src/HOL/Tools/inductive_package.ML
 author wenzelm Tue Jan 12 13:54:51 1999 +0100 (1999-01-12) changeset 6092 d9db67970c73 parent 5891 92e0f5e6fd17 child 6141 a6922171b396 permissions -rw-r--r--
eliminated tthm type and Attribute structure;
1 (*  Title:      HOL/Tools/inductive_package.ML
2     ID:         \$Id\$
3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
4                 Stefan Berghofer,   TU Muenchen
5     Copyright   1994  University of Cambridge
6                 1998  TU Muenchen
8 (Co)Inductive Definition module for HOL
10 Features:
11 * least or greatest fixedpoints
12 * user-specified product and sum constructions
13 * mutually recursive definitions
14 * definitions involving arbitrary monotone operators
15 * automatically proves introduction and elimination rules
17 The recursive sets must *already* be declared as constants in parent theory!
19   Introduction rules have the form
20   [| ti:M(Sj), ..., P(x), ... |] ==> t: Sk |]
21   where M is some monotone operator (usually the identity)
22   P(x) is any side condition on the free variables
23   ti, t are any terms
24   Sj, Sk are two of the sets being defined in mutual recursion
26 Sums are used only for mutual recursion;
27 Products are used only to derive "streamlined" induction rules for relations
28 *)
30 signature INDUCTIVE_PACKAGE =
31 sig
32   val quiet_mode : bool ref
33   val add_inductive_i : bool -> bool -> bstring -> bool -> bool -> bool -> term list ->
34     term list -> thm list -> thm list -> theory -> theory *
35       {defs:thm list, elims:thm list, raw_induct:thm, induct:thm,
36        intrs:thm list,
37        mk_cases:thm list -> string -> thm, mono:thm,
38        unfold:thm}
39   val add_inductive : bool -> bool -> string list -> string list
40     -> xstring list -> xstring list -> theory -> theory *
41       {defs:thm list, elims:thm list, raw_induct:thm, induct:thm,
42        intrs:thm list,
43        mk_cases:thm list -> string -> thm, mono:thm,
44        unfold:thm}
45 end;
47 structure InductivePackage : INDUCTIVE_PACKAGE =
48 struct
50 val quiet_mode = ref false;
51 fun message s = if !quiet_mode then () else writeln s;
53 (*For proving monotonicity of recursion operator*)
54 val basic_monos = [subset_refl, imp_refl, disj_mono, conj_mono,
55                    ex_mono, Collect_mono, in_mono, vimage_mono];
57 val Const _ \$ (vimage_f \$ _) \$ _ = HOLogic.dest_Trueprop (concl_of vimageD);
59 (*Delete needless equality assumptions*)
60 val refl_thin = prove_goal HOL.thy "!!P. [| a=a;  P |] ==> P"
61      (fn _ => [assume_tac 1]);
63 (*For simplifying the elimination rule*)
64 val elim_rls = [asm_rl, FalseE, refl_thin, conjE, exE, Pair_inject];
66 val vimage_name = Sign.intern_const (sign_of Vimage.thy) "op -``";
67 val mono_name = Sign.intern_const (sign_of Ord.thy) "mono";
69 (* make injections needed in mutually recursive definitions *)
71 fun mk_inj cs sumT c x =
72   let
73     fun mk_inj' T n i =
74       if n = 1 then x else
75       let val n2 = n div 2;
76           val Type (_, [T1, T2]) = T
77       in
78         if i <= n2 then
79           Const ("Inl", T1 --> T) \$ (mk_inj' T1 n2 i)
80         else
81           Const ("Inr", T2 --> T) \$ (mk_inj' T2 (n - n2) (i - n2))
82       end
83   in mk_inj' sumT (length cs) (1 + find_index_eq c cs)
84   end;
86 (* make "vimage" terms for selecting out components of mutually rec.def. *)
88 fun mk_vimage cs sumT t c = if length cs < 2 then t else
89   let
90     val cT = HOLogic.dest_setT (fastype_of c);
91     val vimageT = [cT --> sumT, HOLogic.mk_setT sumT] ---> HOLogic.mk_setT cT
92   in
93     Const (vimage_name, vimageT) \$
94       Abs ("y", cT, mk_inj cs sumT c (Bound 0)) \$ t
95   end;
97 (**************************** well-formedness checks **************************)
99 fun err_in_rule sign t msg = error ("Ill-formed introduction rule\n" ^
100   (Sign.string_of_term sign t) ^ "\n" ^ msg);
102 fun err_in_prem sign t p msg = error ("Ill-formed premise\n" ^
103   (Sign.string_of_term sign p) ^ "\nin introduction rule\n" ^
104   (Sign.string_of_term sign t) ^ "\n" ^ msg);
106 val msg1 = "Conclusion of introduction rule must have form\
107           \ ' t : S_i '";
108 val msg2 = "Premises mentioning recursive sets must have form\
109           \ ' t : M S_i '";
110 val msg3 = "Recursion term on left of member symbol";
112 fun check_rule sign cs r =
113   let
114     fun check_prem prem = if exists (Logic.occs o (rpair prem)) cs then
115          (case prem of
116            (Const ("op :", _) \$ t \$ u) =>
117              if exists (Logic.occs o (rpair t)) cs then
118                err_in_prem sign r prem msg3 else ()
119          | _ => err_in_prem sign r prem msg2)
120         else ()
122   in (case (HOLogic.dest_Trueprop o Logic.strip_imp_concl) r of
123         (Const ("op :", _) \$ _ \$ u) =>
124           if u mem cs then map (check_prem o HOLogic.dest_Trueprop)
125             (Logic.strip_imp_prems r)
126           else err_in_rule sign r msg1
127       | _ => err_in_rule sign r msg1)
128   end;
130 fun try' f msg sign t = (f t) handle _ => error (msg ^ Sign.string_of_term sign t);
132 (*********************** properties of (co)inductive sets *********************)
134 (***************************** elimination rules ******************************)
136 fun mk_elims cs cTs params intr_ts =
137   let
138     val used = foldr add_term_names (intr_ts, []);
139     val [aname, pname] = variantlist (["a", "P"], used);
140     val P = HOLogic.mk_Trueprop (Free (pname, HOLogic.boolT));
142     fun dest_intr r =
143       let val Const ("op :", _) \$ t \$ u =
144         HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
145       in (u, t, Logic.strip_imp_prems r) end;
147     val intrs = map dest_intr intr_ts;
149     fun mk_elim (c, T) =
150       let
151         val a = Free (aname, T);
153         fun mk_elim_prem (_, t, ts) =
154           list_all_free (map dest_Free ((foldr add_term_frees (t::ts, [])) \\ params),
155             Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (a, t)) :: ts, P));
156       in
157         Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (a, c)) ::
158           map mk_elim_prem (filter (equal c o #1) intrs), P)
159       end
160   in
161     map mk_elim (cs ~~ cTs)
162   end;
164 (***************** premises and conclusions of induction rules ****************)
166 fun mk_indrule cs cTs params intr_ts =
167   let
168     val used = foldr add_term_names (intr_ts, []);
170     (* predicates for induction rule *)
172     val preds = map Free (variantlist (if length cs < 2 then ["P"] else
173       map (fn i => "P" ^ string_of_int i) (1 upto length cs), used) ~~
174         map (fn T => T --> HOLogic.boolT) cTs);
176     (* transform an introduction rule into a premise for induction rule *)
178     fun mk_ind_prem r =
179       let
180         val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
182         fun subst (prem as (Const ("op :", T) \$ t \$ u), prems) =
183               let val n = find_index_eq u cs in
184                 if n >= 0 then prem :: (nth_elem (n, preds)) \$ t :: prems else
185                   (subst_free (map (fn (c, P) => (c, HOLogic.mk_binop "op Int"
186                     (c, HOLogic.Collect_const (HOLogic.dest_setT
187                       (fastype_of c)) \$ P))) (cs ~~ preds)) prem)::prems
188               end
189           | subst (prem, prems) = prem::prems;
191         val Const ("op :", _) \$ t \$ u =
192           HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
194       in list_all_free (frees,
195            Logic.list_implies (map HOLogic.mk_Trueprop (foldr subst
196              (map HOLogic.dest_Trueprop (Logic.strip_imp_prems r), [])),
197                HOLogic.mk_Trueprop (nth_elem (find_index_eq u cs, preds) \$ t)))
198       end;
200     val ind_prems = map mk_ind_prem intr_ts;
202     (* make conclusions for induction rules *)
204     fun mk_ind_concl ((c, P), (ts, x)) =
205       let val T = HOLogic.dest_setT (fastype_of c);
206           val Ts = HOLogic.prodT_factors T;
207           val (frees, x') = foldr (fn (T', (fs, s)) =>
208             ((Free (s, T'))::fs, bump_string s)) (Ts, ([], x));
209           val tuple = HOLogic.mk_tuple T frees;
210       in ((HOLogic.mk_binop "op -->"
211         (HOLogic.mk_mem (tuple, c), P \$ tuple))::ts, x')
212       end;
214     val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 (app HOLogic.conj)
215         (fst (foldr mk_ind_concl (cs ~~ preds, ([], "xa")))))
217   in (preds, ind_prems, mutual_ind_concl)
218   end;
220 (********************** proofs for (co)inductive sets *************************)
222 (**************************** prove monotonicity ******************************)
224 fun prove_mono setT fp_fun monos thy =
225   let
226     val _ = message "  Proving monotonicity...";
228     val mono = prove_goalw_cterm [] (cterm_of (sign_of thy) (HOLogic.mk_Trueprop
229       (Const (mono_name, (setT --> setT) --> HOLogic.boolT) \$ fp_fun)))
230         (fn _ => [rtac monoI 1, REPEAT (ares_tac (basic_monos @ monos) 1)])
232   in mono end;
234 (************************* prove introduction rules ***************************)
236 fun prove_intrs coind mono fp_def intr_ts con_defs rec_sets_defs thy =
237   let
238     val _ = message "  Proving the introduction rules...";
240     val unfold = standard (mono RS (fp_def RS
241       (if coind then def_gfp_Tarski else def_lfp_Tarski)));
243     fun select_disj 1 1 = []
244       | select_disj _ 1 = [rtac disjI1]
245       | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
247     val intrs = map (fn (i, intr) => prove_goalw_cterm rec_sets_defs
248       (cterm_of (sign_of thy) intr) (fn prems =>
249        [(*insert prems and underlying sets*)
250        cut_facts_tac prems 1,
251        stac unfold 1,
252        REPEAT (resolve_tac [vimageI2, CollectI] 1),
253        (*Now 1-2 subgoals: the disjunction, perhaps equality.*)
254        EVERY1 (select_disj (length intr_ts) i),
255        (*Not ares_tac, since refl must be tried before any equality assumptions;
256          backtracking may occur if the premises have extra variables!*)
257        DEPTH_SOLVE_1 (resolve_tac [refl,exI,conjI] 1 APPEND assume_tac 1),
258        (*Now solve the equations like Inl 0 = Inl ?b2*)
259        rewrite_goals_tac con_defs,
260        REPEAT (rtac refl 1)])) (1 upto (length intr_ts) ~~ intr_ts)
262   in (intrs, unfold) end;
264 (*************************** prove elimination rules **************************)
266 fun prove_elims cs cTs params intr_ts unfold rec_sets_defs thy =
267   let
268     val _ = message "  Proving the elimination rules...";
270     val rules1 = [CollectE, disjE, make_elim vimageD];
271     val rules2 = [exE, conjE, Inl_neq_Inr, Inr_neq_Inl] @
272       map make_elim [Inl_inject, Inr_inject];
274     val elims = map (fn t => prove_goalw_cterm rec_sets_defs
275       (cterm_of (sign_of thy) t) (fn prems =>
276         [cut_facts_tac [hd prems] 1,
277          dtac (unfold RS subst) 1,
278          REPEAT (FIRSTGOAL (eresolve_tac rules1)),
279          REPEAT (FIRSTGOAL (eresolve_tac rules2)),
280          EVERY (map (fn prem =>
281            DEPTH_SOLVE_1 (ares_tac [prem, conjI] 1)) (tl prems))]))
282       (mk_elims cs cTs params intr_ts)
284   in elims end;
286 (** derivation of simplified elimination rules **)
288 (*Applies freeness of the given constructors, which *must* be unfolded by
289   the given defs.  Cannot simply use the local con_defs because con_defs=[]
290   for inference systems.
291  *)
292 fun con_elim_tac simps =
293   let val elim_tac = REPEAT o (eresolve_tac elim_rls)
294   in ALLGOALS(EVERY'[elim_tac,
295                  asm_full_simp_tac (simpset_of NatDef.thy addsimps simps),
296                  elim_tac,
297                  REPEAT o bound_hyp_subst_tac])
298      THEN prune_params_tac
299   end;
301 (*String s should have the form t:Si where Si is an inductive set*)
302 fun mk_cases elims simps s =
303   let val prem = assume (read_cterm (sign_of_thm (hd elims)) (s, propT));
304       val elims' = map (try (fn r =>
305         rule_by_tactic (con_elim_tac simps) (prem RS r) |> standard)) elims
306   in case find_first is_some elims' of
307        Some (Some r) => r
308      | None => error ("mk_cases: string '" ^ s ^ "' not of form 't : S_i'")
309   end;
311 (**************************** prove induction rule ****************************)
313 fun prove_indrule cs cTs sumT rec_const params intr_ts mono
314     fp_def rec_sets_defs thy =
315   let
316     val _ = message "  Proving the induction rule...";
318     val sign = sign_of thy;
320     val (preds, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
322     (* make predicate for instantiation of abstract induction rule *)
324     fun mk_ind_pred _ [P] = P
325       | mk_ind_pred T Ps =
326          let val n = (length Ps) div 2;
327              val Type (_, [T1, T2]) = T
328          in Const ("sum_case",
329            [T1 --> HOLogic.boolT, T2 --> HOLogic.boolT, T] ---> HOLogic.boolT) \$
330              mk_ind_pred T1 (take (n, Ps)) \$ mk_ind_pred T2 (drop (n, Ps))
331          end;
333     val ind_pred = mk_ind_pred sumT preds;
335     val ind_concl = HOLogic.mk_Trueprop
336       (HOLogic.all_const sumT \$ Abs ("x", sumT, HOLogic.mk_binop "op -->"
337         (HOLogic.mk_mem (Bound 0, rec_const), ind_pred \$ Bound 0)));
339     (* simplification rules for vimage and Collect *)
341     val vimage_simps = if length cs < 2 then [] else
342       map (fn c => prove_goalw_cterm [] (cterm_of sign
343         (HOLogic.mk_Trueprop (HOLogic.mk_eq
344           (mk_vimage cs sumT (HOLogic.Collect_const sumT \$ ind_pred) c,
345            HOLogic.Collect_const (HOLogic.dest_setT (fastype_of c)) \$
346              nth_elem (find_index_eq c cs, preds)))))
347         (fn _ => [rtac vimage_Collect 1, rewrite_goals_tac
348            (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
349           rtac refl 1])) cs;
351     val induct = prove_goalw_cterm [] (cterm_of sign
352       (Logic.list_implies (ind_prems, ind_concl))) (fn prems =>
353         [rtac (impI RS allI) 1,
354          DETERM (etac (mono RS (fp_def RS def_induct)) 1),
355          rewrite_goals_tac (map mk_meta_eq (vimage_Int::vimage_simps)),
356          fold_goals_tac rec_sets_defs,
357          (*This CollectE and disjE separates out the introduction rules*)
358          REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE])),
359          (*Now break down the individual cases.  No disjE here in case
360            some premise involves disjunction.*)
361          REPEAT (FIRSTGOAL (eresolve_tac [IntE, CollectE, exE, conjE]
362                      ORELSE' hyp_subst_tac)),
363          rewrite_goals_tac (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
364          EVERY (map (fn prem =>
365            DEPTH_SOLVE_1 (ares_tac [prem, conjI, refl] 1)) prems)]);
367     val lemma = prove_goalw_cterm rec_sets_defs (cterm_of sign
368       (Logic.mk_implies (ind_concl, mutual_ind_concl))) (fn prems =>
369         [cut_facts_tac prems 1,
370          REPEAT (EVERY
371            [REPEAT (resolve_tac [conjI, impI] 1),
372             TRY (dtac vimageD 1), etac allE 1, dtac mp 1, atac 1,
373             rewrite_goals_tac (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
374             atac 1])])
376   in standard (split_rule (induct RS lemma))
377   end;
379 (*************** definitional introduction of (co)inductive sets **************)
381 fun add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs
382     intr_ts monos con_defs thy params paramTs cTs cnames =
383   let
384     val _ = if verbose then message ("Proofs for " ^
385       (if coind then "co" else "") ^ "inductive set(s) " ^ commas cnames) else ();
387     val sumT = fold_bal (fn (T, U) => Type ("+", [T, U])) cTs;
388     val setT = HOLogic.mk_setT sumT;
390     val fp_name = if coind then Sign.intern_const (sign_of Gfp.thy) "gfp"
391       else Sign.intern_const (sign_of Lfp.thy) "lfp";
393     val used = foldr add_term_names (intr_ts, []);
394     val [sname, xname] = variantlist (["S", "x"], used);
396     (* transform an introduction rule into a conjunction  *)
397     (*   [| t : ... S_i ... ; ... |] ==> u : S_j          *)
398     (* is transformed into                                *)
399     (*   x = Inj_j u & t : ... Inj_i -`` S ... & ...      *)
401     fun transform_rule r =
402       let
403         val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
404         val subst = subst_free
405           (cs ~~ (map (mk_vimage cs sumT (Free (sname, setT))) cs));
406         val Const ("op :", _) \$ t \$ u =
407           HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
409       in foldr (fn ((x, T), P) => HOLogic.mk_exists (x, T, P))
410         (frees, foldr1 (app HOLogic.conj)
411           (((HOLogic.eq_const sumT) \$ Free (xname, sumT) \$ (mk_inj cs sumT u t))::
412             (map (subst o HOLogic.dest_Trueprop)
413               (Logic.strip_imp_prems r))))
414       end
416     (* make a disjunction of all introduction rules *)
418     val fp_fun = absfree (sname, setT, (HOLogic.Collect_const sumT) \$
419       absfree (xname, sumT, foldr1 (app HOLogic.disj) (map transform_rule intr_ts)));
421     (* add definiton of recursive sets to theory *)
423     val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
424     val full_rec_name = Sign.full_name (sign_of thy) rec_name;
426     val rec_const = list_comb
427       (Const (full_rec_name, paramTs ---> setT), params);
429     val fp_def_term = Logic.mk_equals (rec_const,
430       Const (fp_name, (setT --> setT) --> setT) \$ fp_fun)
432     val def_terms = fp_def_term :: (if length cs < 2 then [] else
433       map (fn c => Logic.mk_equals (c, mk_vimage cs sumT rec_const c)) cs);
435     val thy' = thy |>
436       (if declare_consts then
437         Theory.add_consts_i (map (fn (c, n) =>
438           (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
439        else I) |>
440       (if length cs < 2 then I else
441        Theory.add_consts_i [(rec_name, paramTs ---> setT, NoSyn)]) |>
442       Theory.add_path rec_name |>
443       PureThy.add_defss_i [(("defs", def_terms), [])];
445     (* get definitions from theory *)
447     val fp_def::rec_sets_defs = get_thms thy' "defs";
449     (* prove and store theorems *)
451     val mono = prove_mono setT fp_fun monos thy';
452     val (intrs, unfold) = prove_intrs coind mono fp_def intr_ts con_defs
453       rec_sets_defs thy';
454     val elims = if no_elim then [] else
455       prove_elims cs cTs params intr_ts unfold rec_sets_defs thy';
456     val raw_induct = if no_ind then TrueI else
457       if coind then standard (rule_by_tactic
458         (rewrite_tac [mk_meta_eq vimage_Un] THEN
459           fold_tac rec_sets_defs) (mono RS (fp_def RS def_Collect_coinduct)))
460       else
461         prove_indrule cs cTs sumT rec_const params intr_ts mono fp_def
462           rec_sets_defs thy';
463     val induct = if coind orelse no_ind orelse length cs > 1 then raw_induct
464       else standard (raw_induct RSN (2, rev_mp));
466     val thy'' = thy' |>
467       PureThy.add_thmss [(("intrs", intrs), [])] |>
468       (if no_elim then I else PureThy.add_thmss
469         [(("elims", elims), [])]) |>
470       (if no_ind then I else PureThy.add_thms
471         [(((if coind then "co" else "") ^ "induct", induct), [])]) |>
472       Theory.parent_path;
474   in (thy'',
475     {defs = fp_def::rec_sets_defs,
476      mono = mono,
477      unfold = unfold,
478      intrs = intrs,
479      elims = elims,
480      mk_cases = mk_cases elims,
481      raw_induct = raw_induct,
482      induct = induct})
483   end;
485 (***************** axiomatic introduction of (co)inductive sets ***************)
487 fun add_ind_axm verbose declare_consts alt_name coind no_elim no_ind cs
488     intr_ts monos con_defs thy params paramTs cTs cnames =
489   let
490     val _ = if verbose then message ("Adding axioms for " ^
491       (if coind then "co" else "") ^ "inductive set(s) " ^ commas cnames) else ();
493     val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
495     val elim_ts = mk_elims cs cTs params intr_ts;
497     val (_, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
498     val ind_t = Logic.list_implies (ind_prems, mutual_ind_concl);
500     val thy' = thy |>
501       (if declare_consts then
502         Theory.add_consts_i (map (fn (c, n) =>
503           (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
504        else I) |>
505       Theory.add_path rec_name |>
506       PureThy.add_axiomss_i [(("intrs", intr_ts), []), (("elims", elim_ts), [])] |>
507       (if coind then I
508        else PureThy.add_axioms_i [(("internal_induct", ind_t), [])]);
510     val intrs = get_thms thy' "intrs";
511     val elims = get_thms thy' "elims";
512     val raw_induct = if coind then TrueI else
513       standard (split_rule (get_thm thy' "internal_induct"));
514     val induct = if coind orelse length cs > 1 then raw_induct
515       else standard (raw_induct RSN (2, rev_mp));
517     val thy'' = thy' |>
518       (if coind then I
519        else PureThy.add_thms [(("induct", induct), [])]) |>
520       Theory.parent_path
522   in (thy'',
523     {defs = [],
524      mono = TrueI,
525      unfold = TrueI,
526      intrs = intrs,
527      elims = elims,
528      mk_cases = mk_cases elims,
529      raw_induct = raw_induct,
530      induct = induct})
531   end;
533 (********************** introduction of (co)inductive sets ********************)
535 fun add_inductive_i verbose declare_consts alt_name coind no_elim no_ind cs
536     intr_ts monos con_defs thy =
537   let
538     val _ = Theory.requires thy "Inductive"
539       ((if coind then "co" else "") ^ "inductive definitions");
541     val sign = sign_of thy;
543     (*parameters should agree for all mutually recursive components*)
544     val (_, params) = strip_comb (hd cs);
545     val paramTs = map (try' (snd o dest_Free) "Parameter in recursive\
546       \ component is not a free variable: " sign) params;
548     val cTs = map (try' (HOLogic.dest_setT o fastype_of)
549       "Recursive component not of type set: " sign) cs;
551     val cnames = map (try' (Sign.base_name o fst o dest_Const o head_of)
552       "Recursive set not previously declared as constant: " sign) cs;
554     val _ = assert_all Syntax.is_identifier cnames
555        (fn a => "Base name of recursive set not an identifier: " ^ a);
557     val _ = map (check_rule sign cs) intr_ts;
559   in
560     (if !quick_and_dirty then add_ind_axm else add_ind_def)
561       verbose declare_consts alt_name coind no_elim no_ind cs intr_ts monos
562         con_defs thy params paramTs cTs cnames
563   end;
565 (***************************** external interface *****************************)
567 fun add_inductive verbose coind c_strings intr_strings monos con_defs thy =
568   let
569     val sign = sign_of thy;
570     val cs = map (readtm (sign_of thy) HOLogic.termTVar) c_strings;
571     val intr_ts = map (readtm (sign_of thy) propT) intr_strings;
573     (* the following code ensures that each recursive set *)
574     (* always has the same type in all introduction rules *)
576     val {tsig, ...} = Sign.rep_sg sign;
577     val add_term_consts_2 =
578       foldl_aterms (fn (cs, Const c) => c ins cs | (cs, _) => cs);
579     fun varify (t, (i, ts)) =
580       let val t' = map_term_types (incr_tvar (i + 1)) (Type.varify (t, []))
581       in (maxidx_of_term t', t'::ts) end;
582     val (i, cs') = foldr varify (cs, (~1, []));
583     val (i', intr_ts') = foldr varify (intr_ts, (i, []));
584     val rec_consts = foldl add_term_consts_2 ([], cs');
585     val intr_consts = foldl add_term_consts_2 ([], intr_ts');
586     fun unify (env, (cname, cT)) =
587       let val consts = map snd (filter (fn c => fst c = cname) intr_consts)
588       in (foldl (fn ((env', j'), Tp) => Type.unify tsig j' env' Tp)
589         (env, (replicate (length consts) cT) ~~ consts)) handle _ =>
590           error ("Occurrences of constant '" ^ cname ^
591             "' have incompatible types")
592       end;
593     val (env, _) = foldl unify (([], i'), rec_consts);
594     fun typ_subst_TVars_2 env T = let val T' = typ_subst_TVars env T
595       in if T = T' then T else typ_subst_TVars_2 env T' end;
596     val subst = fst o Type.freeze_thaw o
597       (map_term_types (typ_subst_TVars_2 env));
598     val cs'' = map subst cs';
599     val intr_ts'' = map subst intr_ts';
601   in add_inductive_i verbose false "" coind false false cs'' intr_ts''
602     (PureThy.get_thmss thy monos)
603     (PureThy.get_thmss thy con_defs) thy
604   end;
606 end;