid_objs\<rbrace>
lookup_ipc_buffer is_receiver thread
\<lbrace>\<lambda>rv _. ipc_buffer_has_read_auth aag (pasObjectAbs aag thread) rv\<rbrace>"
and dmo_loadWord_reads_respects:
"reads_respects aag l (K (for_each_byte_of_word (\<lambda> x. aag_can_read_or_affect aag l x) p))
(do_machine_op (loadWord p))"
and arch_derive_cap_reads_respects:
"reads_respects aag l \<top> (arch_derive_cap acap)"
and arch_derive_cap_rev:
"reads_equiv_valid_inv A aag \<top> (arch_derive_cap acap)"
and cptrs_in_ipc_buffer:
"\<lbrakk> n \<in> set [buffer_cptr_index ..< buffer_cptr_index + unat (mi_extra_caps mi)];
is_aligned p msg_align_bits;
buffer_cptr_index + unat (mi_extra_caps mi) < 2 ^ (msg_align_bits - word_size_bits) \<rbrakk>
\<Longrightarrow> ptr_range (p + of_nat n * of_nat word_size) word_size_bits \<subseteq> ptr_range p msg_align_bits"
and msg_in_ipc_buffer:
"\<lbrakk> n = msg_max_length \<or> n < msg_max_length; is_aligned p msg_align_bits;
unat (mi_length mi) < 2 ^ (msg_align_bits - word_size_bits) \<rbrakk>
\<Longrightarrow> ptr_range (p + of_nat n * of_nat word_size) word_size_bits \<subseteq> ptr_range p msg_align_bits"
and captransfer_in_ipc_buffer:
"\<lbrakk> is_aligned (buf :: obj_ref) msg_align_bits; p \<in> {0..2} \<rbrakk>
\<Longrightarrow> ptr_range (buf + (2 + (of_nat msg_max_length + of_nat msg_max_extra_caps))
* word_size + p * word_size) word_size_bits
\<subseteq> ptr_range buf msg_align_bits"
and mrs_in_ipc_buffer:
"\<lbrakk> n \<in> set [length msg_registers + 1 ..< Suc n'];
is_aligned buf msg_align_bits; n' < 2 ^ (msg_align_bits - word_size_bits) \<rbrakk>
\<Longrightarrow> ptr_range (buf + of_nat n * of_nat word_size) word_size_bits
\<subseteq> ptr_range buf msg_align_bits"
and complete_signal_reads_respects:
"pas_domains_distinct aag
\<Longrightarrow> reads_respects aag l (K (aag_can_read aag nptr \<or> aag_can_affect aag l nptr))
(complete_signal nptr receiver)"
and handle_arch_fault_reply_reads_respects:
"reads_respects aag l (K (aag_can_read aag thread)) (handle_arch_fault_reply afault thread x y)"
and arch_get_sanitise_register_info_reads_respects[wp]:
"reads_respects aag l \<top> (arch_get_sanitise_register_info t)"
and arch_get_sanitise_register_info_valid_global_objs[wp]:
"arch_get_sanitise_register_info t \<lbrace>\<lambda>s :: det_state. valid_global_objs s\<rbrace>"
and handle_arch_fault_reply_valid_global_objs[wp]:
"handle_arch_fault_reply vmf thread x y \<lbrace>\<lambda>s :: det_state. valid_global_objs s\<rbrace>"
and lookup_ipc_buffer_ptr_range':
"\<lbrace>valid_objs\<rbrace>
lookup_ipc_buffer True t
\<lbrace>\<lambda>rv s :: det_state. rv = Some buf' \<longrightarrow> auth_ipc_buffers s t = ptr_range buf' msg_align_bits\<rbrace>"
and lookup_ipc_buffer_aligned':
"\<lbrace>valid_objs\<rbrace>
lookup_ipc_buffer True t
\<lbrace>\<lambda>rv s :: det_state. rv = Some buf' \<longrightarrow> is_aligned buf' msg_align_bits\<rbrace>"
and handle_arch_fault_reply_globals_equiv:
"\<lbrace>globals_equiv st and valid_arch_state and (\<lambda>s. thread \<noteq> idle_thread s)\<rbrace>
handle_arch_fault_reply vmf thread x y
\<lbrace>\<lambda>_. globals_equiv st\<rbrace>"
begin
lemma store_word_offs_equiv_but_for_labels:
"\<lbrace>equiv_but_for_labels aag L st and
K (for_each_byte_of_word (\<lambda>x. pasObjectAbs aag x \<in> L) (ptr + of_nat offs * of_nat word_size))\<rbrace>
store_word_offs ptr offs v
\<lbrace>\<lambda>_. equiv_but_for_labels aag L st\<rbrace>"
unfolding store_word_offs_def
apply (wp modify_wp | simp add: do_machine_op_def split_def)+
apply clarsimp
apply (erule use_valid[OF _ storeWord_equiv_but_for_labels])
apply simp
done
(* FIXME: many redundant conditions *)
lemma update_waiting_ntfn_reads_respects:
assumes domains_distinct[wp]: "pas_domains_distinct aag"
shows
"reads_respects aag l (pspace_aligned and valid_vspace_objs and valid_arch_state and valid_objs
and sym_refs \<circ> state_refs_of and pas_refined aag
and pas_cur_domain aag and ko_at (Notification ntfn) nptr
and (\<lambda>s. is_subject aag (cur_thread s))
and K (ntfn_obj ntfn = WaitingNtfn queue))
(update_waiting_ntfn nptr queue bound_tcb badge)"
unfolding update_waiting_ntfn_def fun_app_def
apply (wp assert_sp possible_switch_to_reads_respects gets_cur_thread_ev | simp add: split_def)+
by (wp as_user_set_register_reads_respects' set_thread_state_reads_respects
set_simple_ko_reads_respects set_thread_state_pas_refined
set_simple_ko_valid_objs hoare_vcg_disj_lift set_simple_ko_pas_refined
| simp add: split_def)+
lemma update_waiting_ntfn_equiv_but_for_labels:
"\<lbrace>equiv_but_for_labels aag L st and pas_refined aag and pspace_aligned and valid_vspace_objs and
valid_arch_state and valid_objs and ko_at (Notification ntfn) nptr and sym_refs \<circ> state_refs_of and
(\<lambda>s. \<forall>t\<in> set list. etcb_at (\<lambda>etcb. tcb_domain etcb \<noteq> cur_domain s) t s) and
K (ntfn_obj ntfn = WaitingNtfn list \<and> pasObjectAbs aag nptr \<in> L \<and>
all_with_auth_to aag Receive (pasObjectAbs aag nptr) \<subseteq> L \<and>
\<Union> (all_to_which_has_auth aag Write ` all_with_auth_to aag Receive (pasObjectAbs aag nptr)) \<subseteq> L)\<rbrace>
update_waiting_ntfn nptr list boundtcb badge
\<lbrace>\<lambda>_. equiv_but_for_labels aag L st\<rbrace>"
unfolding update_waiting_ntfn_def
apply (wp hoare_weak_lift_imp as_user_equiv_but_for_labels set_thread_state_runnable_equiv_but_for_labels
set_thread_state_pas_refined set_notification_equiv_but_for_labels
set_simple_ko_pred_tcb_at set_simple_ko_pas_refined
hoare_vcg_disj_lift possible_switch_to_equiv_but_for_labels
| wpc | simp add: split_def)+
apply clarsimp
apply (frule_tac P="receive_blocked_on nptr" and t="hd list" in ntfn_queued_st_tcb_at')
apply (fastforce)
apply assumption
apply assumption
apply simp
apply (subgoal_tac "pasObjectAbs aag (hd list) \<in> all_with_auth_to aag Receive (pasObjectAbs aag nptr)")
apply (fastforce)
apply (clarsimp simp: all_with_auth_to_def)
apply (erule pas_refined_mem[rotated])
apply (rule sta_ts)
apply (clarsimp simp: thread_st_auth_def tcb_states_of_state_def st_tcb_def2)
apply (case_tac "tcb_state tcb", simp_all)
done
end
lemma invisible_ntfn_invisible_receivers_and_ipcbuffers:
"\<lbrakk> labels_are_invisible aag l {pasObjectAbs aag nptr};
(pasSubject aag, Notify, pasObjectAbs aag nptr) \<in> pasPolicy aag\<rbrakk>
\<Longrightarrow> labels_are_invisible aag l ({pasObjectAbs aag nptr} \<union>
all_with_auth_to aag Receive (pasObjectAbs aag nptr) \<union>
\<Union>(all_to_which_has_auth aag Write
` all_with_auth_to aag Receive (pasObjectAbs aag nptr)))"
by (auto simp: labels_are_invisible_def aag_can_affect_label_def
all_to_which_has_auth_def all_with_auth_to_def
dest: reads_read_page_read_thread reads_read_queued_thread_read_ep)
lemma invisible_ntfn_invisible_receivers_and_receivers[rotated 1]:
"\<lbrakk> auth \<in> {Notify,Receive,SyncSend}; labels_are_invisible aag l {pasObjectAbs aag nptr};
(pasSubject aag, auth, pasObjectAbs aag nptr) \<in> pasPolicy aag \<rbrakk>
\<Longrightarrow> labels_are_invisible aag l ({pasObjectAbs aag nptr} \<union>
all_with_auth_to aag Receive (pasObjectAbs aag nptr) \<union>
(\<Union>(all_to_which_has_auth aag Receive
` all_with_auth_to aag Receive (pasObjectAbs aag nptr))) \<union>
(\<Union>(all_to_which_has_auth aag Write
` all_with_auth_to aag Receive (pasObjectAbs aag nptr))))"
by (auto simp: labels_are_invisible_def aag_can_affect_label_def
all_to_which_has_auth_def all_with_auth_to_def
dest: read_sync_ep_read_senders read_sync_ep_read_receivers
reads_read_queued_thread_read_ep reads_read_page_read_thread reads_ep)
lemma read_queued_thread_reads_ntfn:
"\<lbrakk> ko_at (Notification ntfn) ntfnptr s; t \<in> set queue; aag_can_read aag t; valid_objs s;
sym_refs (state_refs_of s); pas_refined aag s; ntfn_obj ntfn = WaitingNtfn queue;
(pasSubject aag, Notify, pasObjectAbs aag ntfnptr) \<in> pasPolicy aag \<rbrakk>
\<Longrightarrow> aag_can_read aag ntfnptr"
apply (frule_tac P="receive_blocked_on ntfnptr" and t=t in ntfn_queued_st_tcb_at')
apply (fastforce)
apply assumption
apply assumption
apply simp
apply (rule_tac t="pasObjectAbs aag t" and auth="Receive" and auth'="Notify"
in reads_read_queued_thread_read_ep)
apply assumption
apply simp
apply (erule pas_refined_mem[rotated])
apply (rule sta_ts)
apply (clarsimp simp: thread_st_auth_def tcb_states_of_state_def st_tcb_def2)
apply (case_tac "tcb_state tcb", simp_all)[1]
apply simp
apply simp
done
lemma not_etcb_at_not_cdom_can_read:
assumes domains_distinct[wp]: "pas_domains_distinct aag"
shows "\<lbrakk> \<not> etcb_at (\<lambda>etcb. tcb_domain etcb \<noteq> cur_domain s) t s;
tcb_at t s; valid_etcbs s; pas_refined aag s; pas_cur_domain aag s \<rbrakk>
\<Longrightarrow> aag_can_read aag t"
apply (clarsimp simp: valid_etcbs_def tcb_at_st_tcb_at etcb_at_def is_etcb_at_def
pas_refined_def tcb_domain_map_wellformed_aux_def)
apply (erule_tac x="(t, cur_domain s)" in ballE)
apply (force dest: domains_distinct[THEN pas_domains_distinct_inj])
apply (force intro: domtcbs)
done
lemma tcb_at_ntfn_queue:
"\<lbrakk> valid_objs s; t \<in> set q; ko_at (Notification ntfn) nptr s; ntfn_obj ntfn = WaitingNtfn q \<rbrakk>
\<Longrightarrow> tcb_at t s"
by (fastforce simp: obj_at_def valid_obj_def valid_ntfn_def)
lemma invisible_ep_invisible_receiver:
"\<lbrakk> labels_are_invisible aag l {pasObjectAbs aag epptr};
(pasObjectAbs aag tcb, Receive, pasObjectAbs aag epptr) \<in> pasPolicy aag;
(pasObjectAbs aag tcb, Reset, pasObjectAbs aag epptr) \<in> pasPolicy aag \<rbrakk>
\<Longrightarrow> labels_are_invisible aag l ({pasObjectAbs aag epptr} \<union> {pasObjectAbs aag tcb})"
by (auto simp: labels_are_invisible_def aag_can_affect_label_def all_with_auth_to_def
dest: reads_ep reads_read_queued_thread_read_ep)
lemma no_fail_gts:
"no_fail (tcb_at tcb) (get_thread_state tcb)"
apply (clarsimp simp: get_thread_state_def thread_get_def)
apply (rule no_fail_pre)
apply wp
by (clarsimp simp: get_tcb_def tcb_at_def)
lemma sts_noop:
"monadic_rewrite True True (tcb_at tcb and (\<lambda>s. tcb \<noteq> cur_thread s))
(set_thread_state_ext tcb) (return ())"
unfolding set_thread_state_ext_def when_def
apply (monadic_rewrite_l monadic_rewrite_if_l_False \<open>wpsimp wp: gts_wp\<close>)
apply (monadic_rewrite_symb_exec_l_drop)+
apply (rule monadic_rewrite_refl)
by (auto simp: pred_tcb_at_def obj_at_def is_tcb_def get_tcb_def)
lemma sts_to_modify':
"monadic_rewrite True True (tcb_at tcb and (\<lambda>s :: det_state. tcb \<noteq> cur_thread s))
(set_thread_state tcb st)
(modify (\<lambda>s. s\<lparr>kheap := (kheap s)(tcb \<mapsto> TCB (the (get_tcb tcb s)\<lparr>tcb_state := st\<rparr>))\<rparr>))"
apply (clarsimp simp: set_thread_state_def set_object_def)
apply (monadic_rewrite_l sts_noop \<open>wpsimp wp: get_object_wp\<close>)
apply (simp add: bind_assoc)
apply monadic_rewrite_symb_exec_l+
apply (rule_tac P="\<lambda>s'. s' = s \<and> tcba = the (get_tcb tcb s)" in monadic_rewrite_pre_imp_eq)
apply (clarsimp simp: put_def modify_def get_def bind_def)
apply (wpsimp wp: get_object_wp)+
by (clarsimp simp: get_tcb_def tcb_at_def)
lemma sts_no_fail:
"no_fail (\<lambda>s :: det_state. tcb_at tcb s) (set_thread_state tcb st)"
apply (simp add: set_thread_state_def set_object_def)
apply (simp add: set_thread_state_ext_def get_thread_state_def
thread_get_def set_scheduler_action_def)
apply (rule no_fail_pre)
apply (wpsimp wp: get_object_wp)+
apply (clarsimp simp: get_tcb_def tcb_at_def obj_at_def a_type_def is_tcb_def
split: kernel_object.splits option.splits)
by (metis kernel_object.exhaust option.inject)
lemmas sts_to_modify =
monadic_rewrite_weaken_failure[OF sts_to_modify' sts_no_fail no_fail_modify,simplified]
definition "blocked_cancel_ipc_nosts tcb \<equiv>
do state <- get_thread_state tcb;
epptr \<leftarrow> get_blocking_object state;
ep \<leftarrow> get_endpoint epptr;
queue \<leftarrow> get_ep_queue ep;
queue' \<leftarrow> return $ remove1 tcb queue;
ep' \<leftarrow> return (case queue' of [] \<Rightarrow> IdleEP | a # list \<Rightarrow> update_ep_queue ep queue');
set_endpoint epptr ep';
set_thread_state tcb Running
od"
lemma cancel_ipc_to_blocked_nosts:
"monadic_rewrite False False (\<lambda>s :: det_state. st_tcb_at receive_blocked tcb s \<and> cur_thread s \<noteq> tcb)
(blocked_cancel_ipc_nosts tcb)
(cancel_ipc tcb >>= (\<lambda>_. set_thread_state tcb Running))"
apply (simp add: cancel_ipc_def bind_assoc blocked_cancel_ipc_nosts_def)
apply (rule monadic_rewrite_bind_tail)
apply (rule monadic_rewrite_transverse)
apply (rename_tac state)
apply (rule_tac P="\<lambda>_. \<exists>xa pl. state = BlockedOnReceive xa pl" in monadic_rewrite_bind_head)
apply (rule monadic_rewrite_gen_asm[where Q=\<top>,simplified])
apply clarsimp
apply (rule monadic_rewrite_refl)
apply (simp add: blocked_cancel_ipc_def blocked_cancel_ipc_nosts_def bind_assoc)
apply (rule monadic_rewrite_bind_tail)
apply (rule monadic_rewrite_bind_tail)
apply (rule monadic_rewrite_bind_tail)
apply (rule monadic_rewrite_bind_tail)
apply (rule monadic_rewrite_trans)
apply (rule sts_to_modify)
apply (rule monadic_rewrite_transverse)
apply (rule monadic_rewrite_bind)
apply (rule sts_to_modify)
apply (rule sts_to_modify)
apply (rule hoare_modifyE_var[where P="tcb_at tcb and (\<lambda>s. tcb \<noteq> cur_thread s)"])
apply (clarsimp simp: tcb_at_def get_tcb_def)
apply (simp add: modify_modify)
apply (rule monadic_rewrite_is_refl)
apply (fastforce simp add: simpler_modify_def o_def get_tcb_def)
apply (wp gts_wp)+
apply (simp add: set_thread_state_def bind_assoc gets_the_def)
apply (clarsimp simp: pred_tcb_at_def receive_blocked_def obj_at_def is_tcb_def)
by (case_tac "tcb_state tcba"; fastforce)
lemma gts_reads_respects:
"reads_respects aag l (K (aag_can_read aag t \<or> aag_can_affect aag l t)) (get_thread_state t)"
unfolding get_thread_state_def
by (wp thread_get_reads_respects)
lemma ev2_invisible_simple:
assumes domains_distinct: "pas_domains_distinct aag"
shows "\<lbrakk> labels_are_invisible aag l L; modifies_at_most aag L Q f \<rbrakk>
\<Longrightarrow> reads_respects aag l Q (f :: (det_state, unit) nondet_monad)"
apply (simp add: equiv_valid_def2)
apply (rule equiv_valid_2_guard_imp)
apply (rule ev2_invisible[OF domains_distinct])
by fastforce+
crunch blocked_cancel_ipc_nosts
for silc_inv[wp]: "silc_inv aag st"
context Ipc_IF_1 begin
lemma blocked_cancel_ipc_nosts_equiv_but_for_labels:
"\<lbrace>pas_refined aag and st_tcb_at (\<lambda>st. st = BlockedOnReceive x pl) t
and bound_tcb_at ((=) (Some ntfnptr)) t
and equiv_but_for_labels aag L st
and K (pasObjectAbs aag x \<in> L)
and K (pasObjectAbs aag t \<in> L)\<rbrace>
blocked_cancel_ipc_nosts t
\<lbrace>\<lambda>_. equiv_but_for_labels aag L st\<rbrace>"
unfolding blocked_cancel_ipc_nosts_def get_blocking_object_def
apply (wp set_endpoint_equiv_but_for_labels get_object_wp gts_wp
set_thread_state_runnable_equiv_but_for_labels
| wpc | simp)+
by (clarsimp simp: pred_tcb_at_def obj_at_def)
lemma blocked_cancel_ipc_nosts_reads_respects:
assumes domains_distinct[wp]: "pas_domains_distinct aag"
shows
"reads_respects aag l
(pas_refined aag and st_tcb_at (\<lambda>st. \<exists>xa. st = (BlockedOnReceive x pl)) t
and bound_tcb_at ((=) (Some ntfnptr)) t
and (\<lambda>s. is_subject aag (cur_thread s))
and K ((pasObjectAbs aag t, Receive, pasObjectAbs aag ntfnptr) \<in> pasPolicy aag
\<and> (pasSubject aag, Notify, pasObjectAbs aag ntfnptr) \<in> pasPolicy aag
\<and> (pasObjectAbs aag t, Receive, pasObjectAbs aag x) \<in> pasPolicy aag))
(blocked_cancel_ipc_nosts t)"
unfolding blocked_cancel_ipc_nosts_def
apply (simp only:bind_assoc[symmetric])
apply (rule bind_ev[where P''=\<top>,simplified])
apply (wp set_thread_state_runnable_reads_respects,simp)
subgoal proof (cases "aag_can_read_label aag (pasObjectAbs aag x) \<or> aag_can_affect aag l x")
case True thus ?thesis \<comment> \<open>boring case, can read or affect ep\<close>
unfolding blocked_cancel_ipc_nosts_def get_blocking_object_def
apply clarsimp
apply (rule pre_ev)
apply (wpsimp wp: set_thread_state_reads_respects get_ep_queue_reads_respects
get_simple_ko_reads_respects get_blocking_object_reads_respects
gts_reads_respects set_simple_ko_reads_respects gts_wp
simp: get_blocking_object_def get_thread_state_rev)+
apply (clarsimp simp: pred_tcb_at_def obj_at_def)
by (fastforce dest:read_sync_ep_read_receivers )
next
case False thus ?thesis apply - \<comment> \<open>can't read or affect ep\<close>
apply (rule gen_asm_ev)
apply (drule label_is_invisible[THEN iffD2])
apply clarsimp
apply (rule ev2_invisible_simple[OF domains_distinct],assumption)
apply (simp add: get_blocking_object_def)
apply (rule modifies_at_mostI)
apply (rule hoare_pre)
apply (wpsimp wp: set_thread_state_runnable_equiv_but_for_labels
set_endpoint_equiv_but_for_labels get_object_wp gts_wp
set_thread_state_runnable_equiv_but_for_labels)+
by (fastforce simp: pred_tcb_at_def obj_at_def)
qed
by wp
lemmas blocked_cancel_ipc_nosts_reads_respects_f =
reads_respects_f[where Q=\<top>, simplified,
OF blocked_cancel_ipc_nosts_reads_respects
blocked_cancel_ipc_nosts_silc_inv,
simplified]
end
lemma monadic_rewrite_reads_respects:
"\<lbrakk> monadic_rewrite False False P f f'; reads_respects aag l P' (do x <- f; g x od) \<rbrakk>
\<Longrightarrow> reads_respects aag l (P and P') (do x <- f'; g x od)"
apply (clarsimp simp: monadic_rewrite_def spec_equiv_valid_def
equiv_valid_def equiv_valid_2_def bind_def)
apply (frule_tac x=st in spec)
apply (drule_tac x=t in spec)
by fastforce
lemmas cancel_ipc_reads_respects_rewrite =
monadic_rewrite_reads_respects[OF cancel_ipc_to_blocked_nosts, simplified bind_assoc]
lemmas cancel_ipc_valid_rewrite =
monadic_rewrite_is_valid[OF cancel_ipc_to_blocked_nosts, simplified bind_assoc]
crunch blocked_cancel_ipc_nosts
for etcb_at[wp]: "etcb_at P t"
crunch blocked_cancel_ipc_nosts
for cur_domain[wp]: "\<lambda>s. P (cur_domain s)"
crunch blocked_cancel_ipc_nosts
for pas_refined[wp]: "pas_refined aag"
crunch blocked_cancel_ipc_nosts
for cur_thread[wp]: "\<lambda>s. P (cur_thread s)"
lemma BlockedOnReceive_inj:
"x = (case (BlockedOnReceive x pl) of BlockedOnReceive x pl \<Rightarrow> x)"
"pl = (case (BlockedOnReceive x pl) of BlockedOnReceive x pl \<Rightarrow> pl)"
by auto
lemma receive_blockedD:
"receive_blocked st \<Longrightarrow> \<exists>epptr pl. st = BlockedOnReceive epptr pl"
by (cases st; simp add: receive_blocked_def)
crunch blocked_cancel_ipc_nosts
for pspace_aligned[wp]: pspace_aligned
and valid_vspace_objs[wp]: valid_vspace_objs
and valid_arch_state[wp]: valid_arch_state
context Ipc_IF_1 begin
lemma send_signal_reads_respects:
assumes domains_distinct[wp]: "pas_domains_distinct aag"
notes set_thread_state_owned_reads_respects[wp del]
cancel_ipc_pas_refined[wp del]
shows
"reads_respects aag l
(pas_refined aag and pas_cur_domain aag and pspace_aligned
and valid_vspace_objs and valid_arch_state
and (\<lambda>s. is_subject aag (cur_thread s))
and valid_etcbs and ct_active
and (\<lambda>s. sym_refs (state_refs_of s)) and valid_objs
and K ((pasSubject aag, Notify, pasObjectAbs aag ntfnptr) \<in> pasPolicy aag))
(send_signal ntfnptr badge)"
unfolding send_signal_def fun_app_def
subgoal proof (cases "aag_can_read aag ntfnptr \<or> aag_can_affect aag l ntfnptr")
case True
note visible = this
show ?thesis
apply (rule pre_ev)
apply (simp split del: if_split
| rule_tac ntfnptr=ntfnptr in blocked_cancel_ipc_nosts_reads_respects
| rule cancel_ipc_reads_respects_rewrite
| wp (once) set_simple_ko_reads_respects possible_switch_to_reads_respects
as_user_set_register_reads_respects' set_thread_state_pas_refined
set_simple_ko_reads_respects cancel_ipc_receive_blocked_pas_refined
gts_reads_respects gts_wp hoare_vcg_imp_lift get_simple_ko_wp
get_simple_ko_reads_respects update_waiting_ntfn_reads_respects
| wpc
| simp )+
apply (insert visible)
apply clarsimp
apply (rule conjI[rotated])
apply fastforce
apply (rule disjI2)
apply (intro impI allI)
apply (simp add: obj_at_def)
apply (rule conjI)
apply (frule (3) ntfn_bound_tcb_at[where P="(=) (Some ntfnptr)",OF _ _ _ _ refl])
apply (frule (1) bound_tcb_at_implies_receive)
apply (elim disjE)
apply (rule disjI1)
apply (fastforce dest:read_sync_ep_read_receivers)
apply (rule disjI2)
apply (fastforce dest:read_sync_ep_read_receivers)
apply (clarsimp)
apply (frule (1) ntfn_bound_tcb_at[where P="(=) (Some ntfnptr)",OF _ _ _ _ refl])
apply (fastforce simp: obj_at_def)
apply assumption
apply (rule conjI)
apply (fastforce simp: pred_tcb_at_def receive_blocked_def obj_at_def)
apply (rule conjI[rotated])
apply (frule (1) bound_tcb_at_implies_receive)
apply (frule (1) bound_tcb_at_implies_reset)
apply (clarsimp simp: pred_tcb_at_def get_tcb_def obj_at_def)
apply (rule context_conjI)
apply (fastforce dest!: receive_blockedD intro: BlockedOnReceive_inj)
apply (frule_tac t=x and tcb=tcb and ep = "case (tcb_state tcb) of BlockedOnReceive a pl \<Rightarrow> a"
in get_tcb_recv_blocked_implies_receive)
apply (fastforce simp: pred_tcb_at_def get_tcb_def obj_at_def)
apply (fastforce simp: receive_blocked_def split:thread_state.splits)
apply (fastforce simp: receive_blocked_def intro!: BlockedOnReceive_inj)
by (fastforce simp: pred_tcb_at_def get_tcb_def obj_at_def receive_blocked_def ct_in_state_def)
next
case False note invisible = this show ?thesis
apply (insert label_is_invisible[THEN iffD2, OF invisible])
apply (rule gen_asm_ev)
apply (drule (1) invisible_ntfn_invisible_receivers_and_receivers)
apply simp
apply (rule ev2_invisible_simple[OF domains_distinct],assumption)
apply (rule modifies_at_mostI)
apply (simp split del: if_split
| rule cancel_ipc_valid_rewrite
| wp (once) set_thread_state_pas_refined set_notification_equiv_but_for_labels
possible_switch_to_equiv_but_for_labels as_user_equiv_but_for_labels
set_thread_state_runnable_equiv_but_for_labels get_simple_ko_wp
gts_wp update_waiting_ntfn_equiv_but_for_labels
blocked_cancel_ipc_nosts_equiv_but_for_labels
\<comment> \<open>FIXME: The following line is working around the fact that wp (once) doesn't invoke
wp_pre. If that is changed then it could be removed.\<close>
| wp_pre0
| wpc
| wps)+
apply (elim conjE)
apply (match premises in "ntfn_bound_tcb _ = _" \<Rightarrow> \<open>fail\<close>
\<bar> _ \<Rightarrow> \<open>rule allI impI conjI\<close>)+
prefer 2
apply (intro conjI allI impI; fastforce?)
subgoal waiting_ntfn
apply clarsimp
apply (rule ccontr)
apply (frule (3) not_etcb_at_not_cdom_can_read[OF domains_distinct, rotated 2])
apply (rule tcb_at_ntfn_queue;assumption)
apply (frule (7) read_queued_thread_reads_ntfn)
using invisible
by (fastforce simp add: all_with_auth_to_def all_to_which_has_auth_def)
apply (frule (1) ntfn_bound_tcb_at[where P="(=) (Some ntfnptr)", OF _ _ _ _ refl])
apply (fastforce simp: obj_at_def)
apply assumption
apply (intro allI conjI impI)
apply (fastforce simp: pred_tcb_at_def receive_blocked_def obj_at_def
split: thread_state.splits
intro!: BlockedOnReceive_inj)
apply assumption
apply distinct_subgoals
apply (fold_subgoals (prefix))
apply (frule st_tcb_at_tcb_at)
subgoal bound_ntfn premises prems for st s ntfn x sta
prefer 2
apply (rule disjI2)
apply (rule disjI1)
subgoal bound_tcb_can_receive
using prems
apply (clarsimp simp: all_with_auth_to_def obj_at_def)
by (rule bound_tcb_at_implies_receive;assumption)
apply (rule disjI2)
apply (rule disjI2)
apply (rule disjI1)
subgoal bound_ep_can_receive
apply (rule bexI[OF _ bound_tcb_can_receive])
apply (simp add: all_with_auth_to_def all_to_which_has_auth_def)
using prems
apply (case_tac sta; (clarsimp simp: pred_tcb_at_def obj_at_def receive_blocked_def))
apply (rule get_tcb_recv_blocked_implies_receive, assumption)
apply (fastforce simp: get_tcb_def)
by (fastforce split: thread_state.splits)
apply (rule ccontr)
apply (insert prems)
apply (frule (4) not_etcb_at_not_cdom_can_read[OF domains_distinct])
using bound_tcb_can_receive
apply (fastforce simp: labels_are_invisible_def all_with_auth_to_def all_to_which_has_auth_def)
apply (fastforce simp: pred_tcb_at_def receive_blocked_def obj_at_def)
apply (rule ccontr)
apply clarsimp
using invisible bound_tcb_can_receive reads_ep
by (fastforce simp add: all_with_auth_to_def all_to_which_has_auth_def)
done
qed
done
end
lemma receive_signal_reads_respects:
assumes domains_distinct[wp]: "pas_domains_distinct aag"
shows
"reads_respects aag (l :: 'a subject_label)
(valid_objs and pas_refined aag and (\<lambda>s. is_subject aag (cur_thread s))
and K ((\<forall>ntfnptr \<in> obj_refs_ac cap.
(pasSubject aag, Receive, pasObjectAbs aag ntfnptr) \<in> pasPolicy aag \<and>
is_subject aag thread)))
(receive_signal thread cap is_blocking)"
unfolding receive_signal_def fun_app_def do_nbrecv_failed_transfer_def
by (wp set_simple_ko_reads_respects set_thread_state_reads_respects
as_user_set_register_reads_respects' get_simple_ko_reads_respects hoare_vcg_all_lift
| wpc
| wp (once) hoare_drop_imps
| force dest: reads_ep)+
subsection "Sync IPC"
definition aag_can_read_or_affect_ipc_buffer :: "'a PAS \<Rightarrow> 'a \<Rightarrow> obj_ref option \<Rightarrow> bool" where
"aag_can_read_or_affect_ipc_buffer aag l \<equiv>
case_option True
(\<lambda>buf'. is_aligned buf' msg_align_bits \<and>
(\<forall>x \<in> ptr_range buf' msg_align_bits. aag_can_read aag x \<or> aag_can_affect aag l x))"
lemma for_each_byte_of_word_def2:
"for_each_byte_of_word P ptr \<equiv> (\<forall>x\<in>ptr_range ptr word_size_bits. P x)"
by (simp add: for_each_byte_of_word_def ptr_range_def word_size_size_bits_word add_diff_eq)
context Ipc_IF_1 begin
lemma lookup_ipc_buffer_aag_can_read_or_affect:
"\<lbrace>pas_refined aag and valid_objs and K (aag_can_read aag thread \<or> aag_can_affect aag l thread)\<rbrace>
lookup_ipc_buffer is_receiver thread
\<lbrace>\<lambda>rv s. aag_can_read_or_affect_ipc_buffer aag l rv\<rbrace>"
apply (rule hoare_gen_asm)
apply (rule hoare_strengthen_post[OF lookup_ipc_buffer_has_read_auth])
apply (auto simp: ipc_buffer_has_read_auth_def aag_can_read_or_affect_ipc_buffer_def
intro: reads_read_thread_read_pages
simp: aag_can_affect_label_def split: option.splits)
done
lemma aag_has_auth_to_read_cptrs:
"\<lbrakk> x \<in> set [buffer_cptr_index ..< buffer_cptr_index + unat (mi_extra_caps mi)];
ipc_buffer_has_read_auth aag (pasSubject aag) (Some a);
buffer_cptr_index + unat (mi_extra_caps mi) < 2 ^ (msg_align_bits - word_size_bits) \<rbrakk>
\<Longrightarrow> for_each_byte_of_word (\<lambda> y. aag_can_read aag y) (a + of_nat x * of_nat word_size)"
apply (simp add: for_each_byte_of_word_def2 ipc_buffer_has_read_auth_def)
apply (rule ballI)
apply (rule reads_read)
apply (clarify)
apply (erule bspec)
apply (rule subsetD[OF cptrs_in_ipc_buffer])
apply fastforce
apply assumption
apply assumption
apply assumption
done
lemma get_extra_cptrs_rev:
"reads_equiv_valid_inv A aag
(K (ipc_buffer_has_read_auth aag (pasSubject aag) buffer \<and>
(buffer_cptr_index + unat (mi_extra_caps mi) < 2 ^ (msg_align_bits - word_size_bits))))
(get_extra_cptrs buffer mi)"
unfolding get_extra_cptrs_def
apply (rule gen_asm_ev)
apply clarsimp
apply (case_tac buffer, simp_all add: return_ev_pre)
apply (wp mapM_ev equiv_valid_guard_imp[OF load_word_offs_rev]
| erule (2) aag_has_auth_to_read_cptrs)+
done
lemma lookup_extra_caps_rev:
"reads_equiv_valid_inv A aag
(pas_refined aag and (K (is_subject aag thread)) and
(\<lambda>s. ipc_buffer_has_read_auth aag (pasSubject aag) buffer \<and>
buffer_cptr_index + unat (mi_extra_caps mi) < 2 ^ (msg_align_bits - word_size_bits)))
(lookup_extra_caps thread buffer mi)"
unfolding lookup_extra_caps_def fun_app_def
by (wpsimp wp: mapME_ev cap_fault_on_failure_rev lookup_cap_and_slot_rev get_extra_cptrs_rev)
lemmas lookup_extra_caps_reads_respects_g =
reads_respects_g_from_inv[OF lookup_extra_caps_rev lookup_extra_caps_inv]
lemma aag_has_auth_to_read_msg:
"\<lbrakk> n = msg_max_length \<or> n < msg_max_length;
ipc_buffer_has_read_auth aag (pasSubject aag) (Some p);
unat (mi_length mi) < 2 ^ (msg_align_bits - word_size_bits) \<rbrakk>
\<Longrightarrow> for_each_byte_of_word (aag_can_read aag) (p + of_nat n * of_nat word_size)"
apply (simp add: for_each_byte_of_word_def2 ipc_buffer_has_read_auth_def)
apply (rule ballI)
apply (rule reads_read)
apply (clarify)
apply (erule bspec)
apply (rule subsetD[OF msg_in_ipc_buffer[where n=n]])
apply assumption
apply assumption
apply assumption
apply assumption
done
(* only called within do_reply_transfer for which access assumes sender
and receiver in same domain *)
lemma get_mrs_rev:
"reads_equiv_valid_inv A aag
(K (is_subject aag thread \<and> ipc_buffer_has_read_auth aag (pasSubject aag) buf
\<and> unat (mi_length mi) < 2 ^ (msg_align_bits - word_size_bits)))
(get_mrs thread buf mi)"
unfolding get_mrs_def
apply (rule gen_asm_ev)
apply (wp mapM_ev'' load_word_offs_rev thread_get_rev
| wpc
| rule aag_has_auth_to_read_msg[where mi=mi]
| clarsimp split: if_split_asm)+
done
lemmas get_mrs_reads_respects_g = reads_respects_g_from_inv[OF get_mrs_rev get_mrs_inv]
end
lemma setup_caller_cap_reads_respects:
"reads_respects aag l (K (aag_can_read aag sender \<and> aag_can_read aag receiver))
(setup_caller_cap sender receiver grant)"
unfolding setup_caller_cap_def
by (wp cap_insert_reads_respects set_thread_state_owned_reads_respects | simp)+
lemma const_on_failure_ev:
"equiv_valid_inv I A P m
\<Longrightarrow> equiv_valid_inv I A P (const_on_failure c m)"
unfolding const_on_failure_def catch_def
by (wp | wpc | simp)+
lemma set_extra_badge_reads_respects:
"reads_respects aag l \<top> (set_extra_badge buffer badge n)"
unfolding set_extra_badge_def
by (rule store_word_offs_reads_respects)
lemma reads_equiv_cdt_has_children0:
"\<lbrakk> pas_refined aag s; pas_refined aag s'; aag_can_read aag (fst slot);
equiv_for (aag_can_read aag \<circ> fst) cdt s s' \<rbrakk>
\<Longrightarrow> (cdt s) c = Some slot \<longleftrightarrow> (cdt s') c = Some slot"
apply (rule iffI)
apply (drule equiv_forD)
apply (erule(1) all_children_subjectReads[THEN all_childrenD];fastforce)
apply fastforce
apply (drule equiv_forD)
apply (erule(1) all_children_subjectReads[THEN all_childrenD];fastforce)
apply fastforce
done
lemma reads_equiv_cdt_has_children:
"\<lbrakk> pas_refined aag s; pas_refined aag s'; is_subject aag (fst slot);
equiv_for (aag_can_read aag \<circ> fst) cdt s s' \<rbrakk>
\<Longrightarrow> (\<exists>c. (cdt s) c = Some slot) = (\<exists>c. (cdt s') c = Some slot)"
apply (rule iff_exI)
by (erule reads_equiv_cdt_has_children0; force)
lemma ensure_no_children_rev:
"reads_equiv_valid_inv A aag (pas_refined aag and K (is_subject aag (fst slot)))
(ensure_no_children slot)"
unfolding ensure_no_children_def fun_app_def equiv_valid_def2
apply (rule equiv_valid_rv_guard_imp)
apply (rule_tac Q="\<lambda> rv s. pas_refined aag s \<and> is_subject aag (fst slot) \<and> rv = cdt s"
in equiv_valid_rv_liftE_bindE[OF equiv_valid_rv_guard_imp[OF gets_cdt_revrv']])
apply (rule TrueI)
apply (clarsimp simp: equiv_valid_2_def)
apply (drule reads_equiv_cdt_has_children)
apply assumption
apply assumption
apply (fastforce elim: reads_equivE)
apply (fastforce simp: in_whenE in_throwError)
apply (wp, simp)
done
(* FIXME MOVE *)
lemma ball_subsetE:
"\<lbrakk> \<forall>x \<in> S. P x; S' \<subseteq> S; \<And>x. P x \<Longrightarrow> Q x \<rbrakk>
\<Longrightarrow> \<forall>x \<in> S'. Q x"
by blast
context Ipc_IF_1 begin
lemma derive_cap_rev':
"reads_equiv_valid_inv A aag (\<lambda>s. (\<exists>x xa xb d. cap = cap.UntypedCap d x xa xb)
\<longrightarrow> pas_refined aag s \<and> is_subject aag (fst slot))
(derive_cap slot cap)"
unfolding derive_cap_def
apply (rule equiv_valid_guard_imp)
apply (wp ensure_no_children_rev arch_derive_cap_rev | wpc | simp)+
done
lemma derive_cap_rev:
"reads_equiv_valid_inv A aag (\<lambda>s. pas_refined aag s \<and> is_subject aag (fst slot))
(derive_cap slot cap)"
by (blast intro: equiv_valid_guard_imp[OF derive_cap_rev'])
lemma transfer_caps_loop_reads_respects':
"reads_respects aag l
(pas_refined aag and pspace_aligned and valid_vspace_objs and
valid_arch_state and valid_mdb and valid_objs and
(\<lambda>s. (\<forall>cap\<in>set caps. valid_cap (fst cap) s
\<and> is_subject aag (fst (snd cap))
\<and> pas_cap_cur_auth aag (fst cap)
\<and> cte_wp_at (\<lambda>cp. fst cap \<noteq> NullCap
\<longrightarrow> cp \<noteq> fst cap
\<longrightarrow> cp = masked_as_full (fst cap) (fst cap)) (snd cap) s)
\<and> (\<forall>slot\<in>set slots. is_subject aag (fst slot)
\<and> cte_wp_at ((=) NullCap) slot s
\<and> real_cte_at slot s)
\<and> distinct slots))
(transfer_caps_loop ep rcv_buffer n caps slots mi)"
apply (induct caps arbitrary: slots n mi)
apply simp
apply (rule return_ev_pre)
apply (case_tac a, rename_tac cap obj ind)
apply (simp split del: if_split)
apply (rule equiv_valid_guard_imp)
apply (wp const_on_failure_ev | simp | intro conjI impI)+
apply fast
apply (wp set_extra_badge_reads_respects hoare_vcg_ball_lift | simp)+
apply fast
apply (wp cap_insert_reads_respects cap_insert_pas_refined whenE_throwError_wp
derive_cap_rev derive_cap_cap_cur_auth derive_cap_is_derived
hoare_vcg_ball_lift cap_insert_cte_wp_at
| simp split del: if_split)+
apply (rule_tac Q'="\<lambda>capd s. (capd \<noteq> NullCap
\<longrightarrow> cte_wp_at (is_derived (cdt s) (obj,ind) capd) (obj, ind) s)
\<and> (capd \<noteq> NullCap \<longrightarrow> QM s capd)" for QM
in hoare_strengthen_postE_R)
prefer 2
apply (clarsimp simp: cte_wp_at_caps_of_state split del: if_split)
apply (strengthen is_derived_is_transferable[mk_strg I' O], assumption, solves\<open>simp\<close>)
apply (rule hoare_vcg_conj_liftE_R')
apply (rule derive_cap_is_derived)
apply (wp derive_cap_is_derived_foo')
apply wp
apply (clarsimp simp: remove_rights_cur_auth cte_wp_at_caps_of_state split del: if_split)
apply (rename_tac actual_cap)
apply (strengthen real_cte_tcb_valid)
apply (clarsimp)
apply (intro conjI)
subgoal
by (fastforce simp: masked_as_full_def is_cap_simps cap_master_cap_simps split: if_splits)
apply clarsimp
apply (intro conjI)
apply (fastforce dest: auth_derived_pas_cur_auth)
apply fastforce
subgoal
apply (erule ball_subsetE, fastforce)
by (fastforce simp: cte_wp_at_caps_of_state masked_as_full_def is_cap_simps split: if_splits)
subgoal by (fastforce simp: neq_Nil_conv cte_wp_at_caps_of_state)
by (rule distinct_tl)
lemma transfer_caps_loop_reads_respects:
"reads_respects aag l
(pas_refined aag and pspace_aligned and valid_vspace_objs and
valid_arch_state and valid_mdb and valid_objs and
(\<lambda>s. (\<forall>cap\<in>set caps. valid_cap (fst cap) s
\<and> is_subject aag (fst (snd cap))
\<and> pas_cap_cur_auth aag (fst cap)
\<and> cte_wp_at (\<lambda>cp. fst cap \<noteq> NullCap \<longrightarrow> cp = fst cap) (snd cap) s)
\<and> (\<forall>slot\<in>set slots. is_subject aag (fst slot)
\<and> cte_wp_at ((=) NullCap) slot s
\<and> real_cte_at slot s)
\<and> distinct slots))
(transfer_caps_loop ep rcv_buffer n caps slots mi)"
apply (rule equiv_valid_guard_imp, rule transfer_caps_loop_reads_respects')
by (fastforce elim: cte_wp_at_weakenE)
end
lemma empty_on_failure_ev:
"equiv_valid_inv I A P m \<Longrightarrow>
equiv_valid_inv I A P (empty_on_failure m)"
unfolding empty_on_failure_def catch_def
by (wp | wpc | simp)+
lemma unify_failure_ev:
"equiv_valid_inv I A P m \<Longrightarrow>
equiv_valid_inv I A P (unify_failure m)"
unfolding unify_failure_def handleE'_def
by (wp | wpc | simp)+
lemma lookup_slot_for_cnode_op_rev:
"reads_equiv_valid_inv A aag
(\<lambda>s. (depth \<noteq> 0 \<and> depth \<le> word_bits)
\<longrightarrow> (pas_refined aag s \<and> (is_cnode_cap croot \<longrightarrow> is_subject aag (obj_ref_of croot))))
(lookup_slot_for_cnode_op is_source croot ptr depth)"
unfolding lookup_slot_for_cnode_op_def
apply (clarsimp split del: if_split)
apply (wp resolve_address_bits_rev lookup_error_on_failure_rev
whenE_throwError_wp
| wpc
| rule hoare_strengthen_postE_R[OF wp_post_tautE_R]
| simp add: split_def split del: if_split)+
done
lemma lookup_slot_for_cnode_op_reads_respects:
"reads_respects aag l (pas_refined aag and K (is_subject aag (obj_ref_of croot)))
(lookup_slot_for_cnode_op is_source croot ptr depth)"
apply (rule equiv_valid_guard_imp[OF lookup_slot_for_cnode_op_rev])
by simp
lemma lookup_cap_rev:
"reads_equiv_valid_inv A aag (pas_refined aag and K (is_subject aag thread))
(lookup_cap thread ref)"
unfolding lookup_cap_def split_def fun_app_def
apply (wp lookup_slot_for_thread_rev get_cap_rev | simp | strengthen aag_can_read_self)+
apply (rule lookup_slot_for_thread_authorised)
apply simp
done
lemma word_plus_power_2_offset_le:
"\<lbrakk> is_aligned (p :: 'l :: len word) n; is_aligned q m; p < q; n \<le> m; n < len_of TYPE('l) \<rbrakk>
\<Longrightarrow> p + 2^n \<le> q"
apply (drule is_aligned_weaken, assumption)
apply (clarsimp simp: is_aligned_def)
apply (elim dvdE)
apply (rename_tac k ka)
apply (rule_tac ua=0 and n="int k" and n'="int ka" in udvd_incr')
apply assumption
apply (clarsimp simp: uint_nat)+