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CNode_AC.thy
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(*
* Copyright 2020, Data61, CSIRO (ABN 41 687 119 230)
*
* SPDX-License-Identifier: GPL-2.0-only
*)
theory CNode_AC
imports ArchAccess_AC
begin
section\<open>CNode-specific AC.\<close>
(* FIXME: Move. *)
lemma tcb_domain_map_wellformed_ekheap[intro!, simp]:
"ekheap (P s) = ekheap s \<Longrightarrow> tcb_domain_map_wellformed aag (P s) = tcb_domain_map_wellformed aag s"
by (simp add: tcb_domain_map_wellformed_aux_def get_etcb_def)
(* FIXME: for some reason crunch does not discover the right precondition *)
lemma set_cap_integrity_autarch:
"\<lbrace>integrity aag X st and K (is_subject aag (fst slot))\<rbrace> set_cap cap slot \<lbrace>\<lambda>_. integrity aag X st\<rbrace>"
by (wpsimp simp: set_cap_def wp: set_object_integrity_autarch get_object_wp)
lemma integrity_cdt_list_as_list_integ:
"cdt_list_integrity_state aag st s =
list_integ (cdt_change_allowed aag {pasSubject aag} (cdt st) (tcb_states_of_state st)) st s"
by (fastforce elim: integrity_cdt_listE list_integE intro: list_integI integrity_cdt_list_intros)
crunches cap_swap_ext,cap_move_ext,empty_slot_ext
for ekheap[wp]: "\<lambda>s. P (ekheap s)"
and ready_queues[wp]: "\<lambda>s. P (ready_queues s)"
crunches set_untyped_cap_as_full
for integrity_autarch: "integrity aag X st"
locale CNode_AC_1 =
fixes aag :: "'a PAS"
and val_t :: "'b"
assumes sata_cdt_update[simp]:
"\<And>f. state_asids_to_policy aag (cdt_update f s) = state_asids_to_policy aag s"
and sata_is_original_cap_update[simp]:
"\<And>f. state_asids_to_policy aag (is_original_cap_update f s) = state_asids_to_policy aag s"
and sata_interrupt_states_update[simp]:
"\<And>f. state_asids_to_policy aag (interrupt_states_update f s) = state_asids_to_policy aag s"
and sata_machine_state_update[simp]:
"\<And>f. state_asids_to_policy aag (machine_state_update f s) = state_asids_to_policy aag s"
and sata_update:
"\<lbrakk> pas_wellformed aag; cap_links_asid_slot aag (pasObjectAbs aag (fst ptr)) cap;
state_asids_to_policy_arch aag (caps :: cslot_ptr \<Rightarrow> cap option) as vrefs \<subseteq> pasPolicy aag \<rbrakk>
\<Longrightarrow> state_asids_to_policy_arch aag (caps(ptr \<mapsto> cap)) as vrefs \<subseteq> pasPolicy aag"
and sata_update2:
"\<lbrakk> pas_wellformed aag; cap_links_asid_slot aag (pasObjectAbs aag (fst ptr)) cap;
cap_links_asid_slot aag (pasObjectAbs aag (fst ptr')) cap';
state_asids_to_policy_arch aag caps (as :: arch_state) vrefs \<subseteq> pasPolicy aag \<rbrakk>
\<Longrightarrow> state_asids_to_policy_arch aag (caps(ptr \<mapsto> cap, ptr' \<mapsto> cap')) as vrefs \<subseteq> pasPolicy aag"
and state_vrefs_tcb_upd:
"\<lbrakk> pspace_aligned s; valid_vspace_objs s; valid_arch_state s; tcb_at tptr s \<rbrakk>
\<Longrightarrow> state_vrefs (s\<lparr>kheap := kheap s(tptr \<mapsto> TCB tcb)\<rparr>) = state_vrefs s"
and state_vrefs_simple_type_upd:
"\<lbrakk> pspace_aligned s; valid_vspace_objs s; valid_arch_state s;
ko_at ko p s; is_simple_type ko; a_type ko = a_type (f (val :: 'b)) \<rbrakk>
\<Longrightarrow> state_vrefs (s\<lparr>kheap := kheap s(p \<mapsto> f val)\<rparr>) = state_vrefs s"
and a_type_arch_object_not_tcb[simp]:
"a_type (ArchObj arch_kernel_obj) \<noteq> ATCB"
and set_cap_state_vrefs:
"\<And>P. \<lbrace>pspace_aligned and valid_vspace_objs and valid_arch_state and (\<lambda>s. P (state_vrefs s))\<rbrace>
set_cap cap slot
\<lbrace>\<lambda>_ s :: det_ext state. P (state_vrefs s)\<rbrace>"
and set_cdt_state_vrefs[wp]:
"\<And>P. set_cdt t \<lbrace>\<lambda>s :: det_ext state. P (state_vrefs s)\<rbrace>"
and set_cdt_state_asids_to_policy[wp]:
"\<And>P. set_cdt t \<lbrace>\<lambda>s. P (state_asids_to_policy aag s)\<rbrace>"
and arch_post_cap_deletion_integrity[wp]:
"arch_post_cap_deletion acap \<lbrace>integrity aag X st\<rbrace>"
and arch_post_cap_deletion_cur_domain[wp]:
"\<And>P. arch_post_cap_deletion acap \<lbrace>\<lambda>s. P (cur_domain s)\<rbrace>"
and arch_finalise_cap_cur_domain:
"\<And>P. arch_finalise_cap acap final \<lbrace>\<lambda>s. P (cur_domain s)\<rbrace>"
and prepare_thread_delete_cur_domain:
"\<And>P. prepare_thread_delete p \<lbrace>\<lambda>s. P (cur_domain s)\<rbrace>"
and maskInterrupt_underlying_memory[wp]:
"\<And>P. maskInterrupt m irq \<lbrace>\<lambda>s. P (underlying_memory s)\<rbrace>"
and maskInterrupt_device_state[wp]:
"\<And>P. maskInterrupt m irq \<lbrace>\<lambda>s. P (device_state s)\<rbrace>"
and cap_insert_ext_extended_list_integ_lift:
"\<And>Q a b c d e.
\<lbrakk> \<lbrace>list_integ (cdt_change_allowed aag {pasSubject aag} (cdt st) (tcb_states_of_state st)) st and Q\<rbrace>
cap_insert_ext a b c d e
\<lbrace>\<lambda>_. list_integ (cdt_change_allowed aag {pasSubject aag} (cdt st) (tcb_states_of_state st)) st\<rbrace>;
\<And>P. cap_insert_ext a b c d e \<lbrace>\<lambda>s. P (ekheap s)\<rbrace>; \<And>P. cap_insert_ext a b c d e \<lbrace>\<lambda>s. P (ready_queues s)\<rbrace> \<rbrakk>
\<Longrightarrow> \<lbrace>integrity aag X st and Q\<rbrace> cap_insert_ext a b c d e \<lbrace>\<lambda>_. integrity aag X st\<rbrace>"
and cap_move_ext_list_integ_lift:
"\<And>Q a b c d.
\<lbrakk> \<lbrace>list_integ (cdt_change_allowed aag {pasSubject aag} (cdt st) (tcb_states_of_state st)) st and Q\<rbrace>
cap_move_ext a b c d
\<lbrace>\<lambda>_. list_integ (cdt_change_allowed aag {pasSubject aag} (cdt st) (tcb_states_of_state st)) st\<rbrace>;
\<And>P. cap_move_ext a b c d \<lbrace>\<lambda>s. P (ekheap s)\<rbrace>; \<And>P. cap_move_ext a b c d \<lbrace>\<lambda>s. P (ready_queues s)\<rbrace> \<rbrakk>
\<Longrightarrow> \<lbrace>integrity aag X st and Q\<rbrace> cap_move_ext a b c d \<lbrace>\<lambda>_. integrity aag X st\<rbrace>"
and cap_swap_ext_extended_list_integ_lift:
"\<And>Q a b c d.
\<lbrakk> \<lbrace>list_integ (cdt_change_allowed aag {pasSubject aag} (cdt st) (tcb_states_of_state st)) st and Q\<rbrace>
cap_swap_ext a b c d
\<lbrace>\<lambda>_. list_integ (cdt_change_allowed aag {pasSubject aag} (cdt st) (tcb_states_of_state st)) st\<rbrace>;
\<And>P. cap_swap_ext a b c d \<lbrace>\<lambda>s. P (ekheap s)\<rbrace>; \<And>P. cap_swap_ext a b c d \<lbrace>\<lambda>s. P (ready_queues s)\<rbrace> \<rbrakk>
\<Longrightarrow> \<lbrace>integrity aag X st and Q\<rbrace> cap_swap_ext a b c d \<lbrace>\<lambda>_. integrity aag X st\<rbrace>"
and empty_slot_extended_list_integ_lift:
"\<And>Q a b.
\<lbrakk> \<lbrace>list_integ (cdt_change_allowed aag {pasSubject aag} (cdt st) (tcb_states_of_state st)) st and Q\<rbrace>
empty_slot_ext a b
\<lbrace>\<lambda>_. list_integ (cdt_change_allowed aag {pasSubject aag} (cdt st) (tcb_states_of_state st)) st\<rbrace>;
\<And>P. empty_slot_ext a b \<lbrace>\<lambda>s. P (ekheap s)\<rbrace>; \<And>P. empty_slot_ext a b \<lbrace>\<lambda>s. P (ready_queues s)\<rbrace> \<rbrakk>
\<Longrightarrow> \<lbrace>integrity aag X st and Q\<rbrace> empty_slot_ext a b \<lbrace>\<lambda>_. integrity aag X st\<rbrace>"
begin
lemma set_original_integrity_autarch:
"\<lbrace>integrity aag X st and K (is_subject aag (fst slot))\<rbrace>
set_original slot orig
\<lbrace>\<lambda>rv. integrity aag X st\<rbrace>"
apply (wpsimp simp: set_original_def)
apply (clarsimp simp: integrity_def intro!: integrity_cdt_direct)
done
lemma set_original_integrity:
"\<lbrace>integrity aag X st and cdt_change_allowed' aag slot\<rbrace>
set_original slot orig
\<lbrace>\<lambda>rv. integrity aag X st\<rbrace>"
apply integrity_trans_start
apply (wpsimp simp: set_original_def integrity_def)
done
lemma update_cdt_fun_upd_integrity_autarch:
"\<lbrace>integrity aag X st and K (is_subject aag (fst slot))\<rbrace>
update_cdt (\<lambda>cdt. cdt (slot := v cdt))
\<lbrace>\<lambda>rv. integrity aag X st\<rbrace>"
apply (wpsimp simp: update_cdt_def set_cdt_def)
apply (clarsimp simp: integrity_def intro!: integrity_cdt_direct)
done
lemma cap_insert_integrity_autarch:
"\<lbrace>integrity aag X st and K (is_subject aag (fst src_slot) \<and> is_subject aag (fst dest_slot))\<rbrace>
cap_insert cap src_slot dest_slot
\<lbrace>\<lambda>_. integrity aag X st\<rbrace>"
apply (simp add: cap_insert_def)
apply (wp set_original_integrity_autarch cap_insert_ext_extended_list_integ_lift
cap_insert_list_integrity update_cdt_fun_upd_integrity_autarch gets_inv
set_cap_integrity_autarch set_untyped_cap_as_full_integrity_autarch assert_inv)
apply fastforce
done
end
text\<open>
Establish that the pointers this syscall will change are labelled with
the current agent's label.
NOTE: @{term "(\<subseteq>)"} is used consciously here to block the simplifier
rewriting (the equivalent equalities) in the wp proofs.
\<close>
definition authorised_cnode_inv ::
"'a PAS \<Rightarrow> Invocations_A.cnode_invocation \<Rightarrow> 'z::state_ext state \<Rightarrow> bool" where
"authorised_cnode_inv aag ci \<equiv> K (case ci of
InsertCall cap ptr ptr' \<Rightarrow> pasObjectAbs aag ` {fst ptr, fst ptr'} \<subseteq> {pasSubject aag}
| MoveCall cap ptr ptr' \<Rightarrow> pasObjectAbs aag ` {fst ptr, fst ptr'} \<subseteq> {pasSubject aag}
| RotateCall s_cap p_cap src pivot dest \<Rightarrow>
pasObjectAbs aag ` {fst src, fst pivot, fst dest} \<subseteq> {pasSubject aag}
| SaveCall ptr \<Rightarrow> is_subject aag (fst ptr)
| DeleteCall ptr \<Rightarrow> is_subject aag (fst ptr)
| CancelBadgedSendsCall cap \<Rightarrow> pas_cap_cur_auth aag cap
| RevokeCall ptr \<Rightarrow> is_subject aag (fst ptr))"
lemma resolve_address_bits_authorised_aux:
"s \<turnstile> \<lbrace>pas_refined aag and K (is_cnode_cap (fst (cap, cref))
\<longrightarrow> (\<forall>x \<in> obj_refs (fst (cap, cref)). is_subject aag x))\<rbrace>
resolve_address_bits (cap, cref)
\<lbrace>\<lambda>rv s. is_subject aag (fst (fst rv))\<rbrace>, \<lbrace>\<lambda>rv. \<top>\<rbrace>"
unfolding resolve_address_bits_def
proof (induct arbitrary: s rule: resolve_address_bits'.induct)
case (1 z cap' cref' s')
have P: "\<And>s f P Q. s \<turnstile> \<lbrace>P\<rbrace> throwError f \<lbrace>Q\<rbrace>,\<lbrace>\<lambda>rv s. True\<rbrace>"
by wp+
show ?case
apply (subst resolve_address_bits'.simps)
apply (cases cap', simp_all add: P split del: if_split)
apply (rule hoare_pre_spec_validE)
apply (wp "1.hyps", (assumption | simp add: in_monad | rule conjI)+)
apply (wp get_cap_wp)+
apply (auto simp: cte_wp_at_caps_of_state is_cap_simps cap_auth_conferred_def
dest: caps_of_state_pasObjectAbs_eq)
done
qed
lemma resolve_address_bits_authorised[wp]:
"\<lbrace>pas_refined aag and K (is_cnode_cap cap \<longrightarrow> (\<forall>x \<in> obj_refs cap. is_subject aag x))\<rbrace>
resolve_address_bits (cap, cref)
\<lbrace>\<lambda>rv s. is_subject aag (fst (fst rv))\<rbrace>, -"
apply (unfold validE_R_def)
apply (rule hoare_pre)
apply (rule use_spec(2)[OF resolve_address_bits_authorised_aux])
apply simp
done
lemma lookup_slot_for_cnode_op_authorised[wp]:
"\<lbrace>pas_refined aag and K (is_cnode_cap croot \<longrightarrow> (\<forall>x \<in> obj_refs croot. is_subject aag x))\<rbrace>
lookup_slot_for_cnode_op is_source croot ptr depth
\<lbrace>\<lambda>rv s. is_subject aag (fst rv)\<rbrace>, -"
apply (simp add: lookup_slot_for_cnode_op_def split del: if_split)
apply (wp whenE_throwError_wp hoare_drop_imps
resolve_address_bits_authorised
[THEN hoare_post_imp_R[where Q'="\<lambda>x s. is_subject aag (fst (fst x))"]]
| wpc | fastforce)+
done
(* FIXME MOVE *)
lemma is_cnode_into_is_subject:
"\<lbrakk> pas_cap_cur_auth aag cap; pas_refined aag s; is_cnode_cap cap \<rbrakk>
\<Longrightarrow> \<forall>x\<in>obj_refs cap. is_subject aag x"
by (clarsimp simp: is_cap_simps cap_auth_conferred_def
pas_refined_all_auth_is_owns aag_cap_auth_def)
lemma get_cap_prop_imp:
"\<lbrace>cte_wp_at (\<lambda>cap. P cap \<longrightarrow> Q cap) slot\<rbrace> get_cap slot \<lbrace>\<lambda>rv s. P rv \<longrightarrow> cte_wp_at Q slot s\<rbrace>"
by (wpsimp wp: get_cap_wp simp: cte_wp_at_caps_of_state)
lemma get_cap_prop_imp2:
"\<lbrace>cte_wp_at (\<lambda>cap. P cap) slot\<rbrace> get_cap slot \<lbrace>\<lambda>rv s. P rv\<rbrace>"
by (wpsimp wp: get_cap_wp simp: cte_wp_at_def)
lemma get_cap_cur_auth:
"\<lbrace>pas_refined aag and cte_wp_at (\<lambda>_. True) slot and K (is_subject aag (fst slot))\<rbrace>
get_cap slot
\<lbrace>\<lambda>rv s. pas_cap_cur_auth aag rv\<rbrace>"
apply (wp get_cap_wp)
apply (clarsimp simp: cte_wp_at_caps_of_state cap_cur_auth_caps_of_state)
done
lemma decode_cnode_inv_authorised:
"\<lbrace>pas_refined aag and invs and valid_cap cap
and K (\<forall>c \<in> {cap} \<union> set excaps. pas_cap_cur_auth aag c)\<rbrace>
decode_cnode_invocation label args cap excaps
\<lbrace>\<lambda>rv s. authorised_cnode_inv aag rv s\<rbrace>,-"
apply (simp add: authorised_cnode_inv_def decode_cnode_invocation_def
split_def whenE_def unlessE_def set_eq_iff
cong: if_cong Invocations_A.cnode_invocation.case_cong split del: if_split)
apply (wpsimp wp: hoare_vcg_all_lift hoare_vcg_const_imp_lift_R hoare_vcg_all_lift_R lsfco_cte_at
simp: simp_thms if_simps fst_conv snd_conv Invocations_A.cnode_invocation.simps K_def
| wp (once) get_cap_cur_auth)+
apply (subgoal_tac "\<forall>n. n < length excaps
\<longrightarrow> (is_cnode_cap (excaps ! n)
\<longrightarrow> (\<forall>x\<in>obj_refs (excaps ! n). is_subject aag x))")
apply (fastforce simp: invs_valid_objs is_cnode_into_is_subject)
apply (intro allI impI is_cnode_into_is_subject; fastforce)
done
lemma set_cap_thread_st_auth[wp]:
"set_cap cap ptr \<lbrace>\<lambda>s. P (thread_st_auth s)\<rbrace>"
apply (wpsimp wp: get_object_wp simp: set_cap_def split_def set_object_def)
apply (fastforce simp: obj_at_def get_tcb_def tcb_states_of_state_def
thread_st_auth_def rsubst[where P=P, OF _ ext])
done
lemma set_cap_tcb_states_of_state[wp]:
"set_cap cap ptr \<lbrace>\<lambda>s. P (tcb_states_of_state s)\<rbrace>"
apply (simp add: set_cap_def split_def set_object_def)
apply (wpsimp wp: get_object_wp)
apply (fastforce simp: obj_at_def get_tcb_def tcb_states_of_state_def rsubst[where P=P, OF _ ext])
done
lemma set_cap_thread_bound_ntfns[wp]:
"set_cap cap ptr \<lbrace>\<lambda>s. P (thread_bound_ntfns s)\<rbrace>"
apply (wpsimp wp: get_object_wp simp: set_cap_def split_def set_object_def)
apply (fastforce simp: obj_at_def get_tcb_def thread_bound_ntfns_def rsubst[where P=P, OF _ ext])
done
lemma sita_caps_update:
"\<lbrakk> pas_wellformed aag; state_irqs_to_policy_aux aag caps \<subseteq> pasPolicy aag;
cap_links_irq aag (pasObjectAbs aag (fst ptr)) cap \<rbrakk>
\<Longrightarrow> state_irqs_to_policy_aux aag (caps(ptr \<mapsto> cap)) \<subseteq> pasPolicy aag"
by (fastforce intro: state_irqs_to_policy_aux.intros
elim: state_irqs_to_policy_aux.cases
simp: cap_links_irq_def split: if_splits)
lemma sita_caps_update2:
"\<lbrakk> pas_wellformed aag; state_irqs_to_policy_aux aag caps \<subseteq> pasPolicy aag;
cap_links_irq aag (pasObjectAbs aag (fst ptr')) cap';
cap_links_irq aag (pasObjectAbs aag (fst ptr)) cap \<rbrakk>
\<Longrightarrow> state_irqs_to_policy_aux aag (caps(ptr \<mapsto> cap, ptr' \<mapsto> cap')) \<subseteq> pasPolicy aag"
by (fastforce intro: state_irqs_to_policy_aux.intros
elim: state_irqs_to_policy_aux.cases
simp: cap_links_irq_def split: if_splits)
context CNode_AC_1 begin
lemma set_cap_pas_refined:
"\<lbrace>pas_refined aag and pspace_aligned and valid_vspace_objs and valid_arch_state and
(\<lambda>s. (is_transferable_in ptr s \<and> (\<not> Option.is_none (cdt s ptr)))
\<longrightarrow> is_transferable_cap cap \<or>
abs_has_auth_to aag Control (fst $ the $ cdt s ptr) (fst ptr)) and
K (aag_cap_auth aag (pasObjectAbs aag (fst ptr)) cap)\<rbrace>
set_cap cap ptr
\<lbrace>\<lambda>_. pas_refined aag\<rbrace>"
apply (simp add: pas_refined_def state_objs_to_policy_def aag_cap_auth_def)
apply (rule hoare_pre)
apply (wp set_cap_caps_of_state set_cap_state_vrefs | wps)+
apply clarsimp
apply (intro conjI) \<comment> \<open>auth_graph_map\<close>
apply (clarsimp dest!: auth_graph_map_memD)
apply (erule state_bits_to_policy.cases;
solves\<open>auto simp: cap_links_asid_slot_def label_owns_asid_slot_def
intro: auth_graph_map_memI state_bits_to_policy.intros
split: if_split_asm\<close>)
apply (erule (2) sata_update[unfolded fun_upd_def])
apply (erule (2) sita_caps_update[unfolded fun_upd_def])
done
lemma set_cap_pas_refined_not_transferable:
"\<lbrace>pas_refined aag and pspace_aligned and valid_vspace_objs and valid_arch_state
and cte_wp_at (\<lambda>c. \<not>is_transferable (Some c)) ptr
and K (aag_cap_auth aag (pasObjectAbs aag (fst ptr)) cap)\<rbrace>
set_cap cap ptr
\<lbrace>\<lambda>_. pas_refined aag\<rbrace>"
by (wpsimp wp: set_cap_pas_refined simp: cte_wp_at_caps_of_state)
end
(* FIXME MOVE *)
lemma parent_ofI[intro!]: "m x = Some src \<Longrightarrow> m \<Turnstile> src \<leadsto> x"
by (simp add: cdt_parent_rel_def is_cdt_parent_def)
declare set_original_wp[wp del]
context CNode_AC_1 begin
lemma cap_move_respects[wp]:
"\<lbrace>integrity aag X st and pas_refined aag
and K (is_subject aag (fst dest) \<and> is_subject aag (fst src))\<rbrace>
cap_move cap src dest
\<lbrace>\<lambda>_. integrity aag X st\<rbrace>"
apply (rule hoare_gen_asm)
apply (clarsimp simp: cap_move_def)
apply (wpsimp wp: get_cap_wp set_cap_integrity_autarch set_original_integrity_autarch
cap_move_ext_list_integ_lift[where Q="\<top>"] cap_move_list_integrity
simp: set_cdt_def | blast)+
apply (rule wp_integrity_clean')
apply (simp add: integrity_def integrity_cdt_def)
apply (blast intro: cca_owned)
apply (wpsimp wp: set_cap_integrity_autarch)+
done
lemma cap_swap_respects[wp]:
"\<lbrace>integrity aag X st and pas_refined aag
and K (is_subject aag (fst slot) \<and> is_subject aag (fst slot'))\<rbrace>
cap_swap cap slot cap' slot'
\<lbrace>\<lambda>_. integrity aag X st\<rbrace>"
apply (rule hoare_gen_asm)
apply (clarsimp simp: cap_swap_def)
apply (wp get_cap_wp set_cap_integrity_autarch cap_swap_list_integrity
cap_swap_ext_extended_list_integ_lift[where Q="\<top>"]
set_original_integrity_autarch[unfolded pred_conj_def K_def]
| simp add: set_cdt_def split del: if_split | blast)+
apply (rule wp_integrity_clean')
apply (simp add: integrity_def)
apply (blast intro: cca_owned)
apply (wpsimp wp: set_cap_integrity_autarch set_cap_pas_refined)+
done
lemma cap_swap_for_delete_respects[wp]:
"\<lbrace>integrity aag X st and pas_refined aag
and K (is_subject aag (fst slot) \<and> is_subject aag (fst slot'))\<rbrace>
cap_swap_for_delete slot slot'
\<lbrace>\<lambda>_. integrity aag X st\<rbrace>"
by (wpsimp simp: cap_swap_for_delete_def)
lemma dmo_no_mem_respects:
assumes p: "\<And>P. mop \<lbrace>\<lambda>ms. P (underlying_memory ms)\<rbrace>"
assumes q: "\<And>P. mop \<lbrace>\<lambda>ms. P (device_state ms)\<rbrace>"
shows "do_machine_op mop \<lbrace>integrity aag X st\<rbrace>"
unfolding do_machine_op_def
apply (rule hoare_pre)
apply (simp add: split_def)
apply wp
apply (clarsimp simp: integrity_def)
apply (rule conjI)
apply clarsimp
apply (drule_tac x = x in spec)+
apply (erule (1) use_valid [OF _ p])
apply clarsimp
apply (drule_tac x = x in spec)+
apply (erule (1) use_valid [OF _ q])
done
lemma set_irq_state_respects[wp]:
"\<lbrace>integrity aag X st and K (is_subject_irq aag irq)\<rbrace>
set_irq_state irqst irq
\<lbrace>\<lambda>_. integrity aag X st\<rbrace>"
unfolding set_irq_state_def
by (wpsimp wp: dmo_no_mem_respects simp: integrity_subjects_def integrity_interrupts_def)
end
(* FIXME: MOVE *)
(* Only works after a hoare_pre! *)
lemma dmo_wp:
assumes mopv: "\<And>s. \<lbrace>P s\<rbrace> mop \<lbrace>\<lambda>a b. R a (s\<lparr>machine_state := b\<rparr>)\<rbrace>"
shows "\<lbrace>\<lambda>s. P s (machine_state s)\<rbrace> do_machine_op mop \<lbrace>R\<rbrace>"
by (wpsimp simp: do_machine_op_def use_valid[OF _ mopv])
lemmas cases_simp_options = cases_simp_option cases_simp_option[where 'a="'b \<times> 'c", simplified]
(* FIXME MOVE *)
lemma cdt_change_allowed_all_children:
"all_children (cdt_change_allowed aag subject (cdt s) (tcb_states_of_state s)) (cdt s)"
by (rule all_childrenI) (erule cdt_change_allowed_to_child)
abbreviation cleanup_info_wf :: "cap \<Rightarrow> 'a PAS \<Rightarrow> bool" where
"cleanup_info_wf c aag \<equiv> c \<noteq> NullCap \<and> \<not>is_arch_cap c
\<longrightarrow> (\<exists>irq. c = (IRQHandlerCap irq) \<and> is_subject_irq aag irq)"
(* FIXME: MOVE *)
named_theorems wp_transferable
named_theorems wp_not_transferable
context CNode_AC_1 begin
crunch respects[wp]: deleted_irq_handler "integrity aag X st"
lemma post_cap_deletion_integrity[wp]:
"\<lbrace>integrity aag X s and K (cleanup_info_wf cleanup_info aag)\<rbrace>
post_cap_deletion cleanup_info
\<lbrace>\<lambda>_. integrity aag X s\<rbrace>"
by (wpsimp simp: post_cap_deletion_def is_cap_simps wp: arch_post_cap_deletion_integrity)
lemma empty_slot_integrity_spec:
notes split_paired_All[simp del]
shows
"s \<turnstile> \<lbrace>valid_list and valid_mdb and valid_objs and pas_refined aag
and K (is_subject aag (fst slot) \<and> cleanup_info_wf cleanup_info aag)\<rbrace>
empty_slot slot cleanup_info
\<lbrace>\<lambda>_. integrity aag X s\<rbrace>"
apply (simp add: spec_valid_def)
apply (simp add: empty_slot_def)
apply (wp add: get_cap_wp set_cap_integrity_autarch set_original_integrity_autarch
empty_slot_extended_list_integ_lift empty_slot_list_integrity[where m="cdt s"]
| simp add: set_cdt_def | wpc)+
apply (safe; \<comment> \<open>for speedup\<close>
clarsimp simp add: integrity_def,
blast intro: cca_owned cdt_change_allowed_all_children)
done
lemma empty_slot_integrity[wp,wp_not_transferable]:
"\<lbrace>integrity aag X st and valid_list and valid_objs and valid_mdb and pas_refined aag
and K (is_subject aag (fst slot) \<and> cleanup_info_wf c aag)\<rbrace>
empty_slot slot c
\<lbrace>\<lambda>_. integrity aag X st\<rbrace>"
apply (integrity_trans_start)
apply (rule hoare_pre)
apply (wp empty_slot_integrity_spec[simplified spec_valid_def])
by force
end
lemma reply_masters_mdbD1:
"\<lbrakk> reply_masters_mdb m cs ; cs slot = Some (ReplyCap t True R) \<rbrakk>
\<Longrightarrow> m slot = None"
by (fastforce simp:reply_masters_mdb_def simp del:split_paired_All)
lemma reply_cap_no_grand_parent:
"\<lbrakk> m \<Turnstile> pptr \<rightarrow>* slot ; reply_mdb m cs ; cs slot = Some (ReplyCap t False R) \<rbrakk>
\<Longrightarrow> pptr = slot \<or> (m \<Turnstile> pptr \<leadsto> slot \<and> (\<exists> R'. cs pptr = Some (ReplyCap t True R')))"
apply (clarsimp simp: reply_mdb_def del: disjCI)
apply (erule(1) reply_caps_mdbE)
apply (drule(1) reply_masters_mdbD1)
apply (erule rtrancl.cases, blast)
apply (erule rtrancl.cases, simp add: cdt_parent_of_def)
apply (simp add: cdt_parent_of_def)
done
(* FIXME MOVE ? *)
crunches set_cdt_list, update_cdt_list
for cdt[wp]: "\<lambda>s. P (cdt s)"
and kheap[wp]: "\<lambda>s. P (kheap s)"
and valid_mdb[wp]: "\<lambda>s. P (valid_mdb s)"
and valid_objs[wp]: "\<lambda>s. P (valid_objs s)"
and arch_state[wp]: "\<lambda>s. P (arch_state s)"
and thread_st_auth[wp]: "\<lambda>s. P (thread_st_auth s)"
and caps_of_state[wp]: "\<lambda>s. P (caps_of_state s)"
and is_original_cap[wp]: "\<lambda>s. P (is_original_cap s)"
and interrupt_irq_node[wp]: "\<lambda>s. P (interrupt_irq_node s)"
and thread_bound_ntfns[wp]: "\<lambda>s. P (thread_bound_ntfns s)"
locale CNode_AC_2 = CNode_AC_1 +
assumes integrity_asids_set_cap_Nullcap:
"\<lbrace>(=) s\<rbrace> set_cap NullCap slot \<lbrace>\<lambda>_. integrity_asids aag subjects x (s :: det_ext state)\<rbrace>"
and set_original_state_asids_to_policy[wp]:
"\<And>P. set_original slot v \<lbrace>\<lambda>s. P (state_asids_to_policy aag s)\<rbrace>"
and set_original_state_objs_to_policy[wp]:
"\<And>P. set_original slot v \<lbrace>\<lambda>s. P (state_objs_to_policy s)\<rbrace>"
and set_cdt_list_state_vrefs[wp]:
"\<And>P. set_cdt_list t \<lbrace>\<lambda>s. P (state_vrefs s)\<rbrace>"
and set_cdt_list_state_asids_to_policy[wp]:
"\<And>P. set_cdt_list t \<lbrace>\<lambda>s. P (state_asids_to_policy aag s)\<rbrace>"
and update_cdt_list_state_vrefs[wp]:
"\<And>P. update_cdt_list f \<lbrace>\<lambda>s. P (state_vrefs s)\<rbrace>"
and update_cdt_list_state_asids_to_policy[wp]:
"\<And>P. update_cdt_list f \<lbrace>\<lambda>s. P (state_asids_to_policy aag s)\<rbrace>"
begin
crunches set_original
for tcb_domain_map_wellformed[wp]: "\<lambda>s. P (tcb_domain_map_wellformed aag s)"
and state_irqs_to_policy[wp]: "\<lambda>s. P (state_irqs_to_policy aag s)"
and cdt_change_allowed[wp]: "\<lambda>s. P (cdt_change_allowed' aag slot s)"
and irq_map_wellformed[wp]: "\<lambda>s. P (irq_map_wellformed aag s)"
and pas_refined[wp]: "\<lambda>s. P (pas_refined aag s)"
and valid_objs[wp]: "\<lambda>s. P (valid_objs s)"
and cte_wp_at[wp]: "cte_wp_at P slot"
(simp: state_objs_to_policy_def pas_refined_def)
lemma set_cap_integrity_deletion_aux:
"\<lbrace>integrity aag X st and valid_mdb and valid_objs and pas_refined aag and is_transferable_in slot
and cdt_change_allowed' aag slot and K(\<not> is_subject aag (fst slot))\<rbrace>
set_cap NullCap slot
\<lbrace>\<lambda>_. integrity aag X st\<rbrace>"
apply (integrity_trans_start)
apply (rule hoare_pre)
apply (unfold integrity_subjects_def)[1]
apply (wp hoare_wp_combs)
apply (unfold set_cap_def)[1]
apply (wpc)
apply (wp set_object_wp)
apply wpc
apply wp+
apply (wp get_object_wp)
apply wps
apply (wp integrity_asids_set_cap_Nullcap hoare_vcg_all_lift)
apply (safe ; clarsimp simp add: cte_wp_at_caps_of_state dest!: ko_atD)
(* cnode *)
subgoal for s obj addr cnode_size content cap'
apply (rule tro_cnode, simp, simp)
apply (rule cnode_integrityI)
apply simp
apply (intro impI disjI2)
apply (frule_tac addr=addr in caps_of_state_cnode, simp)
apply clarsimp
apply (erule is_transferable.cases, blast)
apply (fastforce intro: reply_cap_deletion_integrity_intros)
apply clarsimp
apply (rule reply_cap_deletion_integrityI2[OF refl refl])
apply (elim cdt_change_allowedE cdt_direct_change_allowed.cases)
apply (drule reply_cap_no_grand_parent[where cs="caps_of_state s"]; fastforce?)
apply (fastforce simp: aag_cap_auth_def cap_auth_conferred_def reply_cap_rights_to_auth_def
dest: cap_auth_caps_of_state pas_refined_Control)
apply (fastforce dest: tcb_states_of_state_kheapD descendant_of_caller_slot[OF _ _ tcb_atI]
parent_of_rtrancl_no_descendant)
done
(* tcb_ctable *)
subgoal for s obj tcb
apply (rule_tac tro_tcb_empty_ctable, simp, simp, simp)
apply (frule_tac addr="tcb_cnode_index 0" in caps_of_state_tcb)
apply clarsimp
apply (elim is_transferable.cases, simp)
apply (fastforce intro: reply_cap_deletion_integrity_intros)
apply clarsimp
apply (rule reply_cap_deletion_integrityI2[OF refl refl])
apply (elim cdt_change_allowedE cdt_direct_change_allowed.cases)
apply (force simp: aag_cap_auth_def cap_auth_conferred_def reply_cap_rights_to_auth_def
dest: reply_cap_no_grand_parent cap_auth_caps_of_state pas_refined_Control)
apply (fastforce simp: direct_call_def
dest: tcb_caller_slot_empty_on_recieve parent_of_rtrancl_no_descendant
descendant_of_caller_slot[OF _ _ tcb_atI] tcb_states_of_state_kheapD)
done
(* tcb_vtable *)
apply (rename_tac s obj tcb)
apply (rule tro_orefl)
apply (fastforce simp: caps_of_state_tcb valid_obj_def valid_tcb_def ran_tcb_cap_cases
elim:pspace_valid_objsE[OF _ invs_valid_objs] elim!:is_transferable.cases)
(* tcb_reply *)
apply (rename_tac s obj tcb)
apply (rule tro_orefl)
apply (fastforce simp: is_cap_simps caps_of_state_tcb valid_obj_def valid_tcb_def
ran_tcb_cap_cases
elim: pspace_valid_objsE[OF _ invs_valid_objs] elim!:is_transferable.cases)
(* tcb_caller *)
subgoal for s obj tcb
apply (rule_tac tro_tcb_empty_caller, simp, simp, simp)
apply (frule_tac addr="tcb_cnode_index 3" in caps_of_state_tcb)
apply clarsimp
apply (elim is_transferable.cases, simp)
apply (fastforce intro: reply_cap_deletion_integrity_intros)
apply clarsimp
apply (rule reply_cap_deletion_integrityI2[OF refl refl])
apply (elim cdt_change_allowedE cdt_direct_change_allowed.cases)
apply (force simp:aag_cap_auth_def cap_auth_conferred_def reply_cap_rights_to_auth_def
dest: reply_cap_no_grand_parent cap_auth_caps_of_state pas_refined_Control)
apply (fastforce simp: direct_call_def
dest: tcb_caller_slot_empty_on_recieve parent_of_rtrancl_no_descendant
descendant_of_caller_slot[OF _ _ tcb_atI] tcb_states_of_state_kheapD)
done
(* tcb_ipcframe*)
apply (rename_tac s obj tcb)
apply (rule tro_orefl)
apply (fastforce simp: is_nondevice_page_cap_simps caps_of_state_tcb
valid_obj_def valid_tcb_def ran_tcb_cap_cases
elim: pspace_valid_objsE[OF _ invs_valid_objs] elim!:is_transferable.cases)
done
lemma set_cap_integrity_deletion[wp_transferable]:
"\<lbrace>integrity aag X st and valid_mdb and valid_objs
and pas_refined aag and cdt_change_allowed' aag slot\<rbrace>
set_cap NullCap slot
\<lbrace>\<lambda>_. integrity aag X st\<rbrace>"
apply (cases "is_subject aag (fst slot)")
apply (wpsimp wp: set_cap_integrity_autarch)
apply (wpsimp wp: set_cap_integrity_deletion_aux)
by (fastforce dest: cca_to_transferable_or_subject simp: cte_wp_at_caps_of_state)
lemma update_cdt_list_pas_refined[wp]:
"update_cdt_list f \<lbrace>pas_refined aag\<rbrace>"
by (wpsimp simp: pas_refined_def state_objs_to_policy_def | wps)+
end
text \<open>
For the @{const empty_slot} proof, we need to rearrange the operations
so that the CDT is updated after emptying the slot. Here we prove the
rearrangement is valid.
\<close>
(* Flesh out the monad_commute framework.
* FIXME: MOVE *)
lemma monad_commuteI2:
"monad_commute P (f :: ('s, unit) nondet_monad) g \<Longrightarrow> (\<And>s. P s) \<Longrightarrow>
(do f; g od) = (do g; f od)"
by (monad_eq simp: monad_commute_def)
lemmas monad_commute_split2 = monad_commute_split[THEN commute_commute]
lemma modify_modify_commute:
"monad_commute (\<lambda>s. f (g s) = g (f s)) (modify f) (modify g)"
by (monad_eq simp: monad_commute_def)
lemma modify_gets_commute:
"monad_commute (\<lambda>s. g (f s) = g s) (modify f) (gets g)"
by (monad_eq simp: monad_commute_def)
lemma set_eq_iff_imp:
"(A = B) = ((\<forall>x. x \<in> A \<longrightarrow> x \<in> B) \<and> (\<forall>x. x \<in> B \<longrightarrow> x \<in> A))"
by blast
lemma modify_get_commute:
"(\<And>s0. \<lbrace>(=) s0\<rbrace> g \<lbrace>\<lambda>r t. s0 = t\<rbrace>)
\<Longrightarrow> monad_commute (\<lambda>s. fst ` fst (g (f s)) = fst ` fst (g s) \<and>
snd (g (f s)) = snd (g s)) (modify f) g"
(* FIXME: proof cleanup *)
apply (monad_eq simp: monad_commute_def valid_def
set_eq_iff_imp[where A="fst ` fst _"] image_iff)
apply atomize
apply (intro conjI; clarsimp)
apply (rename_tac s0 r t)
apply (clarsimp split: prod.splits)
apply (rule_tac x=s0 in exI)
apply (rule conjI)
apply (drule_tac x=s0 in spec)
apply fastforce
apply fastforce
apply (rename_tac s0 r t)
apply (clarsimp split: prod.splits)
apply (subgoal_tac "t = s0")
apply (drule_tac x="f t" in spec)
apply fastforce
apply fastforce
done
(* We use this version for the automation: the precond that falls out
* will look like "\<forall>x. (\<exists>r. r \<in> fst (gets ?foo (?upd s)) \<and> x = fst r) = \<dots>"
* which the monad_eq method can easily reduce with in_monad rules. *)
lemmas modify_get_commute' =
modify_get_commute[simplified set_eq_iff image_iff Ball_def Bex_def]
lemma put_as_modify:
"put t = modify (\<lambda>_. t)"
by monad_eq
lemma put_commuteI:
"monad_commute P f (modify (\<lambda>_. t)) \<Longrightarrow> monad_commute P f (put t)"
by (simp add: put_as_modify)
lemma get_commuteI:
"monad_commute P f (gets (\<lambda>s. s)) \<Longrightarrow> monad_commute P f get"
by (simp add: gets_def)
lemma gets_gets_commute:
"monad_commute \<top> (gets f) (gets g)"
by (monad_eq simp: monad_commute_def)
lemma gets_get_commute:
"(\<And>s0. \<lbrace>(=) s0\<rbrace> g \<lbrace>\<lambda>r t. s0 = t\<rbrace>) \<Longrightarrow>
monad_commute \<top> (gets f) g"
by (monad_eq simp: monad_commute_def valid_def) fastforce
lemma assert_commute':
"empty_fail f \<Longrightarrow> monad_commute \<top> (assert G) f"
by (monad_eq simp: monad_commute_def empty_fail_def) fastforce
named_theorems monad_commute_wp
lemmas[monad_commute_wp] =
monad_commute_split
monad_commute_split2
modify_modify_commute
gets_gets_commute
put_commuteI put_commuteI[THEN commute_commute]
get_commuteI get_commuteI[THEN commute_commute]
return_commute return_commute[THEN commute_commute]
assert_commute' assert_commute'[THEN commute_commute]
(* Sort-of VCG for monad_commute goals *)
lemma wpc_helper_monad_commute:
"monad_commute P f g \<Longrightarrow> wpc_helper (P, P') (Q, Q') (monad_commute P f g)"
by (clarsimp simp: wpc_helper_def)
wpc_setup "\<lambda>m. monad_commute P f m" wpc_helper_monad_commute
method monad_commute_wpc =
(match conclusion in "monad_commute _ _ _" \<Rightarrow> succeed),
(wpc | (rule commute_commute, wpc))
method monad_commute_step methods more_solver =
determ \<open>wp monad_commute_wp\<close>
| (* Conditional rules for fully schematic programs fragments:
* make sure to solve the first condition before continuing *)
(rule modify_get_commute' modify_get_commute'[THEN commute_commute],
solves \<open>(changed \<open>wp | more_solver\<close>)+\<close>)
| more_solver
method monad_commute methods more_solver =
((monad_commute_wpc; rule monad_commute_guard_imp),
(monad_commute more_solver, more_solver)+)
| (monad_commute_step more_solver,
((changed \<open>monad_commute more_solver\<close>)+)?)[1]
method monad_commute_default =
monad_commute \<open>solves \<open>monad_eq\<close>
| solves \<open>(wpc, (changed \<open>wp | fastforce\<close>)+)\<close>
| solves \<open>(changed \<open>wp | fastforce\<close>)+\<close>
| fastforce\<close>
(* Now the commute steps *)
(* FIXME: remove and generalise version in ainvs *)
lemma set_original_set_cap_comm:
"(do set_original slot' val; set_cap cap slot od) =
(do set_cap cap slot; set_original slot' val od)"
apply (rule ext)
apply (clarsimp simp: bind_def split_def set_cap_def set_original_def
get_object_def set_object_def get_def put_def
simpler_gets_def simpler_modify_def
assert_def fail_def)
apply (case_tac y; simp add: return_def fail_def)
done
lemma set_cdt_set_cap_comm:
"(do set_cdt c; set_cap cap slot od) =
(do set_cap cap slot; set_cdt c od)"
apply (rule ext)
apply (clarsimp simp: bind_def split_def set_cap_def set_cdt_def
get_object_def set_object_def get_def put_def
simpler_gets_def simpler_modify_def
assert_def fail_def)
apply (case_tac y; simp add: return_def fail_def)
done
lemma set_cdt_set_original_comm:
"(do set_cdt c; set_original slot val od) =
(do set_original slot val; set_cdt c od)"
apply (clarsimp simp: set_cdt_def[folded modify_def]
set_original_def[folded gets_modify_def]
get_object_def set_object_def
simp del: K_bind_def)
apply (simp only: modify_def[symmetric])
apply (rule monad_commuteI2)
apply monad_commute_default
apply monad_eq
done
lemma set_cdt_empty_slot_ext_comm:
"(do set_cdt c; empty_slot_ext slot slot_p od) =
(do empty_slot_ext slot slot_p; set_cdt c od)"
supply K_bind_def[simp del]
apply (clarsimp simp: set_cdt_def empty_slot_ext_def
update_cdt_list_def set_cdt_list_def)
apply (simp only: modify_def[symmetric])
apply (rule monad_commuteI2)
apply monad_commute_default
apply monad_eq
done
lemma set_cap_empty_slot_ext_comm:
"(do set_cap cap slot; empty_slot_ext slot' slot_p od) =
(do empty_slot_ext slot' slot_p; set_cap cap slot od)"
apply (rule ext)
apply (clarsimp simp: bind_def split_def set_cap_def empty_slot_ext_def
update_cdt_list_def set_cdt_list_def
get_object_def set_object_def get_def put_def
simpler_gets_def simpler_modify_def
assert_def fail_def)
apply (case_tac y; simp add: return_def fail_def split: option.splits)
done
(* FIXME: MOVE *)
lemmas bind_eqI' = NonDetMonadVCG.bind_eqI[OF _ refl]
lemma K_bind_assoc:
"(do (do f; g od); h od) = (do f; g; h od)"
by (simp add: bind_assoc)
lemmas K_bind_eqI = arg_cong2[where f="\<lambda>f g. do f; g od"]
lemmas K_bind_eqI' = K_bind_eqI[OF _ refl]
lemma aag_cap_auth_max_free_index_update[simp]:
"aag_cap_auth aag (pasObjectAbs aag x) (max_free_index_update y) =
aag_cap_auth aag (pasObjectAbs aag x) y"
by (clarsimp simp: aag_cap_auth_def free_index_update_def cap_links_asid_slot_def cap_links_irq_def
split: cap.splits)
context CNode_AC_2 begin
(* Putting it all together *)
lemma empty_slot_shuffle:
"(do set_cdt c;
empty_slot_ext slot slot_p;
set_original slot False;
set_cap NullCap slot;
post_cap_deletion NullCap od) =
(do set_cap NullCap slot;
empty_slot_ext slot slot_p;
set_original slot False;
set_cdt c;
post_cap_deletion NullCap od :: (det_ext state \<Rightarrow> _))"
by (simp only: set_cdt_empty_slot_ext_comm[THEN K_bind_eqI', simplified K_bind_assoc]
set_cdt_set_original_comm[THEN K_bind_eqI', simplified K_bind_assoc]
set_cdt_set_cap_comm[THEN K_bind_eqI', simplified K_bind_assoc]
set_original_set_cap_comm[THEN K_bind_eqI', simplified K_bind_assoc]
set_cap_empty_slot_ext_comm[THEN K_bind_eqI', simplified K_bind_assoc])
lemma empty_slot_integrity_transferable[wp_transferable]:
"\<lbrace>integrity aag X st and valid_list and valid_objs and valid_mdb and pas_refined aag
and cdt_change_allowed' aag slot and K (c = NullCap)\<rbrace>
empty_slot slot c
\<lbrace>\<lambda>_. integrity aag X st\<rbrace>"
apply integrity_trans_start
apply (rule hoare_pre)
apply (simp add: empty_slot_def)
apply (simp add: empty_slot_shuffle[simplified])
apply (simp add: set_cdt_def)
apply (wp set_original_wp)
apply (rename_tac cdtv x)
apply (rule_tac Q = "\<lambda>_ s'. integrity aag X s s'\<and> cdtv = cdt s \<and>
is_original_cap s = is_original_cap s'"
in hoare_post_imp)
apply (clarsimp simp add: integrity_def)
apply (frule all_childrenD[OF cdt_change_allowed_all_children];fastforce)
apply (wp empty_slot_extended_list_integ_lift)
apply (rule hoare_pre)
apply (rule_tac m = "cdt s" in empty_slot_list_integrity)
apply simp
apply wp+
apply (wp set_cap_integrity_deletion gets_wp get_cap_wp)+
by (fastforce intro: cdt_change_allowed_all_children)
lemma set_cdt_pas_refined:
notes split_paired_All[simp del] split_paired_Ex[simp del]
shows "\<lbrace>pas_refined aag and (\<lambda>s. \<forall>x y. c x = Some y \<and> cdt s x \<noteq> Some y
\<longrightarrow> (is_transferable (caps_of_state s x) \<or>
abs_has_auth_to aag Control (fst y) (fst x)) \<and>
abs_has_auth_to aag DeleteDerived (fst y) (fst x))\<rbrace>
set_cdt c
\<lbrace>\<lambda>_. pas_refined aag\<rbrace>"
apply (simp add: pas_refined_def state_objs_to_policy_def set_cdt_def)
apply (wp | simp | simp_all)+
apply (clarsimp dest!: auth_graph_map_memD)
apply (subgoal_tac
"\<forall>x y. c x = Some y \<longrightarrow>
(is_transferable (caps_of_state s x) \<or> abs_has_auth_to aag Control (fst y) (fst x))
\<and> abs_has_auth_to aag DeleteDerived (fst y) (fst x)")
defer
apply (intro allI, case_tac "cdt s x = Some y")
apply (solves\<open>auto intro: auth_graph_map_memI state_bits_to_policy.intros\<close>)
apply (fastforce dest!: spec elim!: mp)
apply (erule state_bits_to_policy.cases)
apply (auto intro: auth_graph_map_memI state_bits_to_policy.intros
split: if_split_asm | blast)+
done
lemma pas_refined_original_cap_update[simp]:
"pas_refined aag (is_original_cap_update f s) = pas_refined aag s"
by (simp add: pas_refined_def state_objs_to_policy_def)
lemma pas_refined_machine_state_update[simp]:
"pas_refined aag (machine_state_update f s) = pas_refined aag s"
by (simp add: pas_refined_def state_objs_to_policy_def state_refs_of_def)
lemma pas_refined_interrupt_states_update[simp]:
"pas_refined aag (interrupt_states_update f s) = pas_refined aag s"
by (simp add: pas_refined_def state_objs_to_policy_def state_refs_of_def)
crunches deleted_irq_handler
for pas_refined[wp]: "pas_refined aag"
crunches set_untyped_cap_as_full
for pas_refined: "pas_refined aag"
lemmas set_untyped_cap_as_full_pas_refined'[wp] = set_untyped_cap_as_full_pas_refined[simplified]
lemma update_cdt_pas_refined:
"\<lbrace>pas_refined aag and (\<lambda>s. \<forall>x y. c (cdt s) x = Some y \<and> cdt s x \<noteq> Some y
\<longrightarrow> (is_transferable (caps_of_state s x) \<or>
abs_has_auth_to aag Control (fst y) (fst x))
\<and> abs_has_auth_to aag DeleteDerived (fst y) (fst x))\<rbrace>
update_cdt c
\<lbrace>\<lambda>_. pas_refined aag\<rbrace>"
apply (simp add: update_cdt_def)
apply (wp set_cdt_pas_refined)
apply simp
done
lemma state_objs_to_policy_more_update[simp]:
"state_objs_to_policy (trans_state f s) =
state_objs_to_policy s"
by (simp add: state_objs_to_policy_def)
end
lemma set_untyped_cap_as_full_cdt_is_original_cap:
"\<lbrace>\<lambda>s. P (cdt s) (is_original_cap s)\<rbrace>
set_untyped_cap_as_full src_cap new_cap src_slot
\<lbrace>\<lambda>_ s. P (cdt s) (is_original_cap s)\<rbrace>"
unfolding set_untyped_cap_as_full_def
apply (rule hoare_pre)
apply (wp set_cap_caps_of_state2)
apply clarsimp
done
(* FIXME MOVE *)
lemma untyped_not_transferable:
"is_untyped_cap cap \<Longrightarrow> \<not> is_transferable (Some cap)"
by (fastforce simp: is_cap_simps elim!: is_transferable.cases)
(* FIXME MOVE *)
lemma is_transferable_max_free_index_update[simp]:
"is_transferable (Some (max_free_index_update cap)) = is_transferable (Some cap)"
by (simp add: is_transferable.simps free_index_update_def split: cap.splits)
lemma set_untyped_cap_as_full_is_transferable[wp]:
"set_untyped_cap_as_full src_cap new_cap slot \<lbrace>\<lambda>s. \<not> is_transferable (caps_of_state s other_slot)\<rbrace>"
apply (clarsimp simp: set_untyped_cap_as_full_def)
apply wp
using untyped_not_transferable max_free_index_update_preserve_untyped by simp
lemma set_untyped_cap_as_full_is_transferable':
"\<lbrace>\<lambda>s. is_transferable ((caps_of_state s(slot2 \<mapsto> new_cap)) slot3) \<and>
Some src_cap = (caps_of_state s slot)\<rbrace>
set_untyped_cap_as_full src_cap new_cap slot
\<lbrace>\<lambda>_ s. is_transferable ((caps_of_state s(slot2 \<mapsto> new_cap)) slot3)\<rbrace>"
apply (clarsimp simp: set_untyped_cap_as_full_def)
apply safe
apply (wp,fastforce)+
done
lemma cap_links_irq_Nullcap [simp]:
"cap_links_irq aag l NullCap" unfolding cap_links_irq_def by simp
lemma aag_cap_auth_NullCap [simp]:
"aag_cap_auth aag l NullCap"
unfolding aag_cap_auth_def
by (simp add: clas_no_asid)
crunch thread_st_auth[wp]: set_cdt "\<lambda>s. P (thread_st_auth s)"
crunch thread_bound_ntfns[wp]: set_cdt "\<lambda>s. P (thread_bound_ntfns s)"
locale CNode_AC_3 = CNode_AC_2 +
assumes cap_move_ext_pas_refined_tcb_domain_map_wellformed[wp]:
"\<And>a b c d. cap_move_ext a b c d \<lbrace>tcb_domain_map_wellformed aag\<rbrace>
\<Longrightarrow> cap_move_ext a b c d \<lbrace>pas_refined aag\<rbrace>"