976 lines
46 KiB
Plaintext
976 lines
46 KiB
Plaintext
(*
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* Copyright 2014, General Dynamics C4 Systems
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*
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* This software may be distributed and modified according to the terms of
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* the GNU General Public License version 2. Note that NO WARRANTY is provided.
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* See "LICENSE_GPLv2.txt" for details.
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*
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* @TAG(GD_GPL)
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*)
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theory Recycle_C
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imports Delete_C Retype_C
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begin
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context kernel_m
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begin
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definition
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"replicateHider \<equiv> replicate"
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lemma collapse_foldl_replicate:
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"replicate (length xs) v = xs \<Longrightarrow>
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foldl (@) [] (map (\<lambda>_. xs) ys)
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= replicateHider (length xs * length ys) v"
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apply (induct ys rule: rev_induct)
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apply (simp add: replicateHider_def)
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apply (simp add: replicateHider_def)
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apply (subst add.commute, simp add: replicate_add)
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done
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lemma coerce_memset_to_heap_update_user_data:
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"heap_update_list x (replicateHider 4096 0)
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= heap_update (Ptr x :: user_data_C ptr)
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(user_data_C (FCP (\<lambda>_. 0)))"
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apply (intro ext, simp add: heap_update_def)
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apply (rule_tac f="\<lambda>xs. heap_update_list x xs a b" for a b in arg_cong)
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apply (simp add: to_bytes_def size_of_def typ_info_simps user_data_C_tag_def)
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apply (simp add: ti_typ_pad_combine_empty_ti ti_typ_pad_combine_td align_of_def padup_def
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final_pad_def size_td_lt_ti_typ_pad_combine Let_def size_of_def)
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apply (simp add: typ_info_simps
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user_context_C_tag_def thread_state_C_tag_def seL4_Fault_C_tag_def
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lookup_fault_C_tag_def update_ti_t_ptr_0s
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ti_typ_pad_combine_empty_ti ti_typ_pad_combine_td
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align_of_def padup_def
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final_pad_def size_td_lt_ti_typ_pad_combine Let_def size_of_def
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align_td_array' size_td_array)
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apply (simp add: typ_info_array')
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apply (subst access_ti_list_array)
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apply simp
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apply simp
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apply (simp add: fcp_beta typ_info_word typ_info_ptr word_rsplit_0)
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apply fastforce
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apply (simp add: collapse_foldl_replicate)
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done
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lemma clift_foldl_hrs_mem_update:
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"\<lbrakk> \<forall>x \<in> set xs. hrs_htd s \<Turnstile>\<^sub>t f x;
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\<And>x s. hrs_htd s \<Turnstile>\<^sub>t f x \<Longrightarrow> clift (hrs_mem_update (heap_update (f x) v) s)
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= g (clift s :: ('a :: c_type) ptr \<rightharpoonup> 'a) x \<rbrakk>
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\<Longrightarrow>
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clift (hrs_mem_update (\<lambda>s. foldl (\<lambda>s x. heap_update (f x) v s) s xs) s)
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= foldl g (clift s :: 'a ptr \<rightharpoonup> 'a) xs"
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using [[hypsubst_thin]]
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apply (cases s, clarsimp)
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apply (induct xs arbitrary: a b)
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apply (simp add: hrs_mem_update_def)
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apply (clarsimp simp add: hrs_mem_update_def split_def hrs_htd_def)
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done
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lemma map_to_user_data_aligned:
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"\<lbrakk> map_to_user_data (ksPSpace s) x = Some y; pspace_aligned' s \<rbrakk>
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\<Longrightarrow> is_aligned x pageBits"
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apply (clarsimp simp: map_comp_eq projectKOs split: option.split_asm)
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apply (drule(1) pspace_alignedD')
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apply (simp add: objBits_simps)
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done
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lemma help_force_intvl_range_conv:
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"\<lbrakk> is_aligned (p::word32) n; v = 2 ^ n; n < word_bits \<rbrakk>
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\<Longrightarrow> {p ..+ v} = {p .. p + 2 ^ n - 1}"
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by (simp add: intvl_range_conv word_bits_def)
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lemma cmap_relation_If_upd:
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"\<lbrakk> cmap_relation f g ptrfun rel; rel v v'; ptrfun ` S = S'; inj ptrfun \<rbrakk>
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\<Longrightarrow> cmap_relation (\<lambda>x. if x \<in> S then Some v else f x)
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(\<lambda>y. if y \<in> S' then Some v' else g y)
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ptrfun rel"
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apply (simp add: cmap_relation_def dom_If_Some)
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apply (rule context_conjI)
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apply blast
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apply clarsimp
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apply (case_tac "x \<in> S")
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apply simp
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apply clarsimp
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apply (subst if_not_P)
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apply (clarsimp simp: inj_eq)
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apply (drule bspec, erule domI)
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apply simp
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done
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lemma length_replicateHider [simp]:
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"length (replicateHider n x) = n"
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by (simp add: replicateHider_def)
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lemma coerce_heap_update_to_heap_updates':
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"n = chunk * m \<Longrightarrow>
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heap_update_list x (replicateHider n 0)
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= (\<lambda>s. foldl (\<lambda>s x. heap_update_list x (replicateHider chunk 0) s) s
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(map (\<lambda>n. x + (of_nat n * of_nat chunk)) [0 ..< m]))"
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using [[hypsubst_thin]]
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apply clarsimp
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apply (induct m arbitrary: x)
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apply (rule ext, simp)
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apply (simp add: replicateHider_def)
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apply (rule ext)
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apply (simp only: map_upt_unfold map_Suc_upt[symmetric])
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apply (simp add: replicate_add[folded replicateHider_def]
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heap_update_list_concat_unfold
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o_def field_simps
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length_replicate[folded replicateHider_def])
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done
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lemma h_t_valid_dom_s:
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"\<lbrakk> h_t_valid htd c_guard p; x = ptr_val (p :: ('a :: mem_type) ptr);
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n = size_of TYPE ('a) \<rbrakk>
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\<Longrightarrow> {x ..+ n} \<times> {SIndexVal, SIndexTyp 0} \<subseteq> dom_s htd"
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apply (clarsimp simp: h_t_valid_def valid_footprint_def Let_def
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intvl_def)
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apply (drule_tac x=k in spec, simp add: size_of_def)
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apply (clarsimp simp: dom_s_def)
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apply (drule_tac x=0 in map_leD, simp_all)
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done
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lemma user_data_at_rf_sr_dom_s:
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"\<lbrakk> typ_at' UserDataT x s; (s, s') \<in> rf_sr \<rbrakk>
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\<Longrightarrow> {x ..+ 2 ^ pageBits} \<times> {SIndexVal, SIndexTyp 0}
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\<subseteq> dom_s (hrs_htd (t_hrs_' (globals s')))"
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apply (drule rf_sr_heap_user_data_relation)
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apply (drule user_data_at_ko)
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apply (erule_tac x=x in cmap_relationE1)
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apply (simp only: heap_to_user_data_def Let_def ko_at_projectKO_opt)
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apply simp
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apply (drule h_t_valid_clift)
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apply (simp add: h_t_valid_dom_s pageBits_def)
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done
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lemma intvl_2_power_times_decomp:
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"\<forall>y < 2 ^ (n - m). {x + y * 2 ^ m ..+ 2 ^ m} \<times> S \<subseteq> T
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\<Longrightarrow> m \<le> n \<Longrightarrow> n < word_bits
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\<Longrightarrow> {(x :: word32) ..+ 2 ^ n} \<times> S \<subseteq> T"
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apply (clarsimp simp: intvl_def)
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apply (drule_tac x="of_nat k >> m" in spec)
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apply (drule mp)
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apply (rule shiftr_less_t2n)
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apply (rule word_of_nat_less)
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apply (simp add: word_of_nat_less)
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apply (erule subsetD)
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apply (clarsimp simp: shiftl_t2n[simplified mult.commute mult.left_commute, symmetric]
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shiftr_shiftl1)
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apply (rule_tac x="unat (of_nat k && mask m :: word32)" in exI)
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apply (simp add: field_simps word_plus_and_or_coroll2)
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apply (simp add: word_bits_def unat_less_power and_mask_less')
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done
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lemma flex_user_data_at_rf_sr_dom_s:
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"\<lbrakk> (\<forall>p<2 ^ (pageBitsForSize sz - pageBits).
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typ_at' UserDataT (x + p * 2 ^ pageBits) s); (s, s') \<in> rf_sr \<rbrakk>
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\<Longrightarrow> {x ..+ 2 ^ pageBitsForSize sz} \<times> {SIndexVal, SIndexTyp 0}
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\<subseteq> dom_s (hrs_htd (t_hrs_' (globals s')))"
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apply (rule_tac m=pageBits in intvl_2_power_times_decomp,
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simp_all add: pbfs_atleast_pageBits pbfs_less_wb')
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apply (erule allEI, clarsimp)
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apply (drule(1) user_data_at_rf_sr_dom_s)
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apply (erule subsetD)
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apply simp
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done
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lemma hrs_mem_update_fold_eq:
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"hrs_mem_update (fold f xs)
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= fold (hrs_mem_update o f) xs"
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apply (rule sym, induct xs)
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apply (simp add: hrs_mem_update_def)
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apply (simp add: hrs_mem_update_def fun_eq_iff)
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done
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lemma power_user_page_foldl_zero_ranges:
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" \<forall>p<2 ^ (pageBitsForSize sz - pageBits).
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hrs_htd hrs \<Turnstile>\<^sub>t (Ptr (ptr + of_nat p * 0x1000) :: user_data_C ptr)
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\<Longrightarrow> zero_ranges_are_zero rngs hrs
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\<Longrightarrow> zero_ranges_are_zero rngs
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(hrs_mem_update (\<lambda>s. foldl (\<lambda>s x. heap_update (Ptr x) (user_data_C (arr x)) s) s
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(map (\<lambda>n. ptr + of_nat n * 0x1000) [0..<2 ^ (pageBitsForSize sz - pageBits)]))
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hrs)"
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apply (simp add: foldl_conv_fold hrs_mem_update_fold_eq)
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apply (rule conjunct1)
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apply (rule fold_invariant[where P="\<lambda>hrs'. zero_ranges_are_zero rngs hrs'
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\<and> hrs_htd hrs' = hrs_htd hrs"
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and xs=xs and Q="\<lambda>x. x \<in> set xs" for xs], simp_all)
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apply (subst zero_ranges_are_zero_update, simp_all)
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apply clarsimp
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done
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declare replicate_numeral [simp]
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lemma coerce_memset_to_heap_update_pte:
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"heap_update_list x (replicateHider 4 0)
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= heap_update (Ptr x :: pte_C ptr)
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(pte_C.pte_C (FCP (\<lambda>x. 0)))"
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apply (intro ext, simp add: heap_update_def)
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apply (rule_tac f="\<lambda>xs. heap_update_list x xs a b" for a b in arg_cong)
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apply (simp add: to_bytes_def size_of_def typ_info_simps pte_C_tag_def)
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apply (simp add: ti_typ_pad_combine_empty_ti ti_typ_pad_combine_td align_of_def padup_def
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final_pad_def size_td_lt_ti_typ_pad_combine Let_def size_of_def)
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apply (simp add: typ_info_simps align_td_array' size_td_array)
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apply (simp add: typ_info_array' typ_info_word word_rsplit_0)
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apply (simp add: replicateHider_def)
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done
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lemma objBits_eq_by_type:
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fixes x :: "'a :: pspace_storable" and y :: 'a
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shows "objBits x = objBits y"
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apply (simp add: objBits_def)
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apply (rule objBits_type)
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apply (simp add: koTypeOf_injectKO)
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done
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lemma mapM_x_store_memset_ccorres_assist:
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fixes val :: "'a :: pspace_storable"
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assumes nofail: "\<not> snd (mapM_x (\<lambda>slot. setObject slot val) slots \<sigma>)"
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assumes slots1: "\<forall>n < length slots. slots ! n = hd slots + (of_nat n << objBits val)"
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assumes slots2: "n = length slots * (2 ^ objBits val)"
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assumes ptr: "ptr = hd slots"
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assumes ko: "\<And>ko :: 'a. updateObject ko = updateObject_default ko"
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"\<And>ko :: 'a. (1 :: word32) < 2 ^ objBits ko"
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assumes restr: "set slots \<subseteq> S"
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assumes worker: "\<And>ptr s s' (ko :: 'a). \<lbrakk> (s, s') \<in> rf_sr; ko_at' ko ptr s; ptr \<in> S \<rbrakk>
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\<Longrightarrow> (s \<lparr> ksPSpace := ksPSpace s (ptr \<mapsto> injectKO val)\<rparr>,
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globals_update (t_hrs_'_update (hrs_mem_update
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(heap_update_list ptr
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(replicateHider (2 ^ objBits val) (ucast c))))) s') \<in> rf_sr"
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assumes rf_sr: "(\<sigma>, s) \<in> rf_sr"
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shows
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"\<exists>(rv, \<sigma>') \<in> fst (mapM_x (\<lambda>slot. setObject slot val) slots \<sigma>).
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(\<sigma>', globals_update (t_hrs_'_update (hrs_mem_update
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(heap_update_list ptr (replicateHider n c)))) s) \<in> rf_sr"
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unfolding slots2 ptr using rf_sr slots1 nofail restr
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proof (induct slots arbitrary: s \<sigma>)
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case Nil
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show ?case
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using Nil.prems
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apply (simp add: mapM_x_def sequence_x_def return_def replicateHider_def)
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apply (simp add: rf_sr_def hrs_mem_update_def cstate_relation_def Let_def
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carch_state_relation_def cmachine_state_relation_def
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h_t_valid_clift_Some_iff)
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done
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next
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case (Cons x xs tPre sPre)
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note nofail_bind = Cons.prems(3)[unfolded mapM_x_Cons K_bind_def]
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have obj_at: "obj_at' (\<lambda>x :: 'a. True) x sPre"
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using not_snd_bindI1[OF nofail_bind]
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apply (subst(asm) setObject_obj_at_pre, simp_all add: ko snd_bind)
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apply (clarsimp simp: stateAssert_def exec_get return_def)
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apply (simp add: koTypeOf_injectKO typ_at_to_obj_at')
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done
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note in_setObject = setObject_eq[OF _ _ objBits_eq_by_type obj_at,
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where ko=val, simplified ko, simplified]
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note nofail_mapM = not_snd_bindI2[OF nofail_bind, OF in_setObject]
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have hd_xs: "xs \<noteq> [] \<Longrightarrow> hd xs = x + (2 ^ objBits val)"
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using Cons.prems(2)[rule_format, where n=1]
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by (simp add: hd_conv_nth)
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show ?case
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using obj_at_ko_at'[OF obj_at] Cons.prems(4)
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apply (clarsimp simp add: mapM_x_Cons bind_def split_def)
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apply (rule rev_bexI, rule in_setObject)
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apply (cut_tac Cons.hyps[OF _ _ nofail_mapM])
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defer
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apply (rule worker, rule Cons.prems, assumption+)
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apply clarsimp
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apply (case_tac "xs = []", simp_all)[1]
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apply (insert Cons.prems, simp)[1]
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apply (frule_tac x="Suc n" in spec)
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apply (simp add: hd_xs shiftl_t2n field_simps)
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apply assumption
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apply clarsimp
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apply (rule rev_bexI, assumption)
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apply (simp add: o_def)
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apply (case_tac "xs = []")
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apply (simp add: hrs_mem_update_def split_def replicateHider_def)
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apply (subst(asm) heap_update_list_concat_fold_hrs_mem)
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apply (simp add: hd_xs replicateHider_def)
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apply (simp add: replicateHider_def replicate_add)
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done
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qed
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lemma invalidateTLBByASID_ccorres:
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"ccorres dc xfdc (valid_pde_mappings' and (\<lambda>_. asid \<le> mask asid_bits))
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(UNIV \<inter> {s. asid_' s = asid}) []
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(invalidateTLBByASID asid) (Call invalidateTLBByASID_'proc)"
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apply (cinit lift: asid_')
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apply (ctac(no_vcg) add: loadHWASID_ccorres)
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apply csymbr
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apply (simp add: case_option_If2 del: Collect_const)
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apply (rule ccorres_if_cond_throws2[where Q=\<top> and Q'=\<top>])
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apply (clarsimp simp: pde_stored_asid_def to_bool_def split: if_split)
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apply (rule ccorres_return_void_C[unfolded dc_def])
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apply (simp add: dc_def[symmetric])
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apply csymbr
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apply (ctac add: invalidateTranslationASID_ccorres)
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apply vcg
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apply (wp hoare_drop_imps)
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apply (clarsimp simp: pde_stored_asid_def to_bool_def)
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done
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end
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lemma option_to_0_user_mem':
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"option_to_0 \<circ> user_mem' as =(\<lambda>x. if x \<in> {y. \<not> pointerInUserData y as} then 0
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else underlying_memory (ksMachineState as) x) "
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apply (rule ext)
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apply (simp add:user_mem'_def option_to_0_def split:if_splits)
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done
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lemma heap_to_user_data_in_user_mem'[simp]:
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"\<lbrakk>pspace_aligned' as;pspace_distinct' as\<rbrakk> \<Longrightarrow> heap_to_user_data (ksPSpace as) (option_to_0 \<circ> user_mem' as) =
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heap_to_user_data (ksPSpace as)(underlying_memory (ksMachineState as))"
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apply (rule ext)+
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apply (clarsimp simp: heap_to_user_data_def option_map_def
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split: option.splits)
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apply (subst option_to_0_user_mem')
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apply (subst map_option_byte_to_word_heap)
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apply (clarsimp simp: projectKO_opt_user_data map_comp_def
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split: option.split_asm kernel_object.split_asm)
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apply (frule(1) pspace_alignedD')
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apply (frule(1) pspace_distinctD')
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apply (subgoal_tac "x + ucast off * 4 + xa && ~~ mask pageBits = x" )
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apply (clarsimp simp: pointerInUserData_def typ_at'_def ko_wp_at'_def)
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apply (simp add: ARM.pageBits_def)
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apply (subst mask_lower_twice2[where n = 2 and m = 12,simplified,symmetric])
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apply (subst is_aligned_add_helper[THEN conjunct2,where n1 = 2])
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apply (erule aligned_add_aligned)
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apply (simp add: is_aligned_mult_triv2[where n = 2,simplified])
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apply (clarsimp simp: objBits_simps ARM.pageBits_def)
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apply simp
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apply (rule is_aligned_add_helper[THEN conjunct2])
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apply (simp add: ARM.pageBits_def objBits_simps)
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apply (rule word_less_power_trans2[where k = 2,simplified])
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apply (rule less_le_trans[OF ucast_less])
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apply simp+
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done
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context begin interpretation Arch . (*FIXME: arch_split*)
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crunch pde_mappings'[wp]: invalidateTLBByASID "valid_pde_mappings'"
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crunch ksArchState[wp]: invalidateTLBByASID "\<lambda>s. P (ksArchState s)"
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crunch gsMaxObjectSize[wp]: invalidateTLBByASID "\<lambda>s. P (gsMaxObjectSize s)"
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crunch gsMaxObjectSize[wp]: deleteASIDPool "\<lambda>s. P (gsMaxObjectSize s)"
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(ignore: setObject getObject wp: crunch_wps getObject_inv loadObject_default_inv
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simp: crunch_simps)
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end
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context kernel_m begin
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lemma page_table_at_rf_sr_dom_s:
|
|
"\<lbrakk> page_table_at' x s; (s, s') \<in> rf_sr \<rbrakk>
|
|
\<Longrightarrow> {x ..+ 2 ^ ptBits} \<times> {SIndexVal, SIndexTyp 0}
|
|
\<subseteq> dom_s (hrs_htd (t_hrs_' (globals s')))"
|
|
apply (rule_tac m=2 in intvl_2_power_times_decomp,
|
|
simp_all add: shiftl_t2n field_simps ptBits_def pageBits_def
|
|
word_bits_def pteBits_def)
|
|
apply (clarsimp simp: page_table_at'_def intvl_def)
|
|
apply (drule spec, drule(1) mp)
|
|
apply (simp add: typ_at_to_obj_at_arches)
|
|
apply (drule obj_at_ko_at', clarsimp)
|
|
apply (erule cmap_relationE1[OF rf_sr_cpte_relation])
|
|
apply (erule ko_at_projectKO_opt)
|
|
apply (drule h_t_valid_clift)
|
|
apply (drule h_t_valid_dom_s[OF _ refl refl])
|
|
apply (erule subsetD)
|
|
apply (auto simp add: intvl_def shiftl_t2n)[1]
|
|
done
|
|
|
|
lemma clearMemory_setObject_PTE_ccorres:
|
|
"ccorres dc xfdc (page_table_at' ptr
|
|
and (\<lambda>s. 2 ^ ptBits \<le> gsMaxObjectSize s)
|
|
and (\<lambda>_. is_aligned ptr ptBits \<and> ptr \<noteq> 0 \<and> pstart = addrFromPPtr ptr))
|
|
(UNIV \<inter> {s. ptr___ptr_to_unsigned_long_' s = Ptr ptr} \<inter> {s. bits_' s = of_nat ptBits}) []
|
|
(do x \<leftarrow> mapM_x (\<lambda>a. setObject a ARM_H.InvalidPTE)
|
|
[ptr , ptr + 2 ^ pteBits .e. ptr + 2 ^ ptBits - 1];
|
|
doMachineOp (cleanCacheRange_PoU ptr (ptr + 2 ^ ptBits - 1) pstart)
|
|
od)
|
|
(Call clearMemory_'proc)"
|
|
apply (rule ccorres_gen_asm)+
|
|
apply (cinit' lift: ptr___ptr_to_unsigned_long_' bits_')
|
|
apply (rule ccorres_Guard_Seq)
|
|
apply (rule ccorres_split_nothrow_novcg_dc)
|
|
apply (rule_tac P="page_table_at' ptr and (\<lambda>s. 2 ^ ptBits \<le> gsMaxObjectSize s)"
|
|
in ccorres_from_vcg_nofail[where P'=UNIV])
|
|
apply (rule allI, rule conseqPre, vcg)
|
|
apply clarsimp
|
|
apply (subst ghost_assertion_size_logic[unfolded o_def])
|
|
apply (simp add: ptBits_def pageBits_def pteBits_def)
|
|
apply simp
|
|
apply (clarsimp simp: replicateHider_def[symmetric])
|
|
apply (frule is_aligned_no_overflow')
|
|
apply (intro conjI)
|
|
apply (clarsimp simp add: ptBits_def pageBits_def pteBits_def
|
|
cong: StateSpace.state.fold_congs globals.fold_congs)
|
|
apply (erule is_aligned_weaken, simp add: ptBits_def pageBits_def)
|
|
apply (clarsimp simp: is_aligned_def ptBits_def pageBits_def pteBits_def)
|
|
apply (simp add: unat_of_nat32 order_less_le_trans[OF pt_bits_stuff(2)]
|
|
word_bits_def page_table_at_rf_sr_dom_s)
|
|
apply (clarsimp simp add: ptBits_def pageBits_def pteBits_def
|
|
cong: StateSpace.state.fold_congs globals.fold_congs)
|
|
apply (simp add: upto_enum_step_def objBits_simps ptBits_def pageBits_def
|
|
field_simps linorder_not_less[symmetric] archObjSize_def
|
|
upto_enum_word split_def pteBits_def)
|
|
apply (erule mapM_x_store_memset_ccorres_assist
|
|
[unfolded split_def, OF _ _ _ _ _ _ subset_refl],
|
|
simp_all add: shiftl_t2n hd_map objBits_simps archObjSize_def pteBits_def)[1]
|
|
apply (rule cmap_relationE1, erule rf_sr_cpte_relation, erule ko_at_projectKO_opt)
|
|
apply (subst coerce_memset_to_heap_update_pte)
|
|
apply (clarsimp simp: rf_sr_def Let_def cstate_relation_def typ_heap_simps)
|
|
apply (rule conjI)
|
|
apply (simp add: cpspace_relation_def typ_heap_simps update_pte_map_tos
|
|
update_pte_map_to_ptes carray_map_relation_upd_triv)
|
|
apply (rule cmap_relation_updI, simp_all)[1]
|
|
apply (simp add: cpte_relation_def Let_def pte_lift_def
|
|
fcp_beta pte_get_tag_def pte_tag_defs)
|
|
apply (simp add: carch_state_relation_def cmachine_state_relation_def
|
|
typ_heap_simps update_pte_map_tos)
|
|
apply csymbr
|
|
apply (rule ccorres_Guard)
|
|
apply (ctac add: cleanCacheRange_PoU_ccorres)
|
|
apply (wp mapM_x_wp' setObject_ksPSpace_only updateObject_default_inv | simp)+
|
|
apply (clarsimp simp: guard_is_UNIV_def ptBits_def pageBits_def pteBits_def)
|
|
apply (clarsimp simp: ptBits_def pageBits_def pteBits_def)
|
|
apply (frule is_aligned_addrFromPPtr_n, simp)
|
|
apply (clarsimp simp: is_aligned_no_overflow'[where n=10, simplified] pageBits_def
|
|
field_simps is_aligned_mask[symmetric] mask_AND_less_0)
|
|
done
|
|
|
|
lemma modify_gets_helper:
|
|
"do y \<leftarrow> modify (ksPSpace_update (\<lambda>_. ps)); ps' \<leftarrow> gets ksPSpace; f ps' od
|
|
= do y \<leftarrow> modify (ksPSpace_update (\<lambda>_. ps)); f ps od"
|
|
by (simp add: bind_def simpler_modify_def simpler_gets_def)
|
|
|
|
lemma snd_lookupAround2_update:
|
|
"ps y \<noteq> None \<Longrightarrow>
|
|
snd (lookupAround2 x (ps (y \<mapsto> v'))) = snd (lookupAround2 x ps)"
|
|
apply (clarsimp simp: lookupAround2_def lookupAround_def Let_def
|
|
dom_fun_upd2
|
|
simp del: dom_fun_upd cong: if_cong option.case_cong)
|
|
apply (clarsimp split: option.split if_split cong: if_cong)
|
|
apply auto
|
|
done
|
|
|
|
lemma double_setEndpoint:
|
|
"do y \<leftarrow> setEndpoint epptr v1; setEndpoint epptr v2 od
|
|
= setEndpoint epptr v2"
|
|
apply (simp add: setEndpoint_def setObject_def bind_assoc split_def
|
|
modify_gets_helper)
|
|
apply (simp add: updateObject_default_def bind_assoc objBits_simps)
|
|
apply (rule ext)
|
|
apply (rule bind_apply_cong, rule refl)+
|
|
apply (clarsimp simp add: in_monad projectKOs magnitudeCheck_assert
|
|
snd_lookupAround2_update)
|
|
apply (simp add: lookupAround2_known1 assert_opt_def projectKO_def projectKO_opt_ep
|
|
alignCheck_assert)
|
|
apply (simp add: bind_def simpler_modify_def)
|
|
done
|
|
|
|
lemma ccorres_inst_voodoo:
|
|
"\<forall>x. ccorres r xf (P x) (P' x) hs (h x) (c x)
|
|
\<Longrightarrow> \<forall>x. ccorres r xf (P x) (P' x) hs (h x) (c x)"
|
|
by simp
|
|
|
|
lemma cpspace_relation_ep_update_ep2:
|
|
"\<lbrakk> ko_at' (ep :: endpoint) epptr s;
|
|
cmap_relation (map_to_eps (ksPSpace s))
|
|
(cslift t) ep_Ptr (cendpoint_relation (cslift t));
|
|
cendpoint_relation (cslift t') ep' endpoint;
|
|
(cslift t' :: tcb_C ptr \<rightharpoonup> tcb_C) = cslift t \<rbrakk>
|
|
\<Longrightarrow> cmap_relation (map_to_eps (ksPSpace s(epptr \<mapsto> KOEndpoint ep')))
|
|
(cslift t(ep_Ptr epptr \<mapsto> endpoint))
|
|
ep_Ptr (cendpoint_relation (cslift t'))"
|
|
apply (rule cmap_relationE1, assumption, erule ko_at_projectKO_opt)
|
|
apply (rule_tac P="\<lambda>a. cmap_relation a b c d" for b c d in rsubst,
|
|
erule cmap_relation_upd_relI, assumption+)
|
|
apply simp+
|
|
apply (rule ext, simp add: map_comp_def projectKO_opt_ep split: if_split)
|
|
done
|
|
|
|
end
|
|
|
|
context begin interpretation Arch . (*FIXME: arch_split*)
|
|
lemma setObject_tcb_ep_obj_at'[wp]:
|
|
"\<lbrace>obj_at' (P :: endpoint \<Rightarrow> bool) ptr\<rbrace> setObject ptr' (tcb :: tcb) \<lbrace>\<lambda>rv. obj_at' P ptr\<rbrace>"
|
|
apply (rule obj_at_setObject2, simp_all)
|
|
apply (clarsimp simp: updateObject_default_def in_monad)
|
|
done
|
|
end
|
|
|
|
crunch ep_obj_at'[wp]: setThreadState "obj_at' (P :: endpoint \<Rightarrow> bool) ptr"
|
|
(ignore: getObject setObject simp: unless_def)
|
|
|
|
context kernel_m begin
|
|
|
|
lemma ccorres_subst_basic_helper:
|
|
"\<lbrakk> \<And>s s'. \<lbrakk> P s; s' \<in> P'; (s, s') \<in> rf_sr \<rbrakk> \<Longrightarrow> f s' = f' s';
|
|
\<And>s s'. \<lbrakk> P s; s' \<in> P'; (s, s') \<in> rf_sr \<rbrakk> \<Longrightarrow> (s, f' s') \<in> rf_sr;
|
|
\<And>s'. xf' (f' s') = v; \<And>rv' t t'. ceqv \<Gamma> xf' rv' t t' c (c' rv');
|
|
ccorres rrel xf Q Q' hs a (c' v) \<rbrakk>
|
|
\<Longrightarrow> ccorres rrel xf (P and Q) {s. s \<in> P' \<and> f' s \<in> Q'} hs a (Basic f ;; c)"
|
|
apply (rule ccorres_guard_imp2)
|
|
apply (rule ccorres_add_return)
|
|
apply (rule ccorres_split_nothrow[where xf'=xf' and r'="\<lambda>rv rv'. rv' = v"])
|
|
apply (rule ccorres_from_vcg[where P=P and P'=P'])
|
|
apply (rule allI, rule conseqPre, vcg)
|
|
apply (clarsimp simp: return_def)
|
|
apply assumption
|
|
apply simp
|
|
apply wp
|
|
apply vcg
|
|
apply clarsimp
|
|
done
|
|
|
|
lemma ctcb_relation_blocking_ipc_badge:
|
|
"\<lbrakk> ctcb_relation tcb ctcb; isBlockedOnSend (tcbState tcb) \<rbrakk> \<Longrightarrow>
|
|
tsType_CL (thread_state_lift (tcbState_C ctcb)) = scast ThreadState_BlockedOnSend"
|
|
"\<lbrakk> ctcb_relation tcb ctcb;
|
|
tsType_CL (thread_state_lift (tcbState_C ctcb)) = scast ThreadState_BlockedOnSend \<rbrakk>
|
|
\<Longrightarrow> blockingIPCBadge (tcbState tcb)
|
|
= blockingIPCBadge_CL (thread_state_lift (tcbState_C ctcb))"
|
|
apply (clarsimp simp add: ctcb_relation_def)
|
|
apply (simp add: isBlockedOnSend_def split: Structures_H.thread_state.split_asm)
|
|
apply (clarsimp simp: cthread_state_relation_def)
|
|
apply (clarsimp simp add: ctcb_relation_def cthread_state_relation_def)
|
|
apply (cases "tcbState tcb", simp_all add: "StrictC'_thread_state_defs")
|
|
done
|
|
|
|
lemma cendpoint_relation_q_cong:
|
|
"\<lbrakk> \<And>t rf. (t, rf) \<in> ep_q_refs_of' ep \<Longrightarrow> hp (tcb_ptr_to_ctcb_ptr t) = hp' (tcb_ptr_to_ctcb_ptr t) \<rbrakk>
|
|
\<Longrightarrow> cendpoint_relation hp ep ep' = cendpoint_relation hp' ep ep'"
|
|
apply (cases ep, simp_all add: cendpoint_relation_def Let_def)
|
|
apply (rule conj_cong [OF refl])
|
|
apply (rule tcb_queue_relation'_cong[OF refl refl refl])
|
|
apply clarsimp
|
|
apply (rule conj_cong [OF refl])
|
|
apply (rule tcb_queue_relation'_cong[OF refl refl refl])
|
|
apply clarsimp
|
|
done
|
|
|
|
lemma cnotification_relation_q_cong:
|
|
"\<lbrakk>\<And>t rf. (t, rf) \<in> ntfn_q_refs_of' (ntfnObj ntfn) \<Longrightarrow> hp (tcb_ptr_to_ctcb_ptr t) = hp' (tcb_ptr_to_ctcb_ptr t)\<rbrakk>
|
|
\<Longrightarrow> cnotification_relation hp ntfn ntfn' = cnotification_relation hp' ntfn ntfn'"
|
|
apply (cases "ntfnObj ntfn", simp_all add: cnotification_relation_def Let_def)
|
|
apply (auto intro: iffD1[OF tcb_queue_relation'_cong[OF refl refl refl]])
|
|
done
|
|
|
|
lemma tcbSchedEnqueue_ep_at:
|
|
"\<lbrace>obj_at' (P :: endpoint \<Rightarrow> bool) ep\<rbrace>
|
|
tcbSchedEnqueue t
|
|
\<lbrace>\<lambda>rv. obj_at' P ep\<rbrace>"
|
|
including no_pre
|
|
apply (simp add: tcbSchedEnqueue_def unless_def null_def)
|
|
apply (wp threadGet_wp, clarsimp, wp+)
|
|
apply (clarsimp split: if_split, wp)
|
|
done
|
|
|
|
lemma ccorres_duplicate_guard:
|
|
"ccorres r xf (P and P) Q hs f f' \<Longrightarrow> ccorres r xf P Q hs f f'"
|
|
by (erule ccorres_guard_imp, auto)
|
|
|
|
|
|
lemma ep_q_refs'_no_NTFNBound[simp]:
|
|
"(x, NTFNBound) \<notin> ep_q_refs_of' ep"
|
|
by (auto simp: ep_q_refs_of'_def split: endpoint.splits)
|
|
|
|
|
|
lemma ntfn_q_refs'_no_NTFNBound[simp]:
|
|
"(x, NTFNBound) \<notin> ntfn_q_refs_of' ntfn"
|
|
by (auto simp: ntfn_q_refs_of'_def split: ntfn.splits)
|
|
|
|
lemma cancelBadgedSends_ccorres:
|
|
"ccorres dc xfdc (invs' and ep_at' ptr)
|
|
(UNIV \<inter> {s. epptr_' s = Ptr ptr} \<inter> {s. badge_' s = bdg}) []
|
|
(cancelBadgedSends ptr bdg) (Call cancelBadgedSends_'proc)"
|
|
apply (cinit lift: epptr_' badge_' simp: whileAnno_def)
|
|
apply (simp add: list_case_return2
|
|
cong: list.case_cong Structures_H.endpoint.case_cong call_ignore_cong
|
|
del: Collect_const)
|
|
apply (rule ccorres_pre_getEndpoint)
|
|
apply (rule_tac R="ko_at' rv ptr" and xf'="ret__unsigned_'"
|
|
and val="case rv of RecvEP q \<Rightarrow> scast EPState_Recv | IdleEP \<Rightarrow> scast EPState_Idle
|
|
| SendEP q \<Rightarrow> scast EPState_Send"
|
|
in ccorres_symb_exec_r_known_rv_UNIV[where R'=UNIV])
|
|
apply vcg
|
|
apply clarsimp
|
|
apply (erule cmap_relationE1 [OF cmap_relation_ep], erule ko_at_projectKO_opt)
|
|
apply (clarsimp simp: typ_heap_simps cendpoint_relation_def Let_def
|
|
split: Structures_H.endpoint.split_asm)
|
|
apply ceqv
|
|
apply wpc
|
|
apply (simp add: dc_def[symmetric] ccorres_cond_iffs)
|
|
apply (rule ccorres_return_Skip)
|
|
apply (simp add: dc_def[symmetric] ccorres_cond_iffs)
|
|
apply (rule ccorres_return_Skip)
|
|
apply (rename_tac list)
|
|
apply (simp add: Collect_True Collect_False endpoint_state_defs
|
|
ccorres_cond_iffs dc_def[symmetric]
|
|
del: Collect_const cong: call_ignore_cong)
|
|
apply (rule ccorres_rhs_assoc)+
|
|
apply (csymbr, csymbr)
|
|
apply (drule_tac s = rv in sym, simp only:)
|
|
apply (rule_tac P="ko_at' rv ptr and invs'" in ccorres_cross_over_guard)
|
|
apply (rule ccorres_symb_exec_r)
|
|
apply (rule ccorres_rhs_assoc2, rule ccorres_rhs_assoc2)
|
|
apply (rule ccorres_split_nothrow[where r'=dc and xf'=xfdc, OF _ ceqv_refl])
|
|
apply (rule_tac P="ko_at' rv ptr"
|
|
in ccorres_from_vcg[where P'=UNIV])
|
|
apply (rule allI, rule conseqPre, vcg)
|
|
apply clarsimp
|
|
apply (rule cmap_relationE1[OF cmap_relation_ep], assumption)
|
|
apply (erule ko_at_projectKO_opt)
|
|
apply (clarsimp simp: typ_heap_simps setEndpoint_def)
|
|
apply (rule rev_bexI)
|
|
apply (rule setObject_eq; simp add: objBits_simps')[1]
|
|
apply (clarsimp simp: rf_sr_def cstate_relation_def
|
|
Let_def carch_state_relation_def
|
|
cmachine_state_relation_def
|
|
)
|
|
apply (clarsimp simp: cpspace_relation_def
|
|
update_ep_map_tos
|
|
typ_heap_simps')
|
|
apply (erule(1) cpspace_relation_ep_update_ep2)
|
|
apply (simp add: cendpoint_relation_def endpoint_state_defs)
|
|
subgoal by simp
|
|
apply (rule ccorres_symb_exec_r)
|
|
apply (rule_tac xs=list in filterM_voodoo)
|
|
apply (rule_tac P="\<lambda>xs s. (\<forall>x \<in> set xs \<union> set list.
|
|
st_tcb_at' (\<lambda>st. isBlockedOnSend st \<and> blockingObject st = ptr) x s)
|
|
\<and> distinct (xs @ list) \<and> ko_at' IdleEP ptr s
|
|
\<and> (\<forall>p. \<forall>x \<in> set (xs @ list). \<forall>rf. (x, rf) \<notin> {r \<in> state_refs_of' s p. snd r \<noteq> NTFNBound})
|
|
\<and> valid_queues s \<and> pspace_aligned' s \<and> pspace_distinct' s
|
|
\<and> sch_act_wf (ksSchedulerAction s) s \<and> valid_objs' s"
|
|
and P'="\<lambda>xs. {s. ep_queue_relation' (cslift s) (xs @ list)
|
|
(head_C (queue_' s)) (end_C (queue_' s))}
|
|
\<inter> {s. thread_' s = (case list of [] \<Rightarrow> tcb_Ptr 0
|
|
| x # xs \<Rightarrow> tcb_ptr_to_ctcb_ptr x)}"
|
|
in ccorres_inst_voodoo)
|
|
apply (induct_tac list)
|
|
apply (rule allI)
|
|
apply (rule iffD1 [OF ccorres_expand_while_iff_Seq])
|
|
apply (rule ccorres_tmp_lift2 [OF _ _ refl])
|
|
apply ceqv
|
|
apply (simp add: ccorres_cond_iffs)
|
|
apply (rule ccorres_rhs_assoc2)
|
|
apply (rule ccorres_duplicate_guard, rule ccorres_split_nothrow_novcg_dc)
|
|
apply (rule ccorres_from_vcg, rule allI, rule conseqPre, vcg)
|
|
apply clarsimp
|
|
apply (drule obj_at_ko_at', clarsimp)
|
|
apply (rule cmap_relationE1[OF cmap_relation_ep], assumption)
|
|
apply (erule ko_at_projectKO_opt)
|
|
apply (clarsimp simp: typ_heap_simps tcb_queue_relation'_def)
|
|
apply (case_tac x)
|
|
apply (clarsimp simp: setEndpoint_def)
|
|
apply (rule rev_bexI, rule setObject_eq,
|
|
(simp add: objBits_simps')+)
|
|
apply (clarsimp simp: rf_sr_def cstate_relation_def Let_def
|
|
carch_state_relation_def
|
|
cmachine_state_relation_def
|
|
cpspace_relation_def typ_heap_simps'
|
|
update_ep_map_tos)
|
|
apply (erule(1) cpspace_relation_ep_update_ep2)
|
|
subgoal by (simp add: cendpoint_relation_def Let_def)
|
|
subgoal by simp
|
|
apply (clarsimp simp: tcb_at_not_NULL[OF pred_tcb_at']
|
|
setEndpoint_def)
|
|
apply (rule rev_bexI, rule setObject_eq,
|
|
(simp add: objBits_simps')+)
|
|
apply (clarsimp simp: rf_sr_def cstate_relation_def Let_def
|
|
carch_state_relation_def
|
|
cmachine_state_relation_def
|
|
cpspace_relation_def typ_heap_simps'
|
|
update_ep_map_tos)
|
|
apply (erule(1) cpspace_relation_ep_update_ep2)
|
|
apply (simp add: cendpoint_relation_def Let_def)
|
|
apply (subgoal_tac "tcb_at' (last (a # list)) \<sigma> \<and> tcb_at' a \<sigma>")
|
|
apply (clarsimp simp: is_aligned_neg_mask_weaken[
|
|
OF is_aligned_tcb_ptr_to_ctcb_ptr[where P=\<top>]])
|
|
subgoal by (simp add: tcb_queue_relation'_def EPState_Send_def mask_def)
|
|
subgoal by (auto split: if_split)
|
|
subgoal by simp
|
|
apply (ctac add: rescheduleRequired_ccorres[unfolded dc_def])
|
|
apply (rule hoare_pre, wp weak_sch_act_wf_lift_linear set_ep_valid_objs')
|
|
apply (clarsimp simp: weak_sch_act_wf_def sch_act_wf_def)
|
|
apply (fastforce simp: valid_ep'_def pred_tcb_at' split: list.splits)
|
|
apply (simp add: guard_is_UNIV_def)
|
|
apply (rule allI)
|
|
apply (rename_tac a lista x)
|
|
apply (rule iffD1 [OF ccorres_expand_while_iff_Seq])
|
|
apply (rule ccorres_init_tmp_lift2, ceqv)
|
|
apply (rule ccorres_guard_imp2)
|
|
apply (simp add: bind_assoc dc_def[symmetric]
|
|
del: Collect_const)
|
|
apply (rule ccorres_cond_true)
|
|
apply (rule ccorres_rhs_assoc)+
|
|
apply (rule ccorres_pre_threadGet[where f=tcbState, folded getThreadState_def])
|
|
apply (rule ccorres_move_c_guard_tcb)
|
|
apply csymbr
|
|
apply (rule ccorres_abstract_cleanup)
|
|
apply csymbr
|
|
apply (rule ccorres_move_c_guard_tcb)
|
|
apply (rule_tac P=\<top>
|
|
and P'="{s. ep_queue_relation' (cslift s) (x @ a # lista)
|
|
(head_C (queue_' s)) (end_C (queue_' s))}"
|
|
and f'="\<lambda>s. s \<lparr> next___ptr_to_struct_tcb_C_' := (case lista of [] \<Rightarrow> tcb_Ptr 0
|
|
| v # vs \<Rightarrow> tcb_ptr_to_ctcb_ptr v) \<rparr>"
|
|
and xf'="next___ptr_to_struct_tcb_C_'"
|
|
in ccorres_subst_basic_helper)
|
|
apply (thin_tac "\<forall>x. P x" for P)
|
|
apply (rule myvars.fold_congs, (rule refl)+)
|
|
apply (clarsimp simp: tcb_queue_relation'_def use_tcb_queue_relation2
|
|
tcb_queue_relation2_concat)
|
|
apply (clarsimp simp: typ_heap_simps split: list.split)
|
|
subgoal by (simp add: rf_sr_def)
|
|
apply simp
|
|
apply ceqv
|
|
apply (rule_tac P="ret__unsigned=blockingIPCBadge rva" in ccorres_gen_asm2)
|
|
apply (rule ccorres_if_bind, rule ccorres_if_lhs)
|
|
apply (simp add: bind_assoc dc_def[symmetric])
|
|
apply (rule ccorres_rhs_assoc)+
|
|
apply (ctac add: setThreadState_ccorres)
|
|
apply (ctac add: tcbSchedEnqueue_ccorres)
|
|
apply (rule_tac P="\<lambda>s. \<forall>t \<in> set (x @ a # lista). tcb_at' t s"
|
|
in ccorres_cross_over_guard)
|
|
apply (rule ccorres_add_return, rule ccorres_split_nothrow[OF _ ceqv_refl])
|
|
apply (rule_tac rrel=dc and xf=xfdc
|
|
and P="\<lambda>s. (\<forall>t \<in> set (x @ a # lista). tcb_at' t s)
|
|
\<and> (\<forall>p. \<forall>t \<in> set (x @ a # lista). \<forall>rf. (t, rf) \<notin> {r \<in> state_refs_of' s p. snd r \<noteq> NTFNBound})
|
|
\<and> valid_queues s \<and> distinct (x @ a # lista)
|
|
\<and> pspace_aligned' s \<and> pspace_distinct' s"
|
|
and P'="{s. ep_queue_relation' (cslift s) (x @ a # lista)
|
|
(head_C (queue_' s)) (end_C (queue_' s))}"
|
|
in ccorres_from_vcg)
|
|
apply (thin_tac "\<forall>x. P x" for P)
|
|
apply (rule allI, rule conseqPre, vcg)
|
|
apply (clarsimp simp: ball_Un)
|
|
apply (rule exI, rule conjI)
|
|
apply (rule exI, erule conjI)
|
|
apply (intro conjI[rotated])
|
|
apply (assumption)
|
|
apply (fold_subgoals (prefix))[3]
|
|
subgoal premises prems using prems by (fastforce intro: pred_tcb_at')+
|
|
apply (clarsimp simp: return_def rf_sr_def cstate_relation_def Let_def)
|
|
apply (rule conjI)
|
|
apply (clarsimp simp: cpspace_relation_def)
|
|
apply (rule conjI, erule ctcb_relation_null_queue_ptrs)
|
|
apply (rule null_ep_queue)
|
|
subgoal by (simp add: o_def)
|
|
apply (rule conjI)
|
|
apply (erule iffD1 [OF cmap_relation_cong, OF refl refl, rotated -1])
|
|
apply clarsimp
|
|
apply (rule cendpoint_relation_q_cong)
|
|
apply (rule sym, erule restrict_map_eqI)
|
|
apply (clarsimp simp: image_iff)
|
|
apply (drule(2) map_to_ko_atI2)
|
|
apply (drule ko_at_state_refs_ofD')
|
|
apply clarsimp
|
|
apply (drule_tac x=p in spec)
|
|
subgoal by fastforce
|
|
apply (erule iffD1 [OF cmap_relation_cong, OF refl refl, rotated -1])
|
|
apply clarsimp
|
|
apply (drule(2) map_to_ko_atI2, drule ko_at_state_refs_ofD')
|
|
|
|
apply (rule cnotification_relation_q_cong)
|
|
apply (rule sym, erule restrict_map_eqI)
|
|
apply (clarsimp simp: image_iff)
|
|
apply (drule_tac x=p in spec)
|
|
subgoal by fastforce
|
|
apply (rule conjI)
|
|
apply (erule cready_queues_relation_not_queue_ptrs,
|
|
auto dest: null_ep_schedD[unfolded o_def] simp: o_def)[1]
|
|
apply (simp add: carch_state_relation_def
|
|
cmachine_state_relation_def
|
|
h_t_valid_clift_Some_iff)
|
|
apply (rule ccorres_symb_exec_r2)
|
|
apply (erule spec)
|
|
apply vcg
|
|
apply (vcg spec=modifies)
|
|
apply wp
|
|
apply simp
|
|
apply vcg
|
|
apply (wp hoare_vcg_const_Ball_lift tcbSchedEnqueue_ep_at
|
|
sch_act_wf_lift)
|
|
apply simp
|
|
apply (vcg exspec=tcbSchedEnqueue_cslift_spec)
|
|
apply (wp hoare_vcg_const_Ball_lift sts_st_tcb_at'_cases
|
|
sts_sch_act sts_valid_queues setThreadState_oa_queued)
|
|
apply (vcg exspec=setThreadState_cslift_spec)
|
|
apply (simp add: ccorres_cond_iffs dc_def[symmetric])
|
|
apply (rule ccorres_symb_exec_r2)
|
|
apply (drule_tac x="x @ [a]" in spec, simp add: dc_def[symmetric])
|
|
apply vcg
|
|
apply (vcg spec=modifies)
|
|
apply (thin_tac "\<forall>x. P x" for P)
|
|
apply (clarsimp simp: pred_tcb_at' ball_Un)
|
|
apply (rule conjI)
|
|
apply (clarsimp split: if_split)
|
|
subgoal by (fastforce simp: valid_tcb_state'_def valid_objs'_maxDomain
|
|
valid_objs'_maxPriority dest: pred_tcb_at')
|
|
apply (clarsimp simp: tcb_at_not_NULL [OF pred_tcb_at'])
|
|
apply (clarsimp simp: typ_heap_simps st_tcb_at'_def)
|
|
apply (drule(1) obj_at_cslift_tcb)
|
|
apply (clarsimp simp: ctcb_relation_blocking_ipc_badge)
|
|
apply (rule conjI, simp add: "StrictC'_thread_state_defs" mask_def)
|
|
apply (rule conjI)
|
|
apply clarsimp
|
|
apply (frule rf_sr_cscheduler_relation)
|
|
apply (clarsimp simp: cscheduler_action_relation_def st_tcb_at'_def
|
|
split: scheduler_action.split_asm)
|
|
apply (rename_tac word)
|
|
apply (frule_tac x=word in tcbSchedEnqueue_cslift_precond_discharge)
|
|
apply simp
|
|
subgoal by clarsimp
|
|
subgoal by clarsimp
|
|
subgoal by clarsimp
|
|
apply clarsimp
|
|
apply (rule conjI)
|
|
apply (frule(3) tcbSchedEnqueue_cslift_precond_discharge)
|
|
subgoal by clarsimp
|
|
apply clarsimp
|
|
apply (rule context_conjI)
|
|
apply (clarsimp simp: tcb_queue_relation'_def)
|
|
apply (erule iffD2[OF ep_queue_relation_shift[rule_format], rotated -1])
|
|
subgoal by simp
|
|
apply (rule_tac x="x @ a # lista" in exI)
|
|
apply (clarsimp simp: ball_Un)
|
|
apply (rule conjI, fastforce)
|
|
subgoal by (clarsimp simp: remove1_append)
|
|
apply vcg
|
|
apply (rule conseqPre, vcg)
|
|
apply clarsimp
|
|
apply (wp hoare_vcg_const_Ball_lift)
|
|
apply (wp obj_at_setObject3[where 'a=endpoint, folded setEndpoint_def])
|
|
apply (simp add: objBits_simps')+
|
|
apply (wp set_ep_valid_objs')
|
|
apply vcg
|
|
apply vcg
|
|
apply (rule conseqPre, vcg)
|
|
apply clarsimp
|
|
apply (clarsimp simp: guard_is_UNIV_def)
|
|
apply (erule cmap_relationE1[OF cmap_relation_ep], erule ko_at_projectKO_opt)
|
|
apply (clarsimp simp: typ_heap_simps)
|
|
apply (clarsimp simp: cendpoint_relation_def Let_def)
|
|
subgoal by (clarsimp simp: tcb_queue_relation'_def neq_Nil_conv
|
|
split: if_split_asm)
|
|
apply clarsimp
|
|
apply (frule ko_at_valid_objs', clarsimp)
|
|
apply (simp add: projectKOs)
|
|
apply (clarsimp simp: valid_obj'_def valid_ep'_def)
|
|
apply (frule sym_refs_ko_atD', clarsimp)
|
|
apply (clarsimp simp: st_tcb_at_refs_of_rev')
|
|
apply (rule conjI)
|
|
subgoal by (auto simp: isBlockedOnSend_def elim!: pred_tcb'_weakenE)
|
|
apply (rule conjI)
|
|
apply (clarsimp split: if_split)
|
|
apply (drule sym_refsD, clarsimp)
|
|
apply (drule(1) bspec)+
|
|
by (auto simp: obj_at'_def projectKOs state_refs_of'_def pred_tcb_at'_def tcb_bound_refs'_def
|
|
dest!: symreftype_inverse')
|
|
|
|
declare Kernel_C.tcb_C_size [simp del]
|
|
|
|
lemma cte_lift_ccte_relation:
|
|
"cte_lift cte' = Some ctel'
|
|
\<Longrightarrow> c_valid_cte cte'
|
|
\<Longrightarrow> ccte_relation (cte_to_H ctel') cte'"
|
|
by (simp add: ccte_relation_def)
|
|
|
|
lemma updateFreeIndex_ccorres:
|
|
"\<forall>s. \<Gamma> \<turnstile> ({s} \<inter> {s. \<exists>cte cte'. cslift s (cte_Ptr srcSlot) = Some cte'
|
|
\<and> cteCap cte = cap' \<and> ccte_relation cte cte'})
|
|
c
|
|
{t. \<exists>cap. cap_untyped_cap_lift cap = (cap_untyped_cap_lift
|
|
(cte_C.cap_C (the (cslift s (cte_Ptr srcSlot)))))
|
|
\<lparr> cap_untyped_cap_CL.capFreeIndex_CL := ((of_nat idx') >> 4) \<rparr>
|
|
\<and> cap_get_tag cap = scast cap_untyped_cap
|
|
\<and> t_hrs_' (globals t) = hrs_mem_update (heap_update (cte_Ptr srcSlot)
|
|
(cte_C.cap_C_update (\<lambda>_. cap) (the (cslift s (cte_Ptr srcSlot)))))
|
|
(t_hrs_' (globals s))
|
|
\<and> t may_only_modify_globals s in [t_hrs]
|
|
}
|
|
\<Longrightarrow> ccorres dc xfdc
|
|
(valid_objs' and cte_wp_at' (\<lambda>cte. isUntypedCap (cteCap cte)
|
|
\<and> cap' = (cteCap cte)) srcSlot
|
|
and untyped_ranges_zero'
|
|
and (\<lambda>_. is_aligned (of_nat idx' :: word32) 4 \<and> idx' \<le> 2 ^ (capBlockSize cap')))
|
|
{s. \<not> capIsDevice cap'
|
|
\<longrightarrow> region_actually_is_zero_bytes (capPtr cap' + of_nat idx') (capFreeIndex cap' - idx') s} hs
|
|
(updateFreeIndex srcSlot idx') c"
|
|
(is "_ \<Longrightarrow> ccorres dc xfdc (valid_objs' and ?cte_wp_at' and _ and _) ?P' hs ?a c")
|
|
apply (rule ccorres_gen_asm)
|
|
apply (simp add: updateFreeIndex_def getSlotCap_def updateCap_def)
|
|
apply (rule ccorres_guard_imp2)
|
|
apply (rule ccorres_split_noop_lhs, rule_tac cap'=cap' in updateTrackedFreeIndex_noop_ccorres)
|
|
apply (rule ccorres_pre_getCTE)+
|
|
apply (rename_tac cte cte2)
|
|
apply (rule_tac P = "\<lambda>s. ?cte_wp_at' s \<and> cte2 = cte \<and> cte_wp_at' ((=) cte) srcSlot s"
|
|
and P'="{s. \<exists>cte cte'. cslift s (cte_Ptr srcSlot) = Some cte'
|
|
\<and> cteCap cte = cap' \<and> ccte_relation cte cte'} \<inter> ?P'" in ccorres_from_vcg)
|
|
apply (rule allI, rule HoarePartial.conseq_exploit_pre, clarify)
|
|
apply (drule_tac x=s in spec, rule conseqPre, erule conseqPost)
|
|
defer
|
|
apply clarsimp
|
|
apply clarsimp
|
|
apply (simp add: cte_wp_at_ctes_of)
|
|
apply wp
|
|
apply (clarsimp simp: isCap_simps cte_wp_at_ctes_of)
|
|
apply (frule(1) rf_sr_ctes_of_clift)
|
|
apply clarsimp
|
|
apply (frule(1) cte_lift_ccte_relation)
|
|
apply (rule exI, intro conjI[rotated], assumption, simp_all)[1]
|
|
apply (clarsimp simp: cte_wp_at_ctes_of)
|
|
apply (erule(1) rf_sr_ctes_of_cliftE)
|
|
apply (frule(1) rf_sr_ctes_of_clift)
|
|
apply clarsimp
|
|
apply (subgoal_tac "ccap_relation (capFreeIndex_update (\<lambda>_. idx')
|
|
(cteCap (the (ctes_of \<sigma> srcSlot)))) cap")
|
|
apply (rule fst_setCTE [OF ctes_of_cte_at], assumption)
|
|
apply (erule bexI [rotated])
|
|
apply (clarsimp simp add: rf_sr_def cstate_relation_def Let_def
|
|
cvariable_array_map_const_add_map_option[where f="tcb_no_ctes_proj"]
|
|
isCap_simps)
|
|
apply (simp add:cpspace_relation_def)
|
|
apply (clarsimp simp:typ_heap_simps' modify_map_def mex_def meq_def)
|
|
apply (rule conjI)
|
|
apply (rule cpspace_cte_relation_upd_capI, assumption+)
|
|
apply (rule conjI)
|
|
apply (rule setCTE_tcb_case, assumption+)
|
|
apply (case_tac s', clarsimp)
|
|
subgoal by (simp add: carch_state_relation_def cmachine_state_relation_def
|
|
typ_heap_simps')
|
|
|
|
apply (clarsimp simp: isCap_simps)
|
|
apply (drule(1) cte_lift_ccte_relation,
|
|
drule ccte_relation_ccap_relation)
|
|
apply (simp add: cte_to_H_def)
|
|
apply (frule cap_get_tag_isCap_unfolded_H_cap)
|
|
apply (clarsimp simp: ccap_relation_def cap_lift_untyped_cap
|
|
cap_to_H_simps cap_untyped_cap_lift_def
|
|
is_aligned_shiftr_shiftl
|
|
dest!: ccte_relation_ccap_relation)
|
|
apply (rule unat_of_nat_eq unat_of_nat_eq[symmetric],
|
|
erule order_le_less_trans,
|
|
rule power_strict_increasing, simp_all)
|
|
apply (rule unat_less_helper, rule order_le_less_trans[OF word_and_le1], simp add: mask_def)
|
|
done
|
|
|
|
end
|
|
|
|
lemma ccap_relation_isDeviceCap2:
|
|
"\<lbrakk>ccap_relation cp cap; isUntypedCap cp
|
|
\<rbrakk> \<Longrightarrow> (capIsDevice_CL (cap_untyped_cap_lift cap) = 0) = (\<not> (capIsDevice cp))"
|
|
apply (frule cap_get_tag_UntypedCap)
|
|
apply (simp add:cap_get_tag_isCap to_bool_def)
|
|
done
|
|
end
|