1(* 2 * Copyright 2014, General Dynamics C4 Systems 3 * 4 * This software may be distributed and modified according to the terms of 5 * the GNU General Public License version 2. Note that NO WARRANTY is provided. 6 * See "LICENSE_GPLv2.txt" for details. 7 * 8 * @TAG(GD_GPL) 9 *) 10 11theory Recycle_C 12imports Delete_C Retype_C 13begin 14 15context kernel_m 16begin 17 18lemma isArchPageCap_ArchObjectCap: 19 "isArchPageCap (ArchObjectCap acap) 20 = isPageCap acap" 21 by (simp add: isArchPageCap_def isPageCap_def) 22 23definition 24 "replicateHider \<equiv> replicate" 25 26lemma collapse_foldl_replicate: 27 "replicate (length xs) v = xs \<Longrightarrow> 28 foldl (@) [] (map (\<lambda>_. xs) ys) 29 = replicateHider (length xs * length ys) v" 30 apply (induct ys rule: rev_induct) 31 apply (simp add: replicateHider_def) 32 apply (simp add: replicateHider_def) 33 apply (subst add.commute, simp add: replicate_add) 34 done 35 36lemma coerce_memset_to_heap_update_user_data: 37 "heap_update_list x (replicateHider 4096 0) 38 = heap_update (Ptr x :: user_data_C ptr) 39 (user_data_C (FCP (\<lambda>_. 0)))" 40 apply (intro ext, simp add: heap_update_def) 41 apply (rule_tac f="\<lambda>xs. heap_update_list x xs a b" for a b in arg_cong) 42 apply (simp add: to_bytes_def size_of_def typ_info_simps user_data_C_tag_def) 43 apply (simp add: ti_typ_pad_combine_empty_ti ti_typ_pad_combine_td align_of_def padup_def 44 final_pad_def size_td_lt_ti_typ_pad_combine Let_def size_of_def) 45 apply (simp add: typ_info_simps 46 user_context_C_tag_def thread_state_C_tag_def seL4_Fault_C_tag_def 47 lookup_fault_C_tag_def update_ti_t_ptr_0s 48 ti_typ_pad_combine_empty_ti ti_typ_pad_combine_td 49 ti_typ_combine_empty_ti ti_typ_combine_td 50 align_of_def padup_def 51 final_pad_def size_td_lt_ti_typ_pad_combine Let_def size_of_def 52 align_td_array' size_td_array) 53 apply (simp add: typ_info_array') 54 apply (subst access_ti_list_array) 55 apply simp 56 apply simp 57 apply (simp add: fcp_beta typ_info_word typ_info_ptr word_rsplit_0) 58 apply fastforce 59 apply (simp add: collapse_foldl_replicate) 60 done 61 62lemma clift_foldl_hrs_mem_update: 63 "\<lbrakk> \<forall>x \<in> set xs. hrs_htd s \<Turnstile>\<^sub>t f x; 64 \<And>x s. hrs_htd s \<Turnstile>\<^sub>t f x \<Longrightarrow> clift (hrs_mem_update (heap_update (f x) v) s) 65 = g (clift s :: ('a :: c_type) ptr \<rightharpoonup> 'a) x \<rbrakk> 66 \<Longrightarrow> 67 clift (hrs_mem_update (\<lambda>s. foldl (\<lambda>s x. heap_update (f x) v s) s xs) s) 68 = foldl g (clift s :: 'a ptr \<rightharpoonup> 'a) xs" 69 using [[hypsubst_thin]] 70 apply (cases s, clarsimp) 71 apply (induct xs arbitrary: a b) 72 apply (simp add: hrs_mem_update_def) 73 apply (clarsimp simp add: hrs_mem_update_def split_def hrs_htd_def) 74 done 75 76lemma map_to_user_data_aligned: 77 "\<lbrakk> map_to_user_data (ksPSpace s) x = Some y; pspace_aligned' s \<rbrakk> 78 \<Longrightarrow> is_aligned x pageBits" 79 apply (clarsimp simp: map_comp_eq projectKOs split: option.split_asm) 80 apply (drule(1) pspace_alignedD') 81 apply (simp add: objBits_simps) 82 done 83 84lemma help_force_intvl_range_conv: 85 "\<lbrakk> is_aligned (p::word32) n; v = 2 ^ n; n < word_bits \<rbrakk> 86 \<Longrightarrow> {p ..+ v} = {p .. p + 2 ^ n - 1}" 87 by (simp add: intvl_range_conv word_bits_def) 88 89lemma cmap_relation_If_upd: 90 "\<lbrakk> cmap_relation f g ptrfun rel; rel v v'; ptrfun ` S = S'; inj ptrfun \<rbrakk> 91 \<Longrightarrow> cmap_relation (\<lambda>x. if x \<in> S then Some v else f x) 92 (\<lambda>y. if y \<in> S' then Some v' else g y) 93 ptrfun rel" 94 apply (simp add: cmap_relation_def dom_If_Some) 95 apply (rule context_conjI) 96 apply blast 97 apply clarsimp 98 apply (case_tac "x \<in> S") 99 apply simp 100 apply clarsimp 101 apply (subst if_not_P) 102 apply (clarsimp simp: inj_eq) 103 apply (drule bspec, erule domI) 104 apply simp 105 done 106 107lemma length_replicateHider [simp]: 108 "length (replicateHider n x) = n" 109 by (simp add: replicateHider_def) 110 111lemma coerce_heap_update_to_heap_updates': 112 "n = chunk * m \<Longrightarrow> 113 heap_update_list x (replicateHider n 0) 114 = (\<lambda>s. foldl (\<lambda>s x. heap_update_list x (replicateHider chunk 0) s) s 115 (map (\<lambda>n. x + (of_nat n * of_nat chunk)) [0 ..< m]))" 116 using [[hypsubst_thin]] 117 apply clarsimp 118 apply (induct m arbitrary: x) 119 apply (rule ext, simp) 120 apply (simp add: replicateHider_def) 121 apply (rule ext) 122 apply (simp only: map_upt_unfold map_Suc_upt[symmetric]) 123 apply (simp add: replicate_add[folded replicateHider_def] 124 heap_update_list_concat_unfold 125 o_def field_simps 126 length_replicate[folded replicateHider_def]) 127 done 128 129lemma h_t_valid_dom_s: 130 "\<lbrakk> h_t_valid htd c_guard p; x = ptr_val (p :: ('a :: mem_type) ptr); 131 n = size_of TYPE ('a) \<rbrakk> 132 \<Longrightarrow> {x ..+ n} \<times> {SIndexVal, SIndexTyp 0} \<subseteq> dom_s htd" 133 apply (clarsimp simp: h_t_valid_def valid_footprint_def Let_def 134 intvl_def) 135 apply (drule_tac x=k in spec, simp add: size_of_def) 136 apply (clarsimp simp: dom_s_def) 137 apply (drule_tac x=0 in map_leD, simp_all) 138 done 139 140lemma user_data_at_rf_sr_dom_s: 141 "\<lbrakk> typ_at' UserDataT x s; (s, s') \<in> rf_sr \<rbrakk> 142 \<Longrightarrow> {x ..+ 2 ^ pageBits} \<times> {SIndexVal, SIndexTyp 0} 143 \<subseteq> dom_s (hrs_htd (t_hrs_' (globals s')))" 144 apply (drule rf_sr_heap_user_data_relation) 145 apply (drule user_data_at_ko) 146 apply (erule_tac x=x in cmap_relationE1) 147 apply (simp only: heap_to_user_data_def Let_def ko_at_projectKO_opt) 148 apply simp 149 apply (drule h_t_valid_clift) 150 apply (simp add: h_t_valid_dom_s pageBits_def) 151 done 152 153lemma device_data_at_rf_sr_dom_s: 154 "\<lbrakk> typ_at' UserDataDeviceT x s; (s, s') \<in> rf_sr \<rbrakk> 155 \<Longrightarrow> {x ..+ 2 ^ pageBits} \<times> {SIndexVal, SIndexTyp 0} 156 \<subseteq> dom_s (hrs_htd (t_hrs_' (globals s')))" 157 apply (drule rf_sr_heap_device_data_relation) 158 apply (drule device_data_at_ko) 159 apply (erule_tac x=x in cmap_relationE1) 160 apply (simp only: heap_to_device_data_def Let_def ko_at_projectKO_opt) 161 apply simp 162 apply (drule h_t_valid_clift) 163 apply (simp add: h_t_valid_dom_s pageBits_def) 164 done 165 166lemma intvl_2_power_times_decomp: 167 "\<forall>y < 2 ^ (n - m). {x + y * 2 ^ m ..+ 2 ^ m} \<times> S \<subseteq> T 168 \<Longrightarrow> m \<le> n \<Longrightarrow> n < word_bits 169 \<Longrightarrow> {(x :: word32) ..+ 2 ^ n} \<times> S \<subseteq> T" 170 apply (clarsimp simp: intvl_def) 171 apply (drule_tac x="of_nat k >> m" in spec) 172 apply (drule mp) 173 apply (rule shiftr_less_t2n) 174 apply (rule word_of_nat_less) 175 apply (simp add: word_of_nat_less) 176 apply (erule subsetD) 177 apply (clarsimp simp: shiftl_t2n[simplified mult.commute mult.left_commute, symmetric] 178 shiftr_shiftl1) 179 apply (rule_tac x="unat (of_nat k && mask m :: word32)" in exI) 180 apply (simp add: field_simps word_plus_and_or_coroll2) 181 apply (simp add: word_bits_def unat_less_power and_mask_less') 182 done 183 184lemma flex_user_data_at_rf_sr_dom_s: 185 "\<lbrakk> (\<forall>p<2 ^ (pageBitsForSize sz - pageBits). 186 typ_at' UserDataT (x + p * 2 ^ pageBits) s); (s, s') \<in> rf_sr \<rbrakk> 187 \<Longrightarrow> {x ..+ 2 ^ pageBitsForSize sz} \<times> {SIndexVal, SIndexTyp 0} 188 \<subseteq> dom_s (hrs_htd (t_hrs_' (globals s')))" 189 apply (rule_tac m=pageBits in intvl_2_power_times_decomp, 190 simp_all add: pbfs_atleast_pageBits pbfs_less_wb') 191 apply (erule allEI, clarsimp) 192 apply (drule(1) user_data_at_rf_sr_dom_s) 193 apply (erule subsetD) 194 apply simp 195 done 196 197lemma hrs_mem_update_fold_eq: 198 "hrs_mem_update (fold f xs) 199 = fold (hrs_mem_update o f) xs" 200 apply (rule sym, induct xs) 201 apply (simp add: hrs_mem_update_def) 202 apply (simp add: hrs_mem_update_def fun_eq_iff) 203 done 204 205lemma power_user_page_foldl_zero_ranges: 206 " \<forall>p<2 ^ (pageBitsForSize sz - pageBits). 207 hrs_htd hrs \<Turnstile>\<^sub>t (Ptr (ptr + of_nat p * 0x1000) :: user_data_C ptr) 208 \<Longrightarrow> zero_ranges_are_zero rngs hrs 209 \<Longrightarrow> zero_ranges_are_zero rngs 210 (hrs_mem_update (\<lambda>s. foldl (\<lambda>s x. heap_update (Ptr x) (user_data_C (arr x)) s) s 211 (map (\<lambda>n. ptr + of_nat n * 0x1000) [0..<2 ^ (pageBitsForSize sz - pageBits)])) 212 hrs)" 213 apply (simp add: foldl_conv_fold hrs_mem_update_fold_eq) 214 apply (rule conjunct1) 215 apply (rule fold_invariant[where P="\<lambda>hrs'. zero_ranges_are_zero rngs hrs' 216 \<and> hrs_htd hrs' = hrs_htd hrs" 217 and xs=xs and Q="\<lambda>x. x \<in> set xs" for xs], simp_all) 218 apply (subst zero_ranges_are_zero_update, simp_all) 219 apply clarsimp 220 done 221 222lemma heap_to_device_data_disj_mdf': 223 "\<lbrakk>is_aligned ptr (pageBitsForSize sz); ksPSpace \<sigma> a = Some obj; objBitsKO obj = pageBits; pspace_aligned' \<sigma>; 224 pspace_distinct' \<sigma>; pspace_no_overlap' ptr (pageBitsForSize sz) \<sigma>\<rbrakk> 225\<Longrightarrow> heap_to_device_data (ksPSpace \<sigma>) 226 (\<lambda>x. if x \<in> {ptr..+2 ^ (pageBitsForSize sz)} then 0 227 else underlying_memory (ksMachineState \<sigma>) x) 228 a = 229 heap_to_device_data (ksPSpace \<sigma>) (underlying_memory (ksMachineState \<sigma>)) a" 230 apply (cut_tac heap_to_device_data_disj_mdf[where ptr = ptr 231 and gbits = "pageBitsForSize sz - pageBits" and n = 1 232 and sz = "pageBitsForSize sz",simplified]) 233 apply (simp add: pbfs_atleast_pageBits pbfs_less_wb' field_simps| intro range_cover_full )+ 234 done 235 236lemma range_cover_nca_neg: "\<And>x p (off :: 10 word). 237 \<lbrakk>(x::word32) < 4; {p..+2 ^pageBits } \<inter> {ptr..ptr + (of_nat n * 2 ^ bits - 1)} = {}; 238 range_cover ptr sz bits n\<rbrakk> 239 \<Longrightarrow> p + ucast off * 4 + x \<notin> {ptr..+n * 2 ^ bits}" 240 apply (case_tac "n = 0") 241 apply simp 242 apply (subst range_cover_intvl,simp) 243 apply simp 244 apply (subgoal_tac " p + ucast off * 4 + x \<in> {p..+2 ^ pageBits}") 245 apply blast 246 apply (clarsimp simp: intvl_def) 247 apply (rule_tac x = "unat off * 4 + unat x" in exI) 248 apply (simp add: ucast_nat_def) 249 apply (rule nat_add_offset_less [where n = 2, simplified]) 250 apply (simp add: word_less_nat_alt) 251 apply (rule unat_lt2p) 252 apply (simp add: pageBits_def objBits_simps) 253 done 254 255 256 257lemma clearMemory_PageCap_ccorres: 258 "ccorres dc xfdc (invs' and valid_cap' (ArchObjectCap (PageCap False ptr undefined sz None)) 259 and (\<lambda>s. 2 ^ pageBitsForSize sz \<le> gsMaxObjectSize s) 260 and K ({ptr .. ptr + 2 ^ (pageBitsForSize sz) - 1} \<inter> kernel_data_refs = {}) 261 ) 262 (UNIV \<inter> {s. bits_' s = of_nat (pageBitsForSize sz)} 263 \<inter> {s. ptr___ptr_to_unsigned_long_' s = Ptr ptr}) 264 [] 265 (doMachineOp (clearMemory ptr (2 ^ pageBitsForSize sz))) (Call clearMemory_'proc)" 266 (is "ccorres dc xfdc ?P ?P' [] ?m ?c") 267 apply (cinit' lift: bits_' ptr___ptr_to_unsigned_long_') 268 apply (rule_tac P="capAligned (ArchObjectCap (PageCap False ptr undefined sz None))" 269 in ccorres_gen_asm) 270 apply (rule ccorres_Guard_Seq) 271 apply (simp add: clearMemory_def) 272 apply (simp add: doMachineOp_bind ef_storeWord) 273 apply (rule ccorres_split_nothrow_novcg_dc) 274 apply (rule_tac P="?P" in ccorres_from_vcg[where P'=UNIV]) 275 apply (rule allI, rule conseqPre, vcg) 276 apply (clarsimp simp: valid_cap'_def capAligned_def 277 is_aligned_no_wrap'[OF _ word32_power_less_1]) 278 apply (subgoal_tac "2 \<le> pageBitsForSize sz") 279 prefer 2 280 apply (simp add: pageBitsForSize_def split: vmpage_size.split) 281 apply (rule conjI) 282 apply (erule is_aligned_weaken) 283 apply (clarsimp simp: pageBitsForSize_def split: vmpage_size.splits) 284 apply (rule conjI) 285 apply (rule is_aligned_power2) 286 apply (clarsimp simp: pageBitsForSize_def split: vmpage_size.splits) 287 apply (clarsimp simp: ghost_assertion_size_logic[unfolded o_def]) 288 apply (simp add: flex_user_data_at_rf_sr_dom_s) 289 apply (clarsimp simp: field_simps word_size_def mapM_x_storeWord_step) 290 apply (simp add: doMachineOp_def split_def exec_gets) 291 apply (simp add: select_f_def simpler_modify_def bind_def) 292 apply (fold replicateHider_def)[1] 293 apply (subst coerce_heap_update_to_heap_updates' 294 [where chunk=4096 and m="2 ^ (pageBitsForSize sz - pageBits)"]) 295 apply (simp add: pageBitsForSize_def pageBits_def 296 split: vmpage_size.split) 297 apply (subst coerce_memset_to_heap_update_user_data) 298 apply (subgoal_tac "\<forall>p<2 ^ (pageBitsForSize sz - pageBits). 299 x \<Turnstile>\<^sub>c (Ptr (ptr + of_nat p * 0x1000) :: user_data_C ptr)") 300 prefer 2 301 apply (erule allfEI[where f=of_nat]) 302 apply clarsimp 303 apply (subst(asm) of_nat_power, assumption) 304 apply simp 305 apply (insert pageBitsForSize_32 [of sz])[1] 306 apply (erule order_le_less_trans [rotated]) 307 apply simp 308 apply (simp, drule ko_at_projectKO_opt[OF user_data_at_ko]) 309 apply (clarsimp simp: rf_sr_def cstate_relation_def Let_def cpspace_relation_def) 310 apply (erule cmap_relationE1, simp(no_asm) add: heap_to_user_data_def Let_def) 311 apply fastforce 312 subgoal by (simp add: pageBits_def typ_heap_simps) 313 apply (clarsimp simp: rf_sr_def cstate_relation_def Let_def) 314 apply (clarsimp simp: cpspace_relation_def typ_heap_simps 315 clift_foldl_hrs_mem_update foldl_id 316 carch_state_relation_def 317 cmachine_state_relation_def 318 foldl_fun_upd_const[unfolded fun_upd_def] 319 power_user_page_foldl_zero_ranges 320 dom_heap_to_device_data) 321 apply (rule conjI[rotated]) 322 apply (simp add:pageBitsForSize_mess_multi) 323 apply (rule cmap_relationI) 324 apply (clarsimp simp: dom_heap_to_device_data cmap_relation_def) 325 apply (simp add:cuser_user_data_device_relation_def) 326 apply (subst help_force_intvl_range_conv, assumption) 327 subgoal by (simp add: pageBitsForSize_def split: vmpage_size.split) 328 apply assumption 329 apply (subst heap_to_user_data_update_region) 330 apply (drule map_to_user_data_aligned, clarsimp) 331 apply (rule aligned_range_offset_mem[where m=pageBits], simp_all)[1] 332 apply (rule pbfs_atleast_pageBits) 333 apply (erule cmap_relation_If_upd) 334 apply (clarsimp simp: cuser_user_data_relation_def fcp_beta 335 order_less_le_trans[OF unat_lt2p]) 336 apply (fold word_rsplit_0, simp add: word_rcat_rsplit)[1] 337 apply (rule image_cong[OF _ refl]) 338 apply (rule set_eqI, rule iffI) 339 apply (clarsimp simp del: atLeastAtMost_iff) 340 apply (drule map_to_user_data_aligned, clarsimp) 341 apply (simp only: mask_in_range[symmetric]) 342 apply (rule_tac x="unat ((xa && mask (pageBitsForSize sz)) >> pageBits)" in image_eqI) 343 apply (simp add: subtract_mask(2)[symmetric]) 344 apply (cut_tac w="xa - ptr" and n=pageBits in and_not_mask[symmetric]) 345 apply (simp add: shiftl_t2n field_simps pageBits_def) 346 apply (subst is_aligned_neg_mask_eq, simp_all)[1] 347 apply (erule aligned_sub_aligned, simp_all add: word_bits_def)[1] 348 apply (erule is_aligned_weaken) 349 apply (rule pbfs_atleast_pageBits[unfolded pageBits_def]) 350 apply simp 351 apply (rule unat_less_power) 352 apply (fold word_bits_def, simp) 353 apply (rule shiftr_less_t2n) 354 apply (simp add: pbfs_atleast_pageBits) 355 apply (rule and_mask_less_size) 356 apply (simp add: word_bits_def word_size) 357 apply (rule IntI) 358 apply (clarsimp simp del: atLeastAtMost_iff) 359 apply (subst aligned_range_offset_mem, assumption, simp_all)[1] 360 apply (rule order_le_less_trans[rotated], erule shiftl_less_t2n [OF of_nat_power], 361 simp_all add: word_bits_def)[1] 362 apply (insert pageBitsForSize_32 [of sz])[1] 363 apply (erule order_le_less_trans [rotated]) 364 subgoal by simp 365 subgoal by (simp add: pageBits_def shiftl_t2n field_simps) 366 apply clarsimp 367 apply (drule_tac x="of_nat n" in spec) 368 apply (simp add: of_nat_power[where 'a=32, folded word_bits_def]) 369 apply (rule exI) 370 subgoal by (simp add: pageBits_def ko_at_projectKO_opt[OF user_data_at_ko]) 371 subgoal by simp 372 apply csymbr 373 apply (ctac add: cleanCacheRange_PoU_ccorres[unfolded dc_def]) 374 apply wp 375 apply (simp add: guard_is_UNIV_def unat_of_nat 376 word_bits_def capAligned_def word_of_nat_less) 377 apply (clarsimp simp: word_bits_def valid_cap'_def 378 capAligned_def word_of_nat_less) 379 apply (frule is_aligned_addrFromPPtr_n, simp add: pageBitsForSize_def split: vmpage_size.splits) 380 by (clarsimp simp: is_aligned_no_overflow'[where n=12, simplified] 381 is_aligned_no_overflow'[where n=16, simplified] 382 is_aligned_no_overflow'[where n=20, simplified] 383 is_aligned_no_overflow'[where n=24, simplified] pageBits_def 384 field_simps is_aligned_mask[symmetric] mask_AND_less_0 385 pageBitsForSize_def split: vmpage_size.splits) 386 387lemma coerce_memset_to_heap_update_asidpool: 388 "heap_update_list x (replicateHider 4096 0) 389 = heap_update (Ptr x :: asid_pool_C ptr) 390 (asid_pool_C (FCP (\<lambda>x. Ptr 0)))" 391 apply (intro ext, simp add: heap_update_def) 392 apply (rule_tac f="\<lambda>xs. heap_update_list x xs a b" for a b in arg_cong) 393 apply (simp add: to_bytes_def size_of_def typ_info_simps asid_pool_C_tag_def) 394 apply (simp add: ti_typ_pad_combine_empty_ti ti_typ_pad_combine_td align_of_def padup_def 395 final_pad_def size_td_lt_ti_typ_pad_combine Let_def size_of_def) 396 apply (simp add: typ_info_simps 397 user_context_C_tag_def thread_state_C_tag_def seL4_Fault_C_tag_def 398 lookup_fault_C_tag_def update_ti_t_ptr_0s 399 ti_typ_pad_combine_empty_ti ti_typ_pad_combine_td 400 ti_typ_combine_empty_ti ti_typ_combine_td 401 align_of_def padup_def 402 final_pad_def size_td_lt_ti_typ_pad_combine Let_def size_of_def 403 align_td_array' size_td_array) 404 apply (simp add: typ_info_array') 405 apply (subst access_ti_list_array) 406 apply simp 407 apply simp 408 apply (simp add: fcp_beta typ_info_word typ_info_ptr word_rsplit_0) 409 apply fastforce 410 apply (simp add: collapse_foldl_replicate) 411 done 412 413declare replicate_numeral [simp] 414 415lemma coerce_memset_to_heap_update_pte: 416 "heap_update_list x (replicateHider 4 0) 417 = heap_update (Ptr x :: pte_C ptr) 418 (pte_C.pte_C (FCP (\<lambda>x. 0)))" 419 apply (intro ext, simp add: heap_update_def) 420 apply (rule_tac f="\<lambda>xs. heap_update_list x xs a b" for a b in arg_cong) 421 apply (simp add: to_bytes_def size_of_def typ_info_simps pte_C_tag_def) 422 apply (simp add: ti_typ_pad_combine_empty_ti ti_typ_pad_combine_td align_of_def padup_def 423 final_pad_def size_td_lt_ti_typ_pad_combine Let_def size_of_def) 424 apply (simp add: typ_info_simps align_td_array' size_td_array) 425 apply (simp add: typ_info_array' typ_info_word word_rsplit_0) 426 apply (simp add: replicateHider_def) 427 done 428 429lemma coerce_memset_to_heap_update_pde: 430 "heap_update_list x (replicateHider 4 0) 431 = heap_update (Ptr x :: pde_C ptr) 432 (pde_C.pde_C (FCP (\<lambda>x. 0)))" 433 apply (intro ext, simp add: heap_update_def) 434 apply (rule_tac f="\<lambda>xs. heap_update_list x xs a b" for a b in arg_cong) 435 apply (simp add: to_bytes_def size_of_def typ_info_simps pde_C_tag_def) 436 apply (simp add: ti_typ_pad_combine_empty_ti ti_typ_pad_combine_td align_of_def padup_def 437 final_pad_def size_td_lt_ti_typ_pad_combine Let_def size_of_def) 438 apply (simp add: typ_info_simps align_td_array' size_td_array) 439 apply (simp add: typ_info_array' typ_info_word word_rsplit_0) 440 apply (simp add: replicateHider_def) 441 done 442 443lemma objBits_eq_by_type: 444 fixes x :: "'a :: pspace_storable" and y :: 'a 445 shows "objBits x = objBits y" 446 apply (simp add: objBits_def) 447 apply (rule objBits_type) 448 apply (simp add: koTypeOf_injectKO) 449 done 450 451lemma mapM_x_store_memset_ccorres_assist: 452 fixes val :: "'a :: pspace_storable" 453 assumes nofail: "\<not> snd (mapM_x (\<lambda>slot. setObject slot val) slots \<sigma>)" 454 assumes slots1: "\<forall>n < length slots. slots ! n = hd slots + (of_nat n << objBits val)" 455 assumes slots2: "n = length slots * (2 ^ objBits val)" 456 assumes ptr: "ptr = hd slots" 457 assumes ko: "\<And>ko :: 'a. updateObject ko = updateObject_default ko" 458 "\<And>ko :: 'a. (1 :: word32) < 2 ^ objBits ko" 459 assumes restr: "set slots \<subseteq> S" 460 assumes worker: "\<And>ptr s s' (ko :: 'a). \<lbrakk> (s, s') \<in> rf_sr; ko_at' ko ptr s; ptr \<in> S \<rbrakk> 461 \<Longrightarrow> (s \<lparr> ksPSpace := ksPSpace s (ptr \<mapsto> injectKO val)\<rparr>, 462 globals_update (t_hrs_'_update (hrs_mem_update 463 (heap_update_list ptr 464 (replicateHider (2 ^ objBits val) (ucast c))))) s') \<in> rf_sr" 465 assumes rf_sr: "(\<sigma>, s) \<in> rf_sr" 466 shows 467 "\<exists>(rv, \<sigma>') \<in> fst (mapM_x (\<lambda>slot. setObject slot val) slots \<sigma>). 468 (\<sigma>', globals_update (t_hrs_'_update (hrs_mem_update 469 (heap_update_list ptr (replicateHider n c)))) s) \<in> rf_sr" 470 unfolding slots2 ptr using rf_sr slots1 nofail restr 471proof (induct slots arbitrary: s \<sigma>) 472 case Nil 473 show ?case 474 using Nil.prems 475 apply (simp add: mapM_x_def sequence_x_def return_def replicateHider_def) 476 apply (simp add: rf_sr_def hrs_mem_update_def cstate_relation_def Let_def 477 carch_state_relation_def cmachine_state_relation_def 478 h_t_valid_clift_Some_iff) 479 done 480next 481 case (Cons x xs tPre sPre) 482 483 note nofail_bind = Cons.prems(3)[unfolded mapM_x_Cons K_bind_def] 484 485 have obj_at: "obj_at' (\<lambda>x :: 'a. True) x sPre" 486 using not_snd_bindI1[OF nofail_bind] 487 apply (subst(asm) setObject_obj_at_pre, simp_all add: ko snd_bind) 488 apply (clarsimp simp: stateAssert_def exec_get return_def) 489 apply (simp add: koTypeOf_injectKO typ_at_to_obj_at') 490 done 491 492 note in_setObject = setObject_eq[OF _ _ objBits_eq_by_type obj_at, 493 where ko=val, simplified ko, simplified] 494 495 note nofail_mapM = not_snd_bindI2[OF nofail_bind, OF in_setObject] 496 497 have hd_xs: "xs \<noteq> [] \<Longrightarrow> hd xs = x + (2 ^ objBits val)" 498 using Cons.prems(2)[rule_format, where n=1] 499 by (simp add: hd_conv_nth) 500 501 show ?case 502 using obj_at_ko_at'[OF obj_at] Cons.prems(4) 503 apply (clarsimp simp add: mapM_x_Cons bind_def split_def) 504 apply (rule rev_bexI, rule in_setObject) 505 apply (cut_tac Cons.hyps[OF _ _ nofail_mapM]) 506 defer 507 apply (rule worker, rule Cons.prems, assumption+) 508 apply clarsimp 509 apply (case_tac "xs = []", simp_all)[1] 510 apply (insert Cons.prems, simp)[1] 511 apply (frule_tac x="Suc n" in spec) 512 apply (simp add: hd_xs shiftl_t2n field_simps) 513 apply assumption 514 apply clarsimp 515 apply (rule rev_bexI, assumption) 516 apply (simp add: o_def) 517 apply (case_tac "xs = []") 518 apply (simp add: hrs_mem_update_def split_def replicateHider_def) 519 apply (subst(asm) heap_update_list_concat_fold_hrs_mem) 520 apply (simp add: hd_xs replicateHider_def) 521 apply (simp add: replicateHider_def replicate_add) 522 done 523qed 524 525lemma invalidateTLBByASID_ccorres: 526 "ccorres dc xfdc (valid_pde_mappings' and (\<lambda>_. asid \<le> mask asid_bits)) 527 (UNIV \<inter> {s. asid_' s = asid}) [] 528 (invalidateTLBByASID asid) (Call invalidateTLBByASID_'proc)" 529 apply (cinit lift: asid_') 530 apply (ctac(no_vcg) add: loadHWASID_ccorres) 531 apply csymbr 532 apply (simp add: case_option_If2 del: Collect_const) 533 apply (rule ccorres_if_cond_throws2[where Q=\<top> and Q'=\<top>]) 534 apply (clarsimp simp: pde_stored_asid_def to_bool_def split: if_split) 535 apply (rule ccorres_return_void_C[unfolded dc_def]) 536 apply (simp add: dc_def[symmetric]) 537 apply csymbr 538 apply (ctac add: invalidateTranslationASID_ccorres) 539 apply vcg 540 apply (wp hoare_drop_imps) 541 apply (clarsimp simp: pde_stored_asid_def to_bool_def) 542 done 543 544(* FIXME: also in VSpace_C *) 545lemma ignoreFailure_liftM: 546 "ignoreFailure = liftM (\<lambda>v. ())" 547 apply (rule ext)+ 548 apply (simp add: ignoreFailure_def liftM_def 549 catch_def) 550 apply (rule bind_apply_cong[OF refl]) 551 apply (simp split: sum.split) 552 done 553 554end 555 556lemma option_to_0_user_mem': 557 "option_to_0 \<circ> user_mem' as =(\<lambda>x. if x \<in> {y. \<not> pointerInUserData y as} then 0 558 else underlying_memory (ksMachineState as) x) " 559 apply (rule ext) 560 apply (simp add:user_mem'_def option_to_0_def split:if_splits) 561 done 562 563lemma heap_to_user_data_in_user_mem'[simp]: 564 "\<lbrakk>pspace_aligned' as;pspace_distinct' as\<rbrakk> \<Longrightarrow> heap_to_user_data (ksPSpace as) (option_to_0 \<circ> user_mem' as) = 565 heap_to_user_data (ksPSpace as)(underlying_memory (ksMachineState as))" 566 apply (rule ext)+ 567 apply (clarsimp simp: heap_to_user_data_def option_map_def 568 split: option.splits) 569 apply (subst option_to_0_user_mem') 570 apply (subst map_option_byte_to_word_heap) 571 apply (clarsimp simp: projectKO_opt_user_data map_comp_def 572 split: option.split_asm kernel_object.split_asm) 573 apply (frule(1) pspace_alignedD') 574 apply (frule(1) pspace_distinctD') 575 apply (subgoal_tac "x + ucast off * 4 + xa && ~~ mask pageBits = x" ) 576 apply (clarsimp simp: pointerInUserData_def typ_at'_def ko_wp_at'_def) 577 apply (simp add: ARM.pageBits_def) 578 apply (subst mask_lower_twice2[where n = 2 and m = 12,simplified,symmetric]) 579 apply (subst is_aligned_add_helper[THEN conjunct2,where n1 = 2]) 580 apply (erule aligned_add_aligned) 581 apply (simp add: is_aligned_mult_triv2[where n = 2,simplified]) 582 apply (clarsimp simp: objBits_simps ARM.pageBits_def) 583 apply simp 584 apply (rule is_aligned_add_helper[THEN conjunct2]) 585 apply (simp add: ARM.pageBits_def objBits_simps) 586 apply (rule word_less_power_trans2[where k = 2,simplified]) 587 apply (rule less_le_trans[OF ucast_less]) 588 apply simp+ 589 done 590 591context begin interpretation Arch . (*FIXME: arch_split*) 592 593crunch pde_mappings'[wp]: invalidateTLBByASID "valid_pde_mappings'" 594crunch ksArchState[wp]: invalidateTLBByASID "\<lambda>s. P (ksArchState s)" 595 596crunch gsMaxObjectSize[wp]: invalidateTLBByASID "\<lambda>s. P (gsMaxObjectSize s)" 597crunch gsMaxObjectSize[wp]: deleteASIDPool "\<lambda>s. P (gsMaxObjectSize s)" 598 (ignore: setObject getObject wp: crunch_wps getObject_inv loadObject_default_inv 599 simp: crunch_simps) 600end 601 602context kernel_m begin 603 604lemma page_table_at_rf_sr_dom_s: 605 "\<lbrakk> page_table_at' x s; (s, s') \<in> rf_sr \<rbrakk> 606 \<Longrightarrow> {x ..+ 2 ^ ptBits} \<times> {SIndexVal, SIndexTyp 0} 607 \<subseteq> dom_s (hrs_htd (t_hrs_' (globals s')))" 608 apply (rule_tac m=2 in intvl_2_power_times_decomp, 609 simp_all add: shiftl_t2n field_simps ptBits_def pageBits_def 610 word_bits_def pteBits_def) 611 apply (clarsimp simp: page_table_at'_def intvl_def) 612 apply (drule spec, drule(1) mp) 613 apply (simp add: typ_at_to_obj_at_arches) 614 apply (drule obj_at_ko_at', clarsimp) 615 apply (erule cmap_relationE1[OF rf_sr_cpte_relation]) 616 apply (erule ko_at_projectKO_opt) 617 apply (drule h_t_valid_clift) 618 apply (drule h_t_valid_dom_s[OF _ refl refl]) 619 apply (erule subsetD) 620 apply (auto simp add: intvl_def shiftl_t2n)[1] 621 done 622 623lemma page_directory_at_rf_sr_dom_s: 624 "\<lbrakk> page_directory_at' x s; (s, s') \<in> rf_sr \<rbrakk> 625 \<Longrightarrow> {x ..+ 2 ^ pdBits} \<times> {SIndexVal, SIndexTyp 0} 626 \<subseteq> dom_s (hrs_htd (t_hrs_' (globals s')))" 627 apply (rule_tac m=2 in intvl_2_power_times_decomp, 628 simp_all add: shiftl_t2n field_simps pdBits_def pageBits_def 629 word_bits_def pdeBits_def) 630 apply (clarsimp simp: page_directory_at'_def intvl_def) 631 apply (drule spec, drule(1) mp) 632 apply (simp add: typ_at_to_obj_at_arches) 633 apply (drule obj_at_ko_at', clarsimp) 634 apply (erule cmap_relationE1[OF rf_sr_cpde_relation]) 635 apply (erule ko_at_projectKO_opt) 636 apply (drule h_t_valid_clift) 637 apply (drule h_t_valid_dom_s[OF _ refl refl]) 638 apply (erule subsetD) 639 apply (auto simp add: intvl_def shiftl_t2n)[1] 640 done 641 642lemma clearMemory_setObject_PTE_ccorres: 643 "ccorres dc xfdc (page_table_at' ptr 644 and (\<lambda>s. 2 ^ ptBits \<le> gsMaxObjectSize s) 645 and (\<lambda>_. is_aligned ptr ptBits \<and> ptr \<noteq> 0 \<and> pstart = addrFromPPtr ptr)) 646 (UNIV \<inter> {s. ptr___ptr_to_unsigned_long_' s = Ptr ptr} \<inter> {s. bits_' s = of_nat ptBits}) [] 647 (do x \<leftarrow> mapM_x (\<lambda>a. setObject a ARM_H.InvalidPTE) 648 [ptr , ptr + 2 ^ pteBits .e. ptr + 2 ^ ptBits - 1]; 649 doMachineOp (cleanCacheRange_PoU ptr (ptr + 2 ^ ptBits - 1) pstart) 650 od) 651 (Call clearMemory_'proc)" 652 apply (rule ccorres_gen_asm)+ 653 apply (cinit' lift: ptr___ptr_to_unsigned_long_' bits_') 654 apply (rule ccorres_Guard_Seq) 655 apply (rule ccorres_split_nothrow_novcg_dc) 656 apply (rule_tac P="page_table_at' ptr and (\<lambda>s. 2 ^ ptBits \<le> gsMaxObjectSize s)" 657 in ccorres_from_vcg_nofail[where P'=UNIV]) 658 apply (rule allI, rule conseqPre, vcg) 659 apply clarsimp 660 apply (subst ghost_assertion_size_logic[unfolded o_def]) 661 apply (simp add: ptBits_def pageBits_def pteBits_def) 662 apply simp 663 apply (clarsimp simp: replicateHider_def[symmetric]) 664 apply (frule is_aligned_no_overflow') 665 apply (intro conjI) 666 apply (clarsimp simp add: ptBits_def pageBits_def pteBits_def 667 cong: StateSpace.state.fold_congs globals.fold_congs) 668 apply (erule is_aligned_weaken, simp add: ptBits_def pageBits_def) 669 apply (clarsimp simp: is_aligned_def ptBits_def pageBits_def pteBits_def) 670 apply (simp add: unat_of_nat32 order_less_le_trans[OF pt_bits_stuff(2)] 671 word_bits_def page_table_at_rf_sr_dom_s) 672 apply (clarsimp simp add: ptBits_def pageBits_def pteBits_def 673 cong: StateSpace.state.fold_congs globals.fold_congs) 674 apply (simp add: upto_enum_step_def objBits_simps ptBits_def pageBits_def 675 field_simps linorder_not_less[symmetric] archObjSize_def 676 upto_enum_word split_def pteBits_def) 677 apply (erule mapM_x_store_memset_ccorres_assist 678 [unfolded split_def, OF _ _ _ _ _ _ subset_refl], 679 simp_all add: shiftl_t2n hd_map objBits_simps archObjSize_def pteBits_def)[1] 680 apply (rule cmap_relationE1, erule rf_sr_cpte_relation, erule ko_at_projectKO_opt) 681 apply (subst coerce_memset_to_heap_update_pte) 682 apply (clarsimp simp: rf_sr_def Let_def cstate_relation_def typ_heap_simps) 683 apply (rule conjI) 684 apply (simp add: cpspace_relation_def typ_heap_simps update_pte_map_tos 685 update_pte_map_to_ptes carray_map_relation_upd_triv) 686 apply (rule cmap_relation_updI, simp_all)[1] 687 apply (simp add: cpte_relation_def Let_def pte_lift_def 688 fcp_beta pte_get_tag_def pte_tag_defs) 689 apply (simp add: carch_state_relation_def cmachine_state_relation_def 690 typ_heap_simps update_pte_map_tos) 691 apply csymbr 692 apply (rule ccorres_Guard) 693 apply (ctac add: cleanCacheRange_PoU_ccorres) 694 apply (wp mapM_x_wp' setObject_ksPSpace_only updateObject_default_inv | simp)+ 695 apply (clarsimp simp: guard_is_UNIV_def ptBits_def pageBits_def pteBits_def) 696 apply (clarsimp simp: ptBits_def pageBits_def pteBits_def) 697 apply (frule is_aligned_addrFromPPtr_n, simp) 698 apply (clarsimp simp: is_aligned_no_overflow'[where n=10, simplified] pageBits_def 699 field_simps is_aligned_mask[symmetric] mask_AND_less_0) 700 done 701 702lemma ccorres_make_xfdc: 703 "ccorresG rf_sr \<Gamma> r xf P P' h a c \<Longrightarrow> ccorresG rf_sr \<Gamma> dc xfdc P P' h a c" 704 apply (erule ccorres_rel_imp) 705 apply simp 706 done 707 708lemma ccorres_if_True_False_simps: 709 "ccorres r xf P P' hs a (IF True THEN c ELSE c' FI) = ccorres r xf P P' hs a c" 710 "ccorres r xf P P' hs a (IF False THEN c ELSE c' FI) = ccorres r xf P P' hs a c'" 711 "ccorres r xf P P' hs a (IF True THEN c ELSE c' FI ;; d) = ccorres r xf P P' hs a (c ;; d)" 712 "ccorres r xf P P' hs a (IF False THEN c ELSE c' FI ;; d) = ccorres r xf P P' hs a (c' ;; d)" 713 by (simp_all add: ccorres_cond_iffs ccorres_seq_simps) 714 715lemmas cap_tag_values = 716 cap_untyped_cap_def 717 cap_endpoint_cap_def 718 cap_notification_cap_def 719 cap_reply_cap_def 720 cap_cnode_cap_def 721 cap_thread_cap_def 722 cap_irq_handler_cap_def 723 cap_null_cap_def 724 cap_irq_control_cap_def 725 cap_zombie_cap_def 726 cap_small_frame_cap_def 727 cap_frame_cap_def 728 cap_page_table_cap_def 729 cap_page_directory_cap_def 730 cap_asid_pool_cap_def 731 732lemma ccorres_return_C_seq: 733 "\<lbrakk>\<And>s f. xf (global_exn_var_'_update f (xfu (\<lambda>_. v s) s)) = v s; \<And>s f. globals (xfu f s) = globals s; wfhandlers hs\<rbrakk> 734 \<Longrightarrow> ccorres_underlying rf_sr \<Gamma> r rvxf arrel xf (\<lambda>_. True) {s. arrel rv (v s)} hs (return rv) (return_C xfu v ;; d)" 735 apply (rule ccorres_guard_imp) 736 apply (rule ccorres_split_throws, rule ccorres_return_C, simp+) 737 apply vcg 738 apply simp_all 739 done 740 741lemma ccap_relation_VPIsDevice: 742 "\<lbrakk>isPageCap cp; ccap_relation (ArchObjectCap cp) cap \<rbrakk> \<Longrightarrow> 743 (generic_frame_cap_get_capFIsDevice_CL (cap_lift cap) = 0) = (\<not> (capVPIsDevice cp))" 744 by (clarsimp elim!:ccap_relationE 745 simp : isPageCap_def generic_frame_cap_get_capFIsDevice_CL_def cap_to_H_def 746 Let_def to_bool_def 747 split: arch_capability.split_asm cap_CL.split_asm if_split_asm) 748 749 750lemma ccap_relation_get_capZombiePtr_CL: 751 "\<lbrakk> ccap_relation cap cap'; isZombie cap; capAligned cap \<rbrakk> 752 \<Longrightarrow> get_capZombiePtr_CL (cap_zombie_cap_lift cap') = capZombiePtr cap" 753 apply (simp only: cap_get_tag_isCap[symmetric]) 754 apply (drule(1) cap_get_tag_to_H) 755 apply (clarsimp simp: get_capZombiePtr_CL_def get_capZombieBits_CL_def Let_def split: if_split) 756 apply (subst less_mask_eq) 757 apply (clarsimp simp add: capAligned_def objBits_simps word_bits_conv) 758 apply unat_arith 759 apply simp 760 done 761 762lemma modify_gets_helper: 763 "do y \<leftarrow> modify (ksPSpace_update (\<lambda>_. ps)); ps' \<leftarrow> gets ksPSpace; f ps' od 764 = do y \<leftarrow> modify (ksPSpace_update (\<lambda>_. ps)); f ps od" 765 by (simp add: bind_def simpler_modify_def simpler_gets_def) 766 767lemma snd_lookupAround2_update: 768 "ps y \<noteq> None \<Longrightarrow> 769 snd (lookupAround2 x (ps (y \<mapsto> v'))) = snd (lookupAround2 x ps)" 770 apply (clarsimp simp: lookupAround2_def lookupAround_def Let_def 771 dom_fun_upd2 772 simp del: dom_fun_upd cong: if_cong option.case_cong) 773 apply (clarsimp split: option.split if_split cong: if_cong) 774 apply auto 775 done 776 777lemma double_setEndpoint: 778 "do y \<leftarrow> setEndpoint epptr v1; setEndpoint epptr v2 od 779 = setEndpoint epptr v2" 780 apply (simp add: setEndpoint_def setObject_def bind_assoc split_def 781 modify_gets_helper) 782 apply (simp add: updateObject_default_def bind_assoc objBits_simps) 783 apply (rule ext) 784 apply (rule bind_apply_cong, rule refl)+ 785 apply (clarsimp simp add: in_monad projectKOs magnitudeCheck_assert 786 snd_lookupAround2_update) 787 apply (simp add: lookupAround2_known1 assert_opt_def projectKO_def projectKO_opt_ep 788 alignCheck_assert) 789 apply (simp add: bind_def simpler_modify_def) 790 done 791 792lemma filterM_setEndpoint_adjustment: 793 "\<lbrakk> \<And>v. do setEndpoint epptr IdleEP; body v od 794 = do v' \<leftarrow> body v; setEndpoint epptr IdleEP; return v' od \<rbrakk> 795 \<Longrightarrow> 796 (do q' \<leftarrow> filterM body q; setEndpoint epptr (f q') od) 797 = (do setEndpoint epptr IdleEP; q' \<leftarrow> filterM body q; setEndpoint epptr (f q') od)" 798 apply (rule sym) 799 apply (induct q arbitrary: f) 800 apply (simp add: double_setEndpoint) 801 apply (simp add: bind_assoc) 802 apply (subst bind_assoc[symmetric], simp, simp add: bind_assoc) 803 done 804 805lemma ccorres_inst_voodoo: 806 "\<forall>x. ccorres r xf (P x) (P' x) hs (h x) (c x) 807 \<Longrightarrow> \<forall>x. ccorres r xf (P x) (P' x) hs (h x) (c x)" 808 by simp 809 810lemma cpspace_relation_ep_update_ep2: 811 "\<lbrakk> ko_at' (ep :: endpoint) epptr s; 812 cmap_relation (map_to_eps (ksPSpace s)) 813 (cslift t) ep_Ptr (cendpoint_relation (cslift t)); 814 cendpoint_relation (cslift t') ep' endpoint; 815 (cslift t' :: tcb_C ptr \<rightharpoonup> tcb_C) = cslift t \<rbrakk> 816 \<Longrightarrow> cmap_relation (map_to_eps (ksPSpace s(epptr \<mapsto> KOEndpoint ep'))) 817 (cslift t(ep_Ptr epptr \<mapsto> endpoint)) 818 ep_Ptr (cendpoint_relation (cslift t'))" 819 apply (rule cmap_relationE1, assumption, erule ko_at_projectKO_opt) 820 apply (rule_tac P="\<lambda>a. cmap_relation a b c d" for b c d in rsubst, 821 erule cmap_relation_upd_relI, assumption+) 822 apply simp+ 823 apply (rule ext, simp add: map_comp_def projectKO_opt_ep split: if_split) 824 done 825 826end 827 828context begin interpretation Arch . (*FIXME: arch_split*) 829lemma setObject_tcb_ep_obj_at'[wp]: 830 "\<lbrace>obj_at' (P :: endpoint \<Rightarrow> bool) ptr\<rbrace> setObject ptr' (tcb :: tcb) \<lbrace>\<lambda>rv. obj_at' P ptr\<rbrace>" 831 apply (rule obj_at_setObject2, simp_all) 832 apply (clarsimp simp: updateObject_default_def in_monad) 833 done 834end 835 836crunch ep_obj_at'[wp]: setThreadState "obj_at' (P :: endpoint \<Rightarrow> bool) ptr" 837 (ignore: getObject setObject simp: unless_def) 838 839context kernel_m begin 840 841lemma ccorres_abstract_h_val: 842 "(\<And>rv. P rv \<Longrightarrow> ccorres r xf G (G' rv) hs a c) \<Longrightarrow> 843 ccorres r xf G ({s. P (h_val (hrs_mem (t_hrs_' (globals s))) p) 844 \<longrightarrow> s \<in> G' (h_val (hrs_mem (t_hrs_' (globals s))) 845 p)} 846 \<inter> {s. P (h_val (hrs_mem (t_hrs_' (globals s))) p)}) hs a c" 847 apply (rule ccorres_tmp_lift1 [where P = P]) 848 apply (clarsimp simp: Collect_conj_eq [symmetric]) 849 apply (fastforce intro: ccorres_guard_imp) 850 done 851 852lemma ccorres_subst_basic_helper: 853 "\<lbrakk> \<And>s s'. \<lbrakk> P s; s' \<in> P'; (s, s') \<in> rf_sr \<rbrakk> \<Longrightarrow> f s' = f' s'; 854 \<And>s s'. \<lbrakk> P s; s' \<in> P'; (s, s') \<in> rf_sr \<rbrakk> \<Longrightarrow> (s, f' s') \<in> rf_sr; 855 \<And>s'. xf' (f' s') = v; \<And>rv' t t'. ceqv \<Gamma> xf' rv' t t' c (c' rv'); 856 ccorres rrel xf Q Q' hs a (c' v) \<rbrakk> 857 \<Longrightarrow> ccorres rrel xf (P and Q) {s. s \<in> P' \<and> f' s \<in> Q'} hs a (Basic f ;; c)" 858 apply (rule ccorres_guard_imp2) 859 apply (rule ccorres_add_return) 860 apply (rule ccorres_split_nothrow[where xf'=xf' and r'="\<lambda>rv rv'. rv' = v"]) 861 apply (rule ccorres_from_vcg[where P=P and P'=P']) 862 apply (rule allI, rule conseqPre, vcg) 863 apply (clarsimp simp: return_def) 864 apply assumption 865 apply simp 866 apply wp 867 apply vcg 868 apply clarsimp 869 done 870 871lemma ctcb_relation_blocking_ipc_badge: 872 "\<lbrakk> ctcb_relation tcb ctcb; isBlockedOnSend (tcbState tcb) \<rbrakk> \<Longrightarrow> 873 tsType_CL (thread_state_lift (tcbState_C ctcb)) = scast ThreadState_BlockedOnSend" 874 "\<lbrakk> ctcb_relation tcb ctcb; 875 tsType_CL (thread_state_lift (tcbState_C ctcb)) = scast ThreadState_BlockedOnSend \<rbrakk> 876 \<Longrightarrow> blockingIPCBadge (tcbState tcb) 877 = blockingIPCBadge_CL (thread_state_lift (tcbState_C ctcb))" 878 apply (clarsimp simp add: ctcb_relation_def) 879 apply (simp add: isBlockedOnSend_def split: Structures_H.thread_state.split_asm) 880 apply (clarsimp simp: cthread_state_relation_def) 881 apply (clarsimp simp add: ctcb_relation_def cthread_state_relation_def) 882 apply (cases "tcbState tcb", simp_all add: "StrictC'_thread_state_defs") 883 done 884 885lemma cendpoint_relation_q_cong: 886 "\<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> 887 \<Longrightarrow> cendpoint_relation hp ep ep' = cendpoint_relation hp' ep ep'" 888 apply (cases ep, simp_all add: cendpoint_relation_def Let_def) 889 apply (rule conj_cong [OF refl]) 890 apply (rule tcb_queue_relation'_cong[OF refl refl refl]) 891 apply clarsimp 892 apply (rule conj_cong [OF refl]) 893 apply (rule tcb_queue_relation'_cong[OF refl refl refl]) 894 apply clarsimp 895 done 896 897lemma cnotification_relation_q_cong: 898 "\<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> 899 \<Longrightarrow> cnotification_relation hp ntfn ntfn' = cnotification_relation hp' ntfn ntfn'" 900 apply (cases "ntfnObj ntfn", simp_all add: cnotification_relation_def Let_def) 901 apply (auto intro: iffD1[OF tcb_queue_relation'_cong[OF refl refl refl]]) 902 done 903 904lemma tcbSchedEnqueue_ep_at: 905 "\<lbrace>obj_at' (P :: endpoint \<Rightarrow> bool) ep\<rbrace> 906 tcbSchedEnqueue t 907 \<lbrace>\<lambda>rv. obj_at' P ep\<rbrace>" 908 including no_pre 909 apply (simp add: tcbSchedEnqueue_def unless_def null_def) 910 apply (wp threadGet_wp, clarsimp, wp+) 911 apply (clarsimp split: if_split, wp) 912 done 913 914lemma ccorres_duplicate_guard: 915 "ccorres r xf (P and P) Q hs f f' \<Longrightarrow> ccorres r xf P Q hs f f'" 916 by (erule ccorres_guard_imp, auto) 917 918 919lemma ep_q_refs'_no_NTFNBound[simp]: 920 "(x, NTFNBound) \<notin> ep_q_refs_of' ep" 921 by (auto simp: ep_q_refs_of'_def split: endpoint.splits) 922 923 924lemma ntfn_q_refs'_no_NTFNBound[simp]: 925 "(x, NTFNBound) \<notin> ntfn_q_refs_of' ntfn" 926 by (auto simp: ntfn_q_refs_of'_def split: ntfn.splits) 927 928lemma cancelBadgedSends_ccorres: 929 "ccorres dc xfdc (invs' and ep_at' ptr) 930 (UNIV \<inter> {s. epptr_' s = Ptr ptr} \<inter> {s. badge_' s = bdg}) [] 931 (cancelBadgedSends ptr bdg) (Call cancelBadgedSends_'proc)" 932 apply (cinit lift: epptr_' badge_' simp: whileAnno_def) 933 apply (simp add: list_case_return2 934 cong: list.case_cong Structures_H.endpoint.case_cong call_ignore_cong 935 del: Collect_const) 936 apply (rule ccorres_pre_getEndpoint) 937 apply (rule_tac R="ko_at' rv ptr" and xf'="ret__unsigned_'" 938 and val="case rv of RecvEP q \<Rightarrow> scast EPState_Recv | IdleEP \<Rightarrow> scast EPState_Idle 939 | SendEP q \<Rightarrow> scast EPState_Send" 940 in ccorres_symb_exec_r_known_rv_UNIV[where R'=UNIV]) 941 apply vcg 942 apply clarsimp 943 apply (erule cmap_relationE1 [OF cmap_relation_ep], erule ko_at_projectKO_opt) 944 apply (clarsimp simp: typ_heap_simps cendpoint_relation_def Let_def 945 split: Structures_H.endpoint.split_asm) 946 apply ceqv 947 apply wpc 948 apply (simp add: dc_def[symmetric] ccorres_cond_iffs) 949 apply (rule ccorres_return_Skip) 950 apply (simp add: dc_def[symmetric] ccorres_cond_iffs) 951 apply (rule ccorres_return_Skip) 952 apply (rename_tac list) 953 apply (simp add: Collect_True Collect_False endpoint_state_defs 954 ccorres_cond_iffs dc_def[symmetric] 955 del: Collect_const cong: call_ignore_cong) 956 apply (rule ccorres_rhs_assoc)+ 957 apply (csymbr, csymbr) 958 apply (drule_tac s = rv in sym, simp only:) 959 apply (rule_tac P="ko_at' rv ptr and invs'" in ccorres_cross_over_guard) 960 apply (rule ccorres_symb_exec_r) 961 apply (rule ccorres_rhs_assoc2, rule ccorres_rhs_assoc2) 962 apply (rule ccorres_split_nothrow[where r'=dc and xf'=xfdc, OF _ ceqv_refl]) 963 apply (rule_tac P="ko_at' rv ptr" 964 in ccorres_from_vcg[where P'=UNIV]) 965 apply (rule allI, rule conseqPre, vcg) 966 apply clarsimp 967 apply (rule cmap_relationE1[OF cmap_relation_ep], assumption) 968 apply (erule ko_at_projectKO_opt) 969 apply (clarsimp simp: typ_heap_simps setEndpoint_def) 970 apply (rule rev_bexI) 971 apply (rule setObject_eq; simp add: objBits_simps')[1] 972 apply (clarsimp simp: rf_sr_def cstate_relation_def 973 Let_def carch_state_relation_def 974 cmachine_state_relation_def 975 ) 976 apply (clarsimp simp: cpspace_relation_def 977 update_ep_map_tos 978 typ_heap_simps') 979 apply (erule(1) cpspace_relation_ep_update_ep2) 980 apply (simp add: cendpoint_relation_def endpoint_state_defs) 981 subgoal by simp 982 apply (rule ccorres_symb_exec_r) 983 apply (rule_tac xs=list in filterM_voodoo) 984 apply (rule_tac P="\<lambda>xs s. (\<forall>x \<in> set xs \<union> set list. 985 st_tcb_at' (\<lambda>st. isBlockedOnSend st \<and> blockingObject st = ptr) x s) 986 \<and> distinct (xs @ list) \<and> ko_at' IdleEP ptr s 987 \<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}) 988 \<and> valid_queues s \<and> pspace_aligned' s \<and> pspace_distinct' s 989 \<and> sch_act_wf (ksSchedulerAction s) s \<and> valid_objs' s" 990 and P'="\<lambda>xs. {s. ep_queue_relation' (cslift s) (xs @ list) 991 (head_C (queue_' s)) (end_C (queue_' s))} 992 \<inter> {s. thread_' s = (case list of [] \<Rightarrow> tcb_Ptr 0 993 | x # xs \<Rightarrow> tcb_ptr_to_ctcb_ptr x)}" 994 in ccorres_inst_voodoo) 995 apply (induct_tac list) 996 apply (rule allI) 997 apply (rule iffD1 [OF ccorres_expand_while_iff_Seq]) 998 apply (rule ccorres_tmp_lift2 [OF _ _ refl]) 999 apply ceqv 1000 apply (simp add: ccorres_cond_iffs) 1001 apply (rule ccorres_rhs_assoc2) 1002 apply (rule ccorres_duplicate_guard, rule ccorres_split_nothrow_novcg_dc) 1003 apply (rule ccorres_from_vcg, rule allI, rule conseqPre, vcg) 1004 apply clarsimp 1005 apply (drule obj_at_ko_at', clarsimp) 1006 apply (rule cmap_relationE1[OF cmap_relation_ep], assumption) 1007 apply (erule ko_at_projectKO_opt) 1008 apply (clarsimp simp: typ_heap_simps tcb_queue_relation'_def) 1009 apply (case_tac x) 1010 apply (clarsimp simp: setEndpoint_def) 1011 apply (rule rev_bexI, rule setObject_eq, 1012 (simp add: objBits_simps')+) 1013 apply (clarsimp simp: rf_sr_def cstate_relation_def Let_def 1014 carch_state_relation_def 1015 cmachine_state_relation_def 1016 cpspace_relation_def typ_heap_simps' 1017 update_ep_map_tos) 1018 apply (erule(1) cpspace_relation_ep_update_ep2) 1019 subgoal by (simp add: cendpoint_relation_def Let_def) 1020 subgoal by simp 1021 apply (clarsimp simp: tcb_at_not_NULL[OF pred_tcb_at'] 1022 setEndpoint_def) 1023 apply (rule rev_bexI, rule setObject_eq, 1024 (simp add: objBits_simps')+) 1025 apply (clarsimp simp: rf_sr_def cstate_relation_def Let_def 1026 carch_state_relation_def 1027 cmachine_state_relation_def 1028 cpspace_relation_def typ_heap_simps' 1029 update_ep_map_tos) 1030 apply (erule(1) cpspace_relation_ep_update_ep2) 1031 apply (simp add: cendpoint_relation_def Let_def) 1032 apply (subgoal_tac "tcb_at' (last (a # list)) \<sigma> \<and> tcb_at' a \<sigma>") 1033 apply (clarsimp simp: is_aligned_neg_mask_weaken[ 1034 OF is_aligned_tcb_ptr_to_ctcb_ptr[where P=\<top>]]) 1035 subgoal by (simp add: tcb_queue_relation'_def EPState_Send_def mask_def) 1036 subgoal by (auto split: if_split) 1037 subgoal by simp 1038 apply (ctac add: rescheduleRequired_ccorres[unfolded dc_def]) 1039 apply (rule hoare_pre, wp weak_sch_act_wf_lift_linear set_ep_valid_objs') 1040 apply (clarsimp simp: weak_sch_act_wf_def sch_act_wf_def) 1041 apply (fastforce simp: valid_ep'_def pred_tcb_at' split: list.splits) 1042 apply (simp add: guard_is_UNIV_def) 1043 apply (rule allI) 1044 apply (rename_tac a lista x) 1045 apply (rule iffD1 [OF ccorres_expand_while_iff_Seq]) 1046 apply (rule ccorres_init_tmp_lift2, ceqv) 1047 apply (rule ccorres_guard_imp2) 1048 apply (simp add: bind_assoc dc_def[symmetric] 1049 del: Collect_const) 1050 apply (rule ccorres_cond_true) 1051 apply (rule ccorres_rhs_assoc)+ 1052 apply (rule ccorres_pre_threadGet[where f=tcbState, folded getThreadState_def]) 1053 apply (rule ccorres_move_c_guard_tcb) 1054 apply csymbr 1055 apply (rule ccorres_abstract_cleanup) 1056 apply csymbr 1057 apply (rule ccorres_move_c_guard_tcb) 1058 apply (rule_tac P=\<top> 1059 and P'="{s. ep_queue_relation' (cslift s) (x @ a # lista) 1060 (head_C (queue_' s)) (end_C (queue_' s))}" 1061 and f'="\<lambda>s. s \<lparr> next___ptr_to_struct_tcb_C_' := (case lista of [] \<Rightarrow> tcb_Ptr 0 1062 | v # vs \<Rightarrow> tcb_ptr_to_ctcb_ptr v) \<rparr>" 1063 and xf'="next___ptr_to_struct_tcb_C_'" 1064 in ccorres_subst_basic_helper) 1065 apply (thin_tac "\<forall>x. P x" for P) 1066 apply (rule myvars.fold_congs, (rule refl)+) 1067 apply (clarsimp simp: tcb_queue_relation'_def use_tcb_queue_relation2 1068 tcb_queue_relation2_concat) 1069 apply (clarsimp simp: typ_heap_simps split: list.split) 1070 subgoal by (simp add: rf_sr_def) 1071 apply simp 1072 apply ceqv 1073 apply (rule_tac P="ret__unsigned=blockingIPCBadge rva" in ccorres_gen_asm2) 1074 apply (rule ccorres_if_bind, rule ccorres_if_lhs) 1075 apply (simp add: bind_assoc dc_def[symmetric]) 1076 apply (rule ccorres_rhs_assoc)+ 1077 apply (ctac add: setThreadState_ccorres) 1078 apply (ctac add: tcbSchedEnqueue_ccorres) 1079 apply (rule_tac P="\<lambda>s. \<forall>t \<in> set (x @ a # lista). tcb_at' t s" 1080 in ccorres_cross_over_guard) 1081 apply (rule ccorres_add_return, rule ccorres_split_nothrow[OF _ ceqv_refl]) 1082 apply (rule_tac rrel=dc and xf=xfdc 1083 and P="\<lambda>s. (\<forall>t \<in> set (x @ a # lista). tcb_at' t s) 1084 \<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}) 1085 \<and> valid_queues s \<and> distinct (x @ a # lista) 1086 \<and> pspace_aligned' s \<and> pspace_distinct' s" 1087 and P'="{s. ep_queue_relation' (cslift s) (x @ a # lista) 1088 (head_C (queue_' s)) (end_C (queue_' s))}" 1089 in ccorres_from_vcg) 1090 apply (thin_tac "\<forall>x. P x" for P) 1091 apply (rule allI, rule conseqPre, vcg) 1092 apply (clarsimp simp: ball_Un) 1093 apply (rule exI, rule conjI) 1094 apply (rule exI, erule conjI) 1095 apply (intro conjI[rotated]) 1096 apply (assumption) 1097 apply (fold_subgoals (prefix))[3] 1098 subgoal premises prems using prems by (fastforce intro: pred_tcb_at')+ 1099 apply (clarsimp simp: return_def rf_sr_def cstate_relation_def Let_def) 1100 apply (rule conjI) 1101 apply (clarsimp simp: cpspace_relation_def) 1102 apply (rule conjI, erule ctcb_relation_null_queue_ptrs) 1103 apply (rule null_ep_queue) 1104 subgoal by (simp add: o_def) 1105 apply (rule conjI) 1106 apply (erule iffD1 [OF cmap_relation_cong, OF refl refl, rotated -1]) 1107 apply clarsimp 1108 apply (rule cendpoint_relation_q_cong) 1109 apply (rule sym, erule restrict_map_eqI) 1110 apply (clarsimp simp: image_iff) 1111 apply (drule(2) map_to_ko_atI2) 1112 apply (drule ko_at_state_refs_ofD') 1113 apply clarsimp 1114 apply (drule_tac x=p in spec) 1115 subgoal by fastforce 1116 apply (erule iffD1 [OF cmap_relation_cong, OF refl refl, rotated -1]) 1117 apply clarsimp 1118 apply (drule(2) map_to_ko_atI2, drule ko_at_state_refs_ofD') 1119 1120 apply (rule cnotification_relation_q_cong) 1121 apply (rule sym, erule restrict_map_eqI) 1122 apply (clarsimp simp: image_iff) 1123 apply (drule_tac x=p in spec) 1124 subgoal by fastforce 1125 apply (rule conjI) 1126 apply (erule cready_queues_relation_not_queue_ptrs, 1127 auto dest: null_ep_schedD[unfolded o_def] simp: o_def)[1] 1128 apply (simp add: carch_state_relation_def 1129 cmachine_state_relation_def 1130 h_t_valid_clift_Some_iff) 1131 apply (rule ccorres_symb_exec_r2) 1132 apply (erule spec) 1133 apply vcg 1134 apply (vcg spec=modifies) 1135 apply wp 1136 apply simp 1137 apply vcg 1138 apply (wp hoare_vcg_const_Ball_lift tcbSchedEnqueue_ep_at 1139 sch_act_wf_lift) 1140 apply simp 1141 apply (vcg exspec=tcbSchedEnqueue_cslift_spec) 1142 apply (wp hoare_vcg_const_Ball_lift sts_st_tcb_at'_cases 1143 sts_sch_act sts_valid_queues setThreadState_oa_queued) 1144 apply (vcg exspec=setThreadState_cslift_spec) 1145 apply (simp add: ccorres_cond_iffs dc_def[symmetric]) 1146 apply (rule ccorres_symb_exec_r2) 1147 apply (drule_tac x="x @ [a]" in spec, simp add: dc_def[symmetric]) 1148 apply vcg 1149 apply (vcg spec=modifies) 1150 apply (thin_tac "\<forall>x. P x" for P) 1151 apply (clarsimp simp: pred_tcb_at' ball_Un) 1152 apply (rule conjI) 1153 apply (clarsimp split: if_split) 1154 subgoal by (fastforce simp: valid_tcb_state'_def valid_objs'_maxDomain 1155 valid_objs'_maxPriority dest: pred_tcb_at') 1156 apply (clarsimp simp: tcb_at_not_NULL [OF pred_tcb_at']) 1157 apply (clarsimp simp: typ_heap_simps st_tcb_at'_def) 1158 apply (drule(1) obj_at_cslift_tcb) 1159 apply (clarsimp simp: ctcb_relation_blocking_ipc_badge) 1160 apply (rule conjI, simp add: "StrictC'_thread_state_defs" mask_def) 1161 apply (rule conjI) 1162 apply clarsimp 1163 apply (frule rf_sr_cscheduler_relation) 1164 apply (clarsimp simp: cscheduler_action_relation_def st_tcb_at'_def 1165 split: scheduler_action.split_asm) 1166 apply (rename_tac word) 1167 apply (frule_tac x=word in tcbSchedEnqueue_cslift_precond_discharge) 1168 apply simp 1169 subgoal by clarsimp 1170 subgoal by clarsimp 1171 subgoal by clarsimp 1172 apply clarsimp 1173 apply (rule conjI) 1174 apply (frule(3) tcbSchedEnqueue_cslift_precond_discharge) 1175 subgoal by clarsimp 1176 apply clarsimp 1177 apply (rule context_conjI) 1178 apply (clarsimp simp: tcb_queue_relation'_def) 1179 apply (erule iffD2[OF ep_queue_relation_shift[rule_format], rotated -1]) 1180 subgoal by simp 1181 apply (rule_tac x="x @ a # lista" in exI) 1182 apply (clarsimp simp: ball_Un) 1183 apply (rule conjI, fastforce) 1184 subgoal by (clarsimp simp: remove1_append) 1185 apply vcg 1186 apply (rule conseqPre, vcg) 1187 apply clarsimp 1188 apply (wp hoare_vcg_const_Ball_lift) 1189 apply (wp obj_at_setObject3[where 'a=endpoint, folded setEndpoint_def]) 1190 apply (simp add: objBits_simps')+ 1191 apply (wp set_ep_valid_objs') 1192 apply vcg 1193 apply vcg 1194 apply (rule conseqPre, vcg) 1195 apply clarsimp 1196 apply (clarsimp simp: guard_is_UNIV_def) 1197 apply (erule cmap_relationE1[OF cmap_relation_ep], erule ko_at_projectKO_opt) 1198 apply (clarsimp simp: typ_heap_simps) 1199 apply (clarsimp simp: cendpoint_relation_def Let_def) 1200 subgoal by (clarsimp simp: tcb_queue_relation'_def neq_Nil_conv 1201 split: if_split_asm) 1202 apply clarsimp 1203 apply (frule ko_at_valid_objs', clarsimp) 1204 apply (simp add: projectKOs) 1205 apply (clarsimp simp: valid_obj'_def valid_ep'_def) 1206 apply (frule sym_refs_ko_atD', clarsimp) 1207 apply (clarsimp simp: st_tcb_at_refs_of_rev') 1208 apply (rule conjI) 1209 subgoal by (auto simp: isBlockedOnSend_def elim!: pred_tcb'_weakenE) 1210 apply (rule conjI) 1211 apply (clarsimp split: if_split) 1212 apply (drule sym_refsD, clarsimp) 1213 apply (drule(1) bspec)+ 1214 by (auto simp: obj_at'_def projectKOs state_refs_of'_def pred_tcb_at'_def tcb_bound_refs'_def 1215 dest!: symreftype_inverse') 1216 1217 1218lemma tcb_ptr_to_ctcb_ptr_force_fold: 1219 "x + 2 ^ ctcb_size_bits = ptr_val (tcb_ptr_to_ctcb_ptr x)" 1220 by (simp add: tcb_ptr_to_ctcb_ptr_def ctcb_offset_def) 1221 1222 1223lemma coerce_memset_to_heap_update: 1224 "heap_update_list x (replicateHider (size_of (TYPE (tcb_C))) 0) 1225 = heap_update (tcb_Ptr x) 1226 (tcb_C (arch_tcb_C (user_context_C (FCP (\<lambda>x. 0)))) 1227 (thread_state_C (FCP (\<lambda>x. 0))) 1228 (NULL) 1229 (seL4_Fault_C (FCP (\<lambda>x. 0))) 1230 (lookup_fault_C (FCP (\<lambda>x. 0))) 1231 0 0 0 0 0 0 NULL NULL NULL NULL)" 1232 apply (intro ext, simp add: heap_update_def) 1233 apply (rule_tac f="\<lambda>xs. heap_update_list x xs a b" for a b in arg_cong) 1234 apply (simp add: to_bytes_def size_of_def typ_info_simps tcb_C_tag_def) 1235 apply (simp add: ti_typ_pad_combine_empty_ti ti_typ_pad_combine_td align_of_def padup_def 1236 final_pad_def size_td_lt_ti_typ_pad_combine Let_def size_of_def) 1237 apply (simp add: typ_info_simps 1238 user_context_C_tag_def thread_state_C_tag_def seL4_Fault_C_tag_def 1239 lookup_fault_C_tag_def update_ti_t_ptr_0s arch_tcb_C_tag_def 1240 ti_typ_pad_combine_empty_ti ti_typ_pad_combine_td 1241 ti_typ_combine_empty_ti ti_typ_combine_td 1242 align_of_def padup_def 1243 final_pad_def size_td_lt_ti_typ_pad_combine Let_def size_of_def 1244 align_td_array' size_td_array) 1245 apply (simp add: typ_info_array') 1246 apply (simp add: typ_info_word word_rsplit_0 upt_conv_Cons) 1247 apply (simp add: typ_info_word typ_info_ptr word_rsplit_0 1248 replicateHider_def) 1249 done 1250 1251lemma isArchObjectCap_capBits: 1252 "isArchObjectCap cap \<Longrightarrow> capBits cap = acapBits (capCap cap)" 1253 by (clarsimp simp: isCap_simps) 1254 1255declare Kernel_C.tcb_C_size [simp del] 1256 1257lemma cte_lift_ccte_relation: 1258 "cte_lift cte' = Some ctel' 1259 \<Longrightarrow> c_valid_cte cte' 1260 \<Longrightarrow> ccte_relation (cte_to_H ctel') cte'" 1261 by (simp add: ccte_relation_def) 1262 1263lemma updateFreeIndex_ccorres: 1264 "\<forall>s. \<Gamma> \<turnstile> ({s} \<inter> {s. \<exists>cte cte'. cslift s (cte_Ptr srcSlot) = Some cte' 1265 \<and> cteCap cte = cap' \<and> ccte_relation cte cte'}) 1266 c 1267 {t. \<exists>cap. cap_untyped_cap_lift cap = (cap_untyped_cap_lift 1268 (cte_C.cap_C (the (cslift s (cte_Ptr srcSlot))))) 1269 \<lparr> cap_untyped_cap_CL.capFreeIndex_CL := ((of_nat idx') >> 4) \<rparr> 1270 \<and> cap_get_tag cap = scast cap_untyped_cap 1271 \<and> t_hrs_' (globals t) = hrs_mem_update (heap_update (cte_Ptr srcSlot) 1272 (cte_C.cap_C_update (\<lambda>_. cap) (the (cslift s (cte_Ptr srcSlot))))) 1273 (t_hrs_' (globals s)) 1274 \<and> t may_only_modify_globals s in [t_hrs] 1275 } 1276 \<Longrightarrow> ccorres dc xfdc 1277 (valid_objs' and cte_wp_at' (\<lambda>cte. isUntypedCap (cteCap cte) 1278 \<and> cap' = (cteCap cte)) srcSlot 1279 and untyped_ranges_zero' 1280 and (\<lambda>_. is_aligned (of_nat idx' :: word32) 4 \<and> idx' \<le> 2 ^ (capBlockSize cap'))) 1281 {s. \<not> capIsDevice cap' 1282 \<longrightarrow> region_actually_is_zero_bytes (capPtr cap' + of_nat idx') (capFreeIndex cap' - idx') s} hs 1283 (updateFreeIndex srcSlot idx') c" 1284 (is "_ \<Longrightarrow> ccorres dc xfdc (valid_objs' and ?cte_wp_at' and _ and _) ?P' hs ?a c") 1285 apply (rule ccorres_gen_asm) 1286 apply (simp add: updateFreeIndex_def getSlotCap_def updateCap_def) 1287 apply (rule ccorres_guard_imp2) 1288 apply (rule ccorres_split_noop_lhs, rule_tac cap'=cap' in updateTrackedFreeIndex_noop_ccorres) 1289 apply (rule ccorres_pre_getCTE)+ 1290 apply (rename_tac cte cte2) 1291 apply (rule_tac P = "\<lambda>s. ?cte_wp_at' s \<and> cte2 = cte \<and> cte_wp_at' ((=) cte) srcSlot s" 1292 and P'="{s. \<exists>cte cte'. cslift s (cte_Ptr srcSlot) = Some cte' 1293 \<and> cteCap cte = cap' \<and> ccte_relation cte cte'} \<inter> ?P'" in ccorres_from_vcg) 1294 apply (rule allI, rule HoarePartial.conseq_exploit_pre, clarify) 1295 apply (drule_tac x=s in spec, rule conseqPre, erule conseqPost) 1296 defer 1297 apply clarsimp 1298 apply clarsimp 1299 apply (simp add: cte_wp_at_ctes_of) 1300 apply wp 1301 apply (clarsimp simp: isCap_simps cte_wp_at_ctes_of) 1302 apply (frule(1) rf_sr_ctes_of_clift) 1303 apply clarsimp 1304 apply (frule(1) cte_lift_ccte_relation) 1305 apply (rule exI, intro conjI[rotated], assumption, simp_all)[1] 1306 apply (clarsimp simp: cte_wp_at_ctes_of) 1307 apply (erule(1) rf_sr_ctes_of_cliftE) 1308 apply (frule(1) rf_sr_ctes_of_clift) 1309 apply clarsimp 1310 apply (subgoal_tac "ccap_relation (capFreeIndex_update (\<lambda>_. idx') 1311 (cteCap (the (ctes_of \<sigma> srcSlot)))) cap") 1312 apply (rule fst_setCTE [OF ctes_of_cte_at], assumption) 1313 apply (erule bexI [rotated]) 1314 apply (clarsimp simp add: rf_sr_def cstate_relation_def Let_def 1315 cvariable_array_map_const_add_map_option[where f="tcb_no_ctes_proj"] 1316 isCap_simps) 1317 apply (simp add:cpspace_relation_def) 1318 apply (clarsimp simp:typ_heap_simps' modify_map_def mex_def meq_def) 1319 apply (rule conjI) 1320 apply (rule cpspace_cte_relation_upd_capI, assumption+) 1321 apply (rule conjI) 1322 apply (rule setCTE_tcb_case, assumption+) 1323 apply (case_tac s', clarsimp) 1324 subgoal by (simp add: carch_state_relation_def cmachine_state_relation_def 1325 typ_heap_simps') 1326 1327 apply (clarsimp simp: isCap_simps) 1328 apply (drule(1) cte_lift_ccte_relation, 1329 drule ccte_relation_ccap_relation) 1330 apply (simp add: cte_to_H_def) 1331 apply (frule cap_get_tag_isCap_unfolded_H_cap) 1332 apply (clarsimp simp: ccap_relation_def cap_lift_untyped_cap 1333 cap_to_H_simps cap_untyped_cap_lift_def 1334 is_aligned_shiftr_shiftl 1335 dest!: ccte_relation_ccap_relation) 1336 apply (rule unat_of_nat_eq unat_of_nat_eq[symmetric], 1337 erule order_le_less_trans, 1338 rule power_strict_increasing, simp_all) 1339 apply (rule unat_less_helper, rule order_le_less_trans[OF word_and_le1], simp add: mask_def) 1340 done 1341 1342end 1343 1344(* FIXME: Move *) 1345lemma ccap_relation_isDeviceCap: 1346 "\<lbrakk>ccap_relation cp cap; isUntypedCap cp 1347 \<rbrakk> \<Longrightarrow> to_bool (capIsDevice_CL (cap_untyped_cap_lift cap)) = (capIsDevice cp)" 1348 apply (frule cap_get_tag_UntypedCap) 1349 apply (simp add:cap_get_tag_isCap ) 1350 done 1351 1352lemma ccap_relation_isDeviceCap2: 1353 "\<lbrakk>ccap_relation cp cap; isUntypedCap cp 1354 \<rbrakk> \<Longrightarrow> (capIsDevice_CL (cap_untyped_cap_lift cap) = 0) = (\<not> (capIsDevice cp))" 1355 apply (frule cap_get_tag_UntypedCap) 1356 apply (simp add:cap_get_tag_isCap to_bool_def) 1357 done 1358end 1359