1 (* Title: ZF/Tools/inductive_package.ML
2 Author: Lawrence C Paulson, Cambridge University Computer Laboratory
4 Fixedpoint definition module -- for Inductive/Coinductive Definitions
6 The functor will be instantiated for normal sums/products (inductive defs)
7 and non-standard sums/products (coinductive defs)
9 Sums are used only for mutual recursion;
10 Products are used only to derive "streamlined" induction rules for relations
13 type inductive_result =
14 {defs : thm list, (*definitions made in thy*)
15 bnd_mono : thm, (*monotonicity for the lfp definition*)
16 dom_subset : thm, (*inclusion of recursive set in dom*)
17 intrs : thm list, (*introduction rules*)
18 elim : thm, (*case analysis theorem*)
19 mk_cases : string -> thm, (*generates case theorems*)
20 induct : thm, (*main induction rule*)
21 mutual_induct : thm}; (*mutual induction rule*)
24 (*Functor's result signature*)
25 signature INDUCTIVE_PACKAGE =
27 (*Insert definitions for the recursive sets, which
28 must *already* be declared as constants in parent theory!*)
29 val add_inductive_i: bool -> term list * term ->
30 ((binding * term) * attribute list) list ->
31 thm list * thm list * thm list * thm list -> theory -> theory * inductive_result
32 val add_inductive: string list * string ->
33 ((binding * string) * Attrib.src list) list ->
34 (Facts.ref * Attrib.src list) list * (Facts.ref * Attrib.src list) list *
35 (Facts.ref * Attrib.src list) list * (Facts.ref * Attrib.src list) list ->
36 theory -> theory * inductive_result
40 (*Declares functions to add fixedpoint/constructor defs to a theory.
41 Recursive sets must *already* be declared as constants.*)
42 functor Add_inductive_def_Fun
43 (structure Fp: FP and Pr : PR and CP: CARTPROD and Su : SU val coind: bool)
49 val co_prefix = if coind then "co" else "";
54 (*make distinct individual variables a1, a2, a3, ..., an. *)
55 fun mk_frees a [] = []
56 | mk_frees a (T::Ts) = Free(a,T) :: mk_frees (Symbol.bump_string a) Ts;
59 (* add_inductive(_i) *)
61 (*internal version, accepting terms*)
62 fun add_inductive_i verbose (rec_tms, dom_sum)
63 raw_intr_specs (monos, con_defs, type_intrs, type_elims) thy =
65 val _ = Theory.requires thy "Inductive_ZF" "(co)inductive definitions";
66 val ctxt = ProofContext.init thy;
68 val intr_specs = map (apfst (apfst Binding.base_name)) raw_intr_specs;
69 val (intr_names, intr_tms) = split_list (map fst intr_specs);
70 val case_names = RuleCases.case_names intr_names;
72 (*recT and rec_params should agree for all mutually recursive components*)
73 val rec_hds = map head_of rec_tms;
75 val dummy = assert_all is_Const rec_hds
76 (fn t => "Recursive set not previously declared as constant: " ^
77 Syntax.string_of_term ctxt t);
79 (*Now we know they are all Consts, so get their names, type and params*)
80 val rec_names = map (#1 o dest_Const) rec_hds
81 and (Const(_,recT),rec_params) = strip_comb (hd rec_tms);
83 val rec_base_names = map Sign.base_name rec_names;
84 val dummy = assert_all Syntax.is_identifier rec_base_names
85 (fn a => "Base name of recursive set not an identifier: " ^ a);
87 local (*Checking the introduction rules*)
88 val intr_sets = map (#2 o rule_concl_msg thy) intr_tms;
90 case head_of set of Const(a,recT) => a mem rec_names | _ => false;
92 val dummy = assert_all intr_ok intr_sets
93 (fn t => "Conclusion of rule does not name a recursive set: " ^
94 Syntax.string_of_term ctxt t);
97 val dummy = assert_all is_Free rec_params
98 (fn t => "Param in recursion term not a free variable: " ^
99 Syntax.string_of_term ctxt t);
101 (*** Construct the fixedpoint definition ***)
102 val mk_variant = Name.variant (foldr OldTerm.add_term_names [] intr_tms);
104 val z' = mk_variant"z" and X' = mk_variant"X" and w' = mk_variant"w";
106 fun dest_tprop (Const("Trueprop",_) $ P) = P
107 | dest_tprop Q = error ("Ill-formed premise of introduction rule: " ^
108 Syntax.string_of_term ctxt Q);
110 (*Makes a disjunct from an introduction rule*)
111 fun fp_part intr = (*quantify over rule's free vars except parameters*)
112 let val prems = map dest_tprop (Logic.strip_imp_prems intr)
113 val dummy = List.app (fn rec_hd => List.app (chk_prem rec_hd) prems) rec_hds
114 val exfrees = OldTerm.term_frees intr \\ rec_params
115 val zeq = FOLogic.mk_eq (Free(z',iT), #1 (rule_concl intr))
116 in foldr FOLogic.mk_exists
117 (BalancedTree.make FOLogic.mk_conj (zeq::prems)) exfrees
120 (*The Part(A,h) terms -- compose injections to make h*)
121 fun mk_Part (Bound 0) = Free(X',iT) (*no mutual rec, no Part needed*)
122 | mk_Part h = @{const Part} $ Free(X',iT) $ Abs(w',iT,h);
124 (*Access to balanced disjoint sums via injections*)
125 val parts = map mk_Part
126 (BalancedTree.accesses {left = fn t => Su.inl $ t, right = fn t => Su.inr $ t, init = Bound 0}
129 (*replace each set by the corresponding Part(A,h)*)
130 val part_intrs = map (subst_free (rec_tms ~~ parts) o fp_part) intr_tms;
132 val fp_abs = absfree(X', iT,
133 mk_Collect(z', dom_sum,
134 BalancedTree.make FOLogic.mk_disj part_intrs));
136 val fp_rhs = Fp.oper $ dom_sum $ fp_abs
138 val dummy = List.app (fn rec_hd => (Logic.occs (rec_hd, fp_rhs) andalso
139 error "Illegal occurrence of recursion operator"; ()))
142 (*** Make the new theory ***)
145 If no mutual recursion then it equals the one recursive set.
146 If mutual recursion then it differs from all the recursive sets. *)
147 val big_rec_base_name = space_implode "_" rec_base_names;
148 val big_rec_name = Sign.intern_const thy big_rec_base_name;
153 writeln ((if coind then "Coind" else "Ind") ^ "uctive definition " ^ quote big_rec_name)
156 (*Big_rec... is the union of the mutually recursive sets*)
157 val big_rec_tm = list_comb(Const(big_rec_name,recT), rec_params);
159 (*The individual sets must already be declared*)
160 val axpairs = map PrimitiveDefs.mk_defpair
161 ((big_rec_tm, fp_rhs) ::
163 [_] => [] (*no mutual recursion*)
164 | _ => rec_tms ~~ (*define the sets as Parts*)
165 map (subst_atomic [(Free(X',iT),big_rec_tm)]) parts));
167 (*tracing: print the fixedpoint definition*)
168 val dummy = if !Ind_Syntax.trace then
169 writeln (cat_lines (map (Syntax.string_of_term ctxt o #2) axpairs))
172 (*add definitions of the inductive sets*)
175 |> Sign.add_path big_rec_base_name
176 |> PureThy.add_defs false (map (Thm.no_attributes o apfst Binding.name) axpairs);
178 val ctxt1 = ProofContext.init thy1;
181 (*fetch fp definitions from the theory*)
182 val big_rec_def::part_rec_defs =
183 map (Thm.get_def thy1)
184 (case rec_names of [_] => rec_names
185 | _ => big_rec_base_name::rec_names);
189 val dummy = writeln " Proving monotonicity...";
192 Goal.prove_global thy1 [] [] (FOLogic.mk_Trueprop (Fp.bnd_mono $ dom_sum $ fp_abs))
194 [rtac (@{thm Collect_subset} RS @{thm bnd_monoI}) 1,
195 REPEAT (ares_tac (@{thms basic_monos} @ monos) 1)]);
197 val dom_subset = standard (big_rec_def RS Fp.subs);
199 val unfold = standard ([big_rec_def, bnd_mono] MRS Fp.Tarski);
202 val dummy = writeln " Proving the introduction rules...";
204 (*Mutual recursion? Helps to derive subset rules for the
209 | _ => standard (@{thm Part_subset} RS @{thm subset_trans});
211 (*To type-check recursive occurrences of the inductive sets, possibly
212 enclosed in some monotonic operator M.*)
214 [dom_subset] RL (asm_rl :: ([Part_trans] RL monos))
217 (*Type-checking is hardest aspect of proof;
218 disjIn selects the correct disjunct after unfolding*)
219 fun intro_tacsf disjIn =
220 [DETERM (stac unfold 1),
221 REPEAT (resolve_tac [@{thm Part_eqI}, @{thm CollectI}] 1),
222 (*Now 2-3 subgoals: typechecking, the disjunction, perhaps equality.*)
224 (*Not ares_tac, since refl must be tried before equality assumptions;
225 backtracking may occur if the premises have extra variables!*)
226 DEPTH_SOLVE_1 (resolve_tac [refl,exI,conjI] 2 APPEND assume_tac 2),
227 (*Now solve the equations like Tcons(a,f) = Inl(?b4)*)
228 rewrite_goals_tac con_defs,
229 REPEAT (rtac @{thm refl} 2),
230 (*Typechecking; this can fail*)
231 if !Ind_Syntax.trace then print_tac "The type-checking subgoal:"
233 REPEAT (FIRSTGOAL ( dresolve_tac rec_typechecks
234 ORELSE' eresolve_tac (asm_rl::@{thm PartE}::@{thm SigmaE2}::
236 ORELSE' hyp_subst_tac)),
237 if !Ind_Syntax.trace then print_tac "The subgoal after monos, type_elims:"
239 DEPTH_SOLVE (swap_res_tac (@{thm SigmaI}::@{thm subsetI}::type_intrs) 1)];
241 (*combines disjI1 and disjI2 to get the corresponding nested disjunct...*)
242 val mk_disj_rls = BalancedTree.accesses
243 {left = fn rl => rl RS @{thm disjI1},
244 right = fn rl => rl RS @{thm disjI2},
245 init = @{thm asm_rl}};
248 (intr_tms, map intro_tacsf (mk_disj_rls (length intr_tms)))
249 |> ListPair.map (fn (t, tacs) =>
250 Goal.prove_global thy1 [] [] t
251 (fn _ => EVERY (rewrite_goals_tac part_rec_defs :: tacs)))
252 handle MetaSimplifier.SIMPLIFIER (msg, thm) => (Display.print_thm thm; error msg);
255 val dummy = writeln " Proving the elimination rule...";
257 (*Breaks down logical connectives in the monotonic function*)
259 REPEAT (SOMEGOAL (eresolve_tac (Ind_Syntax.elim_rls @ Su.free_SEs)
260 ORELSE' bound_hyp_subst_tac))
261 THEN prune_params_tac
262 (*Mutual recursion: collapse references to Part(D,h)*)
263 THEN (PRIMITIVE (fold_rule part_rec_defs));
266 val elim = rule_by_tactic basic_elim_tac
267 (unfold RS Ind_Syntax.equals_CollectD)
269 (*Applies freeness of the given constructors, which *must* be unfolded by
270 the given defs. Cannot simply use the local con_defs because
271 con_defs=[] for inference systems.
272 Proposition A should have the form t:Si where Si is an inductive set*)
273 fun make_cases ss A =
275 (basic_elim_tac THEN ALLGOALS (asm_full_simp_tac ss) THEN basic_elim_tac)
276 (Thm.assume A RS elim)
278 fun mk_cases a = make_cases (*delayed evaluation of body!*)
280 let val thy = Thm.theory_of_thm elim in cterm_of thy (Syntax.read_prop_global thy a) end;
282 fun induction_rules raw_induct thy =
284 val dummy = writeln " Proving the induction rule...";
286 (*** Prove the main induction rule ***)
288 val pred_name = "P"; (*name for predicate variables*)
290 (*Used to make induction rules;
291 ind_alist = [(rec_tm1,pred1),...] associates predicates with rec ops
292 prem is a premise of an intr rule*)
293 fun add_induct_prem ind_alist (prem as Const (@{const_name Trueprop}, _) $
294 (Const (@{const_name mem}, _) $ t $ X), iprems) =
295 (case AList.lookup (op aconv) ind_alist X of
296 SOME pred => prem :: FOLogic.mk_Trueprop (pred $ t) :: iprems
297 | NONE => (*possibly membership in M(rec_tm), for M monotone*)
298 let fun mk_sb (rec_tm,pred) =
299 (rec_tm, @{const Collect} $ rec_tm $ pred)
300 in subst_free (map mk_sb ind_alist) prem :: iprems end)
301 | add_induct_prem ind_alist (prem,iprems) = prem :: iprems;
303 (*Make a premise of the induction rule.*)
304 fun induct_prem ind_alist intr =
305 let val quantfrees = map dest_Free (OldTerm.term_frees intr \\ rec_params)
306 val iprems = foldr (add_induct_prem ind_alist) []
307 (Logic.strip_imp_prems intr)
308 val (t,X) = Ind_Syntax.rule_concl intr
309 val (SOME pred) = AList.lookup (op aconv) ind_alist X
310 val concl = FOLogic.mk_Trueprop (pred $ t)
311 in list_all_free (quantfrees, Logic.list_implies (iprems,concl)) end
312 handle Bind => error"Recursion term not found in conclusion";
314 (*Minimizes backtracking by delivering the correct premise to each goal.
315 Intro rules with extra Vars in premises still cause some backtracking *)
316 fun ind_tac [] 0 = all_tac
317 | ind_tac(prem::prems) i =
318 DEPTH_SOLVE_1 (ares_tac [prem, refl] i) THEN ind_tac prems (i-1);
320 val pred = Free(pred_name, Ind_Syntax.iT --> FOLogic.oT);
322 val ind_prems = map (induct_prem (map (rpair pred) rec_tms))
325 val dummy = if !Ind_Syntax.trace then
326 (writeln "ind_prems = ";
327 List.app (writeln o Syntax.string_of_term ctxt1) ind_prems;
328 writeln "raw_induct = "; Display.print_thm raw_induct)
332 (*We use a MINIMAL simpset. Even FOL_ss contains too many simpules.
333 If the premises get simplified, then the proofs could fail.*)
334 val min_ss = Simplifier.theory_context thy empty_ss
335 setmksimps (map mk_eq o ZF_atomize o gen_all)
336 setSolver (mk_solver "minimal"
337 (fn prems => resolve_tac (triv_rls@prems)
339 ORELSE' etac FalseE));
342 Goal.prove_global thy1 [] ind_prems
343 (FOLogic.mk_Trueprop (Ind_Syntax.mk_all_imp (big_rec_tm, pred)))
344 (fn {prems, ...} => EVERY
345 [rewrite_goals_tac part_rec_defs,
346 rtac (@{thm impI} RS @{thm allI}) 1,
347 DETERM (etac raw_induct 1),
348 (*Push Part inside Collect*)
349 full_simp_tac (min_ss addsimps [@{thm Part_Collect}]) 1,
350 (*This CollectE and disjE separates out the introduction rules*)
351 REPEAT (FIRSTGOAL (eresolve_tac [@{thm CollectE}, @{thm disjE}])),
352 (*Now break down the individual cases. No disjE here in case
353 some premise involves disjunction.*)
354 REPEAT (FIRSTGOAL (eresolve_tac [@{thm CollectE}, @{thm exE}, @{thm conjE}]
355 ORELSE' bound_hyp_subst_tac)),
356 ind_tac (rev (map (rewrite_rule part_rec_defs) prems)) (length prems)]);
358 val dummy = if !Ind_Syntax.trace then
359 (writeln "quant_induct = "; Display.print_thm quant_induct)
363 (*** Prove the simultaneous induction rule ***)
365 (*Make distinct predicates for each inductive set*)
367 (*The components of the element type, several if it is a product*)
368 val elem_type = CP.pseudo_type dom_sum;
369 val elem_factors = CP.factors elem_type;
370 val elem_frees = mk_frees "za" elem_factors;
371 val elem_tuple = CP.mk_tuple Pr.pair elem_type elem_frees;
373 (*Given a recursive set and its domain, return the "fsplit" predicate
374 and a conclusion for the simultaneous induction rule.
375 NOTE. This will not work for mutually recursive predicates. Previously
376 a summand 'domt' was also an argument, but this required the domain of
377 mutual recursion to invariably be a disjoint sum.*)
378 fun mk_predpair rec_tm =
379 let val rec_name = (#1 o dest_Const o head_of) rec_tm
380 val pfree = Free(pred_name ^ "_" ^ Sign.base_name rec_name,
381 elem_factors ---> FOLogic.oT)
385 (@{const mem} $ elem_tuple $ rec_tm)
386 $ (list_comb (pfree, elem_frees))) elem_frees
387 in (CP.ap_split elem_type FOLogic.oT pfree,
391 val (preds,qconcls) = split_list (map mk_predpair rec_tms);
393 (*Used to form simultaneous induction lemma*)
394 fun mk_rec_imp (rec_tm,pred) =
395 FOLogic.imp $ (@{const mem} $ Bound 0 $ rec_tm) $
398 (*To instantiate the main induction rule*)
401 (Ind_Syntax.mk_all_imp
403 Abs("z", Ind_Syntax.iT,
404 BalancedTree.make FOLogic.mk_conj
405 (ListPair.map mk_rec_imp (rec_tms, preds)))))
406 and mutual_induct_concl =
407 FOLogic.mk_Trueprop(BalancedTree.make FOLogic.mk_conj qconcls);
409 val dummy = if !Ind_Syntax.trace then
410 (writeln ("induct_concl = " ^
411 Syntax.string_of_term ctxt1 induct_concl);
412 writeln ("mutual_induct_concl = " ^
413 Syntax.string_of_term ctxt1 mutual_induct_concl))
417 val lemma_tac = FIRST' [eresolve_tac [@{thm asm_rl}, @{thm conjE}, @{thm PartE}, @{thm mp}],
418 resolve_tac [@{thm allI}, @{thm impI}, @{thm conjI}, @{thm Part_eqI}],
419 dresolve_tac [@{thm spec}, @{thm mp}, Pr.fsplitD]];
421 val need_mutual = length rec_names > 1;
423 val lemma = (*makes the link between the two induction rules*)
425 (writeln " Proving the mutual induction rule...";
426 Goal.prove_global thy1 [] []
427 (Logic.mk_implies (induct_concl, mutual_induct_concl))
429 [rewrite_goals_tac part_rec_defs,
430 REPEAT (rewrite_goals_tac [Pr.split_eq] THEN lemma_tac 1)]))
431 else (writeln " [ No mutual induction rule needed ]"; @{thm TrueI});
433 val dummy = if !Ind_Syntax.trace then
434 (writeln "lemma = "; Display.print_thm lemma)
438 (*Mutual induction follows by freeness of Inl/Inr.*)
440 (*Simplification largely reduces the mutual induction rule to the
443 min_ss addsimps [Su.distinct, Su.distinct', Su.inl_iff, Su.inr_iff];
445 val all_defs = con_defs @ part_rec_defs;
447 (*Removes Collects caused by M-operators in the intro rules. It is very
449 list({v: tf. (v : t --> P_t(v)) & (v : f --> P_f(v))})
450 where t==Part(tf,Inl) and f==Part(tf,Inr) to list({v: tf. P_t(v)}).
451 Instead the following rules extract the relevant conjunct.
453 val cmonos = [@{thm subset_refl} RS @{thm Collect_mono}] RL monos
454 RLN (2,[@{thm rev_subsetD}]);
456 (*Minimizes backtracking by delivering the correct premise to each goal*)
457 fun mutual_ind_tac [] 0 = all_tac
458 | mutual_ind_tac(prem::prems) i =
462 (*Simplify the assumptions and goal by unfolding Part and
463 using freeness of the Sum constructors; proves all but one
464 conjunct by contradiction*)
465 rewrite_goals_tac all_defs THEN
466 simp_tac (mut_ss addsimps [@{thm Part_iff}]) 1 THEN
467 IF_UNSOLVED (*simp_tac may have finished it off!*)
468 ((*simplify assumptions*)
469 (*some risk of excessive simplification here -- might have
470 to identify the bare minimum set of rewrites*)
472 (mut_ss addsimps @{thms conj_simps} @ @{thms imp_simps} @ @{thms quant_simps}) 1
474 (*unpackage and use "prem" in the corresponding place*)
475 REPEAT (rtac impI 1) THEN
476 rtac (rewrite_rule all_defs prem) 1 THEN
477 (*prem must not be REPEATed below: could loop!*)
478 DEPTH_SOLVE (FIRSTGOAL (ares_tac [impI] ORELSE'
479 eresolve_tac (conjE::mp::cmonos))))
481 THEN mutual_ind_tac prems (i-1);
483 val mutual_induct_fsplit =
485 Goal.prove_global thy1 [] (map (induct_prem (rec_tms~~preds)) intr_tms)
487 (fn {prems, ...} => EVERY
488 [rtac (quant_induct RS lemma) 1,
489 mutual_ind_tac (rev prems) (length prems)])
492 (** Uncurrying the predicate in the ordinary induction rule **)
494 (*instantiate the variable to a tuple, if it is non-trivial, in order to
495 allow the predicate to be "opened up".
496 The name "x.1" comes from the "RS spec" !*)
498 case elem_frees of [_] => I
499 | _ => instantiate ([], [(cterm_of thy1 (Var(("x",1), Ind_Syntax.iT)),
500 cterm_of thy1 elem_tuple)]);
502 (*strip quantifier and the implication*)
503 val induct0 = inst (quant_induct RS spec RSN (2, @{thm rev_mp}));
505 val Const (@{const_name Trueprop}, _) $ (pred_var $ _) = concl_of induct0
507 val induct = CP.split_rule_var(pred_var, elem_type-->FOLogic.oT, induct0)
509 and mutual_induct = CP.remove_split mutual_induct_fsplit
511 val ([induct', mutual_induct'], thy') =
513 |> PureThy.add_thms [((Binding.name (co_prefix ^ "induct"), induct),
514 [case_names, Induct.induct_pred big_rec_name]),
515 ((Binding.name "mutual_induct", mutual_induct), [case_names])];
516 in ((thy', induct'), mutual_induct')
517 end; (*of induction_rules*)
519 val raw_induct = standard ([big_rec_def, bnd_mono] MRS Fp.induct)
521 val ((thy2, induct), mutual_induct) =
522 if not coind then induction_rules raw_induct thy1
525 |> PureThy.add_thms [((Binding.name (co_prefix ^ "induct"), raw_induct), [])]
526 |> apfst hd |> Library.swap, TrueI)
527 and defs = big_rec_def :: part_rec_defs
530 val (([bnd_mono', dom_subset', elim'], [defs', intrs']), thy3) =
532 |> IndCases.declare big_rec_name make_cases
534 [((Binding.name "bnd_mono", bnd_mono), []),
535 ((Binding.name "dom_subset", dom_subset), []),
536 ((Binding.name "cases", elim), [case_names, Induct.cases_pred big_rec_name])]
537 ||>> (PureThy.add_thmss o map Thm.no_attributes)
538 [(Binding.name "defs", defs),
539 (Binding.name "intros", intrs)];
540 val (intrs'', thy4) =
542 |> PureThy.add_thms ((map Binding.name intr_names ~~ intrs') ~~ map #2 intr_specs)
543 ||> Sign.parent_path;
547 bnd_mono = bnd_mono',
548 dom_subset = dom_subset',
553 mutual_induct = mutual_induct})
557 fun add_inductive (srec_tms, sdom_sum) intr_srcs
558 (raw_monos, raw_con_defs, raw_type_intrs, raw_type_elims) thy =
560 val ctxt = ProofContext.init thy;
561 val read_terms = map (Syntax.parse_term ctxt #> TypeInfer.constrain Ind_Syntax.iT)
562 #> Syntax.check_terms ctxt;
564 val intr_atts = map (map (Attrib.attribute thy) o snd) intr_srcs;
565 val sintrs = map fst intr_srcs ~~ intr_atts;
566 val rec_tms = read_terms srec_tms;
567 val dom_sum = singleton read_terms sdom_sum;
568 val intr_tms = Syntax.read_props ctxt (map (snd o fst) sintrs);
569 val intr_specs = (map (fst o fst) sintrs ~~ intr_tms) ~~ map snd sintrs;
570 val monos = Attrib.eval_thms ctxt raw_monos;
571 val con_defs = Attrib.eval_thms ctxt raw_con_defs;
572 val type_intrs = Attrib.eval_thms ctxt raw_type_intrs;
573 val type_elims = Attrib.eval_thms ctxt raw_type_elims;
576 |> add_inductive_i true (rec_tms, dom_sum) intr_specs (monos, con_defs, type_intrs, type_elims)
582 local structure P = OuterParse and K = OuterKeyword in
584 val _ = List.app OuterKeyword.keyword
585 ["domains", "intros", "monos", "con_defs", "type_intros", "type_elims"];
587 fun mk_ind (((((doms, intrs), monos), con_defs), type_intrs), type_elims) =
588 #1 o add_inductive doms (map P.triple_swap intrs) (monos, con_defs, type_intrs, type_elims);
591 (P.$$$ "domains" |-- P.!!! (P.enum1 "+" P.term --
592 ((P.$$$ "\<subseteq>" || P.$$$ "<=") |-- P.term))) --
594 P.!!! (Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop))) --
595 Scan.optional (P.$$$ "monos" |-- P.!!! SpecParse.xthms1) [] --
596 Scan.optional (P.$$$ "con_defs" |-- P.!!! SpecParse.xthms1) [] --
597 Scan.optional (P.$$$ "type_intros" |-- P.!!! SpecParse.xthms1) [] --
598 Scan.optional (P.$$$ "type_elims" |-- P.!!! SpecParse.xthms1) []
599 >> (Toplevel.theory o mk_ind);
601 val _ = OuterSyntax.command (co_prefix ^ "inductive")
602 ("define " ^ co_prefix ^ "inductive sets") K.thy_decl ind_decl;