1(* Title: HOL/Tools/BNF/bnf_fp_def_sugar_tactics.ML 2 Author: Jasmin Blanchette, TU Muenchen 3 Author: Martin Desharnais, TU Muenchen 4 Copyright 2012, 2013, 2014 5 6Tactics for datatype and codatatype sugar. 7*) 8 9signature BNF_FP_DEF_SUGAR_TACTICS = 10sig 11 val sumprod_thms_rel: thm list 12 13 val co_induct_inst_as_projs_tac: Proof.context -> int -> tactic 14 val mk_case_transfer_tac: Proof.context -> thm -> thm list -> tactic 15 val mk_coinduct_discharge_prem_tac: Proof.context -> thm list -> thm list -> int -> int -> int -> 16 thm -> thm -> thm -> thm -> thm -> thm list -> thm list list -> thm list list -> int -> tactic 17 val mk_coinduct_tac: Proof.context -> thm list -> int -> int list -> thm -> thm list -> 18 thm list -> thm list -> thm list -> thm list -> thm list list -> thm list list list -> 19 thm list list list -> tactic 20 val mk_corec_tac: thm list -> thm list -> thm -> thm -> thm -> thm -> Proof.context -> tactic 21 val mk_corec_disc_iff_tac: thm list -> thm list -> thm list -> Proof.context -> tactic 22 val mk_co_rec_o_map_tac: Proof.context -> thm -> thm list -> thm list -> thm list -> thm -> thm -> 23 thm Seq.seq 24 val mk_corec_transfer_tac: Proof.context -> cterm list -> cterm list -> thm list -> thm list -> 25 thm list -> thm list -> thm list -> ''a list -> ''a list list -> ''a list list list list -> 26 ''a list list list list -> tactic 27 val mk_ctor_iff_dtor_tac: Proof.context -> ctyp option list -> cterm -> cterm -> thm -> thm -> 28 tactic 29 val mk_ctr_transfer_tac: Proof.context -> thm list -> thm list -> tactic 30 val mk_disc_transfer_tac: Proof.context -> thm -> thm -> thm list -> tactic 31 val mk_exhaust_tac: Proof.context -> int -> thm list -> thm -> thm -> tactic 32 val mk_half_distinct_tac: Proof.context -> thm -> thm -> thm list -> tactic 33 val mk_induct_discharge_prem_tac: Proof.context -> int -> int -> thm list -> thm list -> 34 thm list -> thm list -> int -> int -> int list -> tactic 35 val mk_induct_tac: Proof.context -> int -> int list -> int list list -> int list list list -> 36 thm list -> thm -> thm list -> thm list -> thm list -> thm list list -> tactic 37 val mk_inject_tac: Proof.context -> thm -> thm -> thm -> tactic 38 val mk_map_tac: Proof.context -> thm list -> thm -> thm -> thm list -> thm list -> thm list -> 39 tactic 40 val mk_map_disc_iff_tac: Proof.context -> cterm -> thm -> thm list -> thm list -> tactic 41 val mk_map_sel_tac: Proof.context -> cterm -> thm -> thm list -> thm list -> thm list -> 42 thm list -> tactic 43 val mk_rec_tac: thm list -> thm list -> thm list -> thm -> thm -> thm -> thm -> Proof.context -> 44 tactic 45 val mk_rec_transfer_tac: Proof.context -> int -> int list -> cterm list -> cterm list -> 46 term list list list list -> thm list -> thm list -> thm list -> thm list -> tactic 47 val mk_rel_tac: Proof.context -> thm list -> thm -> thm -> thm list -> thm list -> thm list -> 48 tactic 49 val mk_rel_case_tac: Proof.context -> cterm -> cterm -> thm -> thm list -> thm list -> thm list -> 50 thm list -> thm list -> tactic 51 val mk_rel_coinduct0_tac: Proof.context -> thm -> cterm list -> thm list -> thm list -> 52 thm list list -> thm list list -> thm list list -> thm list -> thm list -> thm list -> 53 thm list -> thm list -> thm list -> tactic 54 val mk_rel_induct0_tac: Proof.context -> thm -> thm list -> cterm list -> thm list -> 55 thm list list -> thm list -> thm list -> thm list -> thm list -> tactic 56 val mk_rel_sel_tac: Proof.context -> cterm -> cterm -> thm -> thm list -> thm list -> thm list -> 57 thm list -> thm list -> thm list -> tactic 58 val mk_sel_transfer_tac: Proof.context -> int -> thm list -> thm -> tactic 59 val mk_set0_tac: Proof.context -> thm list -> thm list -> thm -> thm list -> thm list -> 60 thm list -> thm list -> thm list -> tactic 61 val mk_set_cases_tac: Proof.context -> cterm -> thm list -> thm -> thm list -> tactic 62 val mk_set_induct0_tac: Proof.context -> cterm list -> thm list -> thm list -> thm list -> 63 thm list -> thm list -> thm list -> thm list -> tactic 64 val mk_set_intros_tac: Proof.context -> thm list -> tactic 65 val mk_set_sel_tac: Proof.context -> cterm -> thm -> thm list -> thm list -> thm list -> tactic 66end; 67 68structure BNF_FP_Def_Sugar_Tactics : BNF_FP_DEF_SUGAR_TACTICS = 69struct 70 71open Ctr_Sugar_Util 72open BNF_Tactics 73open BNF_Util 74open BNF_FP_Util 75 76val case_sum_transfer = @{thm case_sum_transfer}; 77val case_sum_transfer_eq = @{thm case_sum_transfer[of "(=)" _ "(=)", simplified sum.rel_eq]}; 78val case_prod_transfer = @{thm case_prod_transfer}; 79val case_prod_transfer_eq = @{thm case_prod_transfer[of "(=)" "(=)", simplified prod.rel_eq]}; 80 81val basic_simp_thms = @{thms simp_thms(7,8,12,14,22,24)}; 82val more_simp_thms = basic_simp_thms @ @{thms simp_thms(11,15,16,21)}; 83val simp_thms' = @{thms simp_thms(6,7,8,11,12,15,16,22,24)}; 84 85val sumprod_thms_map = @{thms id_apply map_prod_simp prod.case sum.case map_sum.simps}; 86val sumprod_thms_rel = @{thms rel_sum_simps rel_prod_inject prod.inject id_apply conj_assoc}; 87val basic_sumprod_thms_set = 88 @{thms UN_empty UN_insert UN_iff Un_empty_left Un_empty_right Un_iff Union_Un_distrib o_apply 89 map_prod_simp mem_Collect_eq prod_set_simps map_sum.simps sum_set_simps}; 90val sumprod_thms_set = @{thms UN_simps(10) image_iff} @ basic_sumprod_thms_set; 91 92fun is_def_looping def = 93 (case Thm.prop_of def of 94 Const (\<^const_name>\<open>Pure.eq\<close>, _) $ lhs $ rhs => Term.exists_subterm (curry (op aconv) lhs) rhs 95 | _ => false); 96 97fun hhf_concl_conv cv ctxt ct = 98 (case Thm.term_of ct of 99 Const (\<^const_name>\<open>Pure.all\<close>, _) $ Abs _ => 100 Conv.arg_conv (Conv.abs_conv (hhf_concl_conv cv o snd) ctxt) ct 101 | _ => Conv.concl_conv ~1 cv ct); 102 103fun co_induct_inst_as_projs ctxt k thm = 104 let 105 val fs = Term.add_vars (Thm.prop_of thm) [] 106 |> filter (fn (_, Type (\<^type_name>\<open>fun\<close>, [_, T'])) => T' <> HOLogic.boolT | _ => false); 107 fun mk_inst (xi, T) = (xi, Thm.cterm_of ctxt (mk_proj T (num_binder_types T) k)); 108 in 109 infer_instantiate ctxt (map mk_inst fs) thm 110 end; 111 112val co_induct_inst_as_projs_tac = PRIMITIVE oo co_induct_inst_as_projs; 113 114fun mk_case_transfer_tac ctxt rel_case cases = 115 let val n = length (tl (Thm.prems_of rel_case)) in 116 REPEAT_DETERM (HEADGOAL (rtac ctxt rel_funI)) THEN 117 HEADGOAL (etac ctxt rel_case) THEN 118 ALLGOALS (hyp_subst_tac ctxt) THEN 119 unfold_thms_tac ctxt cases THEN 120 ALLGOALS (fn k => (select_prem_tac ctxt n (dtac ctxt asm_rl) k) k) THEN 121 ALLGOALS (REPEAT_DETERM o (rotate_tac ~1 THEN' dtac ctxt rel_funD THEN' 122 (assume_tac ctxt THEN' etac ctxt thin_rl ORELSE' rtac ctxt refl)) THEN' assume_tac ctxt) 123 end; 124 125fun mk_ctr_transfer_tac ctxt rel_intros rel_eqs = 126 HEADGOAL Goal.conjunction_tac THEN 127 ALLGOALS (REPEAT o (resolve_tac ctxt (rel_funI :: rel_intros) THEN' 128 TRY o (REPEAT_DETERM1 o (SELECT_GOAL (unfold_thms_tac ctxt rel_eqs) THEN' 129 (assume_tac ctxt ORELSE' hyp_subst_tac ctxt THEN' rtac ctxt refl))))); 130 131fun mk_disc_transfer_tac ctxt rel_sel exhaust_disc distinct_disc = 132 let 133 fun last_disc_tac iffD = 134 HEADGOAL (rtac ctxt (rotate_prems ~1 exhaust_disc) THEN' assume_tac ctxt THEN' 135 REPEAT_DETERM o (rotate_tac ~1 THEN' dtac ctxt (rotate_prems 1 iffD) THEN' 136 assume_tac ctxt THEN' rotate_tac ~1 THEN' 137 etac ctxt (rotate_prems 1 notE) THEN' eresolve_tac ctxt distinct_disc)); 138 in 139 HEADGOAL Goal.conjunction_tac THEN 140 REPEAT_DETERM (HEADGOAL (rtac ctxt rel_funI THEN' dtac ctxt (rel_sel RS iffD1) THEN' 141 REPEAT_DETERM o (etac ctxt conjE) THEN' (assume_tac ctxt ORELSE' rtac ctxt iffI))) THEN 142 TRY (last_disc_tac iffD2) THEN TRY (last_disc_tac iffD1) 143 end; 144 145fun mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor sumEN' = 146 unfold_thms_tac ctxt (ctor_iff_dtor :: ctr_defs) THEN HEADGOAL (rtac ctxt sumEN') THEN 147 HEADGOAL (EVERY' (maps (fn k => [select_prem_tac ctxt n (rotate_tac 1) k, 148 REPEAT_DETERM o dtac ctxt meta_spec, etac ctxt meta_mp, assume_tac ctxt]) (1 upto n))); 149 150fun mk_ctor_iff_dtor_tac ctxt cTs cctor cdtor ctor_dtor dtor_ctor = 151 HEADGOAL (rtac ctxt iffI THEN' 152 EVERY' (@{map 3} (fn cTs => fn cx => fn th => 153 dtac ctxt (Thm.instantiate' cTs [NONE, NONE, SOME cx] arg_cong) THEN' 154 SELECT_GOAL (unfold_thms_tac ctxt [th]) THEN' 155 assume_tac ctxt) [rev cTs, cTs] [cdtor, cctor] [dtor_ctor, ctor_dtor])); 156 157fun mk_half_distinct_tac ctxt ctor_inject abs_inject ctr_defs = 158 unfold_thms_tac ctxt (ctor_inject :: abs_inject :: @{thms sum.inject} @ ctr_defs) THEN 159 HEADGOAL (rtac ctxt @{thm sum.distinct(1)}); 160 161fun mk_inject_tac ctxt ctr_def ctor_inject abs_inject = 162 unfold_thms_tac ctxt [ctr_def] THEN 163 HEADGOAL (rtac ctxt (ctor_inject RS ssubst)) THEN 164 unfold_thms_tac ctxt (abs_inject :: @{thms sum.inject prod.inject conj_assoc}) THEN 165 HEADGOAL (rtac ctxt refl); 166 167val rec_unfold_thms = 168 @{thms comp_def convol_def fst_conv id_def case_prod_Pair_iden snd_conv split_conv 169 case_unit_Unity} @ sumprod_thms_map; 170 171fun mk_co_rec_o_map_tac ctxt co_rec_def pre_map_defs map_ident0s abs_inverses xtor_co_rec_o_map = 172 let 173 val rec_o_map_simps = @{thms o_def[abs_def] id_def case_prod_app case_sum_map_sum map_sum.simps 174 case_prod_map_prod id_bnf_def map_prod_simp map_sum_if_distrib_then map_sum_if_distrib_else 175 if_distrib[THEN sym]}; 176 in 177 HEADGOAL (subst_tac ctxt (SOME [1, 2]) [co_rec_def] THEN' 178 rtac ctxt (xtor_co_rec_o_map RS trans) THEN' 179 CONVERSION Thm.eta_long_conversion THEN' 180 asm_simp_tac (ss_only (pre_map_defs @ distinct Thm.eq_thm_prop (map_ident0s @ abs_inverses) @ 181 rec_o_map_simps) ctxt)) 182 end; 183 184fun mk_rec_tac pre_map_defs map_ident0s rec_defs ctor_rec pre_abs_inverse abs_inverse ctr_def ctxt = 185 HEADGOAL ((if is_def_looping ctr_def then subst_tac ctxt NONE 186 else SELECT_GOAL o unfold_thms_tac ctxt) [ctr_def]) THEN 187 unfold_thms_tac ctxt (ctor_rec :: pre_abs_inverse :: abs_inverse :: rec_defs @ 188 pre_map_defs @ map_ident0s @ rec_unfold_thms) THEN HEADGOAL (rtac ctxt refl); 189 190fun mk_rec_transfer_tac ctxt nn ns actives passives xssss rec_defs ctor_rec_transfers rel_pre_T_defs 191 rel_eqs = 192 let 193 val ctor_rec_transfers' = 194 map (infer_instantiate' ctxt (map SOME (passives @ actives))) ctor_rec_transfers; 195 val total_n = Integer.sum ns; 196 val True = \<^term>\<open>True\<close>; 197 in 198 HEADGOAL Goal.conjunction_tac THEN 199 EVERY (map (fn ctor_rec_transfer => 200 REPEAT_DETERM (HEADGOAL (rtac ctxt rel_funI)) THEN 201 unfold_thms_tac ctxt rec_defs THEN 202 HEADGOAL (etac ctxt (mk_rel_funDN_rotated (nn + 1) ctor_rec_transfer)) THEN 203 unfold_thms_tac ctxt rel_pre_T_defs THEN 204 EVERY (fst (@{fold_map 2} (fn k => fn xsss => fn acc => 205 rpair (k + acc) 206 (HEADGOAL (rtac ctxt (mk_rel_funDN_rotated 2 @{thm comp_transfer})) THEN 207 HEADGOAL (rtac ctxt @{thm vimage2p_rel_fun}) THEN 208 unfold_thms_tac ctxt rel_eqs THEN 209 EVERY (@{map 2} (fn n => fn xss => 210 REPEAT_DETERM (HEADGOAL (resolve_tac ctxt 211 [mk_rel_funDN 2 case_sum_transfer_eq, mk_rel_funDN 2 case_sum_transfer])) THEN 212 HEADGOAL (select_prem_tac ctxt total_n (dtac ctxt asm_rl) (acc + n)) THEN 213 HEADGOAL (SELECT_GOAL (HEADGOAL 214 (REPEAT_DETERM o (assume_tac ctxt ORELSE' resolve_tac ctxt 215 [mk_rel_funDN 1 case_prod_transfer_eq, 216 mk_rel_funDN 1 case_prod_transfer, 217 rel_funI]) THEN_ALL_NEW 218 (Subgoal.FOCUS (fn {prems, ...} => 219 let val thm = prems 220 |> permute_like (op =) (True :: flat xss) (True :: flat_rec_arg_args xss) 221 |> Library.foldl1 (fn (acc, elem) => elem RS (acc RS rel_funD)) 222 in HEADGOAL (rtac ctxt thm) end) ctxt))))) 223 (1 upto k) xsss))) 224 ns xssss 0))) 225 ctor_rec_transfers') 226 end; 227 228val corec_unfold_thms = @{thms id_def} @ sumprod_thms_map; 229 230fun mk_corec_tac corec_defs map_ident0s ctor_dtor_corec pre_map_def abs_inverse ctr_def ctxt = 231 let 232 val ss = ss_only (pre_map_def :: abs_inverse :: map_ident0s @ corec_unfold_thms @ 233 @{thms o_apply vimage2p_def if_True if_False}) ctxt; 234 in 235 unfold_thms_tac ctxt (ctr_def :: corec_defs) THEN 236 HEADGOAL (rtac ctxt (ctor_dtor_corec RS trans) THEN' asm_simp_tac ss) THEN_MAYBE 237 HEADGOAL (rtac ctxt refl ORELSE' rtac ctxt (@{thm unit_eq} RS arg_cong)) 238 end; 239 240fun mk_corec_disc_iff_tac case_splits' corecs discs ctxt = 241 EVERY (@{map 3} (fn case_split_tac => fn corec_thm => fn disc => 242 HEADGOAL case_split_tac THEN unfold_thms_tac ctxt [corec_thm] THEN 243 HEADGOAL (asm_simp_tac (ss_only basic_simp_thms ctxt)) THEN 244 (if is_refl disc then all_tac else HEADGOAL (rtac ctxt disc))) 245 (map (rtac ctxt) case_splits' @ [K all_tac]) corecs discs); 246 247fun mk_corec_transfer_tac ctxt actives passives type_definitions corec_defs dtor_corec_transfers 248 rel_pre_T_defs rel_eqs pgs pss qssss gssss = 249 let 250 val num_pgs = length pgs; 251 fun prem_no_of x = 1 + find_index (curry (op =) x) pgs; 252 253 val Inl_Inr_Pair_tac = REPEAT_DETERM o (resolve_tac ctxt 254 [mk_rel_funDN 1 @{thm Inl_transfer}, 255 mk_rel_funDN 1 @{thm Inl_transfer[of "(=)" "(=)", simplified sum.rel_eq]}, 256 mk_rel_funDN 1 @{thm Inr_transfer}, 257 mk_rel_funDN 1 @{thm Inr_transfer[of "(=)" "(=)", simplified sum.rel_eq]}, 258 mk_rel_funDN 2 @{thm Pair_transfer}, 259 mk_rel_funDN 2 @{thm Pair_transfer[of "(=)" "(=)", simplified prod.rel_eq]}]); 260 261 fun mk_unfold_If_tac total pos = 262 HEADGOAL (Inl_Inr_Pair_tac THEN' 263 rtac ctxt (mk_rel_funDN 3 @{thm If_transfer}) THEN' 264 select_prem_tac ctxt total (dtac ctxt asm_rl) pos THEN' 265 dtac ctxt rel_funD THEN' assume_tac ctxt THEN' assume_tac ctxt); 266 267 fun mk_unfold_Inl_Inr_Pair_tac total pos = 268 HEADGOAL (Inl_Inr_Pair_tac THEN' 269 select_prem_tac ctxt total (dtac ctxt asm_rl) pos THEN' 270 dtac ctxt rel_funD THEN' assume_tac ctxt THEN' assume_tac ctxt); 271 272 fun mk_unfold_arg_tac qs gs = 273 EVERY (map (mk_unfold_If_tac num_pgs o prem_no_of) qs) THEN 274 EVERY (map (mk_unfold_Inl_Inr_Pair_tac num_pgs o prem_no_of) gs); 275 276 fun mk_unfold_ctr_tac type_definition qss gss = 277 HEADGOAL (rtac ctxt (mk_rel_funDN 1 (@{thm Abs_transfer} OF 278 [type_definition, type_definition])) THEN' Inl_Inr_Pair_tac) THEN 279 (case (qss, gss) of 280 ([], []) => HEADGOAL (rtac ctxt refl) 281 | _ => EVERY (map2 mk_unfold_arg_tac qss gss)); 282 283 fun mk_unfold_type_tac type_definition ps qsss gsss = 284 let 285 val p_tacs = map (mk_unfold_If_tac num_pgs o prem_no_of) ps; 286 val qg_tacs = map2 (mk_unfold_ctr_tac type_definition) qsss gsss; 287 fun mk_unfold_ty [] [qg_tac] = qg_tac 288 | mk_unfold_ty (p_tac :: p_tacs) (qg_tac :: qg_tacs) = 289 p_tac THEN qg_tac THEN mk_unfold_ty p_tacs qg_tacs 290 in 291 HEADGOAL (rtac ctxt rel_funI) THEN mk_unfold_ty p_tacs qg_tacs 292 end; 293 294 fun mk_unfold_corec_type_tac dtor_corec_transfer corec_def = 295 let 296 val active :: actives' = actives; 297 val dtor_corec_transfer' = 298 infer_instantiate' ctxt 299 (SOME active :: map SOME passives @ map SOME actives') dtor_corec_transfer; 300 in 301 HEADGOAL Goal.conjunction_tac THEN REPEAT_DETERM (HEADGOAL (rtac ctxt rel_funI)) THEN 302 unfold_thms_tac ctxt [corec_def] THEN 303 HEADGOAL (etac ctxt (mk_rel_funDN_rotated (1 + length actives) dtor_corec_transfer')) THEN 304 unfold_thms_tac ctxt (rel_pre_T_defs @ rel_eqs) 305 end; 306 307 fun mk_unfold_prop_tac dtor_corec_transfer corec_def = 308 mk_unfold_corec_type_tac dtor_corec_transfer corec_def THEN 309 EVERY (@{map 4} mk_unfold_type_tac type_definitions pss qssss gssss); 310 in 311 HEADGOAL Goal.conjunction_tac THEN 312 EVERY (map2 mk_unfold_prop_tac dtor_corec_transfers corec_defs) 313 end; 314 315fun solve_prem_prem_tac ctxt = 316 REPEAT o (eresolve_tac ctxt @{thms bexE rev_bexI} ORELSE' 317 rtac ctxt @{thm rev_bexI[OF UNIV_I]} ORELSE' hyp_subst_tac ctxt ORELSE' 318 resolve_tac ctxt @{thms disjI1 disjI2}) THEN' 319 (rtac ctxt refl ORELSE' assume_tac ctxt ORELSE' rtac ctxt @{thm singletonI}); 320 321fun mk_induct_leverage_prem_prems_tac ctxt nn kks pre_abs_inverses abs_inverses set_maps 322 pre_set_defs = 323 HEADGOAL (EVERY' (maps (fn kk => [select_prem_tac ctxt nn (dtac ctxt meta_spec) kk, 324 etac ctxt meta_mp, 325 SELECT_GOAL (unfold_thms_tac ctxt (pre_set_defs @ pre_abs_inverses @ abs_inverses @ set_maps @ 326 sumprod_thms_set)), 327 solve_prem_prem_tac ctxt]) (rev kks))); 328 329fun mk_induct_discharge_prem_tac ctxt nn n pre_abs_inverses abs_inverses set_maps pre_set_defs m k 330 kks = 331 let val r = length kks in 332 HEADGOAL (EVERY' [select_prem_tac ctxt n (rotate_tac 1) k, rotate_tac ~1, hyp_subst_tac ctxt, 333 REPEAT_DETERM_N m o (dtac ctxt meta_spec THEN' rotate_tac ~1)]) THEN 334 EVERY [REPEAT_DETERM_N r 335 (HEADGOAL (rotate_tac ~1 THEN' dtac ctxt meta_mp THEN' rotate_tac 1) THEN prefer_tac 2), 336 if r > 0 then ALLGOALS (Goal.norm_hhf_tac ctxt) else all_tac, HEADGOAL (assume_tac ctxt), 337 mk_induct_leverage_prem_prems_tac ctxt nn kks pre_abs_inverses abs_inverses set_maps 338 pre_set_defs] 339 end; 340 341fun mk_induct_tac ctxt nn ns mss kksss ctr_defs ctor_induct' pre_abs_inverses abs_inverses set_maps 342 pre_set_defss = 343 let val n = Integer.sum ns in 344 (if exists is_def_looping ctr_defs then 345 EVERY (map (fn def => HEADGOAL (subst_asm_tac ctxt NONE [def])) ctr_defs) 346 else 347 unfold_thms_tac ctxt ctr_defs) THEN 348 HEADGOAL (rtac ctxt ctor_induct') THEN co_induct_inst_as_projs_tac ctxt 0 THEN 349 EVERY (@{map 4} (EVERY oooo @{map 3} o 350 mk_induct_discharge_prem_tac ctxt nn n pre_abs_inverses abs_inverses set_maps) 351 pre_set_defss mss (unflat mss (1 upto n)) kksss) 352 end; 353 354fun mk_coinduct_same_ctr_tac ctxt rel_eqs pre_rel_def pre_abs_inverse abs_inverse dtor_ctor ctr_def 355 discs sels extra_unfolds = 356 hyp_subst_tac ctxt THEN' 357 CONVERSION (hhf_concl_conv 358 (Conv.top_conv (K (Conv.try_conv (Conv.rewr_conv ctr_def))) ctxt) ctxt) THEN' 359 SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: dtor_ctor :: sels)) THEN' 360 SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: pre_abs_inverse :: abs_inverse :: dtor_ctor :: 361 sels @ sumprod_thms_rel @ extra_unfolds @ @{thms o_apply vimage2p_def})) THEN' 362 (assume_tac ctxt ORELSE' REPEAT o etac ctxt conjE THEN' 363 full_simp_tac (ss_only (no_refl discs @ rel_eqs @ more_simp_thms) ctxt) THEN' 364 REPEAT o etac ctxt conjE THEN_MAYBE' REPEAT o hyp_subst_tac ctxt THEN' 365 REPEAT o (resolve_tac ctxt [refl, conjI] ORELSE' assume_tac ctxt)); 366 367fun mk_coinduct_distinct_ctrs_tac ctxt discs discs' = 368 let 369 val discs'' = map (perhaps (try (fn th => th RS @{thm notnotD}))) (discs @ discs') 370 |> distinct Thm.eq_thm_prop; 371 in 372 hyp_subst_tac ctxt THEN' REPEAT o etac ctxt conjE THEN' 373 full_simp_tac (ss_only (refl :: no_refl discs'' @ basic_simp_thms) ctxt) 374 end; 375 376fun mk_coinduct_discharge_prem_tac ctxt extra_unfolds rel_eqs' nn kk n pre_rel_def pre_abs_inverse 377 abs_inverse dtor_ctor exhaust ctr_defs discss selss = 378 let val ks = 1 upto n in 379 EVERY' ([rtac ctxt allI, rtac ctxt allI, rtac ctxt impI, 380 select_prem_tac ctxt nn (dtac ctxt meta_spec) kk, dtac ctxt meta_spec, dtac ctxt meta_mp, 381 assume_tac ctxt, rtac ctxt exhaust, K (co_induct_inst_as_projs_tac ctxt 0), 382 hyp_subst_tac ctxt] @ 383 @{map 4} (fn k => fn ctr_def => fn discs => fn sels => 384 EVERY' ([rtac ctxt exhaust, K (co_induct_inst_as_projs_tac ctxt 1)] @ 385 map2 (fn k' => fn discs' => 386 if k' = k then 387 mk_coinduct_same_ctr_tac ctxt rel_eqs' pre_rel_def pre_abs_inverse abs_inverse 388 dtor_ctor ctr_def discs sels extra_unfolds 389 else 390 mk_coinduct_distinct_ctrs_tac ctxt discs discs') ks discss)) ks ctr_defs discss selss) 391 end; 392 393fun mk_coinduct_tac ctxt rel_eqs' nn ns dtor_coinduct' pre_rel_defs pre_abs_inverses abs_inverses 394 dtor_ctors exhausts ctr_defss discsss selsss = 395 HEADGOAL (rtac ctxt dtor_coinduct' THEN' 396 EVERY' (@{map 10} (mk_coinduct_discharge_prem_tac ctxt [] rel_eqs' nn) 397 (1 upto nn) ns pre_rel_defs pre_abs_inverses abs_inverses dtor_ctors exhausts ctr_defss 398 discsss selsss)); 399 400fun mk_map_tac ctxt abs_inverses pre_map_def map_ctor live_nesting_map_id0s ctr_defs' 401 extra_unfolds = 402 TRYALL Goal.conjunction_tac THEN 403 unfold_thms_tac ctxt (pre_map_def :: map_ctor :: abs_inverses @ live_nesting_map_id0s @ 404 ctr_defs' @ extra_unfolds @ sumprod_thms_map @ 405 @{thms o_apply id_apply id_o o_id}) THEN 406 ALLGOALS (rtac ctxt refl); 407 408fun mk_map_disc_iff_tac ctxt ct exhaust discs maps = 409 TRYALL Goal.conjunction_tac THEN 410 ALLGOALS (rtac ctxt (infer_instantiate' ctxt [SOME ct] exhaust) THEN_ALL_NEW 411 REPEAT_DETERM o hyp_subst_tac ctxt) THEN 412 unfold_thms_tac ctxt maps THEN 413 unfold_thms_tac ctxt (map (fn thm => thm RS eqFalseI 414 handle THM _ => thm RS eqTrueI) discs) THEN 415 ALLGOALS (rtac ctxt refl ORELSE' rtac ctxt TrueI); 416 417fun mk_map_sel_tac ctxt ct exhaust discs maps sels map_id0s = 418 TRYALL Goal.conjunction_tac THEN 419 ALLGOALS (rtac ctxt (infer_instantiate' ctxt [SOME ct] exhaust) THEN_ALL_NEW 420 REPEAT_DETERM o hyp_subst_tac ctxt) THEN 421 unfold_thms_tac ctxt ((discs RL [eqTrueI, eqFalseI]) @ 422 @{thms not_True_eq_False not_False_eq_True}) THEN 423 TRYALL (etac ctxt FalseE ORELSE' etac ctxt @{thm TrueE}) THEN 424 unfold_thms_tac ctxt (@{thm id_apply} :: maps @ sels @ map_id0s) THEN 425 ALLGOALS (rtac ctxt refl); 426 427fun mk_rel_tac ctxt abs_inverses pre_rel_def rel_ctor live_nesting_rel_eqs ctr_defs' extra_unfolds = 428 TRYALL Goal.conjunction_tac THEN 429 unfold_thms_tac ctxt (pre_rel_def :: rel_ctor :: abs_inverses @ live_nesting_rel_eqs @ ctr_defs' @ 430 extra_unfolds @ sumprod_thms_rel @ @{thms vimage2p_def o_apply sum.inject 431 sum.distinct(1)[THEN eq_False[THEN iffD2]] not_False_eq_True}) THEN 432 ALLGOALS (resolve_tac ctxt [TrueI, refl]); 433 434fun mk_rel_case_tac ctxt ct1 ct2 exhaust injects rel_injects distincts rel_distincts rel_eqs = 435 HEADGOAL (rtac ctxt (infer_instantiate' ctxt [SOME ct1] exhaust) THEN_ALL_NEW 436 rtac ctxt (infer_instantiate' ctxt [SOME ct2] exhaust) THEN_ALL_NEW 437 hyp_subst_tac ctxt) THEN 438 unfold_thms_tac ctxt (rel_eqs @ injects @ rel_injects @ 439 @{thms conj_imp_eq_imp_imp simp_thms(6) True_implies_equals} @ 440 map (fn thm => thm RS eqFalseI) (distincts @ rel_distincts) @ 441 map (fn thm => thm RS eqTrueI) rel_injects) THEN 442 TRYALL (assume_tac ctxt ORELSE' etac ctxt FalseE ORELSE' 443 (REPEAT_DETERM o dtac ctxt meta_spec THEN' 444 TRY o filter_prems_tac ctxt 445 (forall (curry (op <>) (HOLogic.mk_Trueprop \<^term>\<open>False\<close>)) o Logic.strip_imp_prems) THEN' 446 REPEAT_DETERM o (dtac ctxt meta_mp THEN' rtac ctxt refl) THEN' 447 (assume_tac ctxt ORELSE' Goal.assume_rule_tac ctxt))); 448 449fun mk_rel_coinduct0_tac ctxt dtor_rel_coinduct cts assms exhausts discss selss ctor_defss 450 dtor_ctors ctor_injects abs_injects rel_pre_defs abs_inverses nesting_rel_eqs = 451 rtac ctxt dtor_rel_coinduct 1 THEN 452 EVERY (@{map 11} (fn ct => fn assm => fn exhaust => fn discs => fn sels => fn ctor_defs => 453 fn dtor_ctor => fn ctor_inject => fn abs_inject => fn rel_pre_def => fn abs_inverse => 454 (rtac ctxt exhaust THEN_ALL_NEW (rtac ctxt exhaust THEN_ALL_NEW 455 (dtac ctxt (rotate_prems ~1 (infer_instantiate' ctxt [NONE, NONE, NONE, NONE, SOME ct] 456 @{thm arg_cong2} RS iffD1)) THEN' 457 assume_tac ctxt THEN' assume_tac ctxt THEN' hyp_subst_tac ctxt THEN' dtac ctxt assm THEN' 458 REPEAT_DETERM o etac ctxt conjE))) 1 THEN 459 unfold_thms_tac ctxt ((discs RL [eqTrueI, eqFalseI]) @ sels @ simp_thms') THEN 460 unfold_thms_tac ctxt (dtor_ctor :: rel_pre_def :: abs_inverse :: ctor_inject :: 461 abs_inject :: ctor_defs @ nesting_rel_eqs @ simp_thms' @ 462 @{thms id_bnf_def rel_sum_simps rel_prod_inject vimage2p_def Inl_Inr_False 463 iffD2[OF eq_False Inr_not_Inl] sum.inject prod.inject}) THEN 464 REPEAT_DETERM (HEADGOAL ((REPEAT_DETERM o etac ctxt conjE) THEN' 465 (REPEAT_DETERM o rtac ctxt conjI) THEN' (rtac ctxt refl ORELSE' assume_tac ctxt)))) 466 cts assms exhausts discss selss ctor_defss dtor_ctors ctor_injects abs_injects rel_pre_defs 467 abs_inverses); 468 469fun mk_rel_induct0_tac ctxt ctor_rel_induct assms cterms exhausts ctor_defss ctor_injects 470 rel_pre_list_defs Abs_inverses nesting_rel_eqs = 471 rtac ctxt ctor_rel_induct 1 THEN EVERY (@{map 6} (fn cterm => fn exhaust => fn ctor_defs => 472 fn ctor_inject => fn rel_pre_list_def => fn Abs_inverse => 473 HEADGOAL (rtac ctxt exhaust THEN_ALL_NEW (rtac ctxt exhaust THEN_ALL_NEW 474 (rtac ctxt (infer_instantiate' ctxt (replicate 4 NONE @ [SOME cterm]) @{thm arg_cong2} 475 RS iffD2) 476 THEN' assume_tac ctxt THEN' assume_tac ctxt THEN' TRY o resolve_tac ctxt assms))) THEN 477 unfold_thms_tac ctxt (ctor_inject :: rel_pre_list_def :: ctor_defs @ nesting_rel_eqs @ 478 @{thms id_bnf_def vimage2p_def}) THEN 479 TRYALL (hyp_subst_tac ctxt) THEN 480 unfold_thms_tac ctxt (Abs_inverse :: @{thms rel_sum_simps rel_prod_inject Inl_Inr_False 481 Inr_Inl_False sum.inject prod.inject}) THEN 482 TRYALL (rtac ctxt refl ORELSE' etac ctxt FalseE ORELSE' 483 (REPEAT_DETERM o etac ctxt conjE) THEN' assume_tac ctxt)) 484 cterms exhausts ctor_defss ctor_injects rel_pre_list_defs Abs_inverses); 485 486fun mk_rel_sel_tac ctxt ct1 ct2 exhaust discs sels rel_injects distincts rel_distincts rel_eqs = 487 HEADGOAL (rtac ctxt (infer_instantiate' ctxt [SOME ct1] exhaust) THEN_ALL_NEW 488 rtac ctxt (infer_instantiate' ctxt [SOME ct2] exhaust) THEN_ALL_NEW hyp_subst_tac ctxt) THEN 489 unfold_thms_tac ctxt (sels @ rel_injects @ rel_eqs @ 490 @{thms simp_thms(6,7,8,11,12,15,16,21,22,24)} @ ((discs @ distincts) RL [eqTrueI, eqFalseI]) @ 491 (rel_injects RL [eqTrueI]) @ (rel_distincts RL [eqFalseI])) THEN 492 TRYALL (resolve_tac ctxt [TrueI, refl]); 493 494fun mk_sel_transfer_tac ctxt n sel_defs case_transfer = 495 TRYALL Goal.conjunction_tac THEN 496 unfold_thms_tac ctxt (map (Local_Defs.abs_def_rule ctxt) sel_defs) THEN 497 ALLGOALS (rtac ctxt (mk_rel_funDN n case_transfer) THEN_ALL_NEW 498 REPEAT_DETERM o (assume_tac ctxt ORELSE' rtac ctxt rel_funI)); 499 500fun mk_set0_tac ctxt abs_inverses pre_set_defs dtor_ctor fp_sets fp_nesting_set_maps 501 live_nesting_set_maps ctr_defs' extra_unfolds = 502 TRYALL Goal.conjunction_tac THEN 503 unfold_thms_tac ctxt ctr_defs' THEN 504 ALLGOALS (subst_tac ctxt NONE fp_sets) THEN 505 unfold_thms_tac ctxt (dtor_ctor :: abs_inverses @ pre_set_defs @ fp_nesting_set_maps @ 506 live_nesting_set_maps @ extra_unfolds @ basic_sumprod_thms_set @ 507 @{thms UN_UN_flatten UN_Un_distrib UN_Un sup_assoc[THEN sym]}) THEN 508 ALLGOALS (rtac ctxt @{thm set_eqI[OF iffI]}) THEN 509 ALLGOALS (REPEAT_DETERM o etac ctxt UnE) THEN 510 ALLGOALS (REPEAT o resolve_tac ctxt @{thms UnI1 UnI2} THEN' assume_tac ctxt); 511 512fun mk_set_sel_tac ctxt ct exhaust discs sels sets = 513 TRYALL Goal.conjunction_tac THEN 514 ALLGOALS (rtac ctxt (infer_instantiate' ctxt [SOME ct] exhaust) THEN_ALL_NEW 515 REPEAT_DETERM o hyp_subst_tac ctxt) THEN 516 unfold_thms_tac ctxt ((discs RL [eqTrueI, eqFalseI]) @ 517 @{thms not_True_eq_False not_False_eq_True}) THEN 518 TRYALL (etac ctxt FalseE ORELSE' etac ctxt @{thm TrueE}) THEN 519 unfold_thms_tac ctxt (sels @ sets) THEN 520 ALLGOALS (REPEAT o (resolve_tac ctxt @{thms UnI1 UnI2 imageI} ORELSE' 521 eresolve_tac ctxt @{thms UN_I UN_I[rotated] imageE} ORELSE' 522 hyp_subst_tac ctxt) THEN' 523 (rtac ctxt @{thm singletonI} ORELSE' assume_tac ctxt)); 524 525fun mk_set_cases_tac ctxt ct assms exhaust sets = 526 HEADGOAL (rtac ctxt (infer_instantiate' ctxt [SOME ct] exhaust) 527 THEN_ALL_NEW hyp_subst_tac ctxt) THEN 528 unfold_thms_tac ctxt sets THEN 529 REPEAT_DETERM (HEADGOAL 530 (eresolve_tac ctxt @{thms FalseE emptyE singletonE UnE UN_E insertE} ORELSE' 531 hyp_subst_tac ctxt ORELSE' 532 SELECT_GOAL (SOLVE (HEADGOAL (eresolve_tac ctxt assms THEN' REPEAT_DETERM o 533 assume_tac ctxt))))); 534 535fun mk_set_intros_tac ctxt sets = 536 TRYALL Goal.conjunction_tac THEN unfold_thms_tac ctxt sets THEN 537 TRYALL (REPEAT o 538 (resolve_tac ctxt @{thms UnI1 UnI2} ORELSE' 539 eresolve_tac ctxt @{thms UN_I UN_I[rotated]}) THEN' 540 (rtac ctxt @{thm singletonI} ORELSE' assume_tac ctxt)); 541 542fun mk_set_induct0_tac ctxt cts assms dtor_set_inducts exhausts set_pre_defs ctor_defs dtor_ctors 543 Abs_pre_inverses = 544 let 545 val assms_tac = 546 let val assms' = map (unfold_thms ctxt (@{thm id_bnf_def} :: ctor_defs)) assms in 547 fold (curry (op ORELSE')) (map (fn thm => 548 funpow (length (Thm.prems_of thm)) (fn tac => tac THEN' assume_tac ctxt) 549 (rtac ctxt thm)) assms') 550 (etac ctxt FalseE) 551 end; 552 val exhausts' = map (fn thm => thm RS @{thm asm_rl[of "P x y" for P x y]}) exhausts 553 |> map2 (fn ct => infer_instantiate' ctxt [NONE, SOME ct]) cts; 554 in 555 ALLGOALS (resolve_tac ctxt dtor_set_inducts) THEN 556 TRYALL (resolve_tac ctxt exhausts' THEN_ALL_NEW 557 (resolve_tac ctxt (map (fn ct => refl RS 558 infer_instantiate' ctxt (replicate 4 NONE @ [SOME ct]) @{thm arg_cong2} RS iffD2) cts) 559 THEN' assume_tac ctxt THEN' hyp_subst_tac ctxt)) THEN 560 unfold_thms_tac ctxt (Abs_pre_inverses @ dtor_ctors @ set_pre_defs @ ctor_defs @ 561 @{thms id_bnf_def o_apply sum_set_simps prod_set_simps UN_empty UN_insert Un_empty_left 562 Un_empty_right empty_iff singleton_iff}) THEN 563 REPEAT (HEADGOAL (hyp_subst_tac ctxt ORELSE' 564 eresolve_tac ctxt @{thms UN_E UnE singletonE} ORELSE' assms_tac)) 565 end; 566 567end; 568