54 lines
2.2 KiB
Plaintext
54 lines
2.2 KiB
Plaintext
(*
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* Copyright 2020, Data61, CSIRO (ABN 41 687 119 230)
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*)
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theory Sep_MP
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imports Sep_Tactic_Helpers Sep_Provers Sep_Cancel_Set
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begin
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lemma sep_mp_gen: "((Q \<longrightarrow>* R) \<and>* Q') s \<Longrightarrow> (\<And>s. Q' s \<Longrightarrow> Q s) \<Longrightarrow> R s"
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by (clarsimp simp: sep_conj_def sep_impl_def)
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lemma sep_mp_frame_gen: "\<lbrakk>((Q \<longrightarrow>* R) \<and>* Q' \<and>* R') s; (\<And>s. Q' s \<Longrightarrow> Q s)\<rbrakk> \<Longrightarrow> (R \<and>* R') s"
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by (metis sep_conj_left_commute sep_globalise sep_mp_frame)
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lemma sep_impl_simpl:
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"(P \<and>* Q \<longrightarrow>* R) s \<Longrightarrow> (P \<longrightarrow>* Q \<longrightarrow>* R) s"
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apply (erule sep_conj_sep_impl)
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apply (erule sep_conj_sep_impl)
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apply (clarsimp simp: sep_conj_assoc)
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apply (erule sep_mp)
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done
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lemma sep_wand_frame_lens: "((P \<longrightarrow>* Q) \<and>* R) s \<Longrightarrow> (\<And>s. T s = R s) ==> ((P \<longrightarrow>* Q) \<and>* T) s"
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by (metis sep_conj_commute sep_conj_impl1)
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ML \<open>
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fun sep_wand_frame_drule ctxt =
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let val lens = dresolve_tac ctxt [@{thm sep_wand_frame_lens}]
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val lens' = dresolve_tac ctxt [@{thm sep_asm_eq}]
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val r = rotator' ctxt
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val sep_cancel_thms = rev (SepCancel_Rules.get ctxt)
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in sep_apply_tactic ctxt (dresolve_tac ctxt [@{thm sep_mp_frame_gen}]) sep_cancel_thms |> r lens |> r lens'
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end;
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fun sep_mp_solver ctxt =
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let val sep_mp = sep_apply_tactic ctxt (dresolve0_tac [@{thm sep_mp_gen}]) ((rev o SepCancel_Rules.get) ctxt)
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val taclist = [sep_drule_comb_tac false [@{thm sep_empty_imp}] ctxt,
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sep_drule_tac sep_mp ctxt,
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sep_drule_tac (sep_drule_tactic ctxt [@{thm sep_impl_simpl}]) ctxt,
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sep_wand_frame_drule ctxt ]
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val check = DETERM o (sep_drule_tac (sep_select_tactic (dresolve0_tac [@{thm sep_wand_frame_lens}]) [1] ctxt) ctxt)
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in CHANGED_PROP o (check THEN_ALL_NEW REPEAT_ALL_NEW ( FIRST' taclist) )
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end;
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val sep_mp_method = SIMPLE_METHOD' o sep_mp_solver
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\<close>
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method_setup sep_mp = \<open>Scan.succeed sep_mp_method\<close>
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end
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