(* Title: HOL/UNITY/UNITY_tactics.ML ID: $Id: UNITY_tactics.ML,v 1.7 2003/02/08 15:05:36 paulson Exp $ Author: Lawrence C Paulson, Cambridge University Computer Laboratory Copyright 2003 University of Cambridge Specialized UNITY tactics, and ML bindings of theorems *) (*ListOrder*) val Le_def = thm "Le_def"; val Ge_def = thm "Ge_def"; val prefix_def = thm "prefix_def"; val Nil_genPrefix = thm "Nil_genPrefix"; val genPrefix_length_le = thm "genPrefix_length_le"; val cons_genPrefixE = thm "cons_genPrefixE"; val Cons_genPrefix_Cons = thm "Cons_genPrefix_Cons"; val refl_genPrefix = thm "refl_genPrefix"; val genPrefix_refl = thm "genPrefix_refl"; val genPrefix_mono = thm "genPrefix_mono"; val append_genPrefix = thm "append_genPrefix"; val genPrefix_trans_O = thm "genPrefix_trans_O"; val genPrefix_trans = thm "genPrefix_trans"; val prefix_genPrefix_trans = thm "prefix_genPrefix_trans"; val genPrefix_prefix_trans = thm "genPrefix_prefix_trans"; val trans_genPrefix = thm "trans_genPrefix"; val genPrefix_antisym = thm "genPrefix_antisym"; val antisym_genPrefix = thm "antisym_genPrefix"; val genPrefix_Nil = thm "genPrefix_Nil"; val same_genPrefix_genPrefix = thm "same_genPrefix_genPrefix"; val genPrefix_Cons = thm "genPrefix_Cons"; val genPrefix_take_append = thm "genPrefix_take_append"; val genPrefix_append_both = thm "genPrefix_append_both"; val append_cons_eq = thm "append_cons_eq"; val append_one_genPrefix = thm "append_one_genPrefix"; val genPrefix_imp_nth = thm "genPrefix_imp_nth"; val nth_imp_genPrefix = thm "nth_imp_genPrefix"; val genPrefix_iff_nth = thm "genPrefix_iff_nth"; val prefix_refl = thm "prefix_refl"; val prefix_trans = thm "prefix_trans"; val prefix_antisym = thm "prefix_antisym"; val prefix_less_le = thm "prefix_less_le"; val set_mono = thm "set_mono"; val Nil_prefix = thm "Nil_prefix"; val prefix_Nil = thm "prefix_Nil"; val Cons_prefix_Cons = thm "Cons_prefix_Cons"; val same_prefix_prefix = thm "same_prefix_prefix"; val append_prefix = thm "append_prefix"; val prefix_appendI = thm "prefix_appendI"; val prefix_Cons = thm "prefix_Cons"; val append_one_prefix = thm "append_one_prefix"; val prefix_length_le = thm "prefix_length_le"; val strict_prefix_length_less = thm "strict_prefix_length_less"; val mono_length = thm "mono_length"; val prefix_iff = thm "prefix_iff"; val prefix_snoc = thm "prefix_snoc"; val prefix_append_iff = thm "prefix_append_iff"; val common_prefix_linear = thm "common_prefix_linear"; val reflexive_Le = thm "reflexive_Le"; val antisym_Le = thm "antisym_Le"; val trans_Le = thm "trans_Le"; val pfixLe_refl = thm "pfixLe_refl"; val pfixLe_trans = thm "pfixLe_trans"; val pfixLe_antisym = thm "pfixLe_antisym"; val prefix_imp_pfixLe = thm "prefix_imp_pfixLe"; val reflexive_Ge = thm "reflexive_Ge"; val antisym_Ge = thm "antisym_Ge"; val trans_Ge = thm "trans_Ge"; val pfixGe_refl = thm "pfixGe_refl"; val pfixGe_trans = thm "pfixGe_trans"; val pfixGe_antisym = thm "pfixGe_antisym"; val prefix_imp_pfixGe = thm "prefix_imp_pfixGe"; (*UNITY*) val mk_total_program_def = thm "mk_total_program_def"; val totalize_act_def = thm "totalize_act_def"; val constrains_def = thm "constrains_def"; val stable_def = thm "stable_def"; val invariant_def = thm "invariant_def"; val increasing_def = thm "increasing_def"; val Allowed_def = thm "Allowed_def"; val Id_in_Acts = thm "Id_in_Acts"; val insert_Id_Acts = thm "insert_Id_Acts"; val Id_in_AllowedActs = thm "Id_in_AllowedActs"; val insert_Id_AllowedActs = thm "insert_Id_AllowedActs"; val Init_eq = thm "Init_eq"; val Acts_eq = thm "Acts_eq"; val AllowedActs_eq = thm "AllowedActs_eq"; val surjective_mk_program = thm "surjective_mk_program"; val program_equalityI = thm "program_equalityI"; val program_equalityE = thm "program_equalityE"; val program_equality_iff = thm "program_equality_iff"; val def_prg_Init = thm "def_prg_Init"; val def_prg_Acts = thm "def_prg_Acts"; val def_prg_AllowedActs = thm "def_prg_AllowedActs"; val def_act_simp = thm "def_act_simp"; val def_set_simp = thm "def_set_simp"; val constrainsI = thm "constrainsI"; val constrainsD = thm "constrainsD"; val constrains_empty = thm "constrains_empty"; val constrains_empty2 = thm "constrains_empty2"; val constrains_UNIV = thm "constrains_UNIV"; val constrains_UNIV2 = thm "constrains_UNIV2"; val constrains_weaken_R = thm "constrains_weaken_R"; val constrains_weaken_L = thm "constrains_weaken_L"; val constrains_weaken = thm "constrains_weaken"; val constrains_Un = thm "constrains_Un"; val constrains_UN = thm "constrains_UN"; val constrains_Un_distrib = thm "constrains_Un_distrib"; val constrains_UN_distrib = thm "constrains_UN_distrib"; val constrains_Int_distrib = thm "constrains_Int_distrib"; val constrains_INT_distrib = thm "constrains_INT_distrib"; val constrains_Int = thm "constrains_Int"; val constrains_INT = thm "constrains_INT"; val constrains_imp_subset = thm "constrains_imp_subset"; val constrains_trans = thm "constrains_trans"; val constrains_cancel = thm "constrains_cancel"; val unlessI = thm "unlessI"; val unlessD = thm "unlessD"; val stableI = thm "stableI"; val stableD = thm "stableD"; val stable_UNIV = thm "stable_UNIV"; val stable_Un = thm "stable_Un"; val stable_UN = thm "stable_UN"; val stable_Int = thm "stable_Int"; val stable_INT = thm "stable_INT"; val stable_constrains_Un = thm "stable_constrains_Un"; val stable_constrains_Int = thm "stable_constrains_Int"; val stable_constrains_stable = thm "stable_constrains_stable"; val invariantI = thm "invariantI"; val invariant_Int = thm "invariant_Int"; val increasingD = thm "increasingD"; val increasing_constant = thm "increasing_constant"; val mono_increasing_o = thm "mono_increasing_o"; val strict_increasingD = thm "strict_increasingD"; val elimination = thm "elimination"; val elimination_sing = thm "elimination_sing"; val constrains_strongest_rhs = thm "constrains_strongest_rhs"; val strongest_rhs_is_strongest = thm "strongest_rhs_is_strongest"; val Un_Diff_Diff = thm "Un_Diff_Diff"; val Int_Union_Union = thm "Int_Union_Union"; val Image_less_than = thm "Image_less_than"; val Image_inverse_less_than = thm "Image_inverse_less_than"; val totalize_constrains_iff = thm "totalize_constrains_iff"; (*WFair*) val stable_transient_empty = thm "stable_transient_empty"; val transient_strengthen = thm "transient_strengthen"; val transientI = thm "transientI"; val totalize_transientI = thm "totalize_transientI"; val transientE = thm "transientE"; val transient_empty = thm "transient_empty"; val ensuresI = thm "ensuresI"; val ensuresD = thm "ensuresD"; val ensures_weaken_R = thm "ensures_weaken_R"; val stable_ensures_Int = thm "stable_ensures_Int"; val stable_transient_ensures = thm "stable_transient_ensures"; val ensures_eq = thm "ensures_eq"; val leadsTo_Basis = thm "leadsTo_Basis"; val leadsTo_Trans = thm "leadsTo_Trans"; val transient_imp_leadsTo = thm "transient_imp_leadsTo"; val leadsTo_Un_duplicate = thm "leadsTo_Un_duplicate"; val leadsTo_Un_duplicate2 = thm "leadsTo_Un_duplicate2"; val leadsTo_Union = thm "leadsTo_Union"; val leadsTo_Union_Int = thm "leadsTo_Union_Int"; val leadsTo_UN = thm "leadsTo_UN"; val leadsTo_Un = thm "leadsTo_Un"; val single_leadsTo_I = thm "single_leadsTo_I"; val leadsTo_induct = thm "leadsTo_induct"; val subset_imp_ensures = thm "subset_imp_ensures"; val subset_imp_leadsTo = thm "subset_imp_leadsTo"; val leadsTo_refl = thm "leadsTo_refl"; val empty_leadsTo = thm "empty_leadsTo"; val leadsTo_UNIV = thm "leadsTo_UNIV"; val leadsTo_induct_pre = thm "leadsTo_induct_pre"; val leadsTo_weaken_R = thm "leadsTo_weaken_R"; val leadsTo_weaken_L = thm "leadsTo_weaken_L"; val leadsTo_Un_distrib = thm "leadsTo_Un_distrib"; val leadsTo_UN_distrib = thm "leadsTo_UN_distrib"; val leadsTo_Union_distrib = thm "leadsTo_Union_distrib"; val leadsTo_weaken = thm "leadsTo_weaken"; val leadsTo_Diff = thm "leadsTo_Diff"; val leadsTo_UN_UN = thm "leadsTo_UN_UN"; val leadsTo_Un_Un = thm "leadsTo_Un_Un"; val leadsTo_cancel2 = thm "leadsTo_cancel2"; val leadsTo_cancel_Diff2 = thm "leadsTo_cancel_Diff2"; val leadsTo_cancel1 = thm "leadsTo_cancel1"; val leadsTo_cancel_Diff1 = thm "leadsTo_cancel_Diff1"; val leadsTo_empty = thm "leadsTo_empty"; val psp_stable = thm "psp_stable"; val psp_stable2 = thm "psp_stable2"; val psp_ensures = thm "psp_ensures"; val psp = thm "psp"; val psp2 = thm "psp2"; val psp_unless = thm "psp_unless"; val leadsTo_wf_induct = thm "leadsTo_wf_induct"; val bounded_induct = thm "bounded_induct"; val lessThan_induct = thm "lessThan_induct"; val lessThan_bounded_induct = thm "lessThan_bounded_induct"; val greaterThan_bounded_induct = thm "greaterThan_bounded_induct"; val wlt_leadsTo = thm "wlt_leadsTo"; val leadsTo_subset = thm "leadsTo_subset"; val leadsTo_eq_subset_wlt = thm "leadsTo_eq_subset_wlt"; val wlt_increasing = thm "wlt_increasing"; val leadsTo_123 = thm "leadsTo_123"; val wlt_constrains_wlt = thm "wlt_constrains_wlt"; val completion = thm "completion"; val finite_completion = thm "finite_completion"; val stable_completion = thm "stable_completion"; val finite_stable_completion = thm "finite_stable_completion"; (*Constrains*) val Increasing_def = thm "Increasing_def"; val reachable_Init = thm "reachable.Init"; val reachable_Acts = thm "reachable.Acts"; val reachable_equiv_traces = thm "reachable_equiv_traces"; val Init_subset_reachable = thm "Init_subset_reachable"; val stable_reachable = thm "stable_reachable"; val invariant_reachable = thm "invariant_reachable"; val invariant_includes_reachable = thm "invariant_includes_reachable"; val constrains_reachable_Int = thm "constrains_reachable_Int"; val Constrains_eq_constrains = thm "Constrains_eq_constrains"; val constrains_imp_Constrains = thm "constrains_imp_Constrains"; val stable_imp_Stable = thm "stable_imp_Stable"; val ConstrainsI = thm "ConstrainsI"; val Constrains_empty = thm "Constrains_empty"; val Constrains_UNIV = thm "Constrains_UNIV"; val Constrains_weaken_R = thm "Constrains_weaken_R"; val Constrains_weaken_L = thm "Constrains_weaken_L"; val Constrains_weaken = thm "Constrains_weaken"; val Constrains_Un = thm "Constrains_Un"; val Constrains_UN = thm "Constrains_UN"; val Constrains_Int = thm "Constrains_Int"; val Constrains_INT = thm "Constrains_INT"; val Constrains_imp_subset = thm "Constrains_imp_subset"; val Constrains_trans = thm "Constrains_trans"; val Constrains_cancel = thm "Constrains_cancel"; val Stable_eq = thm "Stable_eq"; val Stable_eq_stable = thm "Stable_eq_stable"; val StableI = thm "StableI"; val StableD = thm "StableD"; val Stable_Un = thm "Stable_Un"; val Stable_Int = thm "Stable_Int"; val Stable_Constrains_Un = thm "Stable_Constrains_Un"; val Stable_Constrains_Int = thm "Stable_Constrains_Int"; val Stable_UN = thm "Stable_UN"; val Stable_INT = thm "Stable_INT"; val Stable_reachable = thm "Stable_reachable"; val IncreasingD = thm "IncreasingD"; val mono_Increasing_o = thm "mono_Increasing_o"; val strict_IncreasingD = thm "strict_IncreasingD"; val increasing_imp_Increasing = thm "increasing_imp_Increasing"; val Increasing_constant = thm "Increasing_constant"; val Elimination = thm "Elimination"; val Elimination_sing = thm "Elimination_sing"; val AlwaysI = thm "AlwaysI"; val AlwaysD = thm "AlwaysD"; val AlwaysE = thm "AlwaysE"; val Always_imp_Stable = thm "Always_imp_Stable"; val Always_includes_reachable = thm "Always_includes_reachable"; val invariant_imp_Always = thm "invariant_imp_Always"; val Always_reachable = thm "Always_reachable"; val Always_eq_invariant_reachable = thm "Always_eq_invariant_reachable"; val Always_eq_includes_reachable = thm "Always_eq_includes_reachable"; val Always_UNIV_eq = thm "Always_UNIV_eq"; val UNIV_AlwaysI = thm "UNIV_AlwaysI"; val Always_eq_UN_invariant = thm "Always_eq_UN_invariant"; val Always_weaken = thm "Always_weaken"; val Always_Constrains_pre = thm "Always_Constrains_pre"; val Always_Constrains_post = thm "Always_Constrains_post"; val Always_ConstrainsI = thm "Always_ConstrainsI"; val Always_ConstrainsD = thm "Always_ConstrainsD"; val Always_Constrains_weaken = thm "Always_Constrains_weaken"; val Always_Int_distrib = thm "Always_Int_distrib"; val Always_INT_distrib = thm "Always_INT_distrib"; val Always_Int_I = thm "Always_Int_I"; val Always_Compl_Un_eq = thm "Always_Compl_Un_eq"; val Always_thin = thm "Always_thin"; (*FP*) val stable_FP_Orig_Int = thm "stable_FP_Orig_Int"; val FP_Orig_weakest = thm "FP_Orig_weakest"; val stable_FP_Int = thm "stable_FP_Int"; val FP_equivalence = thm "FP_equivalence"; val FP_weakest = thm "FP_weakest"; val Compl_FP = thm "Compl_FP"; val Diff_FP = thm "Diff_FP"; (*SubstAx*) val LeadsTo_eq_leadsTo = thm "LeadsTo_eq_leadsTo"; val Always_LeadsTo_pre = thm "Always_LeadsTo_pre"; val Always_LeadsTo_post = thm "Always_LeadsTo_post"; val Always_LeadsToI = thm "Always_LeadsToI"; val Always_LeadsToD = thm "Always_LeadsToD"; val leadsTo_imp_LeadsTo = thm "leadsTo_imp_LeadsTo"; val LeadsTo_Trans = thm "LeadsTo_Trans"; val LeadsTo_Union = thm "LeadsTo_Union"; val LeadsTo_UNIV = thm "LeadsTo_UNIV"; val LeadsTo_Un_duplicate = thm "LeadsTo_Un_duplicate"; val LeadsTo_Un_duplicate2 = thm "LeadsTo_Un_duplicate2"; val LeadsTo_UN = thm "LeadsTo_UN"; val LeadsTo_Un = thm "LeadsTo_Un"; val single_LeadsTo_I = thm "single_LeadsTo_I"; val subset_imp_LeadsTo = thm "subset_imp_LeadsTo"; val empty_LeadsTo = thm "empty_LeadsTo"; val LeadsTo_weaken_R = thm "LeadsTo_weaken_R"; val LeadsTo_weaken_L = thm "LeadsTo_weaken_L"; val LeadsTo_weaken = thm "LeadsTo_weaken"; val Always_LeadsTo_weaken = thm "Always_LeadsTo_weaken"; val LeadsTo_Un_post = thm "LeadsTo_Un_post"; val LeadsTo_Trans_Un = thm "LeadsTo_Trans_Un"; val LeadsTo_Un_distrib = thm "LeadsTo_Un_distrib"; val LeadsTo_UN_distrib = thm "LeadsTo_UN_distrib"; val LeadsTo_Union_distrib = thm "LeadsTo_Union_distrib"; val LeadsTo_Basis = thm "LeadsTo_Basis"; val EnsuresI = thm "EnsuresI"; val Always_LeadsTo_Basis = thm "Always_LeadsTo_Basis"; val LeadsTo_Diff = thm "LeadsTo_Diff"; val LeadsTo_UN_UN = thm "LeadsTo_UN_UN"; val LeadsTo_UN_UN_noindex = thm "LeadsTo_UN_UN_noindex"; val all_LeadsTo_UN_UN = thm "all_LeadsTo_UN_UN"; val LeadsTo_Un_Un = thm "LeadsTo_Un_Un"; val LeadsTo_cancel2 = thm "LeadsTo_cancel2"; val LeadsTo_cancel_Diff2 = thm "LeadsTo_cancel_Diff2"; val LeadsTo_cancel1 = thm "LeadsTo_cancel1"; val LeadsTo_cancel_Diff1 = thm "LeadsTo_cancel_Diff1"; val LeadsTo_empty = thm "LeadsTo_empty"; val PSP_Stable = thm "PSP_Stable"; val PSP_Stable2 = thm "PSP_Stable2"; val PSP = thm "PSP"; val PSP2 = thm "PSP2"; val PSP_Unless = thm "PSP_Unless"; val Stable_transient_Always_LeadsTo = thm "Stable_transient_Always_LeadsTo"; val LeadsTo_wf_induct = thm "LeadsTo_wf_induct"; val Bounded_induct = thm "Bounded_induct"; val LessThan_induct = thm "LessThan_induct"; val integ_0_le_induct = thm "integ_0_le_induct"; val LessThan_bounded_induct = thm "LessThan_bounded_induct"; val GreaterThan_bounded_induct = thm "GreaterThan_bounded_induct"; val Completion = thm "Completion"; val Finite_completion = thm "Finite_completion"; val Stable_completion = thm "Stable_completion"; val Finite_stable_completion = thm "Finite_stable_completion"; (*Union*) val Init_SKIP = thm "Init_SKIP"; val Acts_SKIP = thm "Acts_SKIP"; val AllowedActs_SKIP = thm "AllowedActs_SKIP"; val reachable_SKIP = thm "reachable_SKIP"; val SKIP_in_constrains_iff = thm "SKIP_in_constrains_iff"; val SKIP_in_Constrains_iff = thm "SKIP_in_Constrains_iff"; val SKIP_in_stable = thm "SKIP_in_stable"; val Init_Join = thm "Init_Join"; val Acts_Join = thm "Acts_Join"; val AllowedActs_Join = thm "AllowedActs_Join"; val JN_empty = thm "JN_empty"; val JN_insert = thm "JN_insert"; val Init_JN = thm "Init_JN"; val Acts_JN = thm "Acts_JN"; val AllowedActs_JN = thm "AllowedActs_JN"; val JN_cong = thm "JN_cong"; val Join_commute = thm "Join_commute"; val Join_assoc = thm "Join_assoc"; val Join_left_commute = thm "Join_left_commute"; val Join_SKIP_left = thm "Join_SKIP_left"; val Join_SKIP_right = thm "Join_SKIP_right"; val Join_absorb = thm "Join_absorb"; val Join_left_absorb = thm "Join_left_absorb"; val Join_ac = thms "Join_ac"; val JN_absorb = thm "JN_absorb"; val JN_Un = thm "JN_Un"; val JN_constant = thm "JN_constant"; val JN_Join_distrib = thm "JN_Join_distrib"; val JN_Join_miniscope = thm "JN_Join_miniscope"; val JN_Join_diff = thm "JN_Join_diff"; val JN_constrains = thm "JN_constrains"; val Join_constrains = thm "Join_constrains"; val Join_unless = thm "Join_unless"; val Join_constrains_weaken = thm "Join_constrains_weaken"; val JN_constrains_weaken = thm "JN_constrains_weaken"; val JN_stable = thm "JN_stable"; val invariant_JN_I = thm "invariant_JN_I"; val Join_stable = thm "Join_stable"; val Join_increasing = thm "Join_increasing"; val invariant_JoinI = thm "invariant_JoinI"; val FP_JN = thm "FP_JN"; val JN_transient = thm "JN_transient"; val Join_transient = thm "Join_transient"; val Join_transient_I1 = thm "Join_transient_I1"; val Join_transient_I2 = thm "Join_transient_I2"; val JN_ensures = thm "JN_ensures"; val Join_ensures = thm "Join_ensures"; val stable_Join_constrains = thm "stable_Join_constrains"; val stable_Join_Always1 = thm "stable_Join_Always1"; val stable_Join_Always2 = thm "stable_Join_Always2"; val stable_Join_ensures1 = thm "stable_Join_ensures1"; val stable_Join_ensures2 = thm "stable_Join_ensures2"; val ok_SKIP1 = thm "ok_SKIP1"; val ok_SKIP2 = thm "ok_SKIP2"; val ok_Join_commute = thm "ok_Join_commute"; val ok_commute = thm "ok_commute"; val ok_sym = thm "ok_sym"; val ok_iff_OK = thm "ok_iff_OK"; val ok_Join_iff1 = thm "ok_Join_iff1"; val ok_Join_iff2 = thm "ok_Join_iff2"; val ok_Join_commute_I = thm "ok_Join_commute_I"; val ok_JN_iff1 = thm "ok_JN_iff1"; val ok_JN_iff2 = thm "ok_JN_iff2"; val OK_iff_ok = thm "OK_iff_ok"; val OK_imp_ok = thm "OK_imp_ok"; val Allowed_SKIP = thm "Allowed_SKIP"; val Allowed_Join = thm "Allowed_Join"; val Allowed_JN = thm "Allowed_JN"; val ok_iff_Allowed = thm "ok_iff_Allowed"; val OK_iff_Allowed = thm "OK_iff_Allowed"; val safety_prop_Acts_iff = thm "safety_prop_Acts_iff"; val safety_prop_AllowedActs_iff_Allowed = thm "safety_prop_AllowedActs_iff_Allowed"; val Allowed_eq = thm "Allowed_eq"; val def_prg_Allowed = thm "def_prg_Allowed"; val def_total_prg_Allowed = thm "def_total_prg_Allowed"; val safety_prop_constrains = thm "safety_prop_constrains"; val safety_prop_stable = thm "safety_prop_stable"; val safety_prop_Int = thm "safety_prop_Int"; val safety_prop_INTER1 = thm "safety_prop_INTER1"; val safety_prop_INTER = thm "safety_prop_INTER"; val def_UNION_ok_iff = thm "def_UNION_ok_iff"; val totalize_JN = thm "totalize_JN"; (*Comp*) val preserves_def = thm "preserves_def"; val funPair_def = thm "funPair_def"; val componentI = thm "componentI"; val component_eq_subset = thm "component_eq_subset"; val component_SKIP = thm "component_SKIP"; val component_refl = thm "component_refl"; val SKIP_minimal = thm "SKIP_minimal"; val component_Join1 = thm "component_Join1"; val component_Join2 = thm "component_Join2"; val Join_absorb1 = thm "Join_absorb1"; val Join_absorb2 = thm "Join_absorb2"; val JN_component_iff = thm "JN_component_iff"; val component_JN = thm "component_JN"; val component_trans = thm "component_trans"; val component_antisym = thm "component_antisym"; val Join_component_iff = thm "Join_component_iff"; val component_constrains = thm "component_constrains"; val program_less_le = thm "program_less_le"; val preservesI = thm "preservesI"; val preserves_imp_eq = thm "preserves_imp_eq"; val Join_preserves = thm "Join_preserves"; val JN_preserves = thm "JN_preserves"; val SKIP_preserves = thm "SKIP_preserves"; val funPair_apply = thm "funPair_apply"; val preserves_funPair = thm "preserves_funPair"; val funPair_o_distrib = thm "funPair_o_distrib"; val fst_o_funPair = thm "fst_o_funPair"; val snd_o_funPair = thm "snd_o_funPair"; val subset_preserves_o = thm "subset_preserves_o"; val preserves_subset_stable = thm "preserves_subset_stable"; val preserves_subset_increasing = thm "preserves_subset_increasing"; val preserves_id_subset_stable = thm "preserves_id_subset_stable"; val safety_prop_preserves = thm "safety_prop_preserves"; val stable_localTo_stable2 = thm "stable_localTo_stable2"; val Increasing_preserves_Stable = thm "Increasing_preserves_Stable"; val component_of_imp_component = thm "component_of_imp_component"; val component_of_refl = thm "component_of_refl"; val component_of_SKIP = thm "component_of_SKIP"; val component_of_trans = thm "component_of_trans"; val strict_component_of_eq = thm "strict_component_of_eq"; val localize_Init_eq = thm "localize_Init_eq"; val localize_Acts_eq = thm "localize_Acts_eq"; val localize_AllowedActs_eq = thm "localize_AllowedActs_eq"; (*Guar*) val guar_def = thm "guar_def"; val OK_insert_iff = thm "OK_insert_iff"; val ex1 = thm "ex1"; val ex2 = thm "ex2"; val ex_prop_finite = thm "ex_prop_finite"; val ex_prop_equiv = thm "ex_prop_equiv"; val uv1 = thm "uv1"; val uv2 = thm "uv2"; val uv_prop_finite = thm "uv_prop_finite"; val guaranteesI = thm "guaranteesI"; val guaranteesD = thm "guaranteesD"; val component_guaranteesD = thm "component_guaranteesD"; val guarantees_weaken = thm "guarantees_weaken"; val subset_imp_guarantees_UNIV = thm "subset_imp_guarantees_UNIV"; val subset_imp_guarantees = thm "subset_imp_guarantees"; val ex_prop_imp = thm "ex_prop_imp"; val guarantees_imp = thm "guarantees_imp"; val ex_prop_equiv2 = thm "ex_prop_equiv2"; val guarantees_UN_left = thm "guarantees_UN_left"; val guarantees_Un_left = thm "guarantees_Un_left"; val guarantees_INT_right = thm "guarantees_INT_right"; val guarantees_Int_right = thm "guarantees_Int_right"; val guarantees_Int_right_I = thm "guarantees_Int_right_I"; val guarantees_INT_right_iff = thm "guarantees_INT_right_iff"; val shunting = thm "shunting"; val contrapositive = thm "contrapositive"; val combining1 = thm "combining1"; val combining2 = thm "combining2"; val all_guarantees = thm "all_guarantees"; val ex_guarantees = thm "ex_guarantees"; val guarantees_Join_Int = thm "guarantees_Join_Int"; val guarantees_Join_Un = thm "guarantees_Join_Un"; val guarantees_JN_INT = thm "guarantees_JN_INT"; val guarantees_JN_UN = thm "guarantees_JN_UN"; val guarantees_Join_I1 = thm "guarantees_Join_I1"; val guarantees_Join_I2 = thm "guarantees_Join_I2"; val guarantees_JN_I = thm "guarantees_JN_I"; val Join_welldef_D1 = thm "Join_welldef_D1"; val Join_welldef_D2 = thm "Join_welldef_D2"; val refines_refl = thm "refines_refl"; val ex_refinement_thm = thm "ex_refinement_thm"; val uv_refinement_thm = thm "uv_refinement_thm"; val guarantees_equiv = thm "guarantees_equiv"; val wg_weakest = thm "wg_weakest"; val wg_guarantees = thm "wg_guarantees"; val wg_equiv = thm "wg_equiv"; val component_of_wg = thm "component_of_wg"; val wg_finite = thm "wg_finite"; val wg_ex_prop = thm "wg_ex_prop"; val wx_subset = thm "wx_subset"; val wx_ex_prop = thm "wx_ex_prop"; val wx_weakest = thm "wx_weakest"; val wx'_ex_prop = thm "wx'_ex_prop"; val wx_equiv = thm "wx_equiv"; val guarantees_wx_eq = thm "guarantees_wx_eq"; val stable_guarantees_Always = thm "stable_guarantees_Always"; val leadsTo_Basis = thm "leadsTo_Basis"; val constrains_guarantees_leadsTo = thm "constrains_guarantees_leadsTo"; (*Extend*) val Restrict_iff = thm "Restrict_iff"; val Restrict_UNIV = thm "Restrict_UNIV"; val Restrict_empty = thm "Restrict_empty"; val Restrict_Int = thm "Restrict_Int"; val Restrict_triv = thm "Restrict_triv"; val Restrict_subset = thm "Restrict_subset"; val Restrict_eq_mono = thm "Restrict_eq_mono"; val Restrict_imageI = thm "Restrict_imageI"; val Domain_Restrict = thm "Domain_Restrict"; val Image_Restrict = thm "Image_Restrict"; val insert_Id_image_Acts = thm "insert_Id_image_Acts"; val good_mapI = thm "good_mapI"; val good_map_is_surj = thm "good_map_is_surj"; val fst_inv_equalityI = thm "fst_inv_equalityI"; val project_set_iff = thm "project_set_iff"; val extend_set_mono = thm "extend_set_mono"; val extend_set_empty = thm "extend_set_empty"; val project_set_Int_subset = thm "project_set_Int_subset"; val Init_extend = thm "Init_extend"; val Init_project = thm "Init_project"; val Acts_project = thm "Acts_project"; val project_set_UNIV = thm "project_set_UNIV"; val project_set_Union = thm "project_set_Union"; val project_act_mono = thm "project_act_mono"; val project_constrains_project_set = thm "project_constrains_project_set"; val project_stable_project_set = thm "project_stable_project_set"; (*Rename*) val good_map_bij = thm "good_map_bij"; val fst_o_inv_eq_inv = thm "fst_o_inv_eq_inv"; val mem_rename_set_iff = thm "mem_rename_set_iff"; val extend_set_eq_image = thm "extend_set_eq_image"; val Init_rename = thm "Init_rename"; val extend_set_inv = thm "extend_set_inv"; val bij_extend_act_eq_project_act = thm "bij_extend_act_eq_project_act"; val bij_extend_act = thm "bij_extend_act"; val bij_project_act = thm "bij_project_act"; val bij_inv_project_act_eq = thm "bij_inv_project_act_eq"; val Acts_project = thm "Acts_project"; val extend_inv = thm "extend_inv"; val rename_inv_rename = thm "rename_inv_rename"; val rename_rename_inv = thm "rename_rename_inv"; val rename_inv_eq = thm "rename_inv_eq"; val bij_extend = thm "bij_extend"; val bij_project = thm "bij_project"; val inv_project_eq = thm "inv_project_eq"; val Allowed_rename = thm "Allowed_rename"; val bij_rename = thm "bij_rename"; val surj_rename = thm "surj_rename"; val inj_rename_imp_inj = thm "inj_rename_imp_inj"; val surj_rename_imp_surj = thm "surj_rename_imp_surj"; val bij_rename_imp_bij = thm "bij_rename_imp_bij"; val bij_rename_iff = thm "bij_rename_iff"; val rename_SKIP = thm "rename_SKIP"; val rename_Join = thm "rename_Join"; val rename_JN = thm "rename_JN"; val rename_constrains = thm "rename_constrains"; val rename_stable = thm "rename_stable"; val rename_invariant = thm "rename_invariant"; val rename_increasing = thm "rename_increasing"; val reachable_rename_eq = thm "reachable_rename_eq"; val rename_Constrains = thm "rename_Constrains"; val rename_Stable = thm "rename_Stable"; val rename_Always = thm "rename_Always"; val rename_Increasing = thm "rename_Increasing"; val rename_transient = thm "rename_transient"; val rename_ensures = thm "rename_ensures"; val rename_leadsTo = thm "rename_leadsTo"; val rename_LeadsTo = thm "rename_LeadsTo"; val rename_rename_guarantees_eq = thm "rename_rename_guarantees_eq"; val rename_guarantees_eq_rename_inv = thm "rename_guarantees_eq_rename_inv"; val rename_preserves = thm "rename_preserves"; val ok_rename_iff = thm "ok_rename_iff"; val OK_rename_iff = thm "OK_rename_iff"; val bij_eq_rename = thm "bij_eq_rename"; val rename_image_constrains = thm "rename_image_constrains"; val rename_image_stable = thm "rename_image_stable"; val rename_image_increasing = thm "rename_image_increasing"; val rename_image_invariant = thm "rename_image_invariant"; val rename_image_Constrains = thm "rename_image_Constrains"; val rename_image_preserves = thm "rename_image_preserves"; val rename_image_Stable = thm "rename_image_Stable"; val rename_image_Increasing = thm "rename_image_Increasing"; val rename_image_Always = thm "rename_image_Always"; val rename_image_leadsTo = thm "rename_image_leadsTo"; val rename_image_LeadsTo = thm "rename_image_LeadsTo"; (*Lift_prog*) val sub_def = thm "sub_def"; val lift_map_def = thm "lift_map_def"; val drop_map_def = thm "drop_map_def"; val insert_map_inverse = thm "insert_map_inverse"; val insert_map_delete_map_eq = thm "insert_map_delete_map_eq"; val insert_map_inject1 = thm "insert_map_inject1"; val insert_map_inject2 = thm "insert_map_inject2"; val insert_map_inject = thm "insert_map_inject"; val insert_map_inject = thm "insert_map_inject"; val lift_map_eq_iff = thm "lift_map_eq_iff"; val drop_map_lift_map_eq = thm "drop_map_lift_map_eq"; val inj_lift_map = thm "inj_lift_map"; val lift_map_drop_map_eq = thm "lift_map_drop_map_eq"; val drop_map_inject = thm "drop_map_inject"; val surj_lift_map = thm "surj_lift_map"; val bij_lift_map = thm "bij_lift_map"; val inv_lift_map_eq = thm "inv_lift_map_eq"; val inv_drop_map_eq = thm "inv_drop_map_eq"; val bij_drop_map = thm "bij_drop_map"; val sub_apply = thm "sub_apply"; val lift_set_empty = thm "lift_set_empty"; val lift_set_iff = thm "lift_set_iff"; val lift_set_iff2 = thm "lift_set_iff2"; val lift_set_mono = thm "lift_set_mono"; val lift_set_Un_distrib = thm "lift_set_Un_distrib"; val lift_set_Diff_distrib = thm "lift_set_Diff_distrib"; val bij_lift = thm "bij_lift"; val lift_SKIP = thm "lift_SKIP"; val lift_Join = thm "lift_Join"; val lift_JN = thm "lift_JN"; val lift_constrains = thm "lift_constrains"; val lift_stable = thm "lift_stable"; val lift_invariant = thm "lift_invariant"; val lift_Constrains = thm "lift_Constrains"; val lift_Stable = thm "lift_Stable"; val lift_Always = thm "lift_Always"; val lift_transient = thm "lift_transient"; val lift_ensures = thm "lift_ensures"; val lift_leadsTo = thm "lift_leadsTo"; val lift_LeadsTo = thm "lift_LeadsTo"; val lift_lift_guarantees_eq = thm "lift_lift_guarantees_eq"; val lift_guarantees_eq_lift_inv = thm "lift_guarantees_eq_lift_inv"; val lift_preserves_snd_I = thm "lift_preserves_snd_I"; val delete_map_eqE = thm "delete_map_eqE"; val delete_map_eqE = thm "delete_map_eqE"; val delete_map_neq_apply = thm "delete_map_neq_apply"; val vimage_o_fst_eq = thm "vimage_o_fst_eq"; val vimage_sub_eq_lift_set = thm "vimage_sub_eq_lift_set"; val mem_lift_act_iff = thm "mem_lift_act_iff"; val preserves_snd_lift_stable = thm "preserves_snd_lift_stable"; val constrains_imp_lift_constrains = thm "constrains_imp_lift_constrains"; val lift_map_image_Times = thm "lift_map_image_Times"; val lift_preserves_eq = thm "lift_preserves_eq"; val lift_preserves_sub = thm "lift_preserves_sub"; val o_equiv_assoc = thm "o_equiv_assoc"; val o_equiv_apply = thm "o_equiv_apply"; val fst_o_lift_map = thm "fst_o_lift_map"; val snd_o_lift_map = thm "snd_o_lift_map"; val extend_act_extend_act = thm "extend_act_extend_act"; val project_act_project_act = thm "project_act_project_act"; val project_act_extend_act = thm "project_act_extend_act"; val act_in_UNION_preserves_fst = thm "act_in_UNION_preserves_fst"; val UNION_OK_lift_I = thm "UNION_OK_lift_I"; val OK_lift_I = thm "OK_lift_I"; val Allowed_lift = thm "Allowed_lift"; val lift_image_preserves = thm "lift_image_preserves"; (*PPROD*) val Init_PLam = thm "Init_PLam"; val PLam_empty = thm "PLam_empty"; val PLam_SKIP = thm "PLam_SKIP"; val PLam_insert = thm "PLam_insert"; val PLam_component_iff = thm "PLam_component_iff"; val component_PLam = thm "component_PLam"; val PLam_constrains = thm "PLam_constrains"; val PLam_stable = thm "PLam_stable"; val PLam_transient = thm "PLam_transient"; val PLam_ensures = thm "PLam_ensures"; val PLam_leadsTo_Basis = thm "PLam_leadsTo_Basis"; val invariant_imp_PLam_invariant = thm "invariant_imp_PLam_invariant"; val PLam_preserves_fst = thm "PLam_preserves_fst"; val PLam_preserves_snd = thm "PLam_preserves_snd"; val guarantees_PLam_I = thm "guarantees_PLam_I"; val Allowed_PLam = thm "Allowed_PLam"; val PLam_preserves = thm "PLam_preserves"; (*Follows*) val mono_Always_o = thm "mono_Always_o"; val mono_LeadsTo_o = thm "mono_LeadsTo_o"; val Follows_constant = thm "Follows_constant"; val mono_Follows_o = thm "mono_Follows_o"; val mono_Follows_apply = thm "mono_Follows_apply"; val Follows_trans = thm "Follows_trans"; val Follows_Increasing1 = thm "Follows_Increasing1"; val Follows_Increasing2 = thm "Follows_Increasing2"; val Follows_Bounded = thm "Follows_Bounded"; val Follows_LeadsTo = thm "Follows_LeadsTo"; val Follows_LeadsTo_pfixLe = thm "Follows_LeadsTo_pfixLe"; val Follows_LeadsTo_pfixGe = thm "Follows_LeadsTo_pfixGe"; val Always_Follows1 = thm "Always_Follows1"; val Always_Follows2 = thm "Always_Follows2"; val increasing_Un = thm "increasing_Un"; val Increasing_Un = thm "Increasing_Un"; val Always_Un = thm "Always_Un"; val Follows_Un = thm "Follows_Un"; val increasing_union = thm "increasing_union"; val Increasing_union = thm "Increasing_union"; val Always_union = thm "Always_union"; val Follows_union = thm "Follows_union"; val Follows_setsum = thm "Follows_setsum"; val Increasing_imp_Stable_pfixGe = thm "Increasing_imp_Stable_pfixGe"; val LeadsTo_le_imp_pfixGe = thm "LeadsTo_le_imp_pfixGe"; (*Lazy unfolding of actions or of sets*) fun simp_of_act def = def RS def_act_simp; fun simp_of_set def = def RS def_set_simp; (*Combines two invariance ASSUMPTIONS into one. USEFUL??*) val Always_Int_tac = dtac Always_Int_I THEN' assume_tac THEN' etac Always_thin (*Combines a list of invariance THEOREMS into one.*) val Always_Int_rule = foldr1 (fn (th1,th2) => [th1,th2] MRS Always_Int_I) (*Proves "co" properties when the program is specified. Any use of invariants (from weak constrains) must have been done already.*) fun gen_constrains_tac(cs,ss) i = SELECT_GOAL (EVERY [REPEAT (Always_Int_tac 1), (*reduce the fancy safety properties to "constrains"*) REPEAT (etac Always_ConstrainsI 1 ORELSE resolve_tac [StableI, stableI, constrains_imp_Constrains] 1), (*for safety, the totalize operator can be ignored*) simp_tac (HOL_ss addsimps [mk_total_program_def, totalize_constrains_iff]) 1, rtac constrainsI 1, full_simp_tac ss 1, REPEAT (FIRSTGOAL (etac disjE)), ALLGOALS (clarify_tac cs), ALLGOALS (asm_lr_simp_tac ss)]) i; (*proves "ensures/leadsTo" properties when the program is specified*) fun gen_ensures_tac(cs,ss) sact = SELECT_GOAL (EVERY [REPEAT (Always_Int_tac 1), etac Always_LeadsTo_Basis 1 ORELSE (*subgoal may involve LeadsTo, leadsTo or ensures*) REPEAT (ares_tac [LeadsTo_Basis, leadsTo_Basis, EnsuresI, ensuresI] 1), (*now there are two subgoals: co & transient*) simp_tac (ss addsimps [mk_total_program_def]) 2, res_inst_tac [("act", sact)] totalize_transientI 2 ORELSE res_inst_tac [("act", sact)] transientI 2, (*simplify the command's domain*) simp_tac (ss addsimps [Domain_def]) 3, gen_constrains_tac (cs,ss) 1, ALLGOALS (clarify_tac cs), ALLGOALS (asm_lr_simp_tac ss)]); fun constrains_tac st = gen_constrains_tac (claset(), simpset()) st; fun ensures_tac sact = gen_ensures_tac (claset(), simpset()) sact; (*Composition equivalences, from Lift_prog*) fun make_o_equivs th = [th, th RS o_equiv_assoc |> simplify (HOL_ss addsimps [o_assoc]), th RS o_equiv_apply |> simplify (HOL_ss addsimps [o_def, sub_def])]; Addsimps (make_o_equivs fst_o_funPair @ make_o_equivs snd_o_funPair); Addsimps (make_o_equivs fst_o_lift_map @ make_o_equivs snd_o_lift_map);