1(* Title: Pure/Isar/obtain.ML 2 Author: Markus Wenzel, TU Muenchen 3 4Generalized existence and cases rules within Isar proof text. 5*) 6 7signature OBTAIN = 8sig 9 val obtain_thesis: Proof.context -> ((string * typ) * term) * Proof.context 10 val obtains_attributes: ('typ, 'term) Element.obtain list -> attribute list 11 val obtains_attribs: ('typ, 'term) Element.obtain list -> Token.src list 12 val read_obtains: Proof.context -> term -> Element.obtains -> (binding * term) list 13 val cert_obtains: Proof.context -> term -> Element.obtains_i -> (binding * term) list 14 val parse_obtains: Proof.context -> term -> Element.obtains -> (binding * term) list 15 val consider: Element.obtains_i -> bool -> Proof.state -> Proof.state 16 val consider_cmd: Element.obtains -> bool -> Proof.state -> Proof.state 17 val obtain: binding -> (binding * typ option * mixfix) list -> 18 (binding * typ option * mixfix) list -> (term * term list) list list -> 19 (Thm.binding * (term * term list) list) list -> bool -> Proof.state -> Proof.state 20 val obtain_cmd: binding -> (binding * string option * mixfix) list -> 21 (binding * string option * mixfix) list -> (string * string list) list list -> 22 (Attrib.binding * (string * string list) list) list -> bool -> Proof.state -> Proof.state 23 val result: (Proof.context -> tactic) -> thm list -> Proof.context -> 24 ((string * cterm) list * thm list) * Proof.context 25 val guess: (binding * typ option * mixfix) list -> bool -> Proof.state -> Proof.state 26 val guess_cmd: (binding * string option * mixfix) list -> bool -> Proof.state -> Proof.state 27end; 28 29structure Obtain: OBTAIN = 30struct 31 32(** specification elements **) 33 34(* obtain_export *) 35 36(* 37 [x, A x] 38 : 39 B 40 -------- 41 B 42*) 43fun eliminate_term ctxt xs tm = 44 let 45 val vs = map (dest_Free o Thm.term_of) xs; 46 val bads = Term.fold_aterms (fn t as Free v => 47 if member (op =) vs v then insert (op aconv) t else I | _ => I) tm []; 48 val _ = null bads orelse 49 error ("Result contains obtained parameters: " ^ 50 space_implode " " (map (Syntax.string_of_term ctxt) bads)); 51 in tm end; 52 53fun eliminate ctxt rule xs As thm = 54 let 55 val _ = eliminate_term ctxt xs (Thm.full_prop_of thm); 56 val _ = Object_Logic.is_judgment ctxt (Thm.concl_of thm) orelse 57 error "Conclusion in obtained context must be object-logic judgment"; 58 59 val ((_, [thm']), ctxt') = Variable.import true [thm] ctxt; 60 val prems = Drule.strip_imp_prems (Thm.cprop_of thm'); 61 in 62 ((Drule.implies_elim_list thm' (map Thm.assume prems) 63 |> Drule.implies_intr_list (map (Drule.norm_hhf_cterm ctxt') As) 64 |> Drule.forall_intr_list xs) 65 COMP rule) 66 |> Drule.implies_intr_list prems 67 |> singleton (Variable.export ctxt' ctxt) 68 end; 69 70fun obtain_export ctxt rule xs _ As = 71 (eliminate ctxt rule xs As, eliminate_term ctxt xs); 72 73 74(* result declaration *) 75 76fun case_names (obtains: ('typ, 'term) Element.obtain list) = 77 obtains |> map_index (fn (i, (b, _)) => 78 if Binding.is_empty b then string_of_int (i + 1) else Name_Space.base_name b); 79 80fun obtains_attributes obtains = 81 [Rule_Cases.consumes (~ (length obtains)), Rule_Cases.case_names (case_names obtains)]; 82 83fun obtains_attribs obtains = 84 [Attrib.consumes (~ (length obtains)), Attrib.case_names (case_names obtains)]; 85 86 87(* obtain thesis *) 88 89fun obtain_thesis ctxt = 90 let 91 val ([x], ctxt') = 92 Proof_Context.add_fixes [(Binding.name Auto_Bind.thesisN, NONE, NoSyn)] ctxt; 93 val t = Object_Logic.fixed_judgment ctxt x; 94 val v = dest_Free (Object_Logic.drop_judgment ctxt t); 95 in ((v, t), ctxt') end; 96 97 98(* obtain clauses *) 99 100local 101 102val mk_all_external = Logic.all_constraint o Variable.default_type; 103 104fun mk_all_internal ctxt (y, z) t = 105 let 106 val T = 107 (case AList.lookup (op =) (Term.add_frees t []) z of 108 SOME T => T 109 | NONE => the_default dummyT (Variable.default_type ctxt z)); 110 in Logic.all_const T $ Term.lambda_name (y, Free (z, T)) t end; 111 112fun prepare_clause prep_var parse_prop mk_all ctxt thesis raw_vars raw_props = 113 let 114 val ((xs', vars), ctxt') = ctxt 115 |> fold_map prep_var raw_vars 116 |-> (fn vars => Proof_Context.add_fixes vars ##>> pair vars); 117 val xs = map (Variable.check_name o #1) vars; 118 in 119 Logic.list_implies (map (parse_prop ctxt') raw_props, thesis) 120 |> fold_rev (mk_all ctxt') (xs ~~ xs') 121 end; 122 123fun prepare_obtains prep_clause check_terms 124 ctxt thesis (raw_obtains: ('typ, 'term) Element.obtain list) = 125 let 126 val clauses = raw_obtains 127 |> map (fn (_, (raw_vars, raw_props)) => prep_clause ctxt thesis raw_vars raw_props) 128 |> check_terms ctxt; 129 in map fst raw_obtains ~~ clauses end; 130 131val parse_clause = prepare_clause Proof_Context.read_var Syntax.parse_prop mk_all_external; 132val cert_clause = prepare_clause Proof_Context.cert_var (K I) mk_all_internal; 133 134in 135 136val read_obtains = prepare_obtains parse_clause Syntax.check_terms; 137val cert_obtains = prepare_obtains cert_clause (K I); 138val parse_obtains = prepare_obtains parse_clause (K I); 139 140end; 141 142 143 144(** consider: generalized elimination and cases rule **) 145 146(* 147 consider (a) x where "A x" | (b) y where "B y" | ... \<equiv> 148 149 have thesis 150 if a [intro?]: "\<And>x. A x \<Longrightarrow> thesis" 151 and b [intro?]: "\<And>y. B y \<Longrightarrow> thesis" 152 and ... 153 for thesis 154 apply (insert that) 155*) 156 157local 158 159fun gen_consider prep_obtains raw_obtains int state = 160 let 161 val _ = Proof.assert_forward_or_chain state; 162 val ctxt = Proof.context_of state; 163 164 val ((_, thesis), thesis_ctxt) = obtain_thesis ctxt; 165 val obtains = prep_obtains thesis_ctxt thesis raw_obtains; 166 val atts = Rule_Cases.cases_open :: obtains_attributes raw_obtains; 167 in 168 state 169 |> Proof.have true NONE (K I) 170 [(Binding.name Auto_Bind.thesisN, NONE, NoSyn)] 171 (map (fn (a, A) => ((a, [Context_Rules.intro_query NONE]), [(A, [])])) obtains) 172 [((Binding.empty, atts), [(thesis, [])])] int 173 |-> Proof.refine_insert 174 end; 175 176in 177 178val consider = gen_consider cert_obtains; 179val consider_cmd = gen_consider read_obtains; 180 181end; 182 183 184 185(** obtain: augmented context based on generalized existence rule **) 186 187(* 188 obtain (a) x where "A x" <proof> \<equiv> 189 190 have thesis if a [intro?]: "\<And>x. A x \<Longrightarrow> thesis" for thesis 191 apply (insert that) 192 <proof> 193 fix x assm <<obtain_export>> "A x" 194*) 195 196local 197 198fun gen_obtain prep_stmt prep_att that_binding raw_decls raw_fixes raw_prems raw_concls int state = 199 let 200 val _ = Proof.assert_forward_or_chain state; 201 202 val ((_, thesis), thesis_ctxt) = obtain_thesis (Proof.context_of state); 203 204 val ({vars, propss, binds, result_binds, ...}, params_ctxt) = 205 prep_stmt (raw_decls @ raw_fixes) (raw_prems @ map #2 raw_concls) thesis_ctxt; 206 val (decls, fixes) = chop (length raw_decls) vars ||> map #2; 207 val (premss, conclss) = chop (length raw_prems) propss; 208 val propss' = (map o map) (Logic.close_prop fixes (flat premss)) conclss; 209 210 val that_prop = 211 Logic.list_rename_params (map (#1 o #2) decls) 212 (fold_rev (Logic.all o #2 o #2) decls (Logic.list_implies (flat propss', thesis))); 213 214 val cparams = map (Thm.cterm_of params_ctxt o #2 o #2) decls; 215 val asms = 216 map (fn ((b, raw_atts), _) => (b, map (prep_att params_ctxt) raw_atts)) raw_concls ~~ 217 map (map (rpair [])) propss'; 218 219 fun after_qed (result_ctxt, results) state' = 220 let val [rule] = Proof_Context.export result_ctxt (Proof.context_of state') (flat results) in 221 state' 222 |> Proof.fix (map #1 decls) 223 |> Proof.map_context (fold (Variable.bind_term o apsnd (Logic.close_term fixes)) binds) 224 |> Proof.assm (obtain_export params_ctxt rule cparams) [] [] asms 225 end; 226 in 227 state 228 |> Proof.have true NONE after_qed 229 [(Binding.name Auto_Bind.thesisN, NONE, NoSyn)] 230 [((that_binding, [Context_Rules.intro_query NONE]), [(that_prop, [])])] 231 [(Binding.empty_atts, [(thesis, [])])] int 232 |-> Proof.refine_insert 233 |> Proof.map_context (fold Variable.bind_term result_binds) 234 end; 235 236in 237 238val obtain = gen_obtain Proof_Context.cert_stmt (K I); 239val obtain_cmd = gen_obtain Proof_Context.read_stmt Attrib.attribute_cmd; 240 241end; 242 243 244 245(** tactical result **) 246 247fun check_result ctxt thesis th = 248 (case Thm.prems_of th of 249 [prem] => 250 if Thm.concl_of th aconv thesis andalso 251 Logic.strip_assums_concl prem aconv thesis then th 252 else error ("Guessed a different clause:\n" ^ Thm.string_of_thm ctxt th) 253 | [] => error "Goal solved -- nothing guessed" 254 | _ => error ("Guess split into several cases:\n" ^ Thm.string_of_thm ctxt th)); 255 256fun result tac facts ctxt = 257 let 258 val ((thesis_var, thesis), thesis_ctxt) = obtain_thesis ctxt; 259 val st = Goal.init (Thm.cterm_of ctxt thesis); 260 val rule = 261 (case SINGLE (Method.insert_tac thesis_ctxt facts 1 THEN tac thesis_ctxt) st of 262 NONE => raise THM ("Obtain.result: tactic failed", 0, facts) 263 | SOME th => 264 check_result thesis_ctxt thesis (Raw_Simplifier.norm_hhf thesis_ctxt (Goal.conclude th))); 265 266 val closed_rule = Thm.forall_intr (Thm.cterm_of ctxt (Free thesis_var)) rule; 267 val ((_, [rule']), ctxt') = Variable.import false [closed_rule] ctxt; 268 val obtain_rule = 269 Thm.forall_elim (Thm.cterm_of ctxt (Logic.varify_global (Free thesis_var))) rule'; 270 val ((params, stmt), fix_ctxt) = Variable.focus_cterm NONE (Thm.cprem_of obtain_rule 1) ctxt'; 271 val (prems, ctxt'') = 272 Assumption.add_assms (obtain_export fix_ctxt obtain_rule (map #2 params)) 273 (Drule.strip_imp_prems stmt) fix_ctxt; 274 in ((params, prems), ctxt'') end; 275 276 277 278(** guess: obtain based on tactical result **) 279 280(* 281 <chain_facts> 282 guess x <proof body> <proof end> \<equiv> 283 284 { 285 fix thesis 286 <chain_facts> have "PROP ?guess" 287 apply magic \<comment> \<open>turn goal into \<open>thesis \<Longrightarrow> #thesis\<close>\<close> 288 <proof body> 289 apply_end magic \<comment> \<open>turn final \<open>(\<And>x. P x \<Longrightarrow> thesis) \<Longrightarrow> #thesis\<close> into\<close> 290 \<comment> \<open>\<open>#((\<And>x. A x \<Longrightarrow> thesis) \<Longrightarrow> thesis)\<close> which is a finished goal state\<close> 291 <proof end> 292 } 293 fix x assm <<obtain_export>> "A x" 294*) 295 296local 297 298fun unify_params vars thesis_var raw_rule ctxt = 299 let 300 val thy = Proof_Context.theory_of ctxt; 301 val string_of_term = Syntax.string_of_term (Config.put show_types true ctxt); 302 303 fun err msg th = error (msg ^ ":\n" ^ Thm.string_of_thm ctxt th); 304 305 val maxidx = fold (Term.maxidx_typ o snd o fst) vars ~1; 306 val rule = Thm.incr_indexes (maxidx + 1) raw_rule; 307 308 val params = Rule_Cases.strip_params (Logic.nth_prem (1, Thm.prop_of rule)); 309 val m = length vars; 310 val n = length params; 311 val _ = m <= n orelse err "More variables than parameters in obtained rule" rule; 312 313 fun unify ((x, T), (y, U)) (tyenv, max) = Sign.typ_unify thy (T, U) (tyenv, max) 314 handle Type.TUNIFY => 315 err ("Failed to unify variable " ^ 316 string_of_term (Free (x, Envir.norm_type tyenv T)) ^ " against parameter " ^ 317 string_of_term (Syntax_Trans.mark_bound_abs (y, Envir.norm_type tyenv U)) ^ " in") rule; 318 val (tyenv, _) = fold unify (map #1 vars ~~ take m params) 319 (Vartab.empty, Int.max (maxidx, Thm.maxidx_of rule)); 320 val norm_type = Envir.norm_type tyenv; 321 322 val xs = map (apsnd norm_type o fst) vars; 323 val ys = map (apsnd norm_type) (drop m params); 324 val ys' = map Name.internal (Name.variant_list (map fst xs) (map fst ys)) ~~ map #2 ys; 325 val terms = map (Drule.mk_term o Thm.cterm_of ctxt o Free) (xs @ ys'); 326 327 val instT = 328 fold (Term.add_tvarsT o #2) params [] 329 |> map (fn v => (v, Thm.ctyp_of ctxt (norm_type (TVar v)))); 330 val closed_rule = rule 331 |> Thm.forall_intr (Thm.cterm_of ctxt (Free thesis_var)) 332 |> Thm.instantiate (instT, []); 333 334 val ((_, rule' :: terms'), ctxt') = Variable.import false (closed_rule :: terms) ctxt; 335 val vars' = 336 map (dest_Free o Thm.term_of o Drule.dest_term) terms' ~~ 337 (map snd vars @ replicate (length ys) NoSyn); 338 val rule'' = Thm.forall_elim (Thm.cterm_of ctxt' (Logic.varify_global (Free thesis_var))) rule'; 339 in ((vars', rule''), ctxt') end; 340 341fun inferred_type (binding, _, mx) ctxt = 342 let 343 val x = Variable.check_name binding; 344 val ((_, T), ctxt') = Proof_Context.inferred_param x ctxt 345 in ((x, T, mx), ctxt') end; 346 347fun polymorphic ctxt vars = 348 let val Ts = map Logic.dest_type (Variable.polymorphic ctxt (map (Logic.mk_type o #2) vars)) 349 in map2 (fn (x, _, mx) => fn T => ((x, T), mx)) vars Ts end; 350 351fun gen_guess prep_var raw_vars int state = 352 let 353 val _ = Proof.assert_forward_or_chain state; 354 val ctxt = Proof.context_of state; 355 val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else []; 356 357 val (thesis_var, thesis) = #1 (obtain_thesis ctxt); 358 val vars = ctxt 359 |> fold_map prep_var raw_vars |-> fold_map inferred_type 360 |> fst |> polymorphic ctxt; 361 362 fun guess_context raw_rule state' = 363 let 364 val ((parms, rule), ctxt') = 365 unify_params vars thesis_var raw_rule (Proof.context_of state'); 366 val (xs, _) = Variable.add_fixes (map (#1 o #1) parms) ctxt'; 367 val ps = xs ~~ map (#2 o #1) parms; 368 val ts = map Free ps; 369 val asms = 370 Logic.strip_assums_hyp (Logic.nth_prem (1, Thm.prop_of rule)) 371 |> map (fn asm => (Term.betapplys (fold_rev Term.abs ps asm, ts), [])); 372 val _ = not (null asms) orelse error "Trivial result -- nothing guessed"; 373 in 374 state' 375 |> Proof.map_context (K ctxt') 376 |> Proof.fix (map (fn ((x, T), mx) => (Binding.name x, SOME T, mx)) parms) 377 |> `Proof.context_of |-> (fn fix_ctxt => Proof.assm 378 (obtain_export fix_ctxt rule (map (Thm.cterm_of ctxt) ts)) 379 [] [] [(Binding.empty_atts, asms)]) 380 |> Proof.map_context (fold Variable.unbind_term Auto_Bind.no_facts) 381 end; 382 383 val goal = Var (("guess", 0), propT); 384 val pos = Position.thread_data (); 385 fun print_result ctxt' (k, [(s, [_, th])]) = 386 Proof_Display.print_results int pos ctxt' (k, [(s, [th])]); 387 val before_qed = 388 Method.primitive_text (fn ctxt => 389 Goal.conclude #> Raw_Simplifier.norm_hhf ctxt #> 390 (fn th => Goal.protect 0 (Conjunction.intr (Drule.mk_term (Thm.cprop_of th)) th))); 391 fun after_qed (result_ctxt, results) state' = 392 let val [_, res] = Proof_Context.export result_ctxt (Proof.context_of state') (flat results) 393 in 394 state' 395 |> Proof.end_block 396 |> guess_context (check_result ctxt thesis res) 397 end; 398 in 399 state 400 |> Proof.enter_forward 401 |> Proof.begin_block 402 |> Proof.fix [(Binding.name Auto_Bind.thesisN, NONE, NoSyn)] 403 |> Proof.chain_facts chain_facts 404 |> Proof.internal_goal print_result Proof_Context.mode_schematic true "guess" 405 (SOME before_qed) after_qed 406 [] [] [(Binding.empty_atts, [(Logic.mk_term goal, []), (goal, [])])] 407 |> snd 408 |> Proof.refine_singleton 409 (Method.primitive_text (fn _ => fn _ => Goal.init (Thm.cterm_of ctxt thesis))) 410 end; 411 412in 413 414val guess = gen_guess Proof_Context.cert_var; 415val guess_cmd = gen_guess Proof_Context.read_var; 416 417end; 418 419end; 420