src/HOL/Tools/inductive_package.ML
 author wenzelm Mon Jun 28 21:48:36 1999 +0200 (1999-06-28) changeset 6851 526c0b90bcef parent 6729 b6e167580a32 child 7020 75ff179df7b7 permissions -rw-r--r--
cond_extern_table;
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 the
18 current theory!
20   Introduction rules have the form
21   [| ti:M(Sj), ..., P(x), ... |] ==> t: Sk |]
22   where M is some monotone operator (usually the identity)
23   P(x) is any side condition on the free variables
24   ti, t are any terms
25   Sj, Sk are two of the sets being defined in mutual recursion
27 Sums are used only for mutual recursion.  Products are used only to
28 derive "streamlined" induction rules for relations.
29 *)
31 signature INDUCTIVE_PACKAGE =
32 sig
33   val quiet_mode: bool ref
34   val get_inductive: theory -> string ->
35     {names: string list, coind: bool} * {defs: thm list, elims: thm list, raw_induct: thm,
36       induct: thm, intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}
37   val print_inductives: theory -> unit
38   val add_inductive_i: bool -> bool -> bstring -> bool -> bool -> bool -> term list ->
39     theory attribute list -> ((bstring * term) * theory attribute list) list ->
40       thm list -> thm list -> theory -> theory *
41       {defs: thm list, elims: thm list, raw_induct: thm, induct: thm,
42        intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}
43   val add_inductive: bool -> bool -> string list -> Args.src list ->
44     ((bstring * string) * Args.src list) list -> (xstring * Args.src list) list ->
45       (xstring * Args.src list) list -> theory -> theory *
46       {defs: thm list, elims: thm list, raw_induct: thm, induct: thm,
47        intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}
48   val setup: (theory -> theory) list
49 end;
51 structure InductivePackage: INDUCTIVE_PACKAGE =
52 struct
54 (** utilities **)
56 (* messages *)
58 val quiet_mode = ref false;
59 fun message s = if !quiet_mode then () else writeln s;
61 fun coind_prefix true = "co"
62   | coind_prefix false = "";
65 (* misc *)
67 (*For proving monotonicity of recursion operator*)
68 val basic_monos = [subset_refl, imp_refl, disj_mono, conj_mono,
69                    ex_mono, Collect_mono, in_mono, vimage_mono];
71 val Const _ \$ (vimage_f \$ _) \$ _ = HOLogic.dest_Trueprop (concl_of vimageD);
73 (*Delete needless equality assumptions*)
74 val refl_thin = prove_goal HOL.thy "!!P. [| a=a;  P |] ==> P"
75      (fn _ => [assume_tac 1]);
77 (*For simplifying the elimination rule*)
78 val elim_rls = [asm_rl, FalseE, refl_thin, conjE, exE, Pair_inject];
80 val vimage_name = Sign.intern_const (Theory.sign_of Vimage.thy) "op -``";
81 val mono_name = Sign.intern_const (Theory.sign_of Ord.thy) "mono";
83 (* make injections needed in mutually recursive definitions *)
85 fun mk_inj cs sumT c x =
86   let
87     fun mk_inj' T n i =
88       if n = 1 then x else
89       let val n2 = n div 2;
90           val Type (_, [T1, T2]) = T
91       in
92         if i <= n2 then
93           Const ("Inl", T1 --> T) \$ (mk_inj' T1 n2 i)
94         else
95           Const ("Inr", T2 --> T) \$ (mk_inj' T2 (n - n2) (i - n2))
96       end
97   in mk_inj' sumT (length cs) (1 + find_index_eq c cs)
98   end;
100 (* make "vimage" terms for selecting out components of mutually rec.def. *)
102 fun mk_vimage cs sumT t c = if length cs < 2 then t else
103   let
104     val cT = HOLogic.dest_setT (fastype_of c);
105     val vimageT = [cT --> sumT, HOLogic.mk_setT sumT] ---> HOLogic.mk_setT cT
106   in
107     Const (vimage_name, vimageT) \$
108       Abs ("y", cT, mk_inj cs sumT c (Bound 0)) \$ t
109   end;
113 (** well-formedness checks **)
115 fun err_in_rule sign t msg = error ("Ill-formed introduction rule\n" ^
116   (Sign.string_of_term sign t) ^ "\n" ^ msg);
118 fun err_in_prem sign t p msg = error ("Ill-formed premise\n" ^
119   (Sign.string_of_term sign p) ^ "\nin introduction rule\n" ^
120   (Sign.string_of_term sign t) ^ "\n" ^ msg);
122 val msg1 = "Conclusion of introduction rule must have form\
123           \ ' t : S_i '";
124 val msg2 = "Premises mentioning recursive sets must have form\
125           \ ' t : M S_i '";
126 val msg3 = "Recursion term on left of member symbol";
128 fun check_rule sign cs r =
129   let
130     fun check_prem prem = if exists (Logic.occs o (rpair prem)) cs then
131          (case prem of
132            (Const ("op :", _) \$ t \$ u) =>
133              if exists (Logic.occs o (rpair t)) cs then
134                err_in_prem sign r prem msg3 else ()
135          | _ => err_in_prem sign r prem msg2)
136         else ()
138   in (case (HOLogic.dest_Trueprop o Logic.strip_imp_concl) r of
139         (Const ("op :", _) \$ _ \$ u) =>
140           if u mem cs then seq (check_prem o HOLogic.dest_Trueprop)
141             (Logic.strip_imp_prems r)
142           else err_in_rule sign r msg1
143       | _ => err_in_rule sign r msg1)
144   end;
146 fun try' f msg sign t = (f t) handle _ => error (msg ^ Sign.string_of_term sign t);
150 (*** theory data ***)
152 (* data kind 'HOL/inductive' *)
154 type inductive_info =
155   {names: string list, coind: bool} * {defs: thm list, elims: thm list, raw_induct: thm,
156     induct: thm, intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm};
158 structure InductiveArgs =
159 struct
160   val name = "HOL/inductive";
161   type T = inductive_info Symtab.table;
163   val empty = Symtab.empty;
164   val copy = I;
165   val prep_ext = I;
166   val merge: T * T -> T = Symtab.merge (K true);
168   fun print sg tab =
169     Pretty.writeln (Pretty.strs ("(co)inductives:" ::
170       map #1 (Sign.cond_extern_table sg Sign.constK tab)));
171 end;
173 structure InductiveData = TheoryDataFun(InductiveArgs);
174 val print_inductives = InductiveData.print;
177 (* get and put data *)
179 fun get_inductive thy name =
180   (case Symtab.lookup (InductiveData.get thy, name) of
181     Some info => info
182   | None => error ("Unknown (co)inductive set " ^ quote name));
184 fun put_inductives names info thy =
185   let
186     fun upd (tab, name) = Symtab.update_new ((name, info), tab);
187     val tab = foldl upd (InductiveData.get thy, names)
188       handle Symtab.DUP name => error ("Duplicate definition of (co)inductive set " ^ quote name);
189   in InductiveData.put tab thy end;
193 (*** properties of (co)inductive sets ***)
195 (** elimination rules **)
197 fun mk_elims cs cTs params intr_ts =
198   let
199     val used = foldr add_term_names (intr_ts, []);
200     val [aname, pname] = variantlist (["a", "P"], used);
201     val P = HOLogic.mk_Trueprop (Free (pname, HOLogic.boolT));
203     fun dest_intr r =
204       let val Const ("op :", _) \$ t \$ u =
205         HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
206       in (u, t, Logic.strip_imp_prems r) end;
208     val intrs = map dest_intr intr_ts;
210     fun mk_elim (c, T) =
211       let
212         val a = Free (aname, T);
214         fun mk_elim_prem (_, t, ts) =
215           list_all_free (map dest_Free ((foldr add_term_frees (t::ts, [])) \\ params),
216             Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (a, t)) :: ts, P));
217       in
218         Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (a, c)) ::
219           map mk_elim_prem (filter (equal c o #1) intrs), P)
220       end
221   in
222     map mk_elim (cs ~~ cTs)
223   end;
227 (** premises and conclusions of induction rules **)
229 fun mk_indrule cs cTs params intr_ts =
230   let
231     val used = foldr add_term_names (intr_ts, []);
233     (* predicates for induction rule *)
235     val preds = map Free (variantlist (if length cs < 2 then ["P"] else
236       map (fn i => "P" ^ string_of_int i) (1 upto length cs), used) ~~
237         map (fn T => T --> HOLogic.boolT) cTs);
239     (* transform an introduction rule into a premise for induction rule *)
241     fun mk_ind_prem r =
242       let
243         val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
245         fun subst (prem as (Const ("op :", T) \$ t \$ u), prems) =
246               let val n = find_index_eq u cs in
247                 if n >= 0 then prem :: (nth_elem (n, preds)) \$ t :: prems else
248                   (subst_free (map (fn (c, P) => (c, HOLogic.mk_binop "op Int"
249                     (c, HOLogic.Collect_const (HOLogic.dest_setT
250                       (fastype_of c)) \$ P))) (cs ~~ preds)) prem)::prems
251               end
252           | subst (prem, prems) = prem::prems;
254         val Const ("op :", _) \$ t \$ u =
255           HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
257       in list_all_free (frees,
258            Logic.list_implies (map HOLogic.mk_Trueprop (foldr subst
259              (map HOLogic.dest_Trueprop (Logic.strip_imp_prems r), [])),
260                HOLogic.mk_Trueprop (nth_elem (find_index_eq u cs, preds) \$ t)))
261       end;
263     val ind_prems = map mk_ind_prem intr_ts;
265     (* make conclusions for induction rules *)
267     fun mk_ind_concl ((c, P), (ts, x)) =
268       let val T = HOLogic.dest_setT (fastype_of c);
269           val Ts = HOLogic.prodT_factors T;
270           val (frees, x') = foldr (fn (T', (fs, s)) =>
271             ((Free (s, T'))::fs, bump_string s)) (Ts, ([], x));
272           val tuple = HOLogic.mk_tuple T frees;
273       in ((HOLogic.mk_binop "op -->"
274         (HOLogic.mk_mem (tuple, c), P \$ tuple))::ts, x')
275       end;
277     val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 (app HOLogic.conj)
278         (fst (foldr mk_ind_concl (cs ~~ preds, ([], "xa")))))
280   in (preds, ind_prems, mutual_ind_concl)
281   end;
285 (*** proofs for (co)inductive sets ***)
287 (** prove monotonicity **)
289 fun prove_mono setT fp_fun monos thy =
290   let
291     val _ = message "  Proving monotonicity ...";
293     val mono = prove_goalw_cterm [] (cterm_of (Theory.sign_of thy) (HOLogic.mk_Trueprop
294       (Const (mono_name, (setT --> setT) --> HOLogic.boolT) \$ fp_fun)))
295         (fn _ => [rtac monoI 1, REPEAT (ares_tac (basic_monos @ monos) 1)])
297   in mono end;
301 (** prove introduction rules **)
303 fun prove_intrs coind mono fp_def intr_ts con_defs rec_sets_defs thy =
304   let
305     val _ = message "  Proving the introduction rules ...";
307     val unfold = standard (mono RS (fp_def RS
308       (if coind then def_gfp_Tarski else def_lfp_Tarski)));
310     fun select_disj 1 1 = []
311       | select_disj _ 1 = [rtac disjI1]
312       | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
314     val intrs = map (fn (i, intr) => prove_goalw_cterm rec_sets_defs
315       (cterm_of (Theory.sign_of thy) intr) (fn prems =>
316        [(*insert prems and underlying sets*)
317        cut_facts_tac prems 1,
318        stac unfold 1,
319        REPEAT (resolve_tac [vimageI2, CollectI] 1),
320        (*Now 1-2 subgoals: the disjunction, perhaps equality.*)
321        EVERY1 (select_disj (length intr_ts) i),
322        (*Not ares_tac, since refl must be tried before any equality assumptions;
323          backtracking may occur if the premises have extra variables!*)
324        DEPTH_SOLVE_1 (resolve_tac [refl,exI,conjI] 1 APPEND assume_tac 1),
325        (*Now solve the equations like Inl 0 = Inl ?b2*)
326        rewrite_goals_tac con_defs,
327        REPEAT (rtac refl 1)])) (1 upto (length intr_ts) ~~ intr_ts)
329   in (intrs, unfold) end;
333 (** prove elimination rules **)
335 fun prove_elims cs cTs params intr_ts unfold rec_sets_defs thy =
336   let
337     val _ = message "  Proving the elimination rules ...";
339     val rules1 = [CollectE, disjE, make_elim vimageD];
340     val rules2 = [exE, conjE, Inl_neq_Inr, Inr_neq_Inl] @
341       map make_elim [Inl_inject, Inr_inject];
343     val elims = map (fn t => prove_goalw_cterm rec_sets_defs
344       (cterm_of (Theory.sign_of thy) t) (fn prems =>
345         [cut_facts_tac [hd prems] 1,
346          dtac (unfold RS subst) 1,
347          REPEAT (FIRSTGOAL (eresolve_tac rules1)),
348          REPEAT (FIRSTGOAL (eresolve_tac rules2)),
349          EVERY (map (fn prem =>
350            DEPTH_SOLVE_1 (ares_tac [prem, conjI] 1)) (tl prems))]))
351       (mk_elims cs cTs params intr_ts)
353   in elims end;
356 (** derivation of simplified elimination rules **)
358 (*Applies freeness of the given constructors, which *must* be unfolded by
359   the given defs.  Cannot simply use the local con_defs because con_defs=[]
360   for inference systems.
361  *)
362 fun con_elim_tac ss =
363   let val elim_tac = REPEAT o (eresolve_tac elim_rls)
364   in ALLGOALS(EVERY'[elim_tac,
365 		     asm_full_simp_tac ss,
366 		     elim_tac,
367 		     REPEAT o bound_hyp_subst_tac])
368      THEN prune_params_tac
369   end;
371 (*String s should have the form t:Si where Si is an inductive set*)
372 fun mk_cases elims s =
373   let val prem = assume (read_cterm (Thm.sign_of_thm (hd elims)) (s, propT))
374       fun mk_elim rl = rule_by_tactic (con_elim_tac (simpset())) (prem RS rl)
375 	               |> standard
376   in case find_first is_some (map (try mk_elim) elims) of
377        Some (Some r) => r
378      | None => error ("mk_cases: string '" ^ s ^ "' not of form 't : S_i'")
379   end;
383 (** prove induction rule **)
385 fun prove_indrule cs cTs sumT rec_const params intr_ts mono
386     fp_def rec_sets_defs thy =
387   let
388     val _ = message "  Proving the induction rule ...";
390     val sign = Theory.sign_of thy;
392     val (preds, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
394     (* make predicate for instantiation of abstract induction rule *)
396     fun mk_ind_pred _ [P] = P
397       | mk_ind_pred T Ps =
398          let val n = (length Ps) div 2;
399              val Type (_, [T1, T2]) = T
400          in Const ("sum_case",
401            [T1 --> HOLogic.boolT, T2 --> HOLogic.boolT, T] ---> HOLogic.boolT) \$
402              mk_ind_pred T1 (take (n, Ps)) \$ mk_ind_pred T2 (drop (n, Ps))
403          end;
405     val ind_pred = mk_ind_pred sumT preds;
407     val ind_concl = HOLogic.mk_Trueprop
408       (HOLogic.all_const sumT \$ Abs ("x", sumT, HOLogic.mk_binop "op -->"
409         (HOLogic.mk_mem (Bound 0, rec_const), ind_pred \$ Bound 0)));
411     (* simplification rules for vimage and Collect *)
413     val vimage_simps = if length cs < 2 then [] else
414       map (fn c => prove_goalw_cterm [] (cterm_of sign
415         (HOLogic.mk_Trueprop (HOLogic.mk_eq
416           (mk_vimage cs sumT (HOLogic.Collect_const sumT \$ ind_pred) c,
417            HOLogic.Collect_const (HOLogic.dest_setT (fastype_of c)) \$
418              nth_elem (find_index_eq c cs, preds)))))
419         (fn _ => [rtac vimage_Collect 1, rewrite_goals_tac
420            (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
421           rtac refl 1])) cs;
423     val induct = prove_goalw_cterm [] (cterm_of sign
424       (Logic.list_implies (ind_prems, ind_concl))) (fn prems =>
425         [rtac (impI RS allI) 1,
426          DETERM (etac (mono RS (fp_def RS def_induct)) 1),
427          rewrite_goals_tac (map mk_meta_eq (vimage_Int::vimage_simps)),
428          fold_goals_tac rec_sets_defs,
429          (*This CollectE and disjE separates out the introduction rules*)
430          REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE])),
431          (*Now break down the individual cases.  No disjE here in case
432            some premise involves disjunction.*)
433          REPEAT (FIRSTGOAL (eresolve_tac [IntE, CollectE, exE, conjE]
434                      ORELSE' hyp_subst_tac)),
435          rewrite_goals_tac (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
436          EVERY (map (fn prem =>
437            DEPTH_SOLVE_1 (ares_tac [prem, conjI, refl] 1)) prems)]);
439     val lemma = prove_goalw_cterm rec_sets_defs (cterm_of sign
440       (Logic.mk_implies (ind_concl, mutual_ind_concl))) (fn prems =>
441         [cut_facts_tac prems 1,
442          REPEAT (EVERY
443            [REPEAT (resolve_tac [conjI, impI] 1),
444             TRY (dtac vimageD 1), etac allE 1, dtac mp 1, atac 1,
445             rewrite_goals_tac (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
446             atac 1])])
448   in standard (split_rule (induct RS lemma))
449   end;
453 (*** specification of (co)inductive sets ****)
455 (** definitional introduction of (co)inductive sets **)
457 fun add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs
458     atts intros monos con_defs thy params paramTs cTs cnames =
459   let
460     val _ = if verbose then message ("Proofs for " ^ coind_prefix coind ^ "inductive set(s) " ^
461       commas_quote cnames) else ();
463     val sumT = fold_bal (fn (T, U) => Type ("+", [T, U])) cTs;
464     val setT = HOLogic.mk_setT sumT;
466     val fp_name = if coind then Sign.intern_const (Theory.sign_of Gfp.thy) "gfp"
467       else Sign.intern_const (Theory.sign_of Lfp.thy) "lfp";
469     val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
471     val used = foldr add_term_names (intr_ts, []);
472     val [sname, xname] = variantlist (["S", "x"], used);
474     (* transform an introduction rule into a conjunction  *)
475     (*   [| t : ... S_i ... ; ... |] ==> u : S_j          *)
476     (* is transformed into                                *)
477     (*   x = Inj_j u & t : ... Inj_i -`` S ... & ...      *)
479     fun transform_rule r =
480       let
481         val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
482         val subst = subst_free
483           (cs ~~ (map (mk_vimage cs sumT (Free (sname, setT))) cs));
484         val Const ("op :", _) \$ t \$ u =
485           HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
487       in foldr (fn ((x, T), P) => HOLogic.mk_exists (x, T, P))
488         (frees, foldr1 (app HOLogic.conj)
489           (((HOLogic.eq_const sumT) \$ Free (xname, sumT) \$ (mk_inj cs sumT u t))::
490             (map (subst o HOLogic.dest_Trueprop)
491               (Logic.strip_imp_prems r))))
492       end
494     (* make a disjunction of all introduction rules *)
496     val fp_fun = absfree (sname, setT, (HOLogic.Collect_const sumT) \$
497       absfree (xname, sumT, foldr1 (app HOLogic.disj) (map transform_rule intr_ts)));
499     (* add definiton of recursive sets to theory *)
501     val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
502     val full_rec_name = Sign.full_name (Theory.sign_of thy) rec_name;
504     val rec_const = list_comb
505       (Const (full_rec_name, paramTs ---> setT), params);
507     val fp_def_term = Logic.mk_equals (rec_const,
508       Const (fp_name, (setT --> setT) --> setT) \$ fp_fun)
510     val def_terms = fp_def_term :: (if length cs < 2 then [] else
511       map (fn c => Logic.mk_equals (c, mk_vimage cs sumT rec_const c)) cs);
513     val thy' = thy |>
514       (if declare_consts then
515         Theory.add_consts_i (map (fn (c, n) =>
516           (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
517        else I) |>
518       (if length cs < 2 then I else
519        Theory.add_consts_i [(rec_name, paramTs ---> setT, NoSyn)]) |>
520       Theory.add_path rec_name |>
521       PureThy.add_defss_i [(("defs", def_terms), [])];
523     (* get definitions from theory *)
525     val fp_def::rec_sets_defs = PureThy.get_thms thy' "defs";
527     (* prove and store theorems *)
529     val mono = prove_mono setT fp_fun monos thy';
530     val (intrs, unfold) = prove_intrs coind mono fp_def intr_ts con_defs
531       rec_sets_defs thy';
532     val elims = if no_elim then [] else
533       prove_elims cs cTs params intr_ts unfold rec_sets_defs thy';
534     val raw_induct = if no_ind then TrueI else
535       if coind then standard (rule_by_tactic
536         (rewrite_tac [mk_meta_eq vimage_Un] THEN
537           fold_tac rec_sets_defs) (mono RS (fp_def RS def_Collect_coinduct)))
538       else
539         prove_indrule cs cTs sumT rec_const params intr_ts mono fp_def
540           rec_sets_defs thy';
541     val induct = if coind orelse no_ind orelse length cs > 1 then raw_induct
542       else standard (raw_induct RSN (2, rev_mp));
544     val thy'' = thy'
545       |> PureThy.add_thmss [(("intrs", intrs), atts)]
546       |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts)
547       |> (if no_elim then I else PureThy.add_thmss [(("elims", elims), [])])
548       |> (if no_ind then I else PureThy.add_thms
549         [((coind_prefix coind ^ "induct", induct), [])])
550       |> Theory.parent_path;
552   in (thy'',
553     {defs = fp_def::rec_sets_defs,
554      mono = mono,
555      unfold = unfold,
556      intrs = intrs,
557      elims = elims,
558      mk_cases = mk_cases elims,
559      raw_induct = raw_induct,
560      induct = induct})
561   end;
565 (** axiomatic introduction of (co)inductive sets **)
567 fun add_ind_axm verbose declare_consts alt_name coind no_elim no_ind cs
568     atts intros monos con_defs thy params paramTs cTs cnames =
569   let
570     val _ = if verbose then message ("Adding axioms for " ^ coind_prefix coind ^
571       "inductive set(s) " ^ commas_quote cnames) else ();
573     val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
575     val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
576     val elim_ts = mk_elims cs cTs params intr_ts;
578     val (_, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
579     val ind_t = Logic.list_implies (ind_prems, mutual_ind_concl);
581     val thy' = thy
582       |> (if declare_consts then
584               (map (fn (c, n) => (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
585          else I)
586       |> Theory.add_path rec_name
587       |> PureThy.add_axiomss_i [(("intrs", intr_ts), atts), (("elims", elim_ts), [])]
588       |> (if coind then I else PureThy.add_axioms_i [(("internal_induct", ind_t), [])]);
590     val intrs = PureThy.get_thms thy' "intrs";
591     val elims = PureThy.get_thms thy' "elims";
592     val raw_induct = if coind then TrueI else
593       standard (split_rule (PureThy.get_thm thy' "internal_induct"));
594     val induct = if coind orelse length cs > 1 then raw_induct
595       else standard (raw_induct RSN (2, rev_mp));
597     val thy'' =
598       thy'
599       |> (if coind then I else PureThy.add_thms [(("induct", induct), [])])
600       |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts)
601       |> Theory.parent_path;
602   in (thy'',
603     {defs = [],
604      mono = TrueI,
605      unfold = TrueI,
606      intrs = intrs,
607      elims = elims,
608      mk_cases = mk_cases elims,
609      raw_induct = raw_induct,
610      induct = induct})
611   end;
615 (** introduction of (co)inductive sets **)
617 fun add_inductive_i verbose declare_consts alt_name coind no_elim no_ind cs
618     atts intros monos con_defs thy =
619   let
620     val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
621     val sign = Theory.sign_of thy;
623     (*parameters should agree for all mutually recursive components*)
624     val (_, params) = strip_comb (hd cs);
625     val paramTs = map (try' (snd o dest_Free) "Parameter in recursive\
626       \ component is not a free variable: " sign) params;
628     val cTs = map (try' (HOLogic.dest_setT o fastype_of)
629       "Recursive component not of type set: " sign) cs;
631     val full_cnames = map (try' (fst o dest_Const o head_of)
632       "Recursive set not previously declared as constant: " sign) cs;
633     val cnames = map Sign.base_name full_cnames;
635     val _ = assert_all Syntax.is_identifier cnames	(* FIXME why? *)
636        (fn a => "Base name of recursive set not an identifier: " ^ a);
637     val _ = seq (check_rule sign cs o snd o fst) intros;
639     val (thy1, result) =
640       (if ! quick_and_dirty then add_ind_axm else add_ind_def)
641         verbose declare_consts alt_name coind no_elim no_ind cs atts intros monos
642         con_defs thy params paramTs cTs cnames;
643     val thy2 = thy1 |> put_inductives full_cnames ({names = full_cnames, coind = coind}, result);
644   in (thy2, result) end;
648 (** external interface **)
650 fun add_inductive verbose coind c_strings srcs intro_srcs raw_monos raw_con_defs thy =
651   let
652     val sign = Theory.sign_of thy;
653     val cs = map (readtm (Theory.sign_of thy) HOLogic.termTVar) c_strings;
655     val atts = map (Attrib.global_attribute thy) srcs;
656     val intr_names = map (fst o fst) intro_srcs;
657     val intr_ts = map (readtm (Theory.sign_of thy) propT o snd o fst) intro_srcs;
658     val intr_atts = map (map (Attrib.global_attribute thy) o snd) intro_srcs;
660     (* the following code ensures that each recursive set *)
661     (* always has the same type in all introduction rules *)
663     val {tsig, ...} = Sign.rep_sg sign;
664     val add_term_consts_2 =
665       foldl_aterms (fn (cs, Const c) => c ins cs | (cs, _) => cs);
666     fun varify (t, (i, ts)) =
667       let val t' = map_term_types (incr_tvar (i + 1)) (Type.varify (t, []))
668       in (maxidx_of_term t', t'::ts) end;
669     val (i, cs') = foldr varify (cs, (~1, []));
670     val (i', intr_ts') = foldr varify (intr_ts, (i, []));
671     val rec_consts = foldl add_term_consts_2 ([], cs');
672     val intr_consts = foldl add_term_consts_2 ([], intr_ts');
673     fun unify (env, (cname, cT)) =
674       let val consts = map snd (filter (fn c => fst c = cname) intr_consts)
675       in (foldl (fn ((env', j'), Tp) => Type.unify tsig j' env' Tp)
676         (env, (replicate (length consts) cT) ~~ consts)) handle _ =>
677           error ("Occurrences of constant '" ^ cname ^
678             "' have incompatible types")
679       end;
680     val (env, _) = foldl unify (([], i'), rec_consts);
681     fun typ_subst_TVars_2 env T = let val T' = typ_subst_TVars env T
682       in if T = T' then T else typ_subst_TVars_2 env T' end;
683     val subst = fst o Type.freeze_thaw o
684       (map_term_types (typ_subst_TVars_2 env));
685     val cs'' = map subst cs';
686     val intr_ts'' = map subst intr_ts';
688     val ((thy', con_defs), monos) = thy
689       |> IsarThy.apply_theorems raw_monos
690       |> apfst (IsarThy.apply_theorems raw_con_defs);
691   in
692     add_inductive_i verbose false "" coind false false cs''
693       atts ((intr_names ~~ intr_ts'') ~~ intr_atts) monos con_defs thy'
694   end;
698 (** package setup **)
700 (* setup theory *)
702 val setup = [InductiveData.init];
705 (* outer syntax *)
707 local structure P = OuterParse and K = OuterSyntax.Keyword in
709 fun mk_ind coind (((sets, (atts, intrs)), monos), con_defs) =
710   #1 o add_inductive true coind sets atts (map P.triple_swap intrs) monos con_defs;
712 fun ind_decl coind =
713   (Scan.repeat1 P.term --| P.marg_comment) --
714   (P.\$\$\$ "intrs" |--
715     P.!!! (P.opt_attribs -- Scan.repeat1 (P.opt_thm_name ":" -- P.term --| P.marg_comment))) --
716   Scan.optional (P.\$\$\$ "monos" |-- P.!!! P.xthms1 --| P.marg_comment) [] --
717   Scan.optional (P.\$\$\$ "con_defs" |-- P.!!! P.xthms1 --| P.marg_comment) []
718   >> (Toplevel.theory o mk_ind coind);
720 val inductiveP =
721   OuterSyntax.command "inductive" "define inductive sets" K.thy_decl (ind_decl false);
723 val coinductiveP =
724   OuterSyntax.command "coinductive" "define coinductive sets" K.thy_decl (ind_decl true);
726 val _ = OuterSyntax.add_keywords ["intrs", "monos", "con_defs"];
727 val _ = OuterSyntax.add_parsers [inductiveP, coinductiveP];
729 end;
732 end;