106 lines
3.7 KiB
Plaintext
106 lines
3.7 KiB
Plaintext
(*
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* Copyright 2014, General Dynamics C4 Systems
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*
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* SPDX-License-Identifier: GPL-2.0-only
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*)
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theory Bits_AI
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imports ArchBits_AI
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begin
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lemmas crunch_wps = hoare_drop_imps mapM_wp' mapM_x_wp'
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lemmas crunch_simps = split_def whenE_def unlessE_def Let_def if_fun_split
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assertE_def zipWithM_mapM zipWithM_x_mapM
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lemma in_set_object:
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"(rv, s') \<in> fst (set_object ptr obj s) \<Longrightarrow> s' = s \<lparr> kheap := kheap s (ptr \<mapsto> obj) \<rparr>"
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by (clarsimp simp: set_object_def get_object_def in_monad)
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lemma cap_fault_injection:
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"cap_fault_on_failure addr b = injection_handler (ExceptionTypes_A.CapFault addr b)"
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apply (rule ext)
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apply (simp add: cap_fault_on_failure_def injection_handler_def o_def)
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done
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lemma lookup_error_injection:
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"lookup_error_on_failure b = injection_handler (ExceptionTypes_A.FailedLookup b)"
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apply (rule ext)
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apply (simp add: lookup_error_on_failure_def injection_handler_def o_def)
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done
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ML \<open>Thm.consolidate @{thms lookup_error_injection}\<close>
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lemmas cap_fault_wp[wp] = injection_wp[OF cap_fault_injection]
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lemmas cap_fault_wp_E[wp] = injection_wp_E[OF cap_fault_injection]
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lemmas cap_fault_bindE = injection_bindE[OF cap_fault_injection cap_fault_injection]
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lemmas cap_fault_liftE[simp] = injection_liftE[OF cap_fault_injection]
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lemmas lookup_error_wp[wp] = injection_wp[OF lookup_error_injection]
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lemmas lookup_error_wp_E[wp] = injection_wp_E[OF lookup_error_injection]
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lemmas lookup_error_bindE = injection_bindE[OF lookup_error_injection lookup_error_injection]
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lemmas lookup_error_liftE[simp] = injection_liftE[OF lookup_error_injection]
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lemma unify_failure_injection:
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"unify_failure = injection_handler (\<lambda>x. ())"
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by (intro ext, simp add: unify_failure_def injection_handler_def)
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lemmas unify_failure_wp[wp] = injection_wp [OF unify_failure_injection]
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lemmas unify_failure_wp_E[wp] = injection_wp_E [OF unify_failure_injection]
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lemma ep_cases_weak_wp:
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assumes "\<lbrace>P_A\<rbrace> a \<lbrace>Q\<rbrace>"
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assumes "\<And>q. \<lbrace>P_B\<rbrace> b q \<lbrace>Q\<rbrace>"
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assumes "\<And>q. \<lbrace>P_C\<rbrace> c q \<lbrace>Q\<rbrace>"
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shows
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"\<lbrace>P_A and P_B and P_C\<rbrace>
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case ts of
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Structures_A.IdleEP \<Rightarrow> a
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| Structures_A.SendEP q \<Rightarrow> b q
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| Structures_A.RecvEP q \<Rightarrow> c q \<lbrace>Q\<rbrace>"
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apply (cases ts)
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apply (simp, rule hoare_weaken_pre, rule assms, simp)+
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done
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lemma ntfn_cases_weak_wp:
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assumes "\<lbrace>P_A\<rbrace> a \<lbrace>Q\<rbrace>"
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assumes "\<And>q. \<lbrace>P_B\<rbrace> b q \<lbrace>Q\<rbrace>"
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assumes "\<And>bdg msg. \<lbrace>P_C\<rbrace> c bdg msg \<lbrace>Q\<rbrace>"
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shows
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"\<lbrace>P_A and P_B and P_C\<rbrace>
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case ts of
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Structures_A.IdleNtfn \<Rightarrow> a
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| Structures_A.WaitingNtfn q \<Rightarrow> b q
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| Structures_A.ActiveNtfn bdg \<Rightarrow> c bdg msg \<lbrace>Q\<rbrace>"
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apply (cases ts)
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apply (simp, rule hoare_weaken_pre, rule assms, simp)+
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done
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lemma NullCap_valid [simp]: "s \<turnstile> cap.NullCap"
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by (simp add: valid_cap_def)
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lemma empty_on_failure_wp[wp]:
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"\<lbrace>P\<rbrace> m \<lbrace>Q\<rbrace>,\<lbrace>\<lambda>rv. Q []\<rbrace>
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\<Longrightarrow> \<lbrace>P\<rbrace> empty_on_failure m \<lbrace>Q\<rbrace>"
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by (simp add: empty_on_failure_def) wp
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lemma gen_invocation_typeI:
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"invocation_type l = GenInvocationLabel x \<Longrightarrow> gen_invocation_type l = x"
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by (simp add: gen_invocation_type_def)
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lemma gen_invocation_type_eq:
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"x \<noteq> InvalidInvocation \<Longrightarrow>
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(invocation_type l = GenInvocationLabel x) = (gen_invocation_type l = x)"
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by (auto simp: gen_invocation_type_def split: invocation_label.splits)
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end
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