(* Title: HOL/UNITY/UNITY_tactics.ML
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 2003 University of Cambridge
Specialized UNITY tactics, and ML bindings of theorems
*)
(*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 insert_map_upd_same = thm "insert_map_upd_same";
val insert_map_upd = thm "insert_map_upd";
val insert_map_eq_diff = thm "insert_map_eq_diff";
val lift_map_eq_diff = thm "lift_map_eq_diff";
val lift_transient_eq_disj = thm "lift_transient_eq_disj";
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";
(*proves "co" properties when the program is specified*)
fun gen_constrains_tac(cs,ss) i =
SELECT_GOAL
(EVERY [REPEAT (Always_Int_tac 1),
REPEAT (etac Always_ConstrainsI 1
ORELSE
resolve_tac [StableI, stableI,
constrains_imp_Constrains] 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 2,
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)]);
(*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);