src/HOL/Tools/inductive_package.ML
 author wenzelm Tue Apr 27 10:50:31 1999 +0200 (1999-04-27) changeset 6521 16c425fc00cb parent 6437 9bdfe07ba8e9 child 6556 daa00919502b permissions -rw-r--r--
intrs attributes;
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 prep_ext = I;
165   val merge: T * T -> T = Symtab.merge (K true);
167   fun print sg tab =
168     Pretty.writeln (Pretty.strs ("(co)inductives:" ::
169       map (Sign.cond_extern sg Sign.constK o fst) (Symtab.dest tab)));
170 end;
172 structure InductiveData = TheoryDataFun(InductiveArgs);
173 val print_inductives = InductiveData.print;
176 (* get and put data *)
178 fun get_inductive thy name =
179   (case Symtab.lookup (InductiveData.get thy, name) of
180     Some info => info
181   | None => error ("Unknown (co)inductive set " ^ quote name));
183 fun put_inductives names info thy =
184   let
185     fun upd (tab, name) = Symtab.update_new ((name, info), tab);
186     val tab = foldl upd (InductiveData.get thy, names)
187       handle Symtab.DUP name => error ("Duplicate definition of (co)inductive set " ^ quote name);
188   in InductiveData.put tab thy end;
192 (*** properties of (co)inductive sets ***)
194 (** elimination rules **)
196 fun mk_elims cs cTs params intr_ts =
197   let
198     val used = foldr add_term_names (intr_ts, []);
199     val [aname, pname] = variantlist (["a", "P"], used);
200     val P = HOLogic.mk_Trueprop (Free (pname, HOLogic.boolT));
202     fun dest_intr r =
203       let val Const ("op :", _) \$ t \$ u =
204         HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
205       in (u, t, Logic.strip_imp_prems r) end;
207     val intrs = map dest_intr intr_ts;
209     fun mk_elim (c, T) =
210       let
211         val a = Free (aname, T);
213         fun mk_elim_prem (_, t, ts) =
214           list_all_free (map dest_Free ((foldr add_term_frees (t::ts, [])) \\ params),
215             Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (a, t)) :: ts, P));
216       in
217         Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (a, c)) ::
218           map mk_elim_prem (filter (equal c o #1) intrs), P)
219       end
220   in
221     map mk_elim (cs ~~ cTs)
222   end;
226 (** premises and conclusions of induction rules **)
228 fun mk_indrule cs cTs params intr_ts =
229   let
230     val used = foldr add_term_names (intr_ts, []);
232     (* predicates for induction rule *)
234     val preds = map Free (variantlist (if length cs < 2 then ["P"] else
235       map (fn i => "P" ^ string_of_int i) (1 upto length cs), used) ~~
236         map (fn T => T --> HOLogic.boolT) cTs);
238     (* transform an introduction rule into a premise for induction rule *)
240     fun mk_ind_prem r =
241       let
242         val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
244         fun subst (prem as (Const ("op :", T) \$ t \$ u), prems) =
245               let val n = find_index_eq u cs in
246                 if n >= 0 then prem :: (nth_elem (n, preds)) \$ t :: prems else
247                   (subst_free (map (fn (c, P) => (c, HOLogic.mk_binop "op Int"
248                     (c, HOLogic.Collect_const (HOLogic.dest_setT
249                       (fastype_of c)) \$ P))) (cs ~~ preds)) prem)::prems
250               end
251           | subst (prem, prems) = prem::prems;
253         val Const ("op :", _) \$ t \$ u =
254           HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
256       in list_all_free (frees,
257            Logic.list_implies (map HOLogic.mk_Trueprop (foldr subst
258              (map HOLogic.dest_Trueprop (Logic.strip_imp_prems r), [])),
259                HOLogic.mk_Trueprop (nth_elem (find_index_eq u cs, preds) \$ t)))
260       end;
262     val ind_prems = map mk_ind_prem intr_ts;
264     (* make conclusions for induction rules *)
266     fun mk_ind_concl ((c, P), (ts, x)) =
267       let val T = HOLogic.dest_setT (fastype_of c);
268           val Ts = HOLogic.prodT_factors T;
269           val (frees, x') = foldr (fn (T', (fs, s)) =>
270             ((Free (s, T'))::fs, bump_string s)) (Ts, ([], x));
271           val tuple = HOLogic.mk_tuple T frees;
272       in ((HOLogic.mk_binop "op -->"
273         (HOLogic.mk_mem (tuple, c), P \$ tuple))::ts, x')
274       end;
276     val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 (app HOLogic.conj)
277         (fst (foldr mk_ind_concl (cs ~~ preds, ([], "xa")))))
279   in (preds, ind_prems, mutual_ind_concl)
280   end;
284 (*** proofs for (co)inductive sets ***)
286 (** prove monotonicity **)
288 fun prove_mono setT fp_fun monos thy =
289   let
290     val _ = message "  Proving monotonicity ...";
292     val mono = prove_goalw_cterm [] (cterm_of (Theory.sign_of thy) (HOLogic.mk_Trueprop
293       (Const (mono_name, (setT --> setT) --> HOLogic.boolT) \$ fp_fun)))
294         (fn _ => [rtac monoI 1, REPEAT (ares_tac (basic_monos @ monos) 1)])
296   in mono end;
300 (** prove introduction rules **)
302 fun prove_intrs coind mono fp_def intr_ts con_defs rec_sets_defs thy =
303   let
304     val _ = message "  Proving the introduction rules ...";
306     val unfold = standard (mono RS (fp_def RS
307       (if coind then def_gfp_Tarski else def_lfp_Tarski)));
309     fun select_disj 1 1 = []
310       | select_disj _ 1 = [rtac disjI1]
311       | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
313     val intrs = map (fn (i, intr) => prove_goalw_cterm rec_sets_defs
314       (cterm_of (Theory.sign_of thy) intr) (fn prems =>
315        [(*insert prems and underlying sets*)
316        cut_facts_tac prems 1,
317        stac unfold 1,
318        REPEAT (resolve_tac [vimageI2, CollectI] 1),
319        (*Now 1-2 subgoals: the disjunction, perhaps equality.*)
320        EVERY1 (select_disj (length intr_ts) i),
321        (*Not ares_tac, since refl must be tried before any equality assumptions;
322          backtracking may occur if the premises have extra variables!*)
323        DEPTH_SOLVE_1 (resolve_tac [refl,exI,conjI] 1 APPEND assume_tac 1),
324        (*Now solve the equations like Inl 0 = Inl ?b2*)
325        rewrite_goals_tac con_defs,
326        REPEAT (rtac refl 1)])) (1 upto (length intr_ts) ~~ intr_ts)
328   in (intrs, unfold) end;
332 (** prove elimination rules **)
334 fun prove_elims cs cTs params intr_ts unfold rec_sets_defs thy =
335   let
336     val _ = message "  Proving the elimination rules ...";
338     val rules1 = [CollectE, disjE, make_elim vimageD];
339     val rules2 = [exE, conjE, Inl_neq_Inr, Inr_neq_Inl] @
340       map make_elim [Inl_inject, Inr_inject];
342     val elims = map (fn t => prove_goalw_cterm rec_sets_defs
343       (cterm_of (Theory.sign_of thy) t) (fn prems =>
344         [cut_facts_tac [hd prems] 1,
345          dtac (unfold RS subst) 1,
346          REPEAT (FIRSTGOAL (eresolve_tac rules1)),
347          REPEAT (FIRSTGOAL (eresolve_tac rules2)),
348          EVERY (map (fn prem =>
349            DEPTH_SOLVE_1 (ares_tac [prem, conjI] 1)) (tl prems))]))
350       (mk_elims cs cTs params intr_ts)
352   in elims end;
355 (** derivation of simplified elimination rules **)
357 (*Applies freeness of the given constructors, which *must* be unfolded by
358   the given defs.  Cannot simply use the local con_defs because con_defs=[]
359   for inference systems.
360  *)
361 fun con_elim_tac ss =
362   let val elim_tac = REPEAT o (eresolve_tac elim_rls)
363   in ALLGOALS(EVERY'[elim_tac,
364 		     asm_full_simp_tac ss,
365 		     elim_tac,
366 		     REPEAT o bound_hyp_subst_tac])
367      THEN prune_params_tac
368   end;
370 (*String s should have the form t:Si where Si is an inductive set*)
371 fun mk_cases elims s =
372   let val prem = assume (read_cterm (Thm.sign_of_thm (hd elims)) (s, propT))
373       fun mk_elim rl = rule_by_tactic (con_elim_tac (simpset())) (prem RS rl)
374 	               |> standard
375   in case find_first is_some (map (try mk_elim) elims) of
376        Some (Some r) => r
377      | None => error ("mk_cases: string '" ^ s ^ "' not of form 't : S_i'")
378   end;
382 (** prove induction rule **)
384 fun prove_indrule cs cTs sumT rec_const params intr_ts mono
385     fp_def rec_sets_defs thy =
386   let
387     val _ = message "  Proving the induction rule ...";
389     val sign = Theory.sign_of thy;
391     val (preds, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
393     (* make predicate for instantiation of abstract induction rule *)
395     fun mk_ind_pred _ [P] = P
396       | mk_ind_pred T Ps =
397          let val n = (length Ps) div 2;
398              val Type (_, [T1, T2]) = T
399          in Const ("sum_case",
400            [T1 --> HOLogic.boolT, T2 --> HOLogic.boolT, T] ---> HOLogic.boolT) \$
401              mk_ind_pred T1 (take (n, Ps)) \$ mk_ind_pred T2 (drop (n, Ps))
402          end;
404     val ind_pred = mk_ind_pred sumT preds;
406     val ind_concl = HOLogic.mk_Trueprop
407       (HOLogic.all_const sumT \$ Abs ("x", sumT, HOLogic.mk_binop "op -->"
408         (HOLogic.mk_mem (Bound 0, rec_const), ind_pred \$ Bound 0)));
410     (* simplification rules for vimage and Collect *)
412     val vimage_simps = if length cs < 2 then [] else
413       map (fn c => prove_goalw_cterm [] (cterm_of sign
414         (HOLogic.mk_Trueprop (HOLogic.mk_eq
415           (mk_vimage cs sumT (HOLogic.Collect_const sumT \$ ind_pred) c,
416            HOLogic.Collect_const (HOLogic.dest_setT (fastype_of c)) \$
417              nth_elem (find_index_eq c cs, preds)))))
418         (fn _ => [rtac vimage_Collect 1, rewrite_goals_tac
419            (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
420           rtac refl 1])) cs;
422     val induct = prove_goalw_cterm [] (cterm_of sign
423       (Logic.list_implies (ind_prems, ind_concl))) (fn prems =>
424         [rtac (impI RS allI) 1,
425          DETERM (etac (mono RS (fp_def RS def_induct)) 1),
426          rewrite_goals_tac (map mk_meta_eq (vimage_Int::vimage_simps)),
427          fold_goals_tac rec_sets_defs,
428          (*This CollectE and disjE separates out the introduction rules*)
429          REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE])),
430          (*Now break down the individual cases.  No disjE here in case
431            some premise involves disjunction.*)
432          REPEAT (FIRSTGOAL (eresolve_tac [IntE, CollectE, exE, conjE]
433                      ORELSE' hyp_subst_tac)),
434          rewrite_goals_tac (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
435          EVERY (map (fn prem =>
436            DEPTH_SOLVE_1 (ares_tac [prem, conjI, refl] 1)) prems)]);
438     val lemma = prove_goalw_cterm rec_sets_defs (cterm_of sign
439       (Logic.mk_implies (ind_concl, mutual_ind_concl))) (fn prems =>
440         [cut_facts_tac prems 1,
441          REPEAT (EVERY
442            [REPEAT (resolve_tac [conjI, impI] 1),
443             TRY (dtac vimageD 1), etac allE 1, dtac mp 1, atac 1,
444             rewrite_goals_tac (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
445             atac 1])])
447   in standard (split_rule (induct RS lemma))
448   end;
452 (*** specification of (co)inductive sets ****)
454 (** definitional introduction of (co)inductive sets **)
456 fun add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs
457     atts intros monos con_defs thy params paramTs cTs cnames =
458   let
459     val _ = if verbose then message ("Proofs for " ^ coind_prefix coind ^ "inductive set(s) " ^
460       commas_quote cnames) else ();
462     val sumT = fold_bal (fn (T, U) => Type ("+", [T, U])) cTs;
463     val setT = HOLogic.mk_setT sumT;
465     val fp_name = if coind then Sign.intern_const (Theory.sign_of Gfp.thy) "gfp"
466       else Sign.intern_const (Theory.sign_of Lfp.thy) "lfp";
468     val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
470     val used = foldr add_term_names (intr_ts, []);
471     val [sname, xname] = variantlist (["S", "x"], used);
473     (* transform an introduction rule into a conjunction  *)
474     (*   [| t : ... S_i ... ; ... |] ==> u : S_j          *)
475     (* is transformed into                                *)
476     (*   x = Inj_j u & t : ... Inj_i -`` S ... & ...      *)
478     fun transform_rule r =
479       let
480         val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
481         val subst = subst_free
482           (cs ~~ (map (mk_vimage cs sumT (Free (sname, setT))) cs));
483         val Const ("op :", _) \$ t \$ u =
484           HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
486       in foldr (fn ((x, T), P) => HOLogic.mk_exists (x, T, P))
487         (frees, foldr1 (app HOLogic.conj)
488           (((HOLogic.eq_const sumT) \$ Free (xname, sumT) \$ (mk_inj cs sumT u t))::
489             (map (subst o HOLogic.dest_Trueprop)
490               (Logic.strip_imp_prems r))))
491       end
493     (* make a disjunction of all introduction rules *)
495     val fp_fun = absfree (sname, setT, (HOLogic.Collect_const sumT) \$
496       absfree (xname, sumT, foldr1 (app HOLogic.disj) (map transform_rule intr_ts)));
498     (* add definiton of recursive sets to theory *)
500     val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
501     val full_rec_name = Sign.full_name (Theory.sign_of thy) rec_name;
503     val rec_const = list_comb
504       (Const (full_rec_name, paramTs ---> setT), params);
506     val fp_def_term = Logic.mk_equals (rec_const,
507       Const (fp_name, (setT --> setT) --> setT) \$ fp_fun)
509     val def_terms = fp_def_term :: (if length cs < 2 then [] else
510       map (fn c => Logic.mk_equals (c, mk_vimage cs sumT rec_const c)) cs);
512     val thy' = thy |>
513       (if declare_consts then
514         Theory.add_consts_i (map (fn (c, n) =>
515           (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
516        else I) |>
517       (if length cs < 2 then I else
518        Theory.add_consts_i [(rec_name, paramTs ---> setT, NoSyn)]) |>
519       Theory.add_path rec_name |>
520       PureThy.add_defss_i [(("defs", def_terms), [])];
522     (* get definitions from theory *)
524     val fp_def::rec_sets_defs = PureThy.get_thms thy' "defs";
526     (* prove and store theorems *)
528     val mono = prove_mono setT fp_fun monos thy';
529     val (intrs, unfold) = prove_intrs coind mono fp_def intr_ts con_defs
530       rec_sets_defs thy';
531     val elims = if no_elim then [] else
532       prove_elims cs cTs params intr_ts unfold rec_sets_defs thy';
533     val raw_induct = if no_ind then TrueI else
534       if coind then standard (rule_by_tactic
535         (rewrite_tac [mk_meta_eq vimage_Un] THEN
536           fold_tac rec_sets_defs) (mono RS (fp_def RS def_Collect_coinduct)))
537       else
538         prove_indrule cs cTs sumT rec_const params intr_ts mono fp_def
539           rec_sets_defs thy';
540     val induct = if coind orelse no_ind orelse length cs > 1 then raw_induct
541       else standard (raw_induct RSN (2, rev_mp));
543     val thy'' = thy'
544       |> PureThy.add_thmss [(("intrs", intrs), atts)]
545       |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts)
546       |> (if no_elim then I else PureThy.add_thmss [(("elims", elims), [])])
547       |> (if no_ind then I else PureThy.add_thms
548         [((coind_prefix coind ^ "induct", induct), [])])
549       |> Theory.parent_path;
551   in (thy'',
552     {defs = fp_def::rec_sets_defs,
553      mono = mono,
554      unfold = unfold,
555      intrs = intrs,
556      elims = elims,
557      mk_cases = mk_cases elims,
558      raw_induct = raw_induct,
559      induct = induct})
560   end;
564 (** axiomatic introduction of (co)inductive sets **)
566 fun add_ind_axm verbose declare_consts alt_name coind no_elim no_ind cs
567     atts intros monos con_defs thy params paramTs cTs cnames =
568   let
569     val _ = if verbose then message ("Adding axioms for " ^ coind_prefix coind ^
570       "inductive set(s) " ^ commas_quote cnames) else ();
572     val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
574     val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
575     val elim_ts = mk_elims cs cTs params intr_ts;
577     val (_, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
578     val ind_t = Logic.list_implies (ind_prems, mutual_ind_concl);
580     val thy' = thy
581       |> (if declare_consts then
583               (map (fn (c, n) => (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
584          else I)
585       |> Theory.add_path rec_name
586       |> PureThy.add_axiomss_i [(("intrs", intr_ts), atts), (("elims", elim_ts), [])]
587       |> (if coind then I else PureThy.add_axioms_i [(("internal_induct", ind_t), [])]);
589     val intrs = PureThy.get_thms thy' "intrs";
590     val elims = PureThy.get_thms thy' "elims";
591     val raw_induct = if coind then TrueI else
592       standard (split_rule (PureThy.get_thm thy' "internal_induct"));
593     val induct = if coind orelse length cs > 1 then raw_induct
594       else standard (raw_induct RSN (2, rev_mp));
596     val thy'' =
597       thy'
598       |> (if coind then I else PureThy.add_thms [(("induct", induct), [])])
599       |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts)
600       |> Theory.parent_path;
601   in (thy'',
602     {defs = [],
603      mono = TrueI,
604      unfold = TrueI,
605      intrs = intrs,
606      elims = elims,
607      mk_cases = mk_cases elims,
608      raw_induct = raw_induct,
609      induct = induct})
610   end;
614 (** introduction of (co)inductive sets **)
616 fun add_inductive_i verbose declare_consts alt_name coind no_elim no_ind cs
617     atts intros monos con_defs thy =
618   let
619     val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
620     val sign = Theory.sign_of thy;
622     (*parameters should agree for all mutually recursive components*)
623     val (_, params) = strip_comb (hd cs);
624     val paramTs = map (try' (snd o dest_Free) "Parameter in recursive\
625       \ component is not a free variable: " sign) params;
627     val cTs = map (try' (HOLogic.dest_setT o fastype_of)
628       "Recursive component not of type set: " sign) cs;
630     val full_cnames = map (try' (fst o dest_Const o head_of)
631       "Recursive set not previously declared as constant: " sign) cs;
632     val cnames = map Sign.base_name full_cnames;
634     val _ = assert_all Syntax.is_identifier cnames	(* FIXME why? *)
635        (fn a => "Base name of recursive set not an identifier: " ^ a);
636     val _ = seq (check_rule sign cs o snd o fst) intros;
638     val (thy1, result) =
639       (if ! quick_and_dirty then add_ind_axm else add_ind_def)
640         verbose declare_consts alt_name coind no_elim no_ind cs atts intros monos
641         con_defs thy params paramTs cTs cnames;
642     val thy2 = thy1 |> put_inductives full_cnames ({names = full_cnames, coind = coind}, result);
643   in (thy2, result) end;
647 (** external interface **)
649 fun add_inductive verbose coind c_strings srcs intro_srcs raw_monos raw_con_defs thy =
650   let
651     val sign = Theory.sign_of thy;
652     val cs = map (readtm (Theory.sign_of thy) HOLogic.termTVar) c_strings;
654     val atts = map (Attrib.global_attribute thy) srcs;
655     val intr_names = map (fst o fst) intro_srcs;
656     val intr_ts = map (readtm (Theory.sign_of thy) propT o snd o fst) intro_srcs;
657     val intr_atts = map (map (Attrib.global_attribute thy) o snd) intro_srcs;
659     (* the following code ensures that each recursive set *)
660     (* always has the same type in all introduction rules *)
662     val {tsig, ...} = Sign.rep_sg sign;
663     val add_term_consts_2 =
664       foldl_aterms (fn (cs, Const c) => c ins cs | (cs, _) => cs);
665     fun varify (t, (i, ts)) =
666       let val t' = map_term_types (incr_tvar (i + 1)) (Type.varify (t, []))
667       in (maxidx_of_term t', t'::ts) end;
668     val (i, cs') = foldr varify (cs, (~1, []));
669     val (i', intr_ts') = foldr varify (intr_ts, (i, []));
670     val rec_consts = foldl add_term_consts_2 ([], cs');
671     val intr_consts = foldl add_term_consts_2 ([], intr_ts');
672     fun unify (env, (cname, cT)) =
673       let val consts = map snd (filter (fn c => fst c = cname) intr_consts)
674       in (foldl (fn ((env', j'), Tp) => Type.unify tsig j' env' Tp)
675         (env, (replicate (length consts) cT) ~~ consts)) handle _ =>
676           error ("Occurrences of constant '" ^ cname ^
677             "' have incompatible types")
678       end;
679     val (env, _) = foldl unify (([], i'), rec_consts);
680     fun typ_subst_TVars_2 env T = let val T' = typ_subst_TVars env T
681       in if T = T' then T else typ_subst_TVars_2 env T' end;
682     val subst = fst o Type.freeze_thaw o
683       (map_term_types (typ_subst_TVars_2 env));
684     val cs'' = map subst cs';
685     val intr_ts'' = map subst intr_ts';
687     val ((thy', con_defs), monos) = thy
688       |> IsarThy.apply_theorems raw_monos
689       |> apfst (IsarThy.apply_theorems raw_con_defs);
690   in
691     add_inductive_i verbose false "" coind false false cs''
692       atts ((intr_names ~~ intr_ts'') ~~ intr_atts) monos con_defs thy'
693   end;
697 (** package setup **)
699 (* setup theory *)
701 val setup = [InductiveData.init];
704 (* outer syntax *)
706 local open OuterParse in
708 fun mk_ind coind (((sets, (atts, intrs)), monos), con_defs) =
709   #1 o add_inductive true coind sets atts (map triple_swap intrs) monos con_defs;
711 fun ind_decl coind =
712   Scan.repeat1 term --
713   (\$\$\$ "intrs" |-- !!! (opt_attribs -- Scan.repeat1 (opt_thm_name ":" -- term))) --
714   Scan.optional (\$\$\$ "monos" |-- !!! xthms1) [] --
715   Scan.optional (\$\$\$ "con_defs" |-- !!! xthms1) []
716   >> (Toplevel.theory o mk_ind coind);
718 val inductiveP = OuterSyntax.command "inductive" "define inductive sets" (ind_decl false);
719 val coinductiveP = OuterSyntax.command "coinductive" "define coinductive sets" (ind_decl true);
721 val _ = OuterSyntax.add_keywords ["intrs", "monos", "con_defs"];
722 val _ = OuterSyntax.add_parsers [inductiveP, coinductiveP];
724 end;
727 end;