80 lines
2.5 KiB
Plaintext
80 lines
2.5 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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header "Toplevel Refinement Statement for nondeterministic specification"
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theory Refine_nondet_C (* FIXME: broken *)
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imports
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Refine_C
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"AInvs.BCorres2_AI"
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begin
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definition (in state_rel)
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cstate_to_AN :: "cstate \<Rightarrow> unit Structures_A.state"
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where
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"cstate_to_AN \<equiv> truncate_state \<circ> absKState \<circ> cstate_to_H \<circ> globals"
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definition (in state_rel)
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"Fin_CN \<equiv> \<lambda>((tc,s),m,e). ((tc, cstate_to_AN s),m,e)"
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lemma truncate_trans[simp]: "truncate_state (trans_state f s) = s"
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by (simp add: trans_state_def)
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context kernel
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begin
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definition
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ADT_C' :: "(cstate global_state, unit observable, global_transition) data_type"
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where
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"ADT_C' \<equiv> \<lparr> Init = Init_C', Fin = Fin_CN,
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Step = global_automaton do_user_op_C (kernel_call_C False) \<rparr>"
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definition
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ADT_FP_C' :: "(cstate global_state, unit observable, global_transition) data_type"
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where
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"ADT_FP_C' \<equiv> \<lparr> Init = Init_C', Fin = Fin_CN,
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Step = global_automaton do_user_op_C (kernel_call_C True) \<rparr>"
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lemma refinement2_both_nondet:
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"\<lparr> Init = Init_C', Fin = Fin_CN,
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Step = global_automaton do_user_op_C (kernel_call_C fp) \<rparr>
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\<sqsubseteq> ADT_H'"
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apply (cut_tac refinement2_both)
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apply (clarsimp simp add: refines_def execution_def ADT_H'_def ADT_H_def)
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apply (clarsimp simp add: Fin_CN_def cstate_to_AN_def Fin_C_def cstate_to_A_def Init_C_def)
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apply (rename_tac js aa ba aaa baa ad bd ae be)
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apply (drule_tac x=js in spec)
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apply (drule_tac x=aa in spec)
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apply (drule_tac x="trans_state (\<lambda>s. undefined) ba" in spec)
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apply (drule_tac x=aaa in spec)
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apply (drule_tac x=baa in spec)
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apply simp
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apply force
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done
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theorem refinement2_nondet:
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"ADT_C' \<sqsubseteq> ADT_H'"
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unfolding ADT_C'_def
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by (rule refinement2_both_nondet)
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theorem fp_refinement_nondet:
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"ADT_FP_C' \<sqsubseteq> ADT_H'"
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unfolding ADT_FP_C'_def
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by (rule refinement2_both_nondet)
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theorem seL4_refinement_nondet:
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"ADT_C' \<sqsubseteq> ADT_A'"
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by (blast intro: refinement_nondet refinement2_nondet refinement_trans)
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theorem seL4_fastpath_refinement_nondet:
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"ADT_FP_C' \<sqsubseteq> ADT_A'"
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by (blast intro: refinement_nondet fp_refinement_nondet refinement_trans)
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end
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