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CNode_DR.thy
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(*
* Copyright 2014, NICTA
*
* This software may be distributed and modified according to the terms of
* the GNU General Public License version 2. Note that NO WARRANTY is provided.
* See "LICENSE_GPLv2.txt" for details.
*
* @TAG(NICTA_GPL)
*)
theory CNode_DR
imports Finalise_DR
begin
definition
translate_cnode_invocation :: "Invocations_A.cnode_invocation \<Rightarrow> cdl_cnode_invocation"
where
"translate_cnode_invocation x \<equiv> case x of
Invocations_A.InsertCall cap src_slot dest_slot
\<Rightarrow> Invocations_D.InsertCall (transform_cap cap)
(transform_cslot_ptr src_slot) (transform_cslot_ptr dest_slot)
| Invocations_A.MoveCall cap src_slot dest_slot
\<Rightarrow> Invocations_D.MoveCall (transform_cap cap)
(transform_cslot_ptr src_slot) (transform_cslot_ptr dest_slot)
| Invocations_A.RevokeCall slot \<Rightarrow> Invocations_D.RevokeCall (transform_cslot_ptr slot)
| Invocations_A.DeleteCall slot \<Rightarrow> Invocations_D.DeleteCall (transform_cslot_ptr slot)
| Invocations_A.SaveCall slot \<Rightarrow> Invocations_D.SaveCall (transform_cslot_ptr slot)
| Invocations_A.RecycleCall slot \<Rightarrow> Invocations_D.RecycleCall (transform_cslot_ptr slot)
| Invocations_A.RotateCall cap1 cap2 slot1 slot2 slot3
\<Rightarrow> Invocations_D.RotateCall (transform_cap cap1) (transform_cap cap2)
(transform_cslot_ptr slot1) (transform_cslot_ptr slot2)
(transform_cslot_ptr slot3)
"
lemma corres_assert_lhs:
"(F \<Longrightarrow> corres_underlying sr False r P P' (f ()) g)
\<Longrightarrow> corres_underlying sr False r (\<lambda>s. F \<and> P s) P' (assert F >>= f) g"
by (cases F, simp_all)
lemma ex_cte_cap_to_not_idle:
"\<lbrakk> ex_cte_cap_wp_to P p s; valid_global_refs s;
valid_idle s; valid_irq_node s \<rbrakk> \<Longrightarrow> fst p \<noteq> idle_thread s"
apply (cases p)
apply (clarsimp simp: ex_cte_cap_wp_to_def cte_wp_at_caps_of_state)
apply (drule(1) valid_global_refsD2)
apply (case_tac cap, simp_all add: cap_range_def global_refs_def)
apply (rename_tac word)
apply (clarsimp simp: valid_idle_def valid_irq_node_def st_tcb_at_def
obj_at_def is_cap_table_def)
apply (drule_tac x=word in spec, simp)
done
definition
"cap_insert_dest_original cap src_cap
= (if is_ep_cap cap then cap_ep_badge cap \<noteq> cap_ep_badge src_cap
else if is_aep_cap cap then cap_ep_badge cap \<noteq> cap_ep_badge src_cap
else if \<exists>irq. cap = cap.IRQHandlerCap irq then src_cap = cap.IRQControlCap else is_untyped_cap cap)"
lemma option_return_modify_modify:
"case_option (return ()) (\<lambda>x. modify (f x))
= (\<lambda>opt. modify (case_option id f opt))"
by (auto split: option.split simp: modify_id_return)
lemma update_cdt_modify:
"update_cdt f = modify (cdt_update f)"
apply (simp add: update_cdt_def set_cdt_modify gets_fold_into_modify)
apply (rule ext, simp add: simpler_modify_def)
done
lemma is_untyped_cap_transform_cap[simp]:
"Types_D.is_untyped_cap (transform_cap src_cap)
= is_untyped_cap src_cap"
apply (case_tac src_cap)
apply (simp_all add:transform_cap_def cap_type_simps)
apply (clarsimp simp:cap_type_simps split:arch_cap.splits)
done
lemma is_untyped_cap_eqD:
"Structures_A.is_untyped_cap src_cap
\<Longrightarrow> \<exists>ptr sz idx. src_cap = cap.UntypedCap ptr sz idx"
by (case_tac src_cap, simp_all)
lemma p2_less_minus:
"2 ^ sz - Suc 0 < 2 ^ sz"
by auto
lemma dcorres_set_untyped_cap_as_full:
"dcorres dc \<top> (K (cap_aligned cap) and cte_wp_at (op = src_cap) src
and valid_objs and not_idle_thread (fst src) and valid_idle and valid_etcbs)
(CSpace_D.set_untyped_cap_as_full (transform_cap src_cap) (transform_cap cap) (transform_cslot_ptr src))
(CSpace_A.set_untyped_cap_as_full src_cap cap src)"
apply (simp add:set_untyped_cap_as_full_def CSpace_D.set_untyped_cap_as_full_def
split del:split_if)
apply (case_tac "is_untyped_cap src_cap \<and> is_untyped_cap cap")
apply (rule dcorres_expand_pfx)
apply (rule corres_guard_imp)
apply (rule corres_if)
apply clarsimp
apply (clarsimp dest!:is_untyped_cap_eqD)
apply (drule(1) cte_wp_valid_cap)
apply (simp add:valid_cap_def cap_aligned_def)
apply (rule iffI)
apply clarsimp
apply (drule two_power_eq[THEN iffD1,rotated 2])
apply (simp add:valid_cap_def word_bits_def cap_aligned_def)
apply (simp add:valid_cap_def word_bits_def cap_aligned_def)
apply simp
apply simp
apply (rule_tac F = "is_untyped_cap src_cap \<and> is_untyped_cap cap" in corres_gen_asm)
apply (clarsimp dest!:is_untyped_cap_eqD)
apply (rule set_cap_corres)
apply (clarsimp simp:transform_cap_def free_range_of_untyped_def cap_aligned_def max_free_index_def
dest!:is_untyped_cap_eqD)
apply (cut_tac sz = sz in p2_less_minus)
apply simp
apply simp
apply simp
apply fastforce
apply (fastforce simp:not_idle_thread_def)
apply auto
done
lemma dcorres_opt_parent_set_parent_helper:
"dcorres dc \<top> P
(gets (opt_parent (transform_cslot_ptr src)) >>=
case_option (return ())
(\<lambda>parent. modify (\<lambda>s. s\<lparr>cdl_cdt := cdl_cdt s(transform_cslot_ptr child \<mapsto> parent)\<rparr>)))
g \<Longrightarrow>
dcorres dc \<top> (\<lambda>s. cdt s child = None \<and> cte_at child s \<and>
mdb_cte_at (swp (cte_wp_at (op \<noteq> cap.NullCap)) s) (cdt s) \<and> P s)
(gets (opt_parent (transform_cslot_ptr src)) >>=
case_option (return ()) (set_parent (transform_cslot_ptr child)))
g"
apply (clarsimp simp:gets_def set_parent_def bind_def
return_def get_def assert_def corres_underlying_def
fail_def
simpler_modify_def split:option.splits)
apply (drule_tac x = b in spec)
apply (intro conjI impI)
apply clarsimp
apply clarsimp
apply (clarsimp simp:KHeap_DR.cdl_cdt_transform)
apply (drule(2) transform_cdt_none)
apply simp
done
lemma dcorres_set_parent_helper:
"dcorres dc \<top> P
(modify (\<lambda>s. s\<lparr>cdl_cdt := cdl_cdt s(transform_cslot_ptr child \<mapsto> parent)\<rparr>))
g \<Longrightarrow>
dcorres dc \<top> (\<lambda>s. cdt s child = None \<and> cte_at child s \<and>
mdb_cte_at (swp (cte_wp_at (op \<noteq> cap.NullCap)) s) (cdt s) \<and> P s)
(set_parent (transform_cslot_ptr child) parent)
g"
apply (clarsimp simp:gets_def set_parent_def bind_def
return_def get_def assert_def corres_underlying_def
fail_def
simpler_modify_def split:option.splits)
apply (drule_tac x = b in spec)
apply (clarsimp simp:KHeap_DR.cdl_cdt_transform)
apply (drule(2) transform_cdt_none)
apply simp
done
lemma insert_cap_sibling_corres:
"dcorres dc \<top>
(\<lambda>s. cte_wp_at (\<lambda>cap'. \<not> should_be_parent_of cap' (is_original_cap s src)
cap (cap_insert_dest_original cap cap')) src s
\<and> cte_wp_at (op = cap.NullCap) sibling s
\<and> cte_at src s
\<and> not_idle_thread (fst sibling) s
\<and> not_idle_thread (fst src) s \<and> valid_etcbs s
\<and> valid_mdb s \<and> valid_idle s \<and> valid_objs s \<and> cap_aligned cap)
(insert_cap_sibling (transform_cap cap) (transform_cslot_ptr src) (transform_cslot_ptr sibling))
(cap_insert cap src sibling)"
apply (simp add: cap_insert_def[folded cap_insert_dest_original_def])
apply (simp add: insert_cap_sibling_def insert_cap_orphan_def bind_assoc
option_return_modify_modify
gets_fold_into_modify update_cdt_modify
set_original_def modify_modify
cap_insert_ext_def update_cdt_list_def set_cdt_list_modify
cong: option.case_cong)
apply (rule stronger_corres_guard_imp)
apply (rule corres_split[OF _ get_cap_corres])+
apply (rule corres_assert_lhs corres_assert_rhs)+
apply (rule_tac F = "src_cap = transform_cap src_capa" in corres_gen_asm)
apply simp
apply (rule corres_split[OF _ dcorres_set_untyped_cap_as_full])
apply (rule corres_split[OF _ set_cap_corres[OF refl refl]])
apply (rule dcorres_opt_parent_set_parent_helper)
apply (clarsimp simp:gets_fold_into_modify dc_def[symmetric]
option_return_modify_modify modify_modify bind_assoc
cong:option.case_cong)
apply (rule_tac P=\<top> and P'="(\<lambda>s. \<not> should_be_parent_of src_capa (is_original_cap s src) cap orig')
and cte_at src and cte_at sibling
and (\<lambda>s. mdb_cte_at (swp cte_at s) (cdt s))
and (\<lambda>s. cdt s sibling = None)" for orig'
in corres_modify)
apply (clarsimp split del: split_if)
apply (subst if_not_P, assumption)+
apply (clarsimp simp: opt_parent_def transform_def
transform_objects_def transform_cdt_def
transform_current_thread_def
transform_asid_table_def
split: option.split)
apply (clarsimp simp: fun_upd_def[symmetric] cong:if_cong)
apply (subgoal_tac "inj_on transform_cslot_ptr ({src, sibling} \<union> dom (cdt s') \<union> ran (cdt s'))")
apply (subst map_lift_over_f_eq map_lift_over_upd,
erule subset_inj_on, fastforce)+
apply (simp add: map_option_is_None[THEN trans [OF eq_commute]]
fun_eq_iff del: inj_on_insert)
apply (subst eq_commute [where a=None])
apply (subst map_lift_over_f_eq map_lift_over_upd,
erule subset_inj_on, fastforce)+
apply clarsimp
apply (rule_tac s=s' in transform_cdt_slot_inj_on_cte_at[where P=\<top>])
apply (auto simp: swp_def dest: mdb_cte_atD
elim!: ranE)[1]
apply ((wp set_cap_caps_of_state2 get_cap_wp static_imp_wp
| simp add: swp_def cte_wp_at_caps_of_state)+)
apply (wp set_cap_idle |
simp add:set_untyped_cap_as_full_def split del: split_if)+
apply (rule_tac Q = "\<lambda>r s. cdt s sibling = None
\<and> \<not> should_be_parent_of src_capa (is_original_cap s sibling) cap (cap_insert_dest_original cap src_capa)
\<and> mdb_cte_at (swp (cte_wp_at (op \<noteq> cap.NullCap)) s) (cdt s)"
in hoare_strengthen_post)
apply (wp set_cap_mdb_cte_at arch_update_cap_valid_mdb)
apply (clarsimp simp:mdb_cte_at_def should_be_parent_of_def
cte_wp_at_caps_of_state has_parent_cte_at is_physical_def
dest!:is_untyped_cap_eqD)
apply fastforce
apply (wp get_cap_wp set_cap_idle static_imp_wp
| simp add:set_untyped_cap_as_full_def
split del: split_if)+
apply (rule_tac Q = "\<lambda>r s. cdt s sibling = None
\<and> (\<exists>cap. caps_of_state s src = Some cap)
\<and> \<not> should_be_parent_of src_capa (is_original_cap s src) cap (cap_insert_dest_original cap src_capa)
\<and> mdb_cte_at (swp (cte_wp_at (op \<noteq> cap.NullCap)) s) (cdt s)"
in hoare_strengthen_post)
apply (wp set_cap_mdb_cte_at arch_update_cap_valid_mdb)
apply (clarsimp simp:mdb_cte_at_def should_be_parent_of_def
cte_wp_at_caps_of_state has_parent_cte_at is_physical_def
dest!:is_untyped_cap_eqD)
apply fastforce
apply (wp get_cap_wp set_cap_idle | simp)+
apply clarsimp
apply (rule conjI)
apply (clarsimp simp: not_idle_thread_def)
apply (clarsimp simp: caps_of_state_transform_opt_cap cte_wp_at_caps_of_state
transform_cap_def)
apply fastforce
apply (clarsimp simp: not_idle_thread_def cte_wp_at_caps_of_state)
apply (clarsimp simp: valid_mdb_def cte_wp_at_cases dest!:invs_mdb)
apply (case_tac "cdt s' sibling", safe intro!: mdb_cte_atI)
apply (auto dest: mdb_cte_atD is_untyped_cap_eqD
simp: valid_mdb_def swp_def cte_wp_at_caps_of_state not_idle_thread_def)
done
lemma insert_cap_child_corres:
"dcorres dc \<top>
(\<lambda>s. cte_wp_at (\<lambda>cap'. should_be_parent_of cap' (is_original_cap s src)
cap (cap_insert_dest_original cap cap')) src s
\<and> not_idle_thread (fst child) s \<and> valid_idle s \<and> valid_etcbs s
\<and> valid_mdb s \<and> not_idle_thread (fst src) s \<and> valid_objs s \<and> cap_aligned cap)
(insert_cap_child (transform_cap cap) (transform_cslot_ptr src) (transform_cslot_ptr child))
(cap_insert cap src child)"
apply (simp add: cap_insert_def[folded cap_insert_dest_original_def])
apply (simp add: insert_cap_child_def insert_cap_orphan_def bind_assoc
option_return_modify_modify
gets_fold_into_modify update_cdt_modify
set_original_def modify_modify
cap_insert_ext_def update_cdt_list_def set_cdt_list_modify
cong: option.case_cong)
apply (rule stronger_corres_guard_imp)
apply (rule corres_split[OF _ get_cap_corres])+
apply (rule_tac P="old_cap \<noteq> cdl_cap.NullCap" and P'="rv' \<noteq> cap.NullCap"
in corres_symmetric_bool_cases)
apply (clarsimp simp :transform_cap_def split:cap.splits arch_cap.splits)
apply (simp add:assert_def)
apply (rule corres_trivial)
apply (simp add:corres_free_fail)
apply (simp add:assert_def)
apply (rule corres_split[OF _ dcorres_set_untyped_cap_as_full])
apply (rule corres_split[OF _ set_cap_corres[OF refl refl]])
apply (rule dcorres_set_parent_helper)
apply (rule_tac P=\<top> and P'="(\<lambda>s. should_be_parent_of src_capa (orig s) cap orig')
and cte_at src and cte_at child
and (\<lambda>s. mdb_cte_at (swp cte_at s) (cdt s))" for orig orig'
in corres_modify)
apply (clarsimp split del: split_if)
apply (subst if_P, assumption)+
apply (clarsimp simp: opt_parent_def transform_def transform_asid_table_def
transform_objects_def transform_cdt_def
transform_current_thread_def)
apply (clarsimp simp: fun_upd_def[symmetric] cong:if_cong)
apply (subgoal_tac "inj_on transform_cslot_ptr ({src, child} \<union> dom (cdt s') \<union> ran (cdt s'))")
apply (subst map_lift_over_f_eq map_lift_over_upd,
erule subset_inj_on, fastforce)+
apply (simp add: fun_eq_iff)
apply (rule_tac s=s' in transform_cdt_slot_inj_on_cte_at[where P=\<top>])
apply (auto simp: swp_def dest: mdb_cte_atD
elim!: ranE)[1]
apply (wp set_cap_caps_of_state2 get_cap_wp static_imp_wp
| simp add: swp_def cte_wp_at_caps_of_state)+
apply (wp set_cap_idle |
simp add:set_untyped_cap_as_full_def split del:split_if)+
apply (rule_tac Q = "\<lambda>r s. not_idle_thread (fst child) s
\<and> should_be_parent_of src_capa (is_original_cap s child) cap (cap_insert_dest_original cap src_capa)
\<and> mdb_cte_at (swp (cte_wp_at (op \<noteq> cap.NullCap)) s) (cdt s)"
in hoare_strengthen_post)
apply (wp set_cap_mdb_cte_at | simp add:not_idle_thread_def)+
apply (clarsimp simp:mdb_cte_at_def cte_wp_at_caps_of_state)
apply fastforce
apply (wp get_cap_wp set_cap_idle static_imp_wp
| simp split del:split_if add:set_untyped_cap_as_full_def)+
apply (rule_tac Q = "\<lambda>r s. not_idle_thread (fst child) s
\<and> (\<exists>cap. caps_of_state s src = Some cap)
\<and> should_be_parent_of src_capa (is_original_cap s src) cap (cap_insert_dest_original cap src_capa)
\<and> mdb_cte_at (swp (cte_wp_at (op \<noteq> cap.NullCap)) s) (cdt s)"
in hoare_strengthen_post)
apply (wp set_cap_mdb_cte_at static_imp_wp | simp add:not_idle_thread_def)+
apply (clarsimp simp:mdb_cte_at_def cte_wp_at_caps_of_state)
apply fastforce
apply clarsimp
apply (wp get_cap_wp |simp)+
apply (clarsimp simp: not_idle_thread_def)
apply (clarsimp simp: caps_of_state_transform_opt_cap cte_wp_at_caps_of_state
transform_cap_def)+
apply (clarsimp simp: valid_mdb_def cte_wp_at_cases dest!:invs_mdb)
apply (case_tac "cdt s' child", safe intro!: mdb_cte_atI)
apply (auto dest: mdb_cte_atD is_untyped_cap_eqD
simp: valid_mdb_def swp_def cte_wp_at_caps_of_state not_idle_thread_def)
done
lemma reply_cap_insert_corres:
"sid \<noteq> did\<Longrightarrow>dcorres dc \<top>
(valid_idle and not_idle_thread did and valid_mdb and st_tcb_at (\<lambda>r. \<not> inactive r \<and> \<not> idle r) sid
and valid_etcbs and tcb_at did and tcb_at sid and valid_objs)
(insert_cap_child (cdl_cap.ReplyCap sid) (sid, tcb_replycap_slot)
(did, tcb_caller_slot))
(cap_insert (cap.ReplyCap sid False) (sid,tcb_cnode_index 2) (did,tcb_cnode_index 3))"
apply (rule corres_guard_imp)
apply (rule insert_cap_child_corres [where cap = "cap.ReplyCap sid False"
and src = "(sid, tcb_cnode_index 2)" and child = "(did, tcb_cnode_index 3)",
unfolded transform_cap_def transform_tcb_slot_simp
,simplified])
apply clarsimp+
apply (frule st_tcb_at_reply_cap_valid)
apply simp+
apply (frule tcb_caller_cap)
apply simp+
apply (clarsimp simp:cte_wp_at_caps_of_state should_be_parent_of_def)
apply (clarsimp simp: word_bits_def is_master_reply_cap_def
split:cap.splits)
apply (rule conjI)
apply (drule caps_of_state_cteD)+
apply (frule(1) cte_wp_tcb_cap_valid)
apply (clarsimp simp:valid_mdb_def reply_master_revocable_def)
apply (drule_tac x = "sid" in spec)
apply (drule_tac x = "tcb_cnode_index 2" in spec)
apply (clarsimp simp:cte_wp_at_caps_of_state is_master_reply_cap_def)
apply (drule caps_of_state_cteD)+
apply (frule(1) cte_wp_tcb_cap_valid[where p = "(did,tcb_cnode_index 3)"])
apply (rule conjI)
apply (clarsimp simp:valid_idle_def not_idle_thread_def)
apply (clarsimp simp:st_tcb_at_def2 obj_at_def)
apply (clarsimp simp:tcb_at_def dest!:get_tcb_SomeD)
apply (drule cte_wp_valid_cap)
apply simp
apply (simp add:valid_cap_def cap_aligned_def)
done
lemma invs_irq_node[elim!]:
"invs s \<Longrightarrow> valid_irq_node s"
by (clarsimp simp: invs_def valid_state_def)
lemma cap_move_swap_ext_def:
"(cap_move new_cap src_slot dest_slot :: (unit, unit) s_monad)=
do CSpaceAcc_A.set_cap new_cap dest_slot;
CSpaceAcc_A.set_cap cap.NullCap src_slot;
src_p \<leftarrow> gets (\<lambda>s. cdt s src_slot);
dest_p \<leftarrow> gets (\<lambda>s. cdt s dest_slot);
cdt \<leftarrow> gets cdt;
parent \<leftarrow> return $ cdt src_slot;
cdt' \<leftarrow> return $ cdt(dest_slot := parent, src_slot := None);
set_cdt
(\<lambda>r. if cdt' r = Some src_slot then Some dest_slot
else cdt' r);
is_original \<leftarrow> gets is_original_cap;
set_original dest_slot (is_original src_slot);
set_original src_slot False;
do_extended_op
(cap_move_ext src_slot dest_slot src_p dest_p)
od"
unfolding cap_move_def
apply (simp add: set_original_def gets_fold_into_modify)
done
lemma move_cap_corres:
"dcorres dc \<top> (cte_wp_at (op = cap.NullCap) p'
and invs and valid_etcbs and cte_wp_at (op \<noteq> cap.NullCap) p
and not_idle_thread (fst p')
and not_idle_thread (fst p))
(move_cap (transform_cap cap) (transform_cslot_ptr p)
(transform_cslot_ptr p'))
(cap_move cap p p')"
proof -
note inj_on_insert[iff del]
have insert_sub_walk:
"\<And>p p' S. p \<noteq> p' \<Longrightarrow> insert p S - {p'} = insert p (S - {p'})"
by auto
show ?thesis
apply (simp add: cap_move_def move_cap_def cap_move_swap_ext_def swap_parents_def
del: fun_upd_apply)
apply (rule stronger_corres_guard_imp)
apply (rule corres_split_nor)
apply (rule corres_split_nor)
apply (rule dcorres_gets_all_param)
apply (rule dcorres_gets_all_param)
apply (simp add: swap_parents_def
set_original_def set_cdt_modify
gets_fold_into_modify modify_modify
cap_move_ext_def bind_assoc update_cdt_list_def set_cdt_list_modify)
apply (rule conjI, clarsimp)
apply (rule_tac P'="cte_at p and cte_at p' and (\<lambda>s. cdt s p' = None)
and (\<lambda>s. p' \<notin> ran (cdt s)) and no_mloop o cdt
and (\<lambda>s. mdb_cte_at (swp cte_at s) (cdt s)) and K (p \<noteq> p')" and P=\<top>
in corres_inst)
apply (rule corres_modify)
apply (clarsimp simp: transform_def transform_current_thread_def
transform_cdt_def transform_asid_table_def
transform_objects_def)
apply clarsimp
apply (rule corres_modify)
apply (clarsimp simp: transform_def transform_current_thread_def
transform_cdt_def transform_asid_table_def
transform_objects_def)
apply (subgoal_tac "inj_on transform_cslot_ptr
({p, p'} \<union> dom (cdt s') \<union> ran (cdt s')) \<and> cdt s' p \<noteq> Some p")
apply (elim conjE)
apply (subst map_lift_over_if_eq)
apply (erule subset_inj_on, auto elim!: ranE split: split_if_asm)[1]
apply (rule sym)
apply (simp add: Fun.swap_def split del: split_if)
apply (subst map_lift_over_upd[unfolded fun_upd_def],
((erule subset_inj_on, auto elim!: ranE split: split_if_asm)[1]))+
apply (rule ext)
apply (cases p, cases p')
apply (simp split del: split_if)
apply simp
apply (subst subset_inj_on map_lift_over_f_eq[OF subset_inj_on],
assumption, fastforce)+
apply (simp add: inj_on_iff[where f="transform_cslot_ptr"]
ranI domI map_option_eq_Some[THEN trans [OF eq_commute]])
apply (auto simp: inj_on_iff[where f="transform_cslot_ptr"]
ranI domI,
auto simp: inj_on_iff[where f="transform_cslot_ptr"]
ranI domI map_lift_over_eq_Some)[1]
apply (clarsimp simp: no_cdt_loop_mloop)
apply (rule_tac s=s' in transform_cdt_slot_inj_on_cte_at[where P=\<top>])
apply (auto simp: swp_def dest: mdb_cte_atD
elim!: ranE)[1]
apply (rule set_cap_corres)
apply (simp add: transform_cap_def)
apply simp
apply (wp set_cap_caps_of_state2
| simp add: swp_def cte_wp_at_caps_of_state)+
apply (simp add: insert_cap_orphan_def)
apply (rule corres_dummy_return_pr[where b="()"])
apply (rule corres_split[where r'=dc])
apply (rule corres_assert_lhs)
apply simp
apply (rule set_cap_corres, simp+)[1]
apply (rule corres_gets_the)
apply simp
apply (rule corres_trivial, rule gets_symb_exec_l)
apply (wp set_cap_caps_of_state2 set_cap_idle)
apply clarsimp
apply (clarsimp simp: cte_wp_at_caps_of_state
caps_of_state_transform_opt_cap
transform_cap_def not_idle_thread_def)
apply (clarsimp simp: mdb_Null_None[OF _ invs_mdb])
apply (frule invs_mdb)
apply (clarsimp simp: cte_wp_at_caps_of_state valid_mdb_def)
apply (safe intro!: mdb_cte_atI)
apply (auto simp: swp_def cte_wp_at_caps_of_state not_idle_thread_def
dest: mdb_cte_atD elim!: ranE)
done
qed
crunch idle_thread[wp]: cap_move "\<lambda>s. P (idle_thread s)"
(wp: dxo_wp_weak)
lemma cap_null_reply_case_If:
"(case cap of cap.ReplyCap t b \<Rightarrow> f t b | cap.NullCap \<Rightarrow> g | _ \<Rightarrow> h)
= (if cap = cap.NullCap then g
else if is_reply_cap cap \<or> is_master_reply_cap cap
then f (obj_ref_of cap) (is_master_reply_cap cap)
else h)"
by (simp add: is_reply_cap_def is_master_reply_cap_def split: cap.split)
(* FIXME: move *)
lemma corres_if_rhs2:
"\<lbrakk> G \<Longrightarrow> corres_underlying sr nf rvr P Q a b;
\<not> G \<Longrightarrow> corres_underlying sr nf rvr P' Q' a c \<rbrakk>
\<Longrightarrow> corres_underlying sr nf rvr (P and P') (\<lambda>s. (G \<longrightarrow> Q s) \<and> (\<not> G \<longrightarrow> Q' s))
a (if G then b else c)"
by (rule corres_guard_imp, rule corres_if_rhs, simp+)
lemma transform_cap_is_Null:
"(transform_cap cap = cdl_cap.NullCap) = (cap = cap.NullCap)"
by (simp add: transform_cap_def split: cap.split arch_cap.split)
lemma delete_cap_corres:
"dcorres (dc \<oplus> dc) (\<lambda>_. True) (cap_table_at (length b) a and invs and valid_etcbs
and valid_pdpt_objs and ct_active)
(delete_cap (transform_cslot_ptr (a, b))) (cap_delete (a, b))"
apply (simp add:delete_cap_def cap_delete_def)
apply (subst rec_del_simps_ext)
apply (simp add:bindE_assoc)
apply (rule corres_guard_imp)
apply (rule corres_splitEE[OF _ dcorres_finalise_slot])
apply (clarsimp simp:bindE_assoc when_def)
apply (rule empty_slot_corres)
apply wp
apply (rule validE_validE_R)
apply (simp add:validE_def weak_valid_mdb_def)
apply (rule hoare_drop_imp)
apply (rule_tac Q = "\<lambda>r. invs and not_idle_thread a and valid_etcbs" in hoare_strengthen_post)
apply (wp rec_del_invs)
apply (simp add:not_idle_thread_def validE_def)
apply wp
apply (clarsimp simp:invs_def valid_state_def valid_mdb_def)
apply clarsimp+
apply (simp add:cap_table_at_cte_at)
apply (clarsimp simp:emptyable_def obj_at_def is_cap_table_def)
apply (clarsimp simp:is_tcb_def split:Structures_A.kernel_object.splits)
apply (clarsimp simp:invs_def valid_state_def)
apply (drule cnode_not_idle,simp)
apply (simp add:not_idle_thread_def)
done
lemma delete_cap_corres':
"dcorres (dc \<oplus> dc) (\<lambda>_. True) (cte_at (a,b) and invs and emptyable (a,b)
and not_idle_thread a and valid_pdpt_objs and valid_etcbs)
(delete_cap (transform_cslot_ptr (a, b))) (cap_delete (a, b))"
apply (simp add:delete_cap_def cap_delete_def)
apply (subst rec_del_simps_ext)
apply (simp add:bindE_assoc)
apply (rule corres_guard_imp)
apply (rule corres_splitEE[OF _ dcorres_finalise_slot])
apply (clarsimp simp:bindE_assoc when_def)
apply (rule empty_slot_corres)
apply wp
apply (rule validE_validE_R)
apply (simp add:validE_def weak_valid_mdb_def)
apply (rule hoare_drop_imp)
apply (rule_tac Q = "\<lambda>r. invs and not_idle_thread a and valid_etcbs" in hoare_strengthen_post)
apply (wp rec_del_invs)
apply (simp add:not_idle_thread_def validE_def)
apply wp
apply (clarsimp simp:invs_def valid_state_def valid_mdb_def)
apply (clarsimp simp:not_idle_thread_def)+
done
definition boolean_exception :: "'c + bool \<Rightarrow> 'a+'b \<Rightarrow> bool"
where "boolean_exception r r' \<equiv> case r' of Inr a \<Rightarrow> r = Inr True | Inl a \<Rightarrow> r = Inr False \<or> (\<exists>k. r = Inl k)"
lemma boolean_exception_corres:
"\<lbrakk>dcorres (boolean_exception) P P' a b\<rbrakk>
\<Longrightarrow> dcorres (dc\<oplus>dc) P P' (doE r \<leftarrow> a; unlessE r Monads_D.throw odE) b"
apply (clarsimp simp:bindE_def lift_def unlessE_def corres_underlying_def bind_def)
apply (erule allE, erule impE, rule conjI, assumption, assumption)
apply (drule_tac x = "(aa,baa)" in bspec)
apply simp
apply clarsimp
apply (rule bexI)
prefer 2
apply assumption
apply (clarsimp simp: boolean_exception_def validE_def valid_def lift_def
throwError_def returnOk_def return_def
split: sum.splits)
done
lemma cdl_Null_descendants:
"\<lbrakk>cte_wp_at (op = cap.NullCap) slot' s';valid_mdb s'\<rbrakk>
\<Longrightarrow> KHeap_D.descendants_of (transform_cslot_ptr slot') (transform s') = {}"
apply (subst descendants_of_eqv,clarsimp simp:valid_mdb_def,simp)
apply (erule cte_wp_at_weakenE,simp_all)
apply (erule mdb_Null_descendants,simp)
done
lemma empty_set_eq: "{x. False} = {}"
by auto
lemma preemption_corres:
"dcorres (dc \<oplus> dc) P P'
(Monads_D.throw \<sqinter> returnOk x)
preemption_point"
apply (simp add: preemption_point_def)
apply (auto simp: preemption_point_def o_def gets_def liftE_def whenE_def getActiveIRQ_def
corres_underlying_def select_def bind_def get_def bindE_def select_f_def modify_def
alternative_def throwError_def returnOk_def return_def lift_def
put_def do_machine_op_def
update_work_units_def wrap_ext_bool_det_ext_ext_def work_units_limit_def
work_units_limit_reached_def OR_choiceE_def reset_work_units_def mk_ef_def
split: option.splits kernel_object.splits)
done
lemma in_monad_cap_delete_invs:
"\<lbrakk> invs sfix;slot \<in> CSpaceAcc_A.descendants_of slot' (cdt sfix);
(r, s) \<in> fst (cap_delete slot sfix)\<rbrakk>
\<Longrightarrow> invs s"
using cap_delete_invs[unfolded valid_def,simplified]
apply clarsimp
apply (case_tac slot)
apply (drule_tac x = a in meta_spec)
apply (drule_tac x = b in meta_spec)
apply (drule_tac x = sfix in spec)
apply (clarsimp simp:emptyable_def)
apply (auto simp:reply_slot_not_descendant)
done
lemma descendants_emptyable:
"\<lbrakk>invs s; slot \<in> CSpaceAcc_A.descendants_of slot' (cdt s)\<rbrakk> \<Longrightarrow> emptyable slot s"
apply (case_tac slot)
apply (clarsimp simp:emptyable_def st_tcb_at_def obj_at_def is_tcb_def)
apply (clarsimp split:Structures_A.kernel_object.splits)
apply (frule reply_slot_not_descendant)
apply (simp add:tcb_at_def)
apply (rule exI)
apply (erule get_tcb_rev)
apply fastforce
done
lemma descendants_not_idle:
"\<lbrakk> invs sfix; (a, b) \<in> CSpaceAcc_A.descendants_of slot' (cdt sfix)\<rbrakk>
\<Longrightarrow> not_idle_thread a sfix"
apply (clarsimp simp:not_idle_thread_def invs_def valid_state_def valid_mdb_def valid_pspace_def)
apply (frule descendants_not_null_cap)
apply simp
apply (frule obj_ref_not_idle)
apply simp+
apply (erule cte_wp_at_weakenE)
apply simp
apply (clarsimp simp:cte_wp_at_caps_of_state)
apply (frule valid_idle_has_null_cap)
apply simp+
done
lemma valid_pdpt_objs_irq_state_independent[intro!, simp]:
"valid_pdpt_objs (s \<lparr> machine_state := machine_state s \<lparr> irq_state := f (irq_state (machine_state s)) \<rparr> \<rparr> )
= valid_pdpt_objs s"
by (simp add: obj_valid_pdpt_def)
lemma cdt_machine_state_independent[intro!, simp]:
"cdt (update_machine x s) = cdt s"
by (simp)
lemma cte_wp_at_machine_state[simp]:
"update_machine z s = s' \<Longrightarrow> cte_wp_at x y s' = cte_wp_at x y s"
by (drule sym, simp add: cte_wp_at_def)
lemma valid_mdb_machine_state[simp]:
"update_machine z s = s' \<Longrightarrow> valid_mdb s' = valid_mdb s"
by (drule sym, simp add: valid_mdb_def swp_def)
lemma valid_idle_machine_state[simp]:
"update_machine z s = s' \<Longrightarrow> valid_idle s' = valid_idle s"
by (drule sym, simp add: valid_idle_def)
lemma not_idle_thread_machine_state[simp]:
"update_machine z s = s'\<Longrightarrow> not_idle_thread x s' = not_idle_thread x s"
by (drule sym, simp add: not_idle_thread_def)
lemma dcorres_select_select_ext:
"\<forall>s'\<in>S'. \<exists>s\<in>S. rvr s s' \<Longrightarrow>
dcorres rvr \<top> \<top> (select S) (select_ext a S')"
by (clarsimp simp: select_def select_ext_def get_def bind_def return_def assert_def fail_def corres_underlying_def)
crunch valid_etcbs[wp]: cap_delete "valid_etcbs"
(wp: rec_del_preservation2 cap_revoke_preservation2)
lemma cap_revoke_corres_helper:
"dcorres boolean_exception (\<lambda>_. True)
(op = s' and invs and valid_pdpt_objs and valid_etcbs)
(monadic_trancl_preemptible
(\<lambda>y. do S \<leftarrow> gets (KHeap_D.descendants_of (transform_cslot_ptr slot'));
if S = {} then returnOk True
else do child \<leftarrow> select S;
cap \<leftarrow> KHeap_D.get_cap child;
doE y \<leftarrow> assertE (cap \<noteq> cdl_cap.NullCap);
y \<leftarrow> delete_cap child;
Monads_D.throw \<sqinter> returnOk False
odE
od
od)
False)
(cap_revoke slot')
"
proof (induct rule: cap_revoke.induct)
case (1 slot' sfix)
show ?case
apply (subst cap_revoke.simps)
apply (rule monadic_rewrite_corres2[where P =\<top>,simplified])
apply (rule Finalise_DR.monadic_trancl_preemptible_step)
apply (rule dcorres_expand_pfx)
apply (clarsimp simp:liftE_bindE)
apply (rule_tac Q'="\<lambda>cap. op = sfix and cte_wp_at (\<lambda>x. x = cap) slot'" in corres_symb_exec_r)
apply (rule dcorres_expand_pfx)
apply (rule_tac Q'="\<lambda>cdt' s. s = sfix \<and> cdt' = cdt sfix" in corres_symb_exec_r)
apply clarsimp
apply (rule dcorres_expand_pfx)
apply clarsimp
apply (case_tac "rv = cap.NullCap")
apply (simp add:gets_def bindE_def bind_assoc whenE_def)
apply (rule dcorres_absorb_get_l)
apply (subst cdl_Null_descendants)
apply (subst identity_eq, simp )
apply (drule invs_mdb, simp)
apply (clarsimp simp:empty_set_eq)+
apply (clarsimp simp:returnOk_def lift_def)
apply (rule corres_guard_imp)
apply (rule monadic_rewrite_corres2[where P=\<top> ,simplified])
apply (rule monadic_trancl_preemptible_return)
apply (rule corres_trivial)
apply (clarsimp simp:returnOk_def boolean_exception_def)+
apply (case_tac "CSpaceAcc_A.descendants_of slot' (cdt sfix) = {}")
apply (clarsimp simp:whenE_def empty_set_eq)
apply (simp add:gets_def bindE_def bind_assoc whenE_def)
apply (rule dcorres_absorb_get_l)
apply (subst descendants_of_eqv)
apply (drule invs_mdb_cte)
apply (drule sym, force simp: swp_def)
apply (rule cte_wp_at_weakenE)
apply simp+
apply (clarsimp simp:lift_def image_empty empty_set_eq )+
apply (rule corres_guard_imp)
apply (rule monadic_rewrite_corres2[where P=\<top> ,simplified])
apply (rule monadic_trancl_preemptible_return)
apply (rule corres_trivial)
apply (clarsimp simp:returnOk_def boolean_exception_def)+
apply (clarsimp simp:whenE_def empty_set_eq)
apply (subst gets_def)
apply (simp add: bind_assoc bindE_def)
apply (rule dcorres_absorb_get_l)
apply (subst descendants_of_eqv)
apply (drule invs_mdb_cte)
apply (drule sym, force simp: swp_def)
apply (rule cte_wp_at_weakenE, simp+)
apply (clarsimp simp:bind_assoc)
apply (rule corres_underlying_split[where r'="\<lambda>slot slot'. slot = transform_cslot_ptr slot'"
and P =" \<lambda>r. \<top>" and P'="\<lambda>r s. s = sfix \<and> r \<in> (CSpaceAcc_A.descendants_of slot' (cdt sfix)) \<and> (r, s) \<in> fst ((select_ext (next_revoke_cap slot') (CSpaceAcc_A.descendants_of slot' (cdt sfix))) sfix)"])
apply (rule corres_guard_imp[OF dcorres_select_select_ext])
apply (subst descendants_of_eqv)
apply (drule invs_mdb_cte)
apply (simp add: swp_def)
apply (erule cte_wp_at_weakenE, simp)
apply (simp,blast)
apply simp+
apply (wp select_wp,(clarsimp simp: select_ext_def in_monad)+)
apply (rule dcorres_expand_pfx)
apply (rule_tac r'="\<lambda>cap cap'. cap = transform_cap cap'"
and P ="\<lambda>r. \<top>" and P'="\<lambda>r s. cte_wp_at (\<lambda>x. x = r) (aa,ba) s \<and> s = sfix" in corres_underlying_split)
apply (rule corres_guard_imp[OF get_cap_corres],simp+)
apply (case_tac "next_revoke_cap slot' sfix")
apply clarsimp
apply (frule(1) descendants_not_idle)
apply (simp add:invs_def valid_state_def)
apply (wp get_cap_cte_wp_at | clarsimp)+
apply (clarsimp simp:assertE_def corres_free_fail returnOk_def lift_def)
apply (simp add:bindE_def[symmetric] return_returnOk)
apply (simp add:bindE_assoc)
apply (simp add:bindE_def)
apply (rule dcorres_expand_pfx)
apply (rule_tac r'= "dc\<oplus>dc" and P =" \<lambda>r. \<top>"
and P'="\<lambda>r s. (r,s)\<in> fst (cap_delete (aa,ba) sfix)" in corres_underlying_split)
apply (case_tac "next_revoke_cap slot' sfix")
apply clarsimp
apply (rule corres_guard_imp[OF delete_cap_corres'])
apply clarsimp+
apply (intro conjI, erule cte_wp_at_weakenE,simp)
apply (rule descendants_emptyable,simp+)
apply (rule descendants_not_idle,simp+)
apply (clarsimp|wp)+
apply (fastforce simp:valid_def)
apply (clarsimp simp:bindE_def[symmetric] lift_def)
apply (case_tac rva)
apply (clarsimp simp:boolean_exception_def)+
apply (simp add:bindE_def)
apply (rule dcorres_expand_pfx)
apply (rule_tac r'= "dc \<oplus> dc" and P =" \<lambda>r s. case r of Inr a \<Rightarrow> a = False | _ \<Rightarrow> True"
and P' = "\<lambda>r s. (case r of Inr rva \<Rightarrow> (r , s) \<in> fst (Exceptions_A.preemption_point s') | _ \<Rightarrow> True)"
in corres_underlying_split)
apply (rule corres_guard_imp[OF corres_trivial[OF preemption_corres]])
apply simp+
apply (rule alternative_valid)
apply (simp add:valid_def throwError_def return_def)
apply (simp add:valid_def returnOk_def return_def)
apply (clarsimp simp: valid_def)
apply clarsimp
apply (case_tac rva)
apply (clarsimp simp:lift_def boolean_exception_def)
apply (rule dcorres_expand_pfx)
apply (clarsimp simp:lift_def assertE_def[symmetric] bindE_def[symmetric])
apply (rule corres_guard_imp)
apply (rule_tac rv = rv and rva = "cdt sfix" and rvb = "descendants_of slot' (cdt sfix)"
and rvc = "(aa,ba)" and rvd = rv' and rve = "()" and rvf = "()"
and st = sfix and sta = sfix and stb = sfix and stc = sfix
and std = sfix and ste = sfix and stf = s' and stg = s'a in "1")
apply ((clarsimp simp:without_preemption_def cte_wp_at_def in_monad select_def select_ext_def | rule refl)+)
apply (erule use_valid[OF _ preemption_point_inv'])
apply simp
apply simp
apply (simp add: in_monad_cap_delete_invs use_valid [OF _ cap_delete_valid_pdpt_objs] use_valid [OF _ cap_delete_valid_etcbs] select_def)
apply (simp add: gets_def valid_def bind_def get_def return_def)
apply ((wp get_cap_cte_wp_at|clarsimp)+)
done
qed
lemma revoke_cap_spec_corres:
"dcorres (dc \<oplus> dc) \<top> (op = s' and invs and valid_pdpt_objs and valid_etcbs)
(revoke_cap (transform_cslot_ptr slot')) (cap_revoke slot')"
apply (subst revoke_cap_def)
apply (rule boolean_exception_corres)
unfolding K_def
apply (clarsimp simp:without_preemption_def liftE_bindE)
apply (rule cap_revoke_corres_helper)
done
lemma revoke_cap_corres:
"slot = transform_cslot_ptr slot'
\<Longrightarrow> dcorres (dc\<oplus>dc) \<top> (invs and valid_pdpt_objs and valid_etcbs)
(revoke_cap (slot)) (cap_revoke (slot'))"
apply (rule dcorres_expand_pfx)
apply clarsimp
apply (rule corres_guard_imp[OF revoke_cap_spec_corres])
apply simp+
done
lemma ep_cancel_badged_sends_def':
"CSpace_D.ep_cancel_badged_sends ep badge =
( do s\<leftarrow>get;
tcb_filter_modify {x. \<exists>tcb. (cdl_objects s) x = Some (Tcb tcb) \<and> is_thread_blocked_on_endpoint tcb ep}
(\<lambda>x. (case x of Some (Tcb tcb ) \<Rightarrow>
if get_tcb_ep_badge tcb = Some badge then Some (Tcb (remove_pending_operation tcb cdl_cap.RestartCap))
else x))
od)"
apply (simp add:CSpace_D.ep_cancel_badged_sends_def get_def simpler_modify_def tcb_filter_modify_def)
apply (clarsimp simp:bind_def)
apply (rule ext)
apply clarsimp
apply (case_tac s)
apply clarsimp
apply (rule ext)
apply (clarsimp simp:option_map_def split:option.splits cdl_object.split)
done
lemma ep_cancel_badged_sends_def'':
"CSpace_D.ep_cancel_badged_sends ep badge =
( do s\<leftarrow>get;
tcb_filter_modify {x. \<exists>tcb. (cdl_objects s) x = Some (Tcb tcb) \<and> is_thread_blocked_on_endpoint tcb ep
\<and> get_tcb_ep_badge tcb = Some badge}
(\<lambda>x. (case x of Some (Tcb tcb) \<Rightarrow> Some (Tcb (remove_pending_operation tcb cdl_cap.RestartCap))))
od)"
apply (simp add:CSpace_D.ep_cancel_badged_sends_def get_def simpler_modify_def tcb_filter_modify_def)
apply (clarsimp simp:bind_def)
apply (rule ext)
apply clarsimp
apply (case_tac s)
apply clarsimp
apply (rule ext)
apply (clarsimp simp:option_map_def split:option.splits cdl_object.split)
done
lemma corres_mapM_to_mapM_x:
"corres_underlying sr fl dc P P' f (mapM_x g xs)
\<Longrightarrow> corres_underlying sr fl dc P P' f (mapM g xs)"
by (simp add: mapM_x_mapM liftM_def[symmetric])
lemma ep_waiting_set_recv_upd_kh:
"ep_at epptr s \<Longrightarrow> (ep_waiting_set_recv epptr (update_kheap (kheap s(epptr \<mapsto> kernel_object.Endpoint X)) s))
= (ep_waiting_set_recv epptr s)"
apply (rule set_eqI)
apply (clarsimp simp:ep_waiting_set_recv_def obj_at_def is_ep_def)
done
lemma ep_waiting_set_send_upd_kh:
"ep_at epptr s \<Longrightarrow> (ep_waiting_set_send epptr (update_kheap (kheap s(epptr \<mapsto> kernel_object.Endpoint X)) s))
= (ep_waiting_set_send epptr s)"
apply (rule set_eqI)
apply (clarsimp simp:ep_waiting_set_send_def obj_at_def is_ep_def)
done
lemma aep_waiting_set_upd_kh:
"ep_at epptr s \<Longrightarrow> (aep_waiting_set epptr (update_kheap (kheap s(epptr \<mapsto> kernel_object.Endpoint X)) s))
= (aep_waiting_set epptr s)"
apply (rule set_eqI)
apply (clarsimp simp:aep_waiting_set_def obj_at_def is_ep_def)
done
lemma dcorres_ep_cancel_badge_sends:
notes hoare_post_taut[wp]
shows
"dcorres dc \<top> (valid_state and valid_etcbs)
(CSpace_D.ep_cancel_badged_sends epptr word2)
(IpcCancel_A.ep_cancel_badged_sends epptr word2)"
apply (clarsimp simp:IpcCancel_A.ep_cancel_badged_sends_def)
apply (rule dcorres_expand_pfx)
apply clarsimp
apply (rule_tac Q' = "\<lambda>r. op = s' and ko_at (kernel_object.Endpoint r) epptr and valid_ep r"
in corres_symb_exec_r)
apply (case_tac rv)
apply (clarsimp simp: ep_cancel_badged_sends_def')
apply (rule dcorres_absorb_get_l)
apply (rule corres_guard_imp[OF filter_modify_empty_corres])
apply (clarsimp simp:invs_def)
apply (frule_tac epptr = epptr in get_endpoint_pick ,simp add:obj_at_def)
apply (cut_tac ep = epptr and s = "transform s'a" in is_thread_blocked_on_sth)
apply (drule_tac x = x in eqset_imp_iff)
apply (clarsimp simp: valid_state_def valid_ep_abstract_def none_is_sending_ep_def
none_is_receiving_ep_def)
apply (clarsimp simp: aep_waiting_set_lift ep_waiting_set_send_lift
ep_waiting_set_recv_lift)
apply (drule ep_not_waiting_aep[rotated])
apply (simp add:valid_pspace_def)
apply auto[1]
apply simp+
apply (rule dcorres_expand_pfx)
apply (rule_tac
Q'="\<lambda>r s. s = (update_kheap ((kheap s')(epptr\<mapsto> (Endpoint Structures_A.endpoint.IdleEP))) s')"
in dcorres_symb_exec_r)
apply (clarsimp simp: filterM_mapM ep_cancel_badged_sends_def')
apply (rule dcorres_absorb_get_l)
apply (rule corres_dummy_return_l)
apply (rule corres_underlying_split[where r'=dc])
apply (rule corres_mapM_to_mapM_x)
apply (rule corres_guard_imp)
apply (rule_tac lift_func = id in set_list_modify_corres_helper)
apply (simp add:valid_ep_def)
apply (simp add:inj_on_def)
apply (simp add:is_thread_blocked_on_sth[simplified])
apply (subgoal_tac "valid_idle s' \<and> valid_etcbs s'")
apply (clarsimp simp: aep_waiting_set_lift ep_waiting_set_send_lift
ep_waiting_set_recv_lift)
apply (subst aep_waiting_set_upd_kh)
apply (simp add:obj_at_def is_ep_def)
apply (subst ep_waiting_set_send_upd_kh)
apply (simp add:obj_at_def is_ep_def)
apply (subst ep_waiting_set_recv_upd_kh)
apply (simp add:obj_at_def is_ep_def)
apply (frule_tac epptr = epptr in get_endpoint_pick)
apply (simp add:obj_at_def)
apply (clarsimp simp:valid_ep_abstract_def none_is_receiving_ep_def)
apply (subst ep_not_waiting_aep)
apply (simp add:valid_state_def valid_pspace_def)
apply (simp add:obj_at_def)
apply (rule set_eqI)
apply (clarsimp simp:image_def)
apply (rule conjI)
apply (clarsimp simp:valid_idle_def valid_state_def st_tcb_at_def obj_at_def)
apply (clarsimp simp: obj_at_def, frule(1) valid_etcbs_ko_etcb)
apply (clarsimp simp: valid_etcbs_def obj_at_def st_tcb_at_def st_tcb_at_kh_def
obj_at_kh_def is_etcb_at_def)
apply (clarsimp simp: tcb_filter_modify_def bind_assoc thread_get_def
get_thread_state_def)
apply (rule_tac
Q'="\<lambda>s. valid_idle s \<and> valid_etcbs s \<and> not_idle_thread a s
\<and> idle_thread s = idle_thread s'a \<and>
st_tcb_at (\<lambda>ts. \<exists>pl. ts = Structures_A.thread_state.BlockedOnSend epptr pl) a s"
in corres_guard_imp[where Q=\<top>])
apply (rule dcorres_absorb_gets_the)
apply (clarsimp simp:st_tcb_at_def obj_at_def dest!:get_tcb_SomeD)
apply (rule conjI)
apply (clarsimp simp:set_thread_state_def bind_assoc | rule conjI)+
apply (rule dcorres_absorb_gets_the)
apply (rule corres_guard_imp)
apply (rule_tac P="op = (transform s'b)" and P'="op = s'b"
and Q=\<top> and Q'=\<top> in corres_split_noop_rhs2)
apply (rule dcorres_rhs_noop_above_True[OF set_thread_state_ext_dcorres])
apply (rule dcorres_rhs_noop_above_True[OF tcb_sched_action_dcorres])
apply simp
apply (clarsimp simp:set_object_def simpler_modify_def get_def return_def
bind_def put_def corres_underlying_def)
apply (clarsimp simp:transform_def transform_cdt_kheap_update
transform_current_thread_def)
apply (rule ext)
apply (frule(1) valid_etcbs_get_tcb_get_etcb)
apply (clarsimp simp:transform_objects_tcb not_idle_thread_def )
apply (clarsimp simp:transform_tcb_def transform_objects_def
get_tcb_ep_badge_def remove_pending_operation_def get_tcb_SomeD get_etcb_SomeD)
apply (clarsimp simp: restrict_map_def map_add_def)
apply (wp | simp)+
apply (clarsimp simp: simpler_modify_def corres_underlying_def return_def
transform_def
dest!: get_tcb_rev)