1 (* Title: HOL/Tools/datatype_package.ML
3 Author: Stefan Berghofer, TU Muenchen
5 Datatype package for Isabelle/HOL.
8 signature BASIC_DATATYPE_PACKAGE =
10 val induct_tac : string -> int -> tactic
11 val induct_thm_tac : thm -> string -> int -> tactic
12 val case_tac : string -> int -> tactic
13 val distinct_simproc : simproc
16 signature DATATYPE_PACKAGE =
18 include BASIC_DATATYPE_PACKAGE
19 val quiet_mode : bool ref
20 val add_datatype : bool -> string list -> (string list * bstring * mixfix *
21 (bstring * string list * mixfix) list) list -> theory ->
22 {distinct : thm list list,
23 inject : thm list list,
24 exhaustion : thm list,
26 case_thms : thm list list,
27 split_thms : (thm * thm) list,
30 simps : thm list} * theory
31 val add_datatype_i : bool -> bool -> string list -> (string list * bstring * mixfix *
32 (bstring * typ list * mixfix) list) list -> theory ->
33 {distinct : thm list list,
34 inject : thm list list,
35 exhaustion : thm list,
37 case_thms : thm list list,
38 split_thms : (thm * thm) list,
41 simps : thm list} * theory
42 val rep_datatype_i : string list option -> (thm list * theory attribute list) list list ->
43 (thm list * theory attribute list) list list -> (thm list * theory attribute list) ->
45 {distinct : thm list list,
46 inject : thm list list,
47 exhaustion : thm list,
49 case_thms : thm list list,
50 split_thms : (thm * thm) list,
53 simps : thm list} * theory
54 val rep_datatype : string list option -> (thmref * Attrib.src list) list list ->
55 (thmref * Attrib.src list) list list -> thmref * Attrib.src list -> theory ->
56 {distinct : thm list list,
57 inject : thm list list,
58 exhaustion : thm list,
60 case_thms : thm list list,
61 split_thms : (thm * thm) list,
64 simps : thm list} * theory
65 val get_datatypes : theory -> DatatypeAux.datatype_info Symtab.table
66 val print_datatypes : theory -> unit
67 val datatype_info : theory -> string -> DatatypeAux.datatype_info option
68 val datatype_info_err : theory -> string -> DatatypeAux.datatype_info
69 val is_datatype : theory -> string -> bool
70 val get_datatype : theory -> string -> ((string * sort) list * string list) option
71 val get_datatype_cons : theory -> string * string -> typ list option
72 val get_datatype_case_consts : theory -> string list
73 val get_case_const_data : theory -> string -> (string * int) list option
74 val get_all_datatype_cons : theory -> (string * string) list
75 val constrs_of : theory -> string -> term list option
76 val case_const_of : theory -> string -> term option
77 val weak_case_congs_of : theory -> thm list
78 val setup: (theory -> theory) list
81 structure DatatypePackage : DATATYPE_PACKAGE =
86 val quiet_mode = quiet_mode;
89 (* data kind 'HOL/datatypes' *)
91 structure DatatypesData = TheoryDataFun
93 val name = "HOL/datatypes";
94 type T = datatype_info Symtab.table;
96 val empty = Symtab.empty;
99 fun merge _ tabs : T = Symtab.merge (K true) tabs;
102 Pretty.writeln (Pretty.strs ("datatypes:" ::
103 map #1 (NameSpace.extern_table (Sign.type_space sg, tab))));
106 val get_datatypes = DatatypesData.get;
107 val put_datatypes = DatatypesData.put;
108 val print_datatypes = DatatypesData.print;
111 (** theory information about datatypes **)
113 val datatype_info = Symtab.lookup o get_datatypes;
115 fun datatype_info_err thy name = (case datatype_info thy name of
117 | NONE => error ("Unknown datatype " ^ quote name));
119 fun constrs_of thy tname = (case datatype_info thy tname of
120 SOME {index, descr, ...} =>
121 let val (_, _, constrs) = valOf (AList.lookup (op =) descr index)
122 in SOME (map (fn (cname, _) => Const (cname, Sign.the_const_type thy cname)) constrs)
126 fun case_const_of thy tname = (case datatype_info thy tname of
127 SOME {case_name, ...} => SOME (Const (case_name, Sign.the_const_type thy case_name))
130 val weak_case_congs_of = map (#weak_case_cong o #2) o Symtab.dest o get_datatypes;
132 fun is_datatype thy dtco =
133 Symtab.lookup (get_datatypes thy) dtco
136 fun get_datatype thy dtco =
138 |> Symtab.lookup (get_datatypes thy)
139 |> Option.map (fn info => (#sorts info,
140 (get_first (fn (_, (dtco', _, cs)) =>
142 then SOME (map fst cs)
143 else NONE) (#descr info) |> the)));
145 fun get_datatype_cons thy (co, dtco) =
149 |> Symtab.lookup (get_datatypes thy)
154 |> get_first (fn (_, (dtco', vs, cs)) =>
164 |> AList.lookup (op =) cs
165 |> Option.map (map (DatatypeAux.typ_of_dtyp descr (map (rpair [])
166 (map DatatypeAux.dest_DtTFree vs)))))
170 fun get_datatype_case_consts thy =
171 Symtab.fold (fn (_, {case_name, ...}) => cons case_name) (get_datatypes thy) [];
173 fun get_case_const_data thy c =
174 case find_first (fn (_, {index, descr, case_name, ...}) =>
176 ) ((Symtab.dest o get_datatypes) thy)
178 | SOME (_, {index, descr, ...}) =>
179 (SOME o map (apsnd length) o #3 o the o AList.lookup (op =) descr) index;
181 fun get_all_datatype_cons thy =
182 Symtab.fold (fn (dtco, _) => fold
183 (fn co => cons (co, dtco))
184 ((snd o the oo get_datatype) thy dtco)) (get_datatypes thy) [];
186 fun find_tname var Bi =
187 let val frees = map dest_Free (term_frees Bi)
188 val params = rename_wrt_term Bi (Logic.strip_params Bi);
189 in case AList.lookup (op =) (frees @ params) var of
190 NONE => error ("No such variable in subgoal: " ^ quote var)
191 | SOME(Type (tn, _)) => tn
192 | _ => error ("Cannot determine type of " ^ quote var)
195 fun infer_tname state i aterm =
197 val sign = Thm.sign_of_thm state;
198 val (_, _, Bi, _) = Thm.dest_state (state, i)
199 val params = Logic.strip_params Bi; (*params of subgoal i*)
200 val params = rev (rename_wrt_term Bi params); (*as they are printed*)
201 val (types, sorts) = types_sorts state;
202 fun types' (a, ~1) = (case AList.lookup (op =) params a of NONE => types(a, ~1) | sm => sm)
203 | types' ixn = types ixn;
204 val (ct, _) = read_def_cterm (sign, types', sorts) [] false (aterm, TypeInfer.logicT);
205 in case #T (rep_cterm ct) of
207 | _ => error ("Cannot determine type of " ^ quote aterm)
210 (*Warn if the (induction) variable occurs Free among the premises, which
211 usually signals a mistake. But calls the tactic either way!*)
212 fun occs_in_prems tacf vars =
213 SUBGOAL (fn (Bi, i) =>
214 (if exists (fn Free (a, _) => a mem vars)
215 (foldr add_term_frees [] (#2 (strip_context Bi)))
216 then warning "Induction variable occurs also among premises!"
221 (* generic induction tactic for datatypes *)
225 fun prep_var (Var (ixn, _), SOME x) = SOME (ixn, x)
228 fun prep_inst (concl, xs) = (*exception UnequalLengths *)
229 let val vs = InductAttrib.vars_of concl
230 in List.mapPartial prep_var (Library.drop (length vs - length xs, vs) ~~ xs) end;
234 fun gen_induct_tac inst_tac (varss, opt_rule) i state =
236 val (_, _, Bi, _) = Thm.dest_state (state, i);
237 val {sign, ...} = Thm.rep_thm state;
238 val (rule, rule_name) =
240 SOME r => (r, "Induction rule")
242 let val tn = find_tname (hd (List.mapPartial I (List.concat varss))) Bi
243 in (#induction (datatype_info_err sign tn), "Induction rule for type " ^ tn) end);
245 val concls = HOLogic.dest_concls (Thm.concl_of rule);
246 val insts = List.concat (map prep_inst (concls ~~ varss)) handle UnequalLengths =>
247 error (rule_name ^ " has different numbers of variables");
248 in occs_in_prems (inst_tac insts rule) (map #2 insts) i state end;
251 gen_induct_tac Tactic.res_inst_tac'
252 (map (Library.single o SOME) (Syntax.read_idents s), NONE);
254 fun induct_thm_tac th s =
255 gen_induct_tac Tactic.res_inst_tac'
256 ([map SOME (Syntax.read_idents s)], SOME th);
261 (* generic case tactic for datatypes *)
263 fun case_inst_tac inst_tac t rule i state =
265 val _ $ Var (ixn, _) $ _ = HOLogic.dest_Trueprop
266 (hd (Logic.strip_assums_hyp (hd (Thm.prems_of rule))));
267 in inst_tac [(ixn, t)] rule i state end;
269 fun gen_case_tac inst_tac (t, SOME rule) i state =
270 case_inst_tac inst_tac t rule i state
271 | gen_case_tac inst_tac (t, NONE) i state =
272 let val tn = infer_tname state i t in
273 if tn = HOLogic.boolN then inst_tac [(("P", 0), t)] case_split_thm i state
274 else case_inst_tac inst_tac t
275 (#exhaustion (datatype_info_err (Thm.sign_of_thm state) tn))
277 end handle THM _ => Seq.empty;
279 fun case_tac t = gen_case_tac Tactic.res_inst_tac' (t, NONE);
283 (** Isar tactic emulations **)
287 val rule_spec = Scan.lift (Args.$$$ "rule" -- Args.$$$ ":");
288 val opt_rule = Scan.option (rule_spec |-- Attrib.local_thm);
291 Args.and_list (Scan.repeat (Scan.unless rule_spec (Scan.lift (Args.maybe Args.name))));
293 val inst_tac = Method.bires_inst_tac false;
295 fun induct_meth ctxt (varss, opt_rule) =
296 gen_induct_tac (inst_tac ctxt) (varss, opt_rule);
297 fun case_meth ctxt (varss, opt_rule) =
298 gen_case_tac (inst_tac ctxt) (varss, opt_rule);
302 val tactic_emulations =
303 [("induct_tac", Method.goal_args_ctxt' (varss -- opt_rule) induct_meth,
304 "induct_tac emulation (dynamic instantiation)"),
305 ("case_tac", Method.goal_args_ctxt' (Scan.lift Args.name -- opt_rule) case_meth,
306 "case_tac emulation (dynamic instantiation)")];
312 (** induct method setup **)
318 fun dt_recs (DtTFree _) = []
319 | dt_recs (DtType (_, dts)) = List.concat (map dt_recs dts)
320 | dt_recs (DtRec i) = [i];
322 fun dt_cases (descr: descr) (_, args, constrs) =
324 fun the_bname i = Sign.base_name (#1 (valOf (AList.lookup (op =) descr i)));
325 val bnames = map the_bname (distinct (List.concat (map dt_recs args)));
326 in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end;
329 fun induct_cases descr =
330 DatatypeProp.indexify_names (List.concat (map (dt_cases descr) (map #2 descr)));
332 fun exhaust_cases descr i = dt_cases descr (valOf (AList.lookup (op =) descr i));
336 fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);
338 fun mk_case_names_exhausts descr new =
339 map (RuleCases.case_names o exhaust_cases descr o #1)
340 (List.filter (fn ((_, (name, _, _))) => name mem_string new) descr);
344 (*Name management for ATP linkup. The suffix here must agree with the one given
345 for notE in Clasimp.addIff*)
347 Thm.name_thm (Thm.name_of_thm th ^ "_iff1", th RS notE);
349 fun add_rules simps case_thms size_thms rec_thms inject distinct
350 weak_case_congs cong_att =
351 (snd o PureThy.add_thmss [(("simps", simps), []),
352 (("", List.concat case_thms @ size_thms @
353 List.concat distinct @ rec_thms), [Attrib.theory Simplifier.simp_add]),
354 (("", size_thms @ rec_thms), [RecfunCodegen.add NONE]),
355 (("", List.concat inject), [Attrib.theory iff_add]),
356 (("", map name_notE (List.concat distinct)), [Attrib.theory (Classical.safe_elim NONE)]),
357 (("", weak_case_congs), [cong_att])]);
360 (* add_cases_induct *)
362 fun add_cases_induct infos induction =
364 val n = length (HOLogic.dest_concls (Thm.concl_of induction));
365 fun proj i = ProjectRule.project induction (i + 1);
367 fun named_rules (name, {index, exhaustion, ...}: datatype_info) =
368 [(("", proj index), [Attrib.theory (InductAttrib.induct_type name)]),
369 (("", exhaustion), [Attrib.theory (InductAttrib.cases_type name)])];
371 (("", proj i), [Drule.kind_internal, Attrib.theory (InductAttrib.induct_type "")]);
374 (List.concat (map named_rules infos) @
375 map unnamed_rule (length infos upto n - 1)) #> snd #>
376 PureThy.add_thmss [(("inducts",
377 map (proj #> standard #> RuleCases.save induction) (0 upto n - 1)), [])] #> snd
382 (**** simplification procedure for showing distinctness of constructors ****)
384 fun stripT (i, Type ("fun", [_, T])) = stripT (i + 1, T)
387 fun stripC (i, f $ x) = stripC (i + 1, f)
390 val distinctN = "constr_distinct";
392 exception ConstrDistinct of term;
394 fun distinct_proc sg ss (t as Const ("op =", _) $ t1 $ t2) =
395 (case (stripC (0, t1), stripC (0, t2)) of
396 ((i, Const (cname1, T1)), (j, Const (cname2, T2))) =>
397 (case (stripT (0, T1), stripT (0, T2)) of
398 ((i', Type (tname1, _)), (j', Type (tname2, _))) =>
399 if tname1 = tname2 andalso not (cname1 = cname2) andalso i = i' andalso j = j' then
400 (case (constrs_of sg tname1) of
401 SOME constrs => let val cnames = map (fst o dest_Const) constrs
402 in if cname1 mem cnames andalso cname2 mem cnames then
403 let val eq_t = Logic.mk_equals (t, Const ("False", HOLogic.boolT));
404 val eq_ct = cterm_of sg eq_t;
405 val Datatype_thy = theory "Datatype";
406 val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] =
407 map (get_thm Datatype_thy o Name)
408 ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"]
409 in (case (#distinct (datatype_info_err sg tname1)) of
410 QuickAndDirty => SOME (Thm.invoke_oracle
411 Datatype_thy distinctN (sg, ConstrDistinct eq_t))
412 | FewConstrs thms => SOME (Goal.prove sg [] [] eq_t (K
413 (EVERY [rtac eq_reflection 1, rtac iffI 1, rtac notE 1,
414 atac 2, resolve_tac thms 1, etac FalseE 1])))
415 | ManyConstrs (thm, simpset) => SOME (Goal.prove sg [] [] eq_t (K
416 (EVERY [rtac eq_reflection 1, rtac iffI 1, dtac thm 1,
417 full_simp_tac (Simplifier.inherit_context ss simpset) 1,
418 REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
419 eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1,
428 | distinct_proc sg _ _ = NONE;
430 val distinct_simproc =
431 Simplifier.simproc HOL.thy distinctN ["s = t"] distinct_proc;
433 val dist_ss = HOL_ss addsimprocs [distinct_simproc];
436 [Theory.add_oracle (distinctN, fn (_, ConstrDistinct t) => t),
437 fn thy => ((change_simpset_of thy) (fn ss => ss addsimprocs [distinct_simproc]); thy)];
440 (**** translation rules for case ****)
442 fun find_first f = Library.find_first f;
444 fun case_tr sg [t, u] =
446 fun case_error s name ts = raise TERM ("Error in case expression" ^
447 getOpt (Option.map (curry op ^ " for datatype ") name, "") ^ ":\n" ^ s, ts);
448 fun dest_case1 (Const ("_case1", _) $ t $ u) = (case strip_comb t of
449 (Const (s, _), ts) => (Sign.intern_const sg s, ts)
450 | (Free (s, _), ts) => (Sign.intern_const sg s, ts)
451 | _ => case_error "Head is not a constructor" NONE [t, u], u)
452 | dest_case1 t = raise TERM ("dest_case1", [t]);
453 fun dest_case2 (Const ("_case2", _) $ t $ u) = t :: dest_case2 u
454 | dest_case2 t = [t];
455 val cases as ((cname, _), _) :: _ = map dest_case1 (dest_case2 u);
456 val tab = Symtab.dest (get_datatypes sg);
457 val (cases', default) = (case split_last cases of
458 (cases', (("dummy_pattern", []), t)) => (cases', SOME t)
459 | _ => (cases, NONE))
460 fun abstr (Free (x, T), body) = Term.absfree (x, T, body)
461 | abstr (Const ("_constrain", _) $ Free (x, T) $ tT, body) =
462 Syntax.const Syntax.constrainAbsC $ Term.absfree (x, T, body) $ tT
463 | abstr (Const ("Pair", _) $ x $ y, body) =
464 Syntax.const "split" $ abstr (x, abstr (y, body))
465 | abstr (t, _) = case_error "Illegal pattern" NONE [t];
466 in case find_first (fn (_, {descr, index, ...}) =>
467 exists (equal cname o fst) (#3 (snd (List.nth (descr, index))))) tab of
468 NONE => case_error ("Not a datatype constructor: " ^ cname) NONE [u]
469 | SOME (tname, {descr, sorts, case_name, index, ...}) =>
471 val _ = if exists (equal "dummy_pattern" o fst o fst) cases' then
472 case_error "Illegal occurrence of '_' dummy pattern" (SOME tname) [u] else ();
473 val (_, (_, dts, constrs)) = List.nth (descr, index);
474 fun find_case (cases, (s, dt)) =
475 (case find_first (equal s o fst o fst) cases' of
476 NONE => (case default of
477 NONE => case_error ("No clause for constructor " ^ s) (SOME tname) [u]
478 | SOME t => (cases, list_abs (map (rpair dummyT) (DatatypeProp.make_tnames
479 (map (typ_of_dtyp descr sorts) dt)), t)))
480 | SOME (c as ((_, vs), t)) =>
481 if length dt <> length vs then
482 case_error ("Wrong number of arguments for constructor " ^ s)
484 else (cases \ c, foldr abstr t vs))
485 val (cases'', fs) = foldl_map find_case (cases', constrs)
486 in case (cases'', length constrs = length cases', default) of
487 ([], true, SOME _) =>
488 case_error "Extra '_' dummy pattern" (SOME tname) [u]
490 let val extra = distinct (map (fst o fst) cases'')
491 in case extra \\ map fst constrs of
492 [] => case_error ("More than one clause for constructor(s) " ^
493 commas extra) (SOME tname) [u]
494 | extra' => case_error ("Illegal constructor(s): " ^ commas extra')
497 | _ => list_comb (Syntax.const case_name, fs) $ t
500 | case_tr sg ts = raise TERM ("case_tr", ts);
502 fun case_tr' constrs sg ts =
503 if length ts <> length constrs + 1 then raise Match else
505 val (fs, x) = split_last ts;
506 fun strip_abs 0 t = ([], t)
507 | strip_abs i (Abs p) =
508 let val (x, u) = Syntax.atomic_abs_tr' p
509 in apfst (cons x) (strip_abs (i-1) u) end
510 | strip_abs i (Const ("split", _) $ t) = (case strip_abs (i+1) t of
511 (v :: v' :: vs, u) => (Syntax.const "Pair" $ v $ v' :: vs, u));
512 fun is_dependent i t =
513 let val k = length (strip_abs_vars t) - i
514 in k < 0 orelse exists (fn j => j >= k)
515 (loose_bnos (strip_abs_body t))
517 val cases = map (fn ((cname, dts), t) =>
518 (Sign.extern_const sg cname,
519 strip_abs (length dts) t, is_dependent (length dts) t))
521 fun count_cases (cs, (_, _, true)) = cs
522 | count_cases (cs, (cname, (_, body), false)) = (case AList.lookup (op =) cs body of
523 NONE => (body, [cname]) :: cs
524 | SOME cnames => AList.update (op =) (body, cnames @ [cname]) cs);
525 val cases' = sort (int_ord o Library.swap o pairself (length o snd))
526 (Library.foldl count_cases ([], cases));
527 fun mk_case1 (cname, (vs, body), _) = Syntax.const "_case1" $
528 list_comb (Syntax.const cname, vs) $ body;
530 Syntax.const "_case_syntax" $ x $
531 foldr1 (fn (t, u) => Syntax.const "_case2" $ t $ u) (map mk_case1
534 | (default, cnames) :: _ =>
535 if length cnames = 1 then cases
536 else if length cnames = length constrs then
537 [hd cases, ("dummy_pattern", ([], default), false)]
539 filter_out (fn (cname, _, _) => cname mem cnames) cases @
540 [("dummy_pattern", ([], default), false)]))
543 fun make_case_tr' case_names descr = List.concat (map
544 (fn ((_, (_, _, constrs)), case_name) => map (rpair (case_tr' constrs))
545 (NameSpace.accesses' case_name)) (descr ~~ case_names));
548 [Theory.add_advanced_trfuns ([], [("_case_syntax", case_tr)], [], [])];
553 fun read_typ sign ((Ts, sorts), str) =
555 val T = Type.no_tvars (Sign.read_typ (sign, AList.lookup (op =)
556 (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg
557 in (Ts @ [T], add_typ_tfrees (T, sorts)) end;
559 fun cert_typ sign ((Ts, sorts), raw_T) =
561 val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle
562 TYPE (msg, _, _) => error msg;
563 val sorts' = add_typ_tfrees (T, sorts)
565 case duplicates (map fst sorts') of
567 | dups => error ("Inconsistent sort constraints for " ^ commas dups))
571 (**** make datatype info ****)
573 fun make_dt_info descr sorts induct reccomb_names rec_thms
574 (((((((((i, (_, (tname, _, _))), case_name), case_thms),
575 exhaustion_thm), distinct_thm), inject), nchotomy), case_cong), weak_case_cong) =
580 rec_names = reccomb_names,
581 rec_rewrites = rec_thms,
582 case_name = case_name,
583 case_rewrites = case_thms,
585 exhaustion = exhaustion_thm,
586 distinct = distinct_thm,
589 case_cong = case_cong,
590 weak_case_cong = weak_case_cong});
593 (********************* axiomatic introduction of datatypes ********************)
595 fun add_and_get_axioms_atts label tnames attss ts thy =
596 foldr (fn (((tname, atts), t), (thy', axs)) =>
600 |> Theory.add_path tname
601 |> PureThy.add_axioms_i [((label, t), atts)];
602 in (Theory.parent_path thy'', ax::axs)
603 end) (thy, []) (tnames ~~ attss ~~ ts) |> swap;
605 fun add_and_get_axioms label tnames =
606 add_and_get_axioms_atts label tnames (replicate (length tnames) []);
608 fun add_and_get_axiomss label tnames tss thy =
609 foldr (fn ((tname, ts), (thy', axss)) =>
613 |> Theory.add_path tname
614 |> PureThy.add_axiomss_i [((label, ts), [])];
615 in (Theory.parent_path thy'', axs::axss)
616 end) (thy, []) (tnames ~~ tss) |> swap;
618 fun add_datatype_axm flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
619 case_names_induct case_names_exhausts thy =
621 val descr' = List.concat descr;
622 val recTs = get_rec_types descr' sorts;
623 val used = foldr add_typ_tfree_names [] recTs;
624 val newTs = Library.take (length (hd descr), recTs);
626 val no_size = exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists
627 (fn dt => is_rec_type dt andalso not (null (fst (strip_dtyp dt))))
628 cargs) constrs) descr';
630 (**** declare new types and constants ****)
632 val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr);
634 val constr_decls = map (fn (((_, (_, _, constrs)), T), constr_syntax') =>
635 map (fn ((_, cargs), (cname, mx)) =>
636 (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
637 (constrs ~~ constr_syntax')) ((hd descr) ~~ newTs ~~ constr_syntax);
639 val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
641 val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
642 val reccomb_names = if length descr' = 1 then [big_reccomb_name] else
643 (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
644 (1 upto (length descr')));
646 val size_names = DatatypeProp.indexify_names
647 (map (fn T => name_of_typ T ^ "_size") (Library.drop (length (hd descr), recTs)));
649 val freeT = TFree (variant used "'t", HOLogic.typeS);
650 val case_fn_Ts = map (fn (i, (_, _, constrs)) =>
651 map (fn (_, cargs) =>
652 let val Ts = map (typ_of_dtyp descr' sorts) cargs
653 in Ts ---> freeT end) constrs) (hd descr);
655 val case_names = map (fn s => (s ^ "_case")) new_type_names;
661 curry (Library.foldr (fn (((name, mx), tvs), thy') => thy' |>
662 TypedefPackage.add_typedecls [(name, tvs, mx)]))
663 (types_syntax ~~ tyvars) |>
664 add_path flat_names (space_implode "_" new_type_names) |>
666 (** primrec combinators **)
668 Theory.add_consts_i (map (fn ((name, T), T') =>
669 (name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
670 (reccomb_names ~~ recTs ~~ rec_result_Ts)) |>
672 (** case combinators **)
674 Theory.add_consts_i (map (fn ((name, T), Ts) =>
675 (name, Ts @ [T] ---> freeT, NoSyn))
676 (case_names ~~ newTs ~~ case_fn_Ts));
678 val reccomb_names' = map (Sign.intern_const thy2') reccomb_names;
679 val case_names' = map (Sign.intern_const thy2') case_names;
683 (** size functions **)
685 (if no_size then I else Theory.add_consts_i (map (fn (s, T) =>
686 (Sign.base_name s, T --> HOLogic.natT, NoSyn))
687 (size_names ~~ Library.drop (length (hd descr), recTs)))) |>
691 parent_path flat_names |>
692 curry (Library.foldr (fn (((((_, (_, _, constrs)), T), tname),
693 constr_syntax'), thy') => thy' |>
694 add_path flat_names tname |>
695 Theory.add_consts_i (map (fn ((_, cargs), (cname, mx)) =>
696 (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
697 (constrs ~~ constr_syntax')) |>
698 parent_path flat_names))
699 (hd descr ~~ newTs ~~ new_type_names ~~ constr_syntax);
701 (**** introduction of axioms ****)
703 val rec_axs = DatatypeProp.make_primrecs new_type_names descr sorts thy2;
704 val size_axs = if no_size then [] else DatatypeProp.make_size descr sorts thy2;
706 val ((([induct], [rec_thms]), inject), thy3) =
708 |> Theory.add_path (space_implode "_" new_type_names)
709 |> PureThy.add_axioms_i [(("induct", DatatypeProp.make_ind descr sorts),
710 [case_names_induct])]
711 ||>> PureThy.add_axiomss_i [(("recs", rec_axs), [])]
712 ||> (if no_size then I else snd o PureThy.add_axiomss_i [(("size", size_axs), [])])
713 ||> Theory.parent_path
714 ||>> add_and_get_axiomss "inject" new_type_names
715 (DatatypeProp.make_injs descr sorts);
716 val size_thms = if no_size then [] else get_thms thy3 (Name "size");
717 val (distinct, thy4) = add_and_get_axiomss "distinct" new_type_names
718 (DatatypeProp.make_distincts new_type_names descr sorts thy3) thy3;
720 val exhaust_ts = DatatypeProp.make_casedists descr sorts;
721 val (exhaustion, thy5) = add_and_get_axioms_atts "exhaust" new_type_names
722 (map Library.single case_names_exhausts) exhaust_ts thy4;
723 val (case_thms, thy6) = add_and_get_axiomss "cases" new_type_names
724 (DatatypeProp.make_cases new_type_names descr sorts thy5) thy5;
725 val (split_ts, split_asm_ts) = ListPair.unzip
726 (DatatypeProp.make_splits new_type_names descr sorts thy6);
727 val (split, thy7) = add_and_get_axioms "split" new_type_names split_ts thy6;
728 val (split_asm, thy8) = add_and_get_axioms "split_asm" new_type_names
730 val (nchotomys, thy9) = add_and_get_axioms "nchotomy" new_type_names
731 (DatatypeProp.make_nchotomys descr sorts) thy8;
732 val (case_congs, thy10) = add_and_get_axioms "case_cong" new_type_names
733 (DatatypeProp.make_case_congs new_type_names descr sorts thy9) thy9;
734 val (weak_case_congs, thy11) = add_and_get_axioms "weak_case_cong" new_type_names
735 (DatatypeProp.make_weak_case_congs new_type_names descr sorts thy10) thy10;
737 val dt_infos = map (make_dt_info descr' sorts induct reccomb_names' rec_thms)
738 ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names' ~~ case_thms ~~
739 exhaustion ~~ replicate (length (hd descr)) QuickAndDirty ~~ inject ~~
740 nchotomys ~~ case_congs ~~ weak_case_congs);
742 val simps = List.concat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
743 val split_thms = split ~~ split_asm;
747 |> Theory.add_advanced_trfuns ([], [], make_case_tr' case_names' (hd descr), [])
748 |> Theory.add_path (space_implode "_" new_type_names)
749 |> add_rules simps case_thms size_thms rec_thms inject distinct
750 weak_case_congs (Attrib.theory Simplifier.cong_add)
751 |> put_datatypes (fold Symtab.update dt_infos dt_info)
752 |> add_cases_induct dt_infos induct
753 |> Theory.parent_path
754 |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd
755 |> DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos)
756 |> fold (CodegenPackage.add_case_const_i get_case_const_data) case_names';
758 ({distinct = distinct,
760 exhaustion = exhaustion,
762 case_thms = case_thms,
763 split_thms = split_thms,
766 simps = simps}, thy12)
770 (******************* definitional introduction of datatypes *******************)
772 fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
773 case_names_induct case_names_exhausts thy =
775 val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
777 val ((inject, distinct, dist_rewrites, simproc_dists, induct), thy2) = thy |>
778 DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts
779 types_syntax constr_syntax case_names_induct;
781 val (casedist_thms, thy3) = DatatypeAbsProofs.prove_casedist_thms new_type_names descr
782 sorts induct case_names_exhausts thy2;
783 val ((reccomb_names, rec_thms), thy4) = DatatypeAbsProofs.prove_primrec_thms
784 flat_names new_type_names descr sorts dt_info inject dist_rewrites dist_ss induct thy3;
785 val ((case_thms, case_names), thy6) = DatatypeAbsProofs.prove_case_thms
786 flat_names new_type_names descr sorts reccomb_names rec_thms thy4;
787 val (split_thms, thy7) = DatatypeAbsProofs.prove_split_thms new_type_names
788 descr sorts inject dist_rewrites casedist_thms case_thms thy6;
789 val (nchotomys, thy8) = DatatypeAbsProofs.prove_nchotomys new_type_names
790 descr sorts casedist_thms thy7;
791 val (case_congs, thy9) = DatatypeAbsProofs.prove_case_congs new_type_names
792 descr sorts nchotomys case_thms thy8;
793 val (weak_case_congs, thy10) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
795 val (size_thms, thy11) = DatatypeAbsProofs.prove_size_thms flat_names new_type_names
796 descr sorts reccomb_names rec_thms thy10;
798 val dt_infos = map (make_dt_info (List.concat descr) sorts induct reccomb_names rec_thms)
799 ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~
800 casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
802 val simps = List.concat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
806 |> Theory.add_advanced_trfuns ([], [], make_case_tr' case_names (hd descr), [])
807 |> Theory.add_path (space_implode "_" new_type_names)
808 |> add_rules simps case_thms size_thms rec_thms inject distinct
809 weak_case_congs (Attrib.theory (Simplifier.attrib (op addcongs)))
810 |> put_datatypes (fold Symtab.update dt_infos dt_info)
811 |> add_cases_induct dt_infos induct
812 |> Theory.parent_path
813 |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd
814 |> DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos)
815 |> fold (CodegenPackage.add_case_const_i get_case_const_data) case_names;
817 ({distinct = distinct,
819 exhaustion = casedist_thms,
821 case_thms = case_thms,
822 split_thms = split_thms,
825 simps = simps}, thy12)
829 (*********************** declare existing type as datatype *********************)
831 fun gen_rep_datatype apply_theorems alt_names raw_distinct raw_inject raw_induction thy0 =
833 val _ = Theory.requires thy0 "Inductive" "datatype representations";
835 val (((distinct, inject), [induction]), thy1) =
837 |> fold_map apply_theorems raw_distinct
838 ||>> fold_map apply_theorems raw_inject
839 ||>> apply_theorems [raw_induction];
840 val sign = Theory.sign_of thy1;
842 val induction' = freezeT induction;
844 fun err t = error ("Ill-formed predicate in induction rule: " ^
845 Sign.string_of_term sign t);
847 fun get_typ (t as _ $ Var (_, Type (tname, Ts))) =
848 ((tname, map dest_TFree Ts) handle TERM _ => err t)
851 val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induction')));
852 val new_type_names = getOpt (alt_names, map fst dtnames);
854 fun get_constr t = (case Logic.strip_assums_concl t of
855 _ $ (_ $ t') => (case head_of t' of
856 Const (cname, cT) => (case strip_type cT of
857 (Ts, Type (tname, _)) => (tname, (cname, map (dtyp_of_typ dtnames) Ts))
862 fun make_dt_spec [] _ _ = []
863 | make_dt_spec ((tname, tvs)::dtnames') i constrs =
864 let val (constrs', constrs'') = take_prefix (equal tname o fst) constrs
865 in (i, (tname, map DtTFree tvs, map snd constrs'))::
866 (make_dt_spec dtnames' (i + 1) constrs'')
869 val descr = make_dt_spec dtnames 0 (map get_constr (prems_of induction'));
870 val sorts = add_term_tfrees (concl_of induction', []);
871 val dt_info = get_datatypes thy1;
873 val case_names_induct = mk_case_names_induct descr;
874 val case_names_exhausts = mk_case_names_exhausts descr (map #1 dtnames);
877 val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
879 val (casedist_thms, thy2) = thy1 |>
880 DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induction
882 val ((reccomb_names, rec_thms), thy3) = DatatypeAbsProofs.prove_primrec_thms
883 false new_type_names [descr] sorts dt_info inject distinct dist_ss induction thy2;
884 val ((case_thms, case_names), thy4) = DatatypeAbsProofs.prove_case_thms false
885 new_type_names [descr] sorts reccomb_names rec_thms thy3;
886 val (split_thms, thy5) = DatatypeAbsProofs.prove_split_thms
887 new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4;
888 val (nchotomys, thy6) = DatatypeAbsProofs.prove_nchotomys new_type_names
889 [descr] sorts casedist_thms thy5;
890 val (case_congs, thy7) = DatatypeAbsProofs.prove_case_congs new_type_names
891 [descr] sorts nchotomys case_thms thy6;
892 val (weak_case_congs, thy8) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
894 val (size_thms, thy9) =
895 if Context.exists_name "NatArith" thy8 then
896 DatatypeAbsProofs.prove_size_thms false new_type_names
897 [descr] sorts reccomb_names rec_thms thy8
900 val ((_, [induction']), thy10) =
902 |> store_thmss "inject" new_type_names inject
903 ||>> store_thmss "distinct" new_type_names distinct
904 ||> Theory.add_path (space_implode "_" new_type_names)
905 ||>> PureThy.add_thms [(("induct", induction), [case_names_induct])];
907 val dt_infos = map (make_dt_info descr sorts induction' reccomb_names rec_thms)
908 ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~ casedist_thms ~~
909 map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
911 val simps = List.concat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
914 Theory.add_advanced_trfuns ([], [], make_case_tr' case_names descr, []) |>
915 add_rules simps case_thms size_thms rec_thms inject distinct
916 weak_case_congs (Attrib.theory (Simplifier.attrib (op addcongs))) |>
917 put_datatypes (fold Symtab.update dt_infos dt_info) |>
918 add_cases_induct dt_infos induction' |>
919 Theory.parent_path |>
920 (snd o store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)) |>
921 DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos);
923 ({distinct = distinct,
925 exhaustion = casedist_thms,
927 case_thms = case_thms,
928 split_thms = split_thms,
929 induction = induction',
931 simps = simps}, thy11)
934 val rep_datatype = gen_rep_datatype IsarThy.apply_theorems;
935 val rep_datatype_i = gen_rep_datatype IsarThy.apply_theorems_i;
939 (******************************** add datatype ********************************)
941 fun gen_add_datatype prep_typ err flat_names new_type_names dts thy =
943 val _ = Theory.requires thy "Datatype_Universe" "datatype definitions";
945 (* this theory is used just for parsing *)
949 Theory.add_types (map (fn (tvs, tname, mx, _) =>
950 (tname, length tvs, mx)) dts);
952 val sign = Theory.sign_of tmp_thy;
954 val (tyvars, _, _, _)::_ = dts;
955 val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) =>
956 let val full_tname = Sign.full_name sign (Syntax.type_name tname mx)
957 in (case duplicates tvs of
958 [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx))
959 else error ("Mutually recursive datatypes must have same type parameters")
960 | dups => error ("Duplicate parameter(s) for datatype " ^ full_tname ^
961 " : " ^ commas dups))
964 val _ = (case duplicates (map fst new_dts) @ duplicates new_type_names of
965 [] => () | dups => error ("Duplicate datatypes: " ^ commas dups));
967 fun prep_dt_spec ((dts', constr_syntax, sorts, i), (tvs, tname, mx, constrs)) =
969 fun prep_constr ((constrs, constr_syntax', sorts'), (cname, cargs, mx')) =
971 val (cargs', sorts'') = Library.foldl (prep_typ sign) (([], sorts'), cargs);
972 val _ = (case foldr add_typ_tfree_names [] cargs' \\ tvs of
974 | vs => error ("Extra type variables on rhs: " ^ commas vs))
975 in (constrs @ [((if flat_names then Sign.full_name sign else
976 Sign.full_name_path sign tname) (Syntax.const_name cname mx'),
977 map (dtyp_of_typ new_dts) cargs')],
978 constr_syntax' @ [(cname, mx')], sorts'')
979 end handle ERROR msg =>
980 cat_error msg ("The error above occured in constructor " ^ cname ^
981 " of datatype " ^ tname);
983 val (constrs', constr_syntax', sorts') =
984 Library.foldl prep_constr (([], [], sorts), constrs)
987 case duplicates (map fst constrs') of
989 (dts' @ [(i, (Sign.full_name sign (Syntax.type_name tname mx),
990 map DtTFree tvs, constrs'))],
991 constr_syntax @ [constr_syntax'], sorts', i + 1)
992 | dups => error ("Duplicate constructors " ^ commas dups ^
993 " in datatype " ^ tname)
996 val (dts', constr_syntax, sorts', i) = Library.foldl prep_dt_spec (([], [], [], 0), dts);
997 val sorts = sorts' @ (map (rpair (Sign.defaultS sign)) (tyvars \\ map fst sorts'));
998 val dt_info = get_datatypes thy;
999 val (descr, _) = unfold_datatypes sign dts' sorts dt_info dts' i;
1000 val _ = check_nonempty descr handle (exn as Datatype_Empty s) =>
1001 if err then error ("Nonemptiness check failed for datatype " ^ s)
1004 val descr' = List.concat descr;
1005 val case_names_induct = mk_case_names_induct descr';
1006 val case_names_exhausts = mk_case_names_exhausts descr' (map #1 new_dts);
1008 (if (!quick_and_dirty) then add_datatype_axm else add_datatype_def)
1009 flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
1010 case_names_induct case_names_exhausts thy
1013 val add_datatype_i = gen_add_datatype cert_typ;
1014 val add_datatype = gen_add_datatype read_typ true;
1018 (** package setup **)
1022 val setup = [DatatypesData.init, Method.add_methods tactic_emulations] @ simproc_setup @ trfun_setup;
1027 local structure P = OuterParse and K = OuterKeyword in
1030 Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
1031 (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix));
1033 fun mk_datatype args =
1035 val names = map (fn ((((NONE, _), t), _), _) => t | ((((SOME t, _), _), _), _) => t) args;
1036 val specs = map (fn ((((_, vs), t), mx), cons) =>
1037 (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
1038 in snd o add_datatype false names specs end;
1041 OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl
1042 (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
1045 val rep_datatype_decl =
1046 Scan.option (Scan.repeat1 P.name) --
1047 Scan.optional (P.$$$ "distinct" |-- P.!!! (P.and_list1 P.xthms1)) [[]] --
1048 Scan.optional (P.$$$ "inject" |-- P.!!! (P.and_list1 P.xthms1)) [[]] --
1049 (P.$$$ "induction" |-- P.!!! P.xthm);
1051 fun mk_rep_datatype (((opt_ts, dss), iss), ind) = #2 o rep_datatype opt_ts dss iss ind;
1054 OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_decl
1055 (rep_datatype_decl >> (Toplevel.theory o mk_rep_datatype));
1058 val _ = OuterSyntax.add_keywords ["distinct", "inject", "induction"];
1059 val _ = OuterSyntax.add_parsers [datatypeP, rep_datatypeP];
1066 structure BasicDatatypePackage: BASIC_DATATYPE_PACKAGE = DatatypePackage;
1067 open BasicDatatypePackage;