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Ipc_DR.thy
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Ipc_DR.thy
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(*
* Copyright 2020, Data61, CSIRO (ABN 41 687 119 230)
*
* SPDX-License-Identifier: GPL-2.0-only
*)
theory Ipc_DR
imports CNode_DR
begin
context begin interpretation Arch . (*FIXME: arch-split*)
abbreviation
"thread_is_running y s \<equiv> st_tcb_at ((=) Structures_A.Running) y s"
lemmas [wp] = abs_typ_at_lifts[OF set_simple_ko_typ_at]
lemma set_object_cur_thread_idle_thread:
"\<lbrace>\<lambda>s. P (cur_thread s) (idle_thread s)\<rbrace> KHeap_A.set_object word x
\<lbrace>\<lambda>yb s. P (cur_thread s) (idle_thread s)\<rbrace>"
by (wpsimp wp: set_object_wp)
lemma set_thread_state_cur_thread_idle_thread:
"\<lbrace>\<lambda>s. P (cur_thread s) (idle_thread s) \<rbrace> set_thread_state thread x \<lbrace>\<lambda>rv s. P (cur_thread s) (idle_thread s)\<rbrace>"
apply (simp add: set_thread_state_def)
apply (wp set_object_cur_thread_idle_thread dxo_wp_weak | simp)+
done
lemma thread_set_cur_thread_idle_thread:
" \<lbrace>\<lambda>s. P (cur_thread s) (idle_thread s)\<rbrace> thread_set (tcb_fault_update Map.empty) word \<lbrace>\<lambda>xg s. P (cur_thread s) (idle_thread s)\<rbrace>"
apply (simp add:thread_set_def)
apply (wp set_object_cur_thread_idle_thread)
apply simp
done
lemma as_user_cur_thread_idle_thread:
"\<lbrace>\<lambda>s. P (cur_thread s) (idle_thread s)\<rbrace> as_user thread x \<lbrace>\<lambda>rv s. P (cur_thread s) (idle_thread s)\<rbrace>"
by (wpsimp wp: set_object_cur_thread_idle_thread simp: as_user_def split_def)
lemma do_fault_transfer_cur_thread_idle_thread:
"\<lbrace>\<lambda>s. P (cur_thread s) (idle_thread s)\<rbrace> do_fault_transfer c a e recv_buffer \<lbrace>\<lambda>rv s. P (cur_thread s) (idle_thread s)\<rbrace>"
apply (simp add:do_fault_transfer_def set_message_info_def)
apply (wp as_user_cur_thread_idle_thread |wpc|clarsimp)+
apply (wps | wp transfer_caps_it copy_mrs_it | simp)+
apply wpc
apply (wp | simp add:thread_get_def)+
done
lemma do_normal_transfer_cur_thread_idle_thread:
"\<lbrace>\<lambda>s. P (cur_thread s) (idle_thread s) \<rbrace> Ipc_A.do_normal_transfer a b c d e f g \<lbrace>\<lambda>rv s. P (cur_thread s) (idle_thread s)\<rbrace>"
apply (simp add:do_normal_transfer_def set_message_info_def cong: if_cong)
apply (wp as_user_cur_thread_idle_thread |wpc|clarsimp)+
apply (wps | wp transfer_caps_it copy_mrs_it)+
apply clarsimp
done
lemma do_ipc_transfer_cur_thread_idle_thread:
"\<lbrace>\<lambda>s. P (cur_thread s) (idle_thread s) \<rbrace> Ipc_A.do_ipc_transfer a b c d e \<lbrace>\<lambda>rv s. P (cur_thread s) (idle_thread s)\<rbrace>"
apply (simp add:do_ipc_transfer_def)
apply (wp do_fault_transfer_cur_thread_idle_thread do_normal_transfer_cur_thread_idle_thread|wpc)+
apply (wp | simp add:thread_get_def)+
done
lemma handle_reply_cur_thread_idle_thread:
"\<lbrace>\<lambda>s. P (cur_thread s) (idle_thread s)\<rbrace> Syscall_A.handle_reply
\<lbrace>\<lambda>rv s. P (cur_thread s) (idle_thread s) \<rbrace>"
apply (simp add:handle_reply_def)
apply (wp do_ipc_transfer_cur_thread_idle_thread|wpc)+
apply (clarsimp simp:Ipc_A.do_reply_transfer_def)
apply (wp set_thread_state_cur_thread_idle_thread dxo_wp_weak
|wpc|simp add: trans_state_def)+
apply ((wps|wp cap_delete_one_it)+)[1]
apply (wp do_ipc_transfer_cur_thread_idle_thread dxo_wp_weak)+
apply (clarsimp simp: trans_state_def)
apply (case_tac rvf)
apply (simp | wp set_thread_state_cur_thread_idle_thread
thread_set_cur_thread_idle_thread)+
apply ((wps | wp)+)[1]
apply wp+
apply ((wps | wp cap_delete_one_it)+)[1]
apply (rule hoare_drop_imp | rule hoare_conjI | rule hoare_allI | wp)+
apply simp+
done
declare pbfs_atleast_pageBits [simp]
lemma dcorres_move_guard:
"dcorres r P P' a c \<Longrightarrow> dcorres r \<top> (P' and (P o transform)) a c"
apply (rule corres_underlyingI)
apply (erule (1) corres_underlyingE, simp_all)[1]
apply (fastforce intro: bexI [rotated])
apply simp
done
lemma dcorres_move_guard_back:
"dcorres r \<top> (P' and (P o transform)) a c \<Longrightarrow> dcorres r P P' a c"
apply (rule corres_underlyingI)
apply (erule (1) corres_underlyingE, rule TrueI)
apply (fastforce intro: bexI [rotated])+
done
lemma dcorres_move_guard_iff:
"dcorres r P P' a c = dcorres r \<top> (P' and (P o transform)) a c"
apply (rule iffI)
apply (erule dcorres_move_guard)
apply (erule dcorres_move_guard_back)
done
lemma transform_cdt_cong:
"\<lbrakk> cdt s = cdt s'; interrupt_irq_node s = interrupt_irq_node s' \<rbrakk> \<Longrightarrow> transform_cdt s = transform_cdt s'"
unfolding transform_cdt_def by (simp)
lemma transform_current_thread_cong:
"\<lbrakk> cur_thread s = cur_thread s'; idle_thread s = idle_thread s' \<rbrakk> \<Longrightarrow> transform_current_thread s = transform_current_thread s'"
unfolding transform_current_thread_def by (simp)
lemma cap_installed_at_irq_weak_cong:
"\<lbrakk> w = w'; caps_of_state s = caps_of_state s'; interrupt_irq_node s = interrupt_irq_node s' \<rbrakk> \<Longrightarrow> cap_installed_at_irq w s = cap_installed_at_irq w' s'"
unfolding cap_installed_at_irq_def by (simp)
lemmas transform_congs = transform_cdt_cong transform_current_thread_cong
cap_installed_at_irq_weak_cong caps_of_state_pspace
lemma is_arch_page_capE:
assumes ispc: "is_arch_page_cap cap"
and rl: "\<And>buf rights sz mapdata dev. \<lbrakk> cap = cap.ArchObjectCap (arch_cap.PageCap dev buf rights sz mapdata)\<rbrakk> \<Longrightarrow> R"
shows "R"
using ispc unfolding is_arch_page_cap_def
apply (simp split: cap.splits arch_cap.splits)
apply (erule rl)
done
lemma get_ipc_buffer_words_Nil:
"get_ipc_buffer_words ms tcb [] = []"
unfolding get_ipc_buffer_words_def
by (auto simp: mapM_Nil split: cap.splits arch_cap.splits)
lemma det_loadWord:
"is_aligned x 2 \<Longrightarrow> det (loadWord x)"
unfolding loadWord_def
by (simp add: is_aligned_mask)
definition
"functional f \<equiv> (\<forall>P. \<lbrace>P\<rbrace> f \<lbrace>\<lambda>_. P\<rbrace>)"
lemma return_functional [simp]:
"functional (return x)"
unfolding functional_def by (rule allI, wp)
lemma functional_from_wp:
"(\<And>P. \<lbrace>P\<rbrace> f \<lbrace>\<lambda>_. P\<rbrace>) \<Longrightarrow> functional f"
unfolding functional_def
by clarsimp
lemma detE:
"\<lbrakk> det f; \<And>a b. fst (f s) = {(a, b)} \<Longrightarrow> R \<rbrakk> \<Longrightarrow> R"
unfolding det_def
apply (drule spec [where x = s])
apply fastforce
done
(* might be an equality *)
lemma evalMonad_from_wp:
"\<lbrakk> \<lbrace>(=) s\<rbrace> f \<lbrace>\<lambda>rv _. P rv\<rbrace>; det f \<rbrakk> \<Longrightarrow> P (the (evalMonad f s))"
apply (erule detE [where s = s])
apply (drule use_valid [rotated])
apply (rule refl)
apply (erule in_singleton)
apply (clarsimp simp: evalMonad_def)
done
lemma evalMonad_bind_functional:
"\<lbrakk> functional f; det f \<rbrakk> \<Longrightarrow> evalMonad (f >>= g) s = evalMonad (g (the (evalMonad f s))) s "
unfolding evalMonad_def
apply (erule detE [where s = s])
apply (clarsimp simp: bind_def)
apply (drule in_inv_by_hoareD [OF _ in_singleton, rotated])
apply (clarsimp simp: functional_def)
apply simp
done
lemma mapM_functional:
assumes fn: "\<And>n. functional (f n)"
shows "functional (mapM f ns)"
apply (rule functional_from_wp)
apply (wp mapM_wp')
apply (rule fn [unfolded functional_def, THEN spec])
apply assumption
done
lemma evalMonad_mapM_functional:
assumes fn: "\<And>n. functional (f n)"
and det: "\<And>n. n \<in> set ns \<Longrightarrow> det (f n)"
shows "the (evalMonad (mapM f ns) s) = map (\<lambda>n. the (evalMonad (f n) s)) ns"
using det
proof (induct ns)
case Nil
thus ?case by (simp add: mapM_Nil)
next
case (Cons n ns')
have det': "det (f n)" using Cons.prems by clarsimp
show ?case
apply (simp add: mapM_Cons evalMonad_bind_functional [OF fn det'])
apply (subst evalMonad_bind_functional)
apply (rule mapM_functional [OF fn])
apply (rule det_mapM [OF Cons.prems])
apply assumption
apply clarsimp
apply simp
apply (subst Cons.hyps)
apply (rule Cons.prems)
apply simp
apply simp
done
qed
lemma loadWord_functional [simp]:
"functional (loadWord n)"
unfolding loadWord_def
apply (rule functional_from_wp)
apply wp
apply simp
done
lemma is_aligned_buffer_offset:
"\<lbrakk> is_aligned buf (pageBitsForSize sz); is_aligned p msg_align_bits \<rbrakk> \<Longrightarrow>
is_aligned (buf + (p && mask (pageBitsForSize sz)) + of_nat n * of_nat word_size) 2"
apply (rule aligned_add_aligned)
apply (erule aligned_add_aligned)
apply (erule is_aligned_andI1)
apply simp
apply simp
apply (simp add: word_size_def is_aligned_mult_triv2[where n = 2, simplified]
word_bits_conv)
done
abbreviation
"ipc_buf_addr buf ptr sz n \<equiv> (buf + (ptr && mask (pageBitsForSize sz)) + of_nat n * of_nat word_size)"
lemma evalMonad_singleton [simp]:
"evalMonad (\<lambda>s. ({(f s, g s)}, b)) s = Some (f s)"
unfolding evalMonad_def by simp
lemma mi_length_dest : "of_nat (unat (mi_length rva)) = mi_length rva"
by (rule word_unat.Rep_inverse)
(* CORRES RULES *)
lemma no_pending_cap_when_active_corres:
"dcorres (\<lambda>cap rv'. cap = cdl_cap.NullCap) \<top> (st_tcb_at (\<lambda>t. \<not> generates_pending t) thread and not_idle_thread thread and valid_etcbs)
(KHeap_D.get_cap (thread, tcb_pending_op_slot))
(return b)"
apply (simp add:gets_the_def gets_def assert_opt_def)
apply (rule dcorres_absorb_get_l)
apply (clarsimp simp:st_tcb_at_def obj_at_def)
apply (frule(1) valid_etcbs_tcb_etcb)
apply (subst opt_cap_tcb)
apply (erule get_tcb_rev)
apply (clarsimp simp: get_etcb_def)
apply (simp add:not_idle_thread_def)
apply (clarsimp simp:tcb_pending_op_slot_def tcb_caller_slot_def tcb_cspace_slot_def tcb_ipcbuffer_slot_def
tcb_replycap_slot_def tcb_vspace_slot_def assert_opt_def)
apply (clarsimp simp:object_slots_def generates_pending_def infer_tcb_pending_op_def return_def
split:Structures_A.thread_state.splits)
done
lemma dummy_finalise_wp[wp]:
"is_pending_cap obj
\<Longrightarrow> \<lbrace>(=) s\<rbrace> PageTableUnmap_D.fast_finalise obj (PageTableUnmap_D.is_final_cap' obj s) \<lbrace>\<lambda>x. (=) s\<rbrace>"
by (clarsimp simp:is_pending_cap_def split:cdl_cap.splits)
lemma cte_at_into_opt_cap:
"cte_at p s = (\<exists>cap. cte_wp_at ((=) cap) p s
\<and> (fst p \<noteq> idle_thread s \<and> valid_etcbs s \<longrightarrow> opt_cap (transform_cslot_ptr p) (transform s) = Some (transform_cap cap)))"
apply (clarsimp simp: cte_wp_at_caps_of_state)
apply (safe, simp_all)
apply (clarsimp simp: caps_of_state_transform_opt_cap)
done
lemma object_slots_has_slots [simp]:
"object_slots obj p = Some v \<Longrightarrow> has_slots obj"
unfolding object_slots_def has_slots_def
by (simp split: cdl_object.splits)
lemma dcorres_when_l:
assumes tc: "R \<Longrightarrow> dcorres dc \<top> P l r"
and fc: "\<not> R \<Longrightarrow> dcorres dc \<top> Q (return ()) r"
shows "dcorres dc \<top> (\<lambda>s. (R \<longrightarrow> P s) \<and> (\<not> R \<longrightarrow> Q s)) (when R l) r"
unfolding when_def
apply (cases R)
apply simp
apply (erule tc)
apply simp
apply (erule fc)
done
lemma corres_guard_from_wp_r:
assumes ac: "corres_underlying sr False False r G G' a c"
and rl: "\<lbrace>\<lambda>s. \<not> P s\<rbrace> c \<lbrace>\<lambda>_ _. False\<rbrace>"
shows "corres_underlying sr False False r G (\<lambda>s. P s \<longrightarrow> G' s) a c"
apply (rule corres_name_pre)
apply (case_tac "P s'")
apply simp
apply (rule corres_guard_imp)
apply (rule ac)
apply simp
apply simp
apply (rule corres_underlyingI)
apply (frule use_valid [OF _ rl])
apply simp
apply simp
apply simp
done
lemma corres_guard_from_wp_bind_r:
assumes ac: "corres_underlying sr False False r G G' a (c >>= d)"
and rl: "\<lbrace>\<lambda>s. \<not> P s\<rbrace> c \<lbrace>\<lambda>_ _. False\<rbrace>"
shows "corres_underlying sr False False r G (\<lambda>s. P s \<longrightarrow> G' s) a (c >>= d)"
apply (rule corres_guard_from_wp_r)
apply (rule ac)
apply (wp rl)
done
lemma thread_set_gwp:
"dcorres dc P P' a (thread_set f p)
\<Longrightarrow> dcorres dc P (\<lambda>s. tcb_at p s \<longrightarrow> P' s) a (thread_set f p)"
unfolding thread_set_def
apply (erule corres_guard_from_wp_r)
apply (wp gets_the_wp)
apply (simp add: tcb_at_def)
done
lemma sts_gwp:
"dcorres dc P P' a (set_thread_state p st)
\<Longrightarrow> dcorres dc P (\<lambda>s. tcb_at p s \<longrightarrow> P' s) a (set_thread_state p st)"
apply (simp add: set_thread_state_thread_set thread_set_def)
apply (erule corres_guard_from_wp_r)
apply (wp gets_the_wp)
apply (simp add: tcb_at_def)
done
lemma block_thread_on_send_corres:
"dcorres dc \<top> (not_idle_thread thread and valid_etcbs)
(KHeap_D.set_cap (thread, tcb_pending_op_slot)
(PendingSyncSendCap epptr badge call can_grant can_grant_reply
False))
(set_thread_state thread
(Structures_A.thread_state.BlockedOnSend epptr
\<lparr>sender_badge = badge, sender_can_grant = can_grant,
sender_can_grant_reply = can_grant_reply, sender_is_call = call\<rparr>))"
apply (clarsimp simp:KHeap_D.set_cap_def set_thread_state_def)
apply (rule dcorres_gets_the, clarsimp)
apply (rule dcorres_rhs_noop_below_True[OF set_thread_state_ext_dcorres])
apply (frule(1) valid_etcbs_get_tcb_get_etcb, clarsimp)
apply (clarsimp simp: obj_at_def not_idle_thread_def opt_object_tcb assert_def
transform_tcb_def has_slots_def split: option.splits)
apply (clarsimp simp:update_slots_def object_slots_def)
apply (clarsimp simp:set_object_def get_object_def in_monad simpler_modify_def KHeap_D.set_object_def
get_def put_def bind_def corres_underlying_def return_def)
apply (clarsimp simp:transform_def transform_objects_def transform_current_thread_def)
apply (rule ext)
apply (clarsimp simp: |rule conjI)+
apply (fastforce dest!: get_tcb_SomeD get_etcb_SomeD
simp: transform_tcb_def infer_tcb_pending_op_def tcb_slot_defs)
apply (clarsimp simp:restrict_map_def map_add_def)
apply (clarsimp, frule(1) valid_etcbs_get_tcb_get_etcb)
apply (fastforce simp:not_idle_thread_def dest!:opt_object_tcb)
done
lemma block_thread_on_recv_corres:
"dcorres dc \<top> (not_idle_thread thread and valid_etcbs)
(KHeap_D.set_cap (thread, tcb_pending_op_slot)
(PendingSyncRecvCap epptr False can_grant))
(set_thread_state thread
(Structures_A.thread_state.BlockedOnReceive epptr \<lparr>receiver_can_grant = can_grant\<rparr>))"
apply (clarsimp simp:KHeap_D.set_cap_def set_thread_state_def)
apply (rule dcorres_gets_the, clarsimp)
apply (rule dcorres_rhs_noop_below_True[OF set_thread_state_ext_dcorres])
apply (frule(1) valid_etcbs_get_tcb_get_etcb, clarsimp)
apply (clarsimp simp:not_idle_thread_def opt_object_tcb assert_def
transform_tcb_def has_slots_def)
apply (clarsimp simp:update_slots_def object_slots_def)
apply (clarsimp simp:set_object_def get_object_def in_monad simpler_modify_def KHeap_D.set_object_def
get_def put_def bind_def corres_underlying_def return_def)
apply (clarsimp simp:transform_def transform_objects_def transform_current_thread_def)
apply (rule ext)
apply (clarsimp simp: get_etcb_def|rule conjI)+
apply (fastforce simp:transform_tcb_def infer_tcb_pending_op_def tcb_slot_defs)
apply (clarsimp simp:restrict_map_def map_add_def)
apply (clarsimp, frule(1) valid_etcbs_get_tcb_get_etcb)
apply (fastforce simp:not_idle_thread_def dest!:opt_object_tcb)
done
lemma block_thread_on_ntfn_recv_corres:
"dcorres dc \<top> (not_idle_thread thread and valid_etcbs)
(KHeap_D.set_cap (thread, tcb_pending_op_slot)
(PendingNtfnRecvCap w))
(set_thread_state thread (Structures_A.thread_state.BlockedOnNotification w))"
apply (clarsimp simp:KHeap_D.set_cap_def set_thread_state_def)
apply (rule dcorres_gets_the, clarsimp)
apply (rule dcorres_rhs_noop_below_True[OF set_thread_state_ext_dcorres])
apply (frule(1) valid_etcbs_get_tcb_get_etcb, clarsimp)
apply (clarsimp simp:not_idle_thread_def opt_object_tcb assert_def
transform_tcb_def has_slots_def)
apply (clarsimp simp:update_slots_def object_slots_def)
apply (clarsimp simp:set_object_def get_object_def in_monad simpler_modify_def KHeap_D.set_object_def
get_def put_def bind_def corres_underlying_def return_def)
apply (clarsimp simp:transform_def transform_objects_def transform_current_thread_def)
apply (rule ext)
apply (clarsimp simp: get_etcb_def|rule conjI)+
apply (fastforce simp:transform_tcb_def infer_tcb_pending_op_def tcb_slot_defs)
apply (clarsimp simp:restrict_map_def map_add_def)
apply (clarsimp, frule(1) valid_etcbs_get_tcb_get_etcb)
apply (fastforce simp:not_idle_thread_def dest!:opt_object_tcb)
done
lemma corres_ignore_ret_lhs: "dcorres rv P P' (do f;g od) f' \<Longrightarrow> dcorres rv P P' (do a\<leftarrow>f;g od) f'"
by (clarsimp simp:corres_underlying_def)
crunch set_thread_state, set_object
for not_idle[wp]: "not_idle_thread y :: 'a::state_ext state \<Rightarrow> bool"
(simp: not_idle_thread_def get_object_def wp: dxo_wp_weak)
lemma set_scheduler_action_dcorres:
"dcorres dc P P' (return ()) (set_scheduler_action sa)"
by (clarsimp simp: set_scheduler_action_def modify_def get_def put_def bind_def return_def corres_underlying_def)
lemma tcb_sched_action_transform_inv: "\<lbrace>\<lambda>ps. transform ps = cs\<rbrace> tcb_sched_action tcb_sched_enqueue t \<lbrace>\<lambda>r s. transform s = cs\<rbrace>"
apply (clarsimp simp: tcb_sched_action_def)
apply (wp | simp)+
done
lemma set_scheduler_action_transform_inv:
"\<lbrace>\<lambda>ps. transform ps = cs\<rbrace> set_scheduler_action act \<lbrace>\<lambda>r s. transform s = cs\<rbrace>"
by (wpsimp simp: set_scheduler_action_def)
lemma possible_switch_to_dcorres:
"dcorres dc P P' (return ()) (possible_switch_to t)"
apply (clarsimp simp: possible_switch_to_def cong: if_cong)
apply (rule dcorres_symb_exec_r)+
apply (rule corres_guard1_imp, rule corres_if_rhs)
apply (rule tcb_sched_action_dcorres[THEN corres_trivial])
apply (rule corres_if_rhs)
apply (rule dcorres_symb_exec_r)+
apply (rule tcb_sched_action_dcorres[THEN corres_trivial])
apply (wp set_scheduler_action_transform_inv tcb_sched_action_transform_inv
| simp add: reschedule_required_def
| wpc
| rule set_scheduler_action_dcorres[THEN corres_trivial])+
done
lemma corres_update_waiting_ntfn_do_notification_transfer:
"dcorres dc \<top>
(pspace_aligned and valid_objs and valid_mdb and pspace_distinct and valid_idle and valid_etcbs and
(st_tcb_at ((=) (Structures_A.thread_state.BlockedOnNotification epptr)) y) and
valid_ntfn (\<lparr>ntfn_obj = case ys of [] \<Rightarrow> Structures_A.ntfn.IdleNtfn | a # list \<Rightarrow> Structures_A.ntfn.WaitingNtfn ys, ntfn_bound_tcb = bound_tcb\<rparr> ))
(Endpoint_D.do_notification_transfer y)
(update_waiting_ntfn epptr (y # ys) bound_tcb badge)"
apply (simp add: Endpoint_D.do_notification_transfer_def update_waiting_ntfn_def assert_def)
apply (rule corres_dummy_return_pl)
apply (rule corres_split_keep_pfx[where r'="dc" and Q="%x. \<top>" and Q'="%x. \<top>"])
apply (rule corres_guard_imp,rule corres_dummy_set_notification,clarsimp+)
apply (rule dcorres_expand_pfx)
apply clarsimp
apply (frule_tac y = y in generates_pending_not_idle)
apply (clarsimp simp:st_tcb_at_def obj_at_def)
apply (drule_tac t = "tcb_state tcb" in sym)
apply (simp add:generates_pending_def)
apply (rule corres_guard_imp)
apply (rule dcorres_dc_rhs_noop_below_2_True[OF allI[OF possible_switch_to_dcorres]])
apply (rule corres_split[OF set_thread_state_corres])
apply (rule set_register_corres)
apply (wp)+
apply simp
apply (frule generates_pending_not_idle[where y = y])
apply (clarsimp simp: pred_tcb_at_def obj_at_def generates_pending_def)
apply (drule_tac t = "tcb_state tcb" in sym)
apply ((clarsimp simp:pred_tcb_at_def obj_at_def not_idle_thread_def split:Structures_A.thread_state.splits)+)[3]
apply (wp set_simple_ko_aligned set_ep_mdb set_simple_ko_valid_objs sts_typ_ats)
apply (simp add: not_idle_thread_def a_type_def ntfn_at_def2[symmetric, simplified])
apply (clarsimp simp: pred_tcb_at_def obj_at_def)
apply (drule valid_tcb_objs,erule get_tcb_rev)
apply (drule_tac t = "tcb_state tcb" in sym)
apply (clarsimp simp: valid_tcb_def valid_tcb_state_def obj_at_def)
done
lemma ntfn_waiting_set_spec:
"\<lbrakk>y\<in> ntfn_waiting_set epptr s\<rbrakk>\<Longrightarrow> st_tcb_at ((=) (Structures_A.thread_state.BlockedOnNotification epptr)) y s"
by (clarsimp simp: ntfn_waiting_set_def st_tcb_at_def obj_at_def)
lemma not_empty_list_not_empty_set:
"a \<noteq> [] \<Longrightarrow> \<exists>x. x \<in> (set a)"
apply (case_tac a)
apply auto
done
lemma set_thread_state_block_on_notification_corres:
"dcorres dc \<top>
(not_idle_thread thread and tcb_at thread and valid_etcbs)
(block_thread_on_ipc thread (PendingNtfnRecvCap w))
(set_thread_state thread (Structures_A.thread_state.BlockedOnNotification w))"
apply (simp add: block_thread_on_ipc_def)
apply (clarsimp simp: KHeap_D.set_cap_def set_thread_state_def)
apply (rule dcorres_dc_rhs_noop_below_2_True[OF allI[OF set_thread_state_ext_dcorres]])
apply (rule dcorres_gets_the)
apply (clarsimp, frule(1) valid_etcbs_get_tcb_get_etcb, clarsimp)
apply (clarsimp simp: not_idle_thread_def opt_object_tcb assert_def transform_tcb_def has_slots_def)
apply (clarsimp simp: update_slots_def object_slots_def)
apply (clarsimp simp: set_object_def get_object_def in_monad simpler_modify_def KHeap_D.set_object_def
get_def put_def bind_def corres_underlying_def return_def)
apply (clarsimp simp: transform_def transform_current_thread_def)
apply (intro ext conjI)
apply (case_tac x)
apply (clarsimp simp: |rule conjI)+
apply (clarsimp simp: transform_tcb_def transform_objects_def infer_tcb_pending_op_def)
apply ((fastforce simp: transform_objects_def restrict_map_def map_add_def tcb_at_def
transform_tcb_def tcb_slot_defs
dest!: get_tcb_SomeD get_etcb_SomeD)+)[2]
apply (clarsimp, frule(1) valid_etcbs_get_tcb_get_etcb, clarsimp)
apply (fastforce simp: not_idle_thread_def dest!:opt_object_tcb get_tcb_rev get_etcb_rev)
done
lemma insert_contr:
"\<lbrakk>\<forall>x. x \<notin> insert y Q\<rbrakk> \<Longrightarrow> P"
apply (drule_tac x = y in spec)
apply (clarsimp simp:insertI1)
done
lemma recv_signal_corres:
"cap = transform_cap cap' \<Longrightarrow>
dcorres dc \<top> (invs and not_idle_thread thread and st_tcb_at active thread and valid_etcbs)
(recv_signal thread cap)
(receive_signal thread cap' is_blocking)"
apply (clarsimp simp:receive_signal_def invs_def recv_signal_def corres_free_fail split:cap.splits)
apply (rename_tac word1 word2 rights)
apply (rule dcorres_expand_pfx)
apply (rule_tac Q' = "\<lambda>r. (=) s' and ko_at (kernel_object.Notification r) word1 and valid_ntfn r" in corres_symb_exec_r)
apply (rule dcorres_expand_pfx)
apply (clarsimp simp:obj_at_def is_ntfn_def)
apply (case_tac "ntfn_obj rv"; simp)
apply (clarsimp simp: ntfn_waiting_set_lift valid_state_def valid_ntfn_abstract_def
none_is_waiting_ntfn_def )
apply (case_tac is_blocking; simp)
apply (rule corres_guard_imp)
apply (rule corres_alternate1)
apply (rule corres_dummy_return_l)
apply (rule corres_split[OF set_thread_state_block_on_notification_corres])
apply (rule corres_dummy_set_notification,simp)
apply (wp|simp)+
apply (clarsimp simp:st_tcb_at_def tcb_at_def obj_at_def get_tcb_rev)
apply (simp add: do_nbrecv_failed_transfer_def)
apply (rule corres_guard_imp)
apply (rule corres_alternate2)
apply (rule corrupt_tcb_intent_as_user_corres)
apply simp
apply simp
(* WaitingNtfn *)
apply (clarsimp simp: ntfn_waiting_set_lift valid_state_def valid_ntfn_abstract_def
none_is_waiting_ntfn_def)
apply (case_tac is_blocking; simp)
apply (rule corres_guard_imp)
apply (rule corres_alternate1)
apply (rule corres_dummy_return_l)
apply (rule corres_split[OF set_thread_state_block_on_notification_corres])
apply (rule corres_dummy_set_notification,simp)
apply (wp|simp)+
apply (clarsimp simp:st_tcb_at_def tcb_at_def obj_at_def get_tcb_rev)
apply (simp add: do_nbrecv_failed_transfer_def)
apply (rule corres_guard_imp)
apply (rule corres_alternate2)
apply (rule corrupt_tcb_intent_as_user_corres)
apply simp
apply simp
(* Active NTFN *)
apply (clarsimp simp: ntfn_waiting_set_lift valid_state_def valid_ntfn_abstract_def
none_is_waiting_ntfn_def)
apply (rule corres_alternate2)
apply (rule corres_guard_imp )
apply (rule corres_dummy_return_l)
apply (rule corres_split[OF set_register_corres corres_dummy_set_notification])
apply (wp |clarsimp)+
apply (rule_tac Q'="\<lambda>r. ko_at (kernel_object.Notification r) word1 and valid_state" in hoare_strengthen_post)
apply (wp get_simple_ko_ko_at | clarsimp)+
apply (rule valid_objs_valid_ntfn_simp)
apply (clarsimp simp:valid_objs_valid_ntfn_simp valid_state_def valid_pspace_def)
apply (simp add:obj_at_def)
apply (clarsimp|wp)+
done
lemma bound_tcb_fold:
"\<lbrakk>kheap s x = Some (TCB tcb); tcb_bound_notification tcb = Some ntfnptr\<rbrakk> \<Longrightarrow> bound_tcb_at (\<lambda>ntfn. ntfn = Some ntfnptr) x s"
by (auto simp: pred_tcb_at_def obj_at_def)
lemma receive_blocked_waiting_syncs:
"\<lbrakk>valid_state s; valid_etcbs s; kheap s ntfnptr = Some (kernel_object.Notification ntfn);
ntfn_bound_tcb ntfn = Some a; get_tcb a s = Some aa; receive_blocked (tcb_state aa)\<rbrakk>
\<Longrightarrow> get_waiting_sync_bound_ntfn_threads ntfnptr (transform s) = {a}"
apply (clarsimp simp: get_waiting_sync_bound_ntfn_threads_def)
apply (frule get_notification_pick, simp)
apply (clarsimp simp: valid_ntfn_abstract_def ntfn_bound_set_def get_tcb_def
split: Structures_A.kernel_object.splits option.splits)
apply (rule set_eqI)
apply clarsimp
apply (rule iffI)
apply (clarsimp)
apply (rule_tac x=aa in exI)
apply (clarsimp simp: valid_state_def valid_pspace_def)
apply (frule (3) ntfn_bound_tcb_at[where P="\<lambda>a. a = Some ntfnptr"], simp)
apply (clarsimp simp: pred_tcb_at_def obj_at_def)
apply (clarsimp simp: transform_def transform_objects_def restrict_map_def map_add_def
split: option.splits)
apply (subst (asm) handy_if_lemma)+
apply clarsimp
apply (case_tac "x \<noteq> idle_thread s")
apply (clarsimp simp: transform_object_def
split: Structures_A.kernel_object.splits ARM_A.arch_kernel_obj.splits
option.splits nat.splits)
apply (frule_tac ptr=x in valid_etcbs_tcb_etcb, simp+)
apply (clarsimp simp add: transform_tcb_def tcb_pending_op_slot_def
tcb_boundntfn_slot_def infer_tcb_bound_notification_def
split: option.splits)
apply (frule_tac tcb="x2a" in bound_tcb_fold, simp)
apply (frule (3) bound_tcb_bound_notification_at)
apply clarsimp
apply clarsimp
apply clarsimp
apply (frule_tac tcb=t in bound_tcb_fold, simp)
apply (clarsimp simp: valid_state_def valid_pspace_def)
apply (frule (3) bound_tcb_bound_notification_at)
apply clarsimp
apply (drule get_tcb_rev)
apply (frule (1) valid_etcbs_get_tcb_get_etcb, clarsimp)
apply (clarsimp simp: transform_def)
apply (frule (1) transform_objects_tcb)
apply (clarsimp simp: valid_idle_def pred_tcb_at_def obj_at_def)
apply (clarsimp simp: transform_tcb_def tcb_pending_op_slot_def tcb_boundntfn_slot_def
infer_tcb_pending_op_def infer_tcb_bound_notification_def receive_blocked_def
split: Structures_A.thread_state.splits)
done
lemma dcorres_dat:
"dcorres dc \<top> (valid_etcbs and not_idle_thread a and valid_idle)
(do_notification_transfer a)
(do y \<leftarrow> set_thread_state a Structures_A.thread_state.Running;
y \<leftarrow> as_user a (set_register badge_register badge);
possible_switch_to a
od)"
apply (simp add: Endpoint_D.do_notification_transfer_def)
apply (rule dcorres_expand_pfx)
apply clarsimp
apply (rule corres_guard_imp)
apply (rule dcorres_dc_rhs_noop_below_2_True[OF allI[OF possible_switch_to_dcorres]])
apply (rule corres_split[OF set_thread_state_corres])
apply (rule set_register_corres)
apply (wp)+
apply simp
apply (clarsimp simp: not_idle_thread_def valid_state_def)
done
lemma not_idle_after_blocked_cancel_ipc:
"\<lbrace>valid_idle and not_idle_thread obj_id' and valid_objs and st_tcb_at ((=) state) obj_id'\<rbrace>
blocked_cancel_ipc state obj_id' \<lbrace>\<lambda>y. valid_idle\<rbrace>"
including no_pre
apply (simp add:blocked_cancel_ipc_def)
apply wp
apply (clarsimp simp:not_idle_thread_def)
apply (clarsimp simp:get_blocking_object_def)
apply (case_tac state)
apply clarsimp+
apply (clarsimp simp:valid_def return_def st_tcb_at_def valid_objs_def obj_at_def)
apply (drule_tac x = obj_id' in bspec)
apply (clarsimp simp:valid_obj_def valid_tcb_def valid_tcb_state_def)+
apply (drule_tac t = "tcb_state tcb" in sym)
apply (clarsimp simp:obj_at_def is_ep_def2)
apply (clarsimp simp:valid_def return_def st_tcb_at_def obj_at_def valid_objs_def)
apply (drule_tac x = obj_id' in bspec)
apply (clarsimp simp:valid_obj_def valid_tcb_def valid_tcb_state_def)+
apply (drule_tac t = "tcb_state tcb" in sym)
apply (clarsimp simp:obj_at_def is_ep_def2)
apply (clarsimp)+
done
lemma valid_idle_set_thread_state:
"\<lbrace>not_idle_thread xa and valid_idle :: det_state \<Rightarrow> bool\<rbrace> set_thread_state xa Structures_A.thread_state.Restart \<lbrace>\<lambda>xa. valid_idle\<rbrace>"
apply (simp add: set_thread_state_def not_idle_thread_def)
apply (simp add: set_object_def get_object_def)
apply wp
apply (clarsimp simp: not_idle_thread_def)
apply (clarsimp simp: obj_at_def dest!:get_tcb_SomeD)
apply (auto simp: valid_idle_def pred_tcb_at_def obj_at_def)
done
crunch tcb_sched_action
for not_idle_thread[wp]: "not_idle_thread a"
(wp: simp: not_idle_thread_def)
lemma tcb_sched_action_tcb_at_not_idle[wp]:
"\<lbrace>\<lambda>s. \<forall>x\<in>set list. tcb_at x s \<and> not_idle_thread x s\<rbrace> tcb_sched_action a b
\<lbrace>\<lambda>x s. \<forall>x\<in>set list. tcb_at x s \<and> not_idle_thread x s\<rbrace>"
by (wp hoare_Ball_helper)
lemma valid_idle_cancel_all_ipc:
"\<lbrace>valid_idle and valid_state :: det_state \<Rightarrow> bool\<rbrace> IpcCancel_A.cancel_all_ipc word1 \<lbrace>\<lambda>a. valid_idle\<rbrace>"
including classic_wp_pre
apply (simp add:cancel_all_ipc_def)
apply (wp|wpc|simp)+
apply (rename_tac queue list)
apply (rule_tac I = "(\<lambda>s. (queue = list) \<and> (\<forall>a\<in> set list. tcb_at a s \<and> not_idle_thread a s))
and ko_at (kernel_object.Endpoint Structures_A.endpoint.IdleEP) word1 and valid_idle" in mapM_x_inv_wp)
apply clarsimp
apply (wp KHeap_DR.tcb_at_set_thread_state_wp)
apply (rule hoare_conjI)
apply (rule_tac P="(\<lambda>s. (queue = list) \<and> (\<forall>a\<in> set list. tcb_at a s \<and> not_idle_thread a s))
and valid_idle and ko_at (kernel_object.Endpoint Structures_A.endpoint.IdleEP) word1"
in hoare_weaken_pre)
apply (wp | clarsimp)+
apply (rule set_thread_state_ko)
apply (simp add:is_tcb_def)
apply (wp valid_idle_set_thread_state)
apply (clarsimp simp:)+
apply wp
apply (rule hoare_vcg_conj_lift)
apply (rule hoare_Ball_helper)
apply (wp simple_obj_set_prop_at | clarsimp simp :get_ep_queue_def not_idle_thread_def)+
apply (rename_tac queue list)
apply (rule_tac I = "(\<lambda>s. (queue = list) \<and> (\<forall>a\<in> set list. tcb_at a s \<and> not_idle_thread a s))
and ko_at (kernel_object.Endpoint Structures_A.endpoint.IdleEP) word1 and valid_idle" in mapM_x_inv_wp)
apply clarsimp
apply (wp KHeap_DR.tcb_at_set_thread_state_wp)
apply (rule hoare_conjI)
apply (rule_tac P="(\<lambda>s. (queue = list) \<and> (\<forall>a\<in> set list. tcb_at a s \<and> not_idle_thread a s))
and valid_idle and ko_at (kernel_object.Endpoint Structures_A.endpoint.IdleEP) word1"
in hoare_weaken_pre)
apply (rule set_thread_state_ko)
apply (simp add:is_tcb_def)
apply (wp valid_idle_set_thread_state)
apply (clarsimp simp:)+
apply wp
apply (rule hoare_vcg_conj_lift)
apply (rule hoare_Ball_helper)
apply (wp simple_obj_set_prop_at | clarsimp simp :get_ep_queue_def not_idle_thread_def)+
apply (rule hoare_strengthen_post[OF get_simple_ko_sp])
apply (clarsimp | rule conjI)+
apply (clarsimp simp:obj_at_def valid_pspace_def valid_state_def)
apply (drule(1) valid_objs_valid_ep_simp)
apply (clarsimp simp:is_tcb_def valid_ep_def obj_at_def)
apply (drule(1) pending_thread_in_send_not_idle)
apply (simp add:not_idle_thread_def obj_at_def is_ep_def)+
apply (clarsimp | rule conjI)+
apply (clarsimp simp:obj_at_def valid_pspace_def valid_state_def)
apply (drule(1) valid_objs_valid_ep_simp)
apply (clarsimp simp:is_tcb_def valid_ep_def obj_at_def)
apply (drule(1) pending_thread_in_recv_not_idle)
apply (simp add:not_idle_thread_def obj_at_def is_ep_def)+
done
lemma valid_idle_cancel_all_signals:
"\<lbrace>valid_idle and valid_state :: det_state \<Rightarrow> bool\<rbrace> IpcCancel_A.cancel_all_signals word1 \<lbrace>\<lambda>a. valid_idle\<rbrace>"
including classic_wp_pre
apply (simp add:cancel_all_signals_def)
apply (wp|wpc|simp)+
apply (rename_tac list)
apply (rule_tac I = "(\<lambda>s. (\<forall>a\<in> set list. tcb_at a s \<and> not_idle_thread a s))
and ko_at (kernel_object.Notification (ntfn_set_obj ntfn Structures_A.ntfn.IdleNtfn)) word1 and valid_idle" in mapM_x_inv_wp)
apply clarsimp
apply (wp KHeap_DR.tcb_at_set_thread_state_wp)
apply (rule hoare_conjI)
apply (rule_tac P="(\<lambda>s. (\<forall>a\<in> set list. tcb_at a s \<and> not_idle_thread a s))
and valid_idle and ko_at (kernel_object.Notification (ntfn_set_obj ntfn Structures_A.ntfn.IdleNtfn)) word1"
in hoare_weaken_pre)
apply (rule set_thread_state_ko)
apply (simp add:is_tcb_def)
apply (wp valid_idle_set_thread_state)+
apply (clarsimp simp:)+
apply (rule hoare_vcg_conj_lift)
apply (rule hoare_Ball_helper)
apply (wp set_simple_ko_tcb| clarsimp simp : not_idle_thread_def)+
apply (wp simple_obj_set_prop_at)+
apply (rule hoare_strengthen_post[OF get_simple_ko_sp])
apply (clarsimp | rule conjI)+
apply (clarsimp simp:obj_at_def valid_pspace_def valid_state_def)
apply (drule(1) valid_objs_valid_ntfn_simp)
apply (clarsimp simp:is_tcb_def valid_ntfn_def obj_at_def)
apply (drule(1) pending_thread_in_wait_not_idle)
apply (simp add:not_idle_thread_def obj_at_def is_ntfn_def)+
done
lemma not_idle_after_reply_cancel_ipc:
"\<lbrace>not_idle_thread obj_id' and invs :: det_state \<Rightarrow> bool \<rbrace> reply_cancel_ipc obj_id'
\<lbrace>\<lambda>y. valid_idle\<rbrace>"
apply (simp add:reply_cancel_ipc_def)
apply wp
apply (simp add:cap_delete_one_def unless_def)
apply wp+
apply (simp add:IpcCancel_A.empty_slot_def)
apply (wp set_cap_idle | simp add: if_apply_def2 imp_conjR
| strengthen imp_consequent[where P="invs s" for s] imp_consequent[where P="valid_idle s" for s])+
apply (strengthen invs_valid_idle)
apply (wp thread_set_invs_trivial | simp add: ran_tcb_cap_cases)+
done
lemma not_idle_thread_cancel_signal:
"\<lbrace>not_idle_thread obj_id' and valid_idle\<rbrace> cancel_signal obj_id' word \<lbrace>\<lambda>r. valid_idle\<rbrace>"
including no_pre
apply (simp add:cancel_signal_def)
apply (wp valid_idle_set_thread_state|wpc)+
apply (rule hoare_strengthen_post[OF get_simple_ko_sp])
apply (clarsimp simp:not_idle_thread_def obj_at_def is_ntfn_def)
done
lemma cancel_ipc_valid_idle:
"\<lbrace>valid_idle and not_idle_thread obj_id' and invs :: det_state \<Rightarrow> bool\<rbrace> IpcCancel_A.cancel_ipc obj_id' \<lbrace>\<lambda>_. valid_idle\<rbrace>"
apply (clarsimp simp: cancel_ipc_def)
apply (wp not_idle_after_blocked_cancel_ipc not_idle_after_reply_cancel_ipc
not_idle_thread_cancel_signal | wpc | simp)+
apply (rule hoare_strengthen_post[where Q'="\<lambda>r. st_tcb_at ((=) r) obj_id'
and not_idle_thread obj_id' and invs"])
apply (wp gts_sp)
apply (clarsimp simp: invs_def valid_state_def valid_pspace_def not_idle_thread_def | rule conjI)+
done
lemma send_signal_corres:
notes if_split [split del]
shows
"ep_id = epptr \<Longrightarrow> dcorres dc \<top> (invs and valid_etcbs)
(Endpoint_D.send_signal ep_id)
(Ipc_A.send_signal epptr badge)"
apply (unfold Endpoint_D.send_signal_def Ipc_A.send_signal_def invs_def)
apply (rule dcorres_expand_pfx)
apply (clarsimp simp:get_simple_ko_def get_object_def gets_def bind_assoc split: if_split)
apply (rule dcorres_absorb_get_r)
apply (clarsimp simp:assert_def corres_free_fail partial_inv_def a_type_def the_equality
split:Structures_A.kernel_object.splits if_split)
apply (rule conjI, clarsimp+)
apply (rename_tac ntfn_ext)
apply (case_tac "ntfn_obj ntfn_ext", clarsimp)
apply (case_tac "ntfn_bound_tcb ntfn_ext", clarsimp)
\<comment> \<open>Idle, not bound\<close>
apply (rule corres_alternate1)
apply (rule dcorres_absorb_get_l)
apply (clarsimp)
apply (frule valid_objs_valid_ntfn_simp[rotated])
apply (simp add:valid_state_def valid_pspace_def)
apply (simp add:gets_def bind_assoc option_select_def)
apply (frule get_notification_pick,simp)
apply (clarsimp simp:ntfn_waiting_set_lift valid_state_def valid_ntfn_abstract_def none_is_waiting_ntfn_def)
apply (rule corres_guard_imp,rule corres_dummy_set_notification,simp+)[1]
\<comment> \<open>Idle, bound\<close>
apply (clarsimp simp: get_thread_state_def thread_get_def gets_the_def gets_def bind_assoc)
apply (rule dcorres_absorb_get_r)
apply (clarsimp simp: assert_opt_def corres_free_fail split: Structures_A.kernel_object.splits option.splits)
apply (case_tac "receive_blocked (tcb_state x2)")
\<comment> \<open>receive_blocked\<close>
apply (clarsimp)
apply (rule corres_alternate2)
apply (clarsimp simp: send_signal_bound_def gets_def)
apply (rule dcorres_absorb_get_l)
apply (clarsimp simp: receive_blocked_waiting_syncs)
apply (clarsimp simp: IpcCancel_A.cancel_ipc_def get_thread_state_def thread_get_def gets_the_def gets_def bind_assoc)
apply (rule dcorres_absorb_get_r)
apply (clarsimp simp: assert_opt_def corres_free_fail split: Structures_A.kernel_object.splits option.splits)
apply (simp add: receive_blocked_def)
apply (case_tac "tcb_state x2";clarsimp)
apply (rule corres_guard_imp)
apply (simp add: blocked_cancel_ipc_def bind_assoc)
apply (rule corres_symb_exec_r)
apply (rule corres_symb_exec_r)
apply (rule corres_symb_exec_r)
apply (rule corres_dummy_return_pl)
apply (rule corres_split[OF corres_dummy_set_sync_ep])
apply (simp add: when_def dc_def[symmetric])
apply (rule corres_split[OF set_thread_state_corres dcorres_dat])
apply (wp cancel_ipc_valid_idle
| simp add: not_idle_thread_def invs_def valid_state_def get_blocking_object_def)+
apply (clarsimp dest!:get_tcb_rev simp:invs_def ep_at_def2[symmetric, simplified])
apply (frule valid_tcb_if_valid_state[rotated], clarsimp simp: valid_state_def)
apply (fastforce dest!: get_tcb_SomeD
simp: receive_blocked_def valid_idle_def pred_tcb_at_def obj_at_def
valid_tcb_def valid_tcb_state_def infer_tcb_pending_op_def
split: Structures_A.thread_state.splits)
apply clarsimp
apply (rule corres_alternate1)
apply (rule dcorres_absorb_get_l)
apply (clarsimp)
apply (frule valid_objs_valid_ntfn_simp[rotated])
apply (simp add:valid_state_def valid_pspace_def)
apply (simp add:gets_def bind_assoc option_select_def)
apply (frule get_notification_pick,simp)
apply (clarsimp simp:ntfn_waiting_set_lift valid_state_def valid_ntfn_abstract_def none_is_waiting_ntfn_def)
apply (rule corres_guard_imp,rule corres_dummy_set_notification,simp+)[1]
\<comment> \<open>Waiting\<close>
apply (rule corres_alternate1)
apply (rule dcorres_absorb_get_l)
apply (clarsimp)
apply (frule valid_objs_valid_ntfn_simp[rotated])
apply (simp add:valid_state_def valid_pspace_def)
apply (simp add:gets_def bind_assoc option_select_def)
apply (frule get_notification_pick,simp)
apply (clarsimp simp:ntfn_waiting_set_lift valid_state_def valid_ntfn_abstract_def split: if_split)
apply (rule conjI)
apply (clarsimp simp: dest!:not_empty_list_not_empty_set)
apply (clarsimp simp:neq_Nil_conv)
apply (rule corres_guard_imp)
apply (rule select_pick_corres)
apply (rule corres_update_waiting_ntfn_do_notification_transfer)
apply (drule_tac s = "insert y (set ys)" in sym)
apply (clarsimp simp: image_def)
apply (drule_tac s = "insert y (set ys)" in sym)
apply (drule_tac A="ntfn_waiting_set epptr s'" and x = y in eqset_imp_iff)
apply (clarsimp simp:valid_pspace_def ntfn_waiting_set_def)
apply (clarsimp simp: pred_tcb_at_def obj_at_def valid_ntfn_def split:list.splits option.splits)
\<comment> \<open>Active\<close>
apply (rule corres_alternate1)
apply (rule dcorres_absorb_get_l)
apply (clarsimp)
apply (frule valid_objs_valid_ntfn_simp[rotated])
apply (simp add:valid_state_def valid_pspace_def)
apply (clarsimp simp:gets_def bind_assoc option_select_def)
apply (frule get_notification_pick,simp)
apply (clarsimp simp:ntfn_waiting_set_lift valid_state_def valid_ntfn_abstract_def none_is_waiting_ntfn_def)
apply (rule corres_guard_imp,rule corres_dummy_set_notification,simp+)
done
lemma set_thread_state_block_on_send_corres:
"dcorres dc \<top>
(not_idle_thread thread and valid_etcbs)
(block_thread_on_ipc thread
(PendingSyncSendCap epptr badge call can_grant can_grant_reply False))
(set_thread_state thread
(Structures_A.thread_state.BlockedOnSend epptr
\<lparr>sender_badge = badge, sender_can_grant = can_grant,
sender_can_grant_reply = can_grant_reply, sender_is_call = call\<rparr>))"
by (simp add:block_thread_on_ipc_def,rule block_thread_on_send_corres)
lemma set_thread_state_block_on_receive_corres:
"dcorres dc \<top> (not_idle_thread thread and valid_etcbs)
(block_thread_on_ipc thread (PendingSyncRecvCap epptr False can_grant))
(set_thread_state thread
(Structures_A.thread_state.BlockedOnReceive epptr \<lparr>receiver_can_grant = can_grant\<rparr>))"
apply (simp add:block_thread_on_ipc_def)
apply (rule block_thread_on_recv_corres)
done
lemma corres_setup_caller_cap:
"sender \<noteq> receiver \<Longrightarrow> dcorres dc \<top>
(valid_mdb and valid_idle and not_idle_thread sender and not_idle_thread receiver
and tcb_at sender and tcb_at receiver
and st_tcb_at (Not \<circ> halted) sender and valid_objs and valid_etcbs)
(inject_reply_cap sender receiver can_grant)
(setup_caller_cap sender receiver can_grant)"
apply (rule dcorres_expand_pfx)
apply (rule corres_guard_imp)
apply (simp add: inject_reply_cap_def setup_caller_cap_def split del: if_split)
apply (rule corres_split[OF set_thread_state_corres])
apply (rule reply_cap_insert_corres)
apply (simp add: not_idle_thread_def)+
apply (wp set_thread_state_it|simp )+
apply (rule hoare_vcg_conj_lift)
apply (clarsimp simp: not_idle_thread_def set_thread_state_def)
apply wp
apply (simp add: set_object_def get_object_def)
apply wp+
apply simp
apply (clarsimp simp: not_idle_thread_def tcb_at_def obj_at_def st_tcb_at_def)
apply (rule conjI|clarsimp simp: is_tcb_def)+
apply (drule valid_tcb_objs)
apply (erule get_tcb_rev)
apply (simp add: valid_tcb_state_def)
done
lemma seq_alt_when:"(do a \<leftarrow> when c (f \<sqinter> g); h a od) = ((do a\<leftarrow>when c f ; h a od)\<sqinter> (do a\<leftarrow>when c g; h a od))"
apply (clarsimp simp:when_def)
apply (subst alternative_bind_distrib)+
apply (clarsimp simp:alternative_def)
done
lemma evalMonad_mapM:
assumes as:"evalMonad (mapM f ls) s = Some v"
assumes "\<And>l. empty_when_fail (f l)"
assumes "\<And>P l. weak_det_spec P (f l)"
assumes wp: "\<And>s l. \<lbrace>(=) s\<rbrace> f l \<lbrace>\<lambda>r. (=) s\<rbrace>"
shows "v = (map (\<lambda>p. the (evalMonad (f p) s)) ls)"
using as
proof (induct ls arbitrary: v)
case Nil
thus ?case
by (clarsimp simp:evalMonad_def mapM_def sequence_def return_def)
next
case (Cons l ls)
show ?case
using Cons.prems
apply clarsimp
apply (clarsimp simp:mapM_Cons)
apply (subst (asm) evalMonad_compose)
apply (simp add: Cons assms)+
apply (clarsimp split:option.splits)
apply (subst (asm) evalMonad_compose)
apply (rule empty_when_fail_mapM)