src/HOL/Tools/inductive_package.ML
 author haftmann Fri Jul 20 14:28:25 2007 +0200 (2007-07-20) changeset 23881 851c74f1bb69 parent 23762 24eef53a9ad3 child 24039 273698405054 permissions -rw-r--r--
moved class ord from Orderings.thy to HOL.thy
```     1 (*  Title:      HOL/Tools/inductive_package.ML
```
```     2     ID:         \$Id\$
```
```     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
```
```     4     Author:     Stefan Berghofer and Markus Wenzel, TU Muenchen
```
```     5
```
```     6 (Co)Inductive Definition module for HOL.
```
```     7
```
```     8 Features:
```
```     9   * least or greatest fixedpoints
```
```    10   * mutually recursive definitions
```
```    11   * definitions involving arbitrary monotone operators
```
```    12   * automatically proves introduction and elimination rules
```
```    13
```
```    14   Introduction rules have the form
```
```    15   [| M Pj ti, ..., Q x, ... |] ==> Pk t
```
```    16   where M is some monotone operator (usually the identity)
```
```    17   Q x is any side condition on the free variables
```
```    18   ti, t are any terms
```
```    19   Pj, Pk are two of the predicates being defined in mutual recursion
```
```    20 *)
```
```    21
```
```    22 signature BASIC_INDUCTIVE_PACKAGE =
```
```    23 sig
```
```    24   val quiet_mode: bool ref
```
```    25   type inductive_result
```
```    26   val morph_result: morphism -> inductive_result -> inductive_result
```
```    27   type inductive_info
```
```    28   val the_inductive: Proof.context -> string -> inductive_info
```
```    29   val print_inductives: Proof.context -> unit
```
```    30   val mono_add: attribute
```
```    31   val mono_del: attribute
```
```    32   val get_monos: Proof.context -> thm list
```
```    33   val mk_cases: Proof.context -> term -> thm
```
```    34   val inductive_forall_name: string
```
```    35   val inductive_forall_def: thm
```
```    36   val rulify: thm -> thm
```
```    37   val inductive_cases: ((bstring * Attrib.src list) * string list) list ->
```
```    38     Proof.context -> thm list list * local_theory
```
```    39   val inductive_cases_i: ((bstring * Attrib.src list) * term list) list ->
```
```    40     Proof.context -> thm list list * local_theory
```
```    41   val add_inductive_i: bool -> bstring -> bool -> bool -> bool ->
```
```    42     (string * typ option * mixfix) list ->
```
```    43     (string * typ option) list -> ((bstring * Attrib.src list) * term) list -> thm list ->
```
```    44       local_theory -> inductive_result * local_theory
```
```    45   val add_inductive: bool -> bool -> (string * string option * mixfix) list ->
```
```    46     (string * string option * mixfix) list ->
```
```    47     ((bstring * Attrib.src list) * string) list -> (thmref * Attrib.src list) list ->
```
```    48     local_theory -> inductive_result * local_theory
```
```    49   val add_inductive_global: bool -> bstring -> bool -> bool -> bool ->
```
```    50     (string * typ option * mixfix) list -> (string * typ option) list ->
```
```    51     ((bstring * Attrib.src list) * term) list -> thm list -> theory -> inductive_result * theory
```
```    52   val arities_of: thm -> (string * int) list
```
```    53   val params_of: thm -> term list
```
```    54   val partition_rules: thm -> thm list -> (string * thm list) list
```
```    55   val unpartition_rules: thm list -> (string * 'a list) list -> 'a list
```
```    56   val infer_intro_vars: thm -> int -> thm list -> term list list
```
```    57   val setup: theory -> theory
```
```    58 end;
```
```    59
```
```    60 signature INDUCTIVE_PACKAGE =
```
```    61 sig
```
```    62   include BASIC_INDUCTIVE_PACKAGE
```
```    63   type add_ind_def
```
```    64   val declare_rules: bstring -> bool -> bool -> string list ->
```
```    65     thm list -> bstring list -> Attrib.src list list -> (thm * string list) list ->
```
```    66     thm -> local_theory -> thm list * thm list * thm * local_theory
```
```    67   val add_ind_def: add_ind_def
```
```    68   val gen_add_inductive_i: add_ind_def ->
```
```    69     bool -> bstring -> bool -> bool -> bool ->
```
```    70     (string * typ option * mixfix) list ->
```
```    71     (string * typ option) list -> ((bstring * Attrib.src list) * term) list -> thm list ->
```
```    72       local_theory -> inductive_result * local_theory
```
```    73   val gen_add_inductive: add_ind_def ->
```
```    74     bool -> bool -> (string * string option * mixfix) list ->
```
```    75     (string * string option * mixfix) list ->
```
```    76     ((bstring * Attrib.src list) * string) list -> (thmref * Attrib.src list) list ->
```
```    77     local_theory -> inductive_result * local_theory
```
```    78   val gen_ind_decl: add_ind_def ->
```
```    79     bool -> OuterParse.token list ->
```
```    80     (Toplevel.transition -> Toplevel.transition) * OuterParse.token list
```
```    81 end;
```
```    82
```
```    83 structure InductivePackage: INDUCTIVE_PACKAGE =
```
```    84 struct
```
```    85
```
```    86
```
```    87 (** theory context references **)
```
```    88
```
```    89 val mono_name = "Orderings.mono";
```
```    90 val gfp_name = "FixedPoint.gfp";
```
```    91 val lfp_name = "FixedPoint.lfp";
```
```    92
```
```    93 val inductive_forall_name = "HOL.induct_forall";
```
```    94 val inductive_forall_def = thm "induct_forall_def";
```
```    95 val inductive_conj_name = "HOL.induct_conj";
```
```    96 val inductive_conj_def = thm "induct_conj_def";
```
```    97 val inductive_conj = thms "induct_conj";
```
```    98 val inductive_atomize = thms "induct_atomize";
```
```    99 val inductive_rulify = thms "induct_rulify";
```
```   100 val inductive_rulify_fallback = thms "induct_rulify_fallback";
```
```   101
```
```   102 val notTrueE = TrueI RSN (2, notE);
```
```   103 val notFalseI = Seq.hd (atac 1 notI);
```
```   104 val simp_thms' = map (fn s => mk_meta_eq (the (find_first
```
```   105   (equal (Sign.read_prop HOL.thy s) o prop_of) simp_thms)))
```
```   106   ["(~True) = False", "(~False) = True",
```
```   107    "(True --> ?P) = ?P", "(False --> ?P) = True",
```
```   108    "(?P & True) = ?P", "(True & ?P) = ?P"];
```
```   109
```
```   110
```
```   111
```
```   112 (** context data **)
```
```   113
```
```   114 type inductive_result =
```
```   115   {preds: term list, elims: thm list, raw_induct: thm,
```
```   116    induct: thm, intrs: thm list};
```
```   117
```
```   118 fun morph_result phi {preds, elims, raw_induct: thm, induct, intrs} =
```
```   119   let
```
```   120     val term = Morphism.term phi;
```
```   121     val thm = Morphism.thm phi;
```
```   122     val fact = Morphism.fact phi;
```
```   123   in
```
```   124    {preds = map term preds, elims = fact elims, raw_induct = thm raw_induct,
```
```   125     induct = thm induct, intrs = fact intrs}
```
```   126   end;
```
```   127
```
```   128 type inductive_info =
```
```   129   {names: string list, coind: bool} * inductive_result;
```
```   130
```
```   131 structure InductiveData = GenericDataFun
```
```   132 (
```
```   133   type T = inductive_info Symtab.table * thm list;
```
```   134   val empty = (Symtab.empty, []);
```
```   135   val extend = I;
```
```   136   fun merge _ ((tab1, monos1), (tab2, monos2)) =
```
```   137     (Symtab.merge (K true) (tab1, tab2), Drule.merge_rules (monos1, monos2));
```
```   138 );
```
```   139
```
```   140 val get_inductives = InductiveData.get o Context.Proof;
```
```   141
```
```   142 fun print_inductives ctxt =
```
```   143   let
```
```   144     val (tab, monos) = get_inductives ctxt;
```
```   145     val space = Consts.space_of (ProofContext.consts_of ctxt);
```
```   146   in
```
```   147     [Pretty.strs ("(co)inductives:" :: map #1 (NameSpace.extern_table (space, tab))),
```
```   148      Pretty.big_list "monotonicity rules:" (map (ProofContext.pretty_thm ctxt) monos)]
```
```   149     |> Pretty.chunks |> Pretty.writeln
```
```   150   end;
```
```   151
```
```   152
```
```   153 (* get and put data *)
```
```   154
```
```   155 fun the_inductive ctxt name =
```
```   156   (case Symtab.lookup (#1 (get_inductives ctxt)) name of
```
```   157     NONE => error ("Unknown (co)inductive predicate " ^ quote name)
```
```   158   | SOME info => info);
```
```   159
```
```   160 fun put_inductives names info = InductiveData.map (apfst (fn tab =>
```
```   161   fold (fn name => Symtab.update_new (name, info)) names tab
```
```   162     handle Symtab.DUP d => error ("Duplicate definition of (co)inductive predicate " ^ quote d)));
```
```   163
```
```   164
```
```   165
```
```   166 (** monotonicity rules **)
```
```   167
```
```   168 val get_monos = #2 o get_inductives;
```
```   169 val map_monos = InductiveData.map o apsnd;
```
```   170
```
```   171 fun mk_mono thm =
```
```   172   let
```
```   173     val concl = concl_of thm;
```
```   174     fun eq2mono thm' = [thm' RS (thm' RS eq_to_mono)] @
```
```   175       (case concl of
```
```   176           (_ \$ (_ \$ (Const ("Not", _) \$ _) \$ _)) => []
```
```   177         | _ => [thm' RS (thm' RS eq_to_mono2)]);
```
```   178     fun dest_less_concl thm = dest_less_concl (thm RS le_funD)
```
```   179       handle THM _ => thm RS le_boolD
```
```   180   in
```
```   181     case concl of
```
```   182       Const ("==", _) \$ _ \$ _ => eq2mono (thm RS meta_eq_to_obj_eq)
```
```   183     | _ \$ (Const ("op =", _) \$ _ \$ _) => eq2mono thm
```
```   184     | _ \$ (Const ("HOL.ord_class.less_eq", _) \$ _ \$ _) =>
```
```   185       [dest_less_concl (Seq.hd (REPEAT (FIRSTGOAL
```
```   186          (resolve_tac [le_funI, le_boolI'])) thm))]
```
```   187     | _ => [thm]
```
```   188   end handle THM _ => error ("Bad monotonicity theorem:\n" ^ string_of_thm thm);
```
```   189
```
```   190 val mono_add = Thm.declaration_attribute (map_monos o fold Drule.add_rule o mk_mono);
```
```   191 val mono_del = Thm.declaration_attribute (map_monos o fold Drule.del_rule o mk_mono);
```
```   192
```
```   193
```
```   194
```
```   195 (** misc utilities **)
```
```   196
```
```   197 val quiet_mode = ref false;
```
```   198 fun message s = if ! quiet_mode then () else writeln s;
```
```   199 fun clean_message s = if ! quick_and_dirty then () else message s;
```
```   200
```
```   201 val note_theorems = LocalTheory.notes Thm.theoremK;
```
```   202 val note_theorem = LocalTheory.note Thm.theoremK;
```
```   203
```
```   204 fun coind_prefix true = "co"
```
```   205   | coind_prefix false = "";
```
```   206
```
```   207 fun log b m n = if m >= n then 0 else 1 + log b (b * m) n;
```
```   208
```
```   209 fun make_bool_args f g [] i = []
```
```   210   | make_bool_args f g (x :: xs) i =
```
```   211       (if i mod 2 = 0 then f x else g x) :: make_bool_args f g xs (i div 2);
```
```   212
```
```   213 fun make_bool_args' xs =
```
```   214   make_bool_args (K HOLogic.false_const) (K HOLogic.true_const) xs;
```
```   215
```
```   216 fun find_arg T x [] = sys_error "find_arg"
```
```   217   | find_arg T x ((p as (_, (SOME _, _))) :: ps) =
```
```   218       apsnd (cons p) (find_arg T x ps)
```
```   219   | find_arg T x ((p as (U, (NONE, y))) :: ps) =
```
```   220       if (T: typ) = U then (y, (U, (SOME x, y)) :: ps)
```
```   221       else apsnd (cons p) (find_arg T x ps);
```
```   222
```
```   223 fun make_args Ts xs =
```
```   224   map (fn (T, (NONE, ())) => Const ("arbitrary", T) | (_, (SOME t, ())) => t)
```
```   225     (fold (fn (t, T) => snd o find_arg T t) xs (map (rpair (NONE, ())) Ts));
```
```   226
```
```   227 fun make_args' Ts xs Us =
```
```   228   fst (fold_map (fn T => find_arg T ()) Us (Ts ~~ map (pair NONE) xs));
```
```   229
```
```   230 fun dest_predicate cs params t =
```
```   231   let
```
```   232     val k = length params;
```
```   233     val (c, ts) = strip_comb t;
```
```   234     val (xs, ys) = chop k ts;
```
```   235     val i = find_index_eq c cs;
```
```   236   in
```
```   237     if xs = params andalso i >= 0 then
```
```   238       SOME (c, i, ys, chop (length ys)
```
```   239         (List.drop (binder_types (fastype_of c), k)))
```
```   240     else NONE
```
```   241   end;
```
```   242
```
```   243 fun mk_names a 0 = []
```
```   244   | mk_names a 1 = [a]
```
```   245   | mk_names a n = map (fn i => a ^ string_of_int i) (1 upto n);
```
```   246
```
```   247
```
```   248
```
```   249 (** process rules **)
```
```   250
```
```   251 local
```
```   252
```
```   253 fun err_in_rule ctxt name t msg =
```
```   254   error (cat_lines ["Ill-formed introduction rule " ^ quote name,
```
```   255     ProofContext.string_of_term ctxt t, msg]);
```
```   256
```
```   257 fun err_in_prem ctxt name t p msg =
```
```   258   error (cat_lines ["Ill-formed premise", ProofContext.string_of_term ctxt p,
```
```   259     "in introduction rule " ^ quote name, ProofContext.string_of_term ctxt t, msg]);
```
```   260
```
```   261 val bad_concl = "Conclusion of introduction rule must be an inductive predicate";
```
```   262
```
```   263 val bad_ind_occ = "Inductive predicate occurs in argument of inductive predicate";
```
```   264
```
```   265 val bad_app = "Inductive predicate must be applied to parameter(s) ";
```
```   266
```
```   267 fun atomize_term thy = MetaSimplifier.rewrite_term thy inductive_atomize [];
```
```   268
```
```   269 in
```
```   270
```
```   271 fun check_rule ctxt cs params ((name, att), rule) =
```
```   272   let
```
```   273     val params' = Term.variant_frees rule (Logic.strip_params rule);
```
```   274     val frees = rev (map Free params');
```
```   275     val concl = subst_bounds (frees, Logic.strip_assums_concl rule);
```
```   276     val prems = map (curry subst_bounds frees) (Logic.strip_assums_hyp rule);
```
```   277     val rule' = Logic.list_implies (prems, concl);
```
```   278     val aprems = map (atomize_term (ProofContext.theory_of ctxt)) prems;
```
```   279     val arule = list_all_free (params', Logic.list_implies (aprems, concl));
```
```   280
```
```   281     fun check_ind err t = case dest_predicate cs params t of
```
```   282         NONE => err (bad_app ^
```
```   283           commas (map (ProofContext.string_of_term ctxt) params))
```
```   284       | SOME (_, _, ys, _) =>
```
```   285           if exists (fn c => exists (fn t => Logic.occs (c, t)) ys) cs
```
```   286           then err bad_ind_occ else ();
```
```   287
```
```   288     fun check_prem' prem t =
```
```   289       if head_of t mem cs then
```
```   290         check_ind (err_in_prem ctxt name rule prem) t
```
```   291       else (case t of
```
```   292           Abs (_, _, t) => check_prem' prem t
```
```   293         | t \$ u => (check_prem' prem t; check_prem' prem u)
```
```   294         | _ => ());
```
```   295
```
```   296     fun check_prem (prem, aprem) =
```
```   297       if can HOLogic.dest_Trueprop aprem then check_prem' prem prem
```
```   298       else err_in_prem ctxt name rule prem "Non-atomic premise";
```
```   299   in
```
```   300     (case concl of
```
```   301        Const ("Trueprop", _) \$ t =>
```
```   302          if head_of t mem cs then
```
```   303            (check_ind (err_in_rule ctxt name rule') t;
```
```   304             List.app check_prem (prems ~~ aprems))
```
```   305          else err_in_rule ctxt name rule' bad_concl
```
```   306      | _ => err_in_rule ctxt name rule' bad_concl);
```
```   307     ((name, att), arule)
```
```   308   end;
```
```   309
```
```   310 val rulify =  (* FIXME norm_hhf *)
```
```   311   hol_simplify inductive_conj
```
```   312   #> hol_simplify inductive_rulify
```
```   313   #> hol_simplify inductive_rulify_fallback
```
```   314   (*#> standard*);
```
```   315
```
```   316 end;
```
```   317
```
```   318
```
```   319
```
```   320 (** proofs for (co)inductive predicates **)
```
```   321
```
```   322 (* prove monotonicity -- NOT subject to quick_and_dirty! *)
```
```   323
```
```   324 fun prove_mono predT fp_fun monos ctxt =
```
```   325  (message "  Proving monotonicity ...";
```
```   326   Goal.prove ctxt [] []   (*NO quick_and_dirty here!*)
```
```   327     (HOLogic.mk_Trueprop
```
```   328       (Const (mono_name, (predT --> predT) --> HOLogic.boolT) \$ fp_fun))
```
```   329     (fn _ => EVERY [rtac monoI 1,
```
```   330       REPEAT (resolve_tac [le_funI, le_boolI'] 1),
```
```   331       REPEAT (FIRST
```
```   332         [atac 1,
```
```   333          resolve_tac (List.concat (map mk_mono monos) @ get_monos ctxt) 1,
```
```   334          etac le_funE 1, dtac le_boolD 1])]));
```
```   335
```
```   336
```
```   337 (* prove introduction rules *)
```
```   338
```
```   339 fun prove_intrs coind mono fp_def k params intr_ts rec_preds_defs ctxt =
```
```   340   let
```
```   341     val _ = clean_message "  Proving the introduction rules ...";
```
```   342
```
```   343     val unfold = funpow k (fn th => th RS fun_cong)
```
```   344       (mono RS (fp_def RS
```
```   345         (if coind then def_gfp_unfold else def_lfp_unfold)));
```
```   346
```
```   347     fun select_disj 1 1 = []
```
```   348       | select_disj _ 1 = [rtac disjI1]
```
```   349       | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
```
```   350
```
```   351     val rules = [refl, TrueI, notFalseI, exI, conjI];
```
```   352
```
```   353     val intrs = map_index (fn (i, intr) => rulify
```
```   354       (SkipProof.prove ctxt (map (fst o dest_Free) params) [] intr (fn _ => EVERY
```
```   355        [rewrite_goals_tac rec_preds_defs,
```
```   356         rtac (unfold RS iffD2) 1,
```
```   357         EVERY1 (select_disj (length intr_ts) (i + 1)),
```
```   358         (*Not ares_tac, since refl must be tried before any equality assumptions;
```
```   359           backtracking may occur if the premises have extra variables!*)
```
```   360         DEPTH_SOLVE_1 (resolve_tac rules 1 APPEND assume_tac 1)]))) intr_ts
```
```   361
```
```   362   in (intrs, unfold) end;
```
```   363
```
```   364
```
```   365 (* prove elimination rules *)
```
```   366
```
```   367 fun prove_elims cs params intr_ts intr_names unfold rec_preds_defs ctxt =
```
```   368   let
```
```   369     val _ = clean_message "  Proving the elimination rules ...";
```
```   370
```
```   371     val ([pname], ctxt') = ctxt |>
```
```   372       Variable.add_fixes (map (fst o dest_Free) params) |> snd |>
```
```   373       Variable.variant_fixes ["P"];
```
```   374     val P = HOLogic.mk_Trueprop (Free (pname, HOLogic.boolT));
```
```   375
```
```   376     fun dest_intr r =
```
```   377       (the (dest_predicate cs params (HOLogic.dest_Trueprop (Logic.strip_assums_concl r))),
```
```   378        Logic.strip_assums_hyp r, Logic.strip_params r);
```
```   379
```
```   380     val intrs = map dest_intr intr_ts ~~ intr_names;
```
```   381
```
```   382     val rules1 = [disjE, exE, FalseE];
```
```   383     val rules2 = [conjE, FalseE, notTrueE];
```
```   384
```
```   385     fun prove_elim c =
```
```   386       let
```
```   387         val Ts = List.drop (binder_types (fastype_of c), length params);
```
```   388         val (anames, ctxt'') = Variable.variant_fixes (mk_names "a" (length Ts)) ctxt';
```
```   389         val frees = map Free (anames ~~ Ts);
```
```   390
```
```   391         fun mk_elim_prem ((_, _, us, _), ts, params') =
```
```   392           list_all (params',
```
```   393             Logic.list_implies (map (HOLogic.mk_Trueprop o HOLogic.mk_eq)
```
```   394               (frees ~~ us) @ ts, P));
```
```   395         val c_intrs = (List.filter (equal c o #1 o #1 o #1) intrs);
```
```   396         val prems = HOLogic.mk_Trueprop (list_comb (c, params @ frees)) ::
```
```   397            map mk_elim_prem (map #1 c_intrs)
```
```   398       in
```
```   399         (SkipProof.prove ctxt'' [] prems P
```
```   400           (fn {prems, ...} => EVERY
```
```   401             [cut_facts_tac [hd prems] 1,
```
```   402              rewrite_goals_tac rec_preds_defs,
```
```   403              dtac (unfold RS iffD1) 1,
```
```   404              REPEAT (FIRSTGOAL (eresolve_tac rules1)),
```
```   405              REPEAT (FIRSTGOAL (eresolve_tac rules2)),
```
```   406              EVERY (map (fn prem =>
```
```   407                DEPTH_SOLVE_1 (ares_tac [rewrite_rule rec_preds_defs prem, conjI] 1)) (tl prems))])
```
```   408           |> rulify
```
```   409           |> singleton (ProofContext.export ctxt'' ctxt),
```
```   410          map #2 c_intrs)
```
```   411       end
```
```   412
```
```   413    in map prove_elim cs end;
```
```   414
```
```   415
```
```   416 (* derivation of simplified elimination rules *)
```
```   417
```
```   418 local
```
```   419
```
```   420 (*delete needless equality assumptions*)
```
```   421 val refl_thin = Goal.prove_global HOL.thy [] []
```
```   422   (Sign.read_prop HOL.thy "!!P. a = a ==> P ==> P")
```
```   423   (fn _ => assume_tac 1);
```
```   424 val elim_rls = [asm_rl, FalseE, refl_thin, conjE, exE];
```
```   425 val elim_tac = REPEAT o Tactic.eresolve_tac elim_rls;
```
```   426
```
```   427 fun simp_case_tac ss i =
```
```   428   EVERY' [elim_tac, asm_full_simp_tac ss, elim_tac, REPEAT o bound_hyp_subst_tac] i;
```
```   429
```
```   430 in
```
```   431
```
```   432 fun mk_cases ctxt prop =
```
```   433   let
```
```   434     val thy = ProofContext.theory_of ctxt;
```
```   435     val ss = Simplifier.local_simpset_of ctxt;
```
```   436
```
```   437     fun err msg =
```
```   438       error (Pretty.string_of (Pretty.block
```
```   439         [Pretty.str msg, Pretty.fbrk, ProofContext.pretty_term ctxt prop]));
```
```   440
```
```   441     val elims = InductAttrib.find_casesS ctxt prop;
```
```   442
```
```   443     val cprop = Thm.cterm_of thy prop;
```
```   444     val tac = ALLGOALS (simp_case_tac ss) THEN prune_params_tac;
```
```   445     fun mk_elim rl =
```
```   446       Thm.implies_intr cprop (Tactic.rule_by_tactic tac (Thm.assume cprop RS rl))
```
```   447       |> singleton (Variable.export (Variable.auto_fixes prop ctxt) ctxt);
```
```   448   in
```
```   449     (case get_first (try mk_elim) elims of
```
```   450       SOME r => r
```
```   451     | NONE => err "Proposition not an inductive predicate:")
```
```   452   end;
```
```   453
```
```   454 end;
```
```   455
```
```   456
```
```   457 (* inductive_cases *)
```
```   458
```
```   459 fun gen_inductive_cases prep_att prep_prop args lthy =
```
```   460   let
```
```   461     val thy = ProofContext.theory_of lthy;
```
```   462     val facts = args |> map (fn ((a, atts), props) =>
```
```   463       ((a, map (prep_att thy) atts),
```
```   464         map (Thm.no_attributes o single o mk_cases lthy o prep_prop lthy) props));
```
```   465   in lthy |> note_theorems facts |>> map snd end;
```
```   466
```
```   467 val inductive_cases = gen_inductive_cases Attrib.intern_src ProofContext.read_prop;
```
```   468 val inductive_cases_i = gen_inductive_cases (K I) ProofContext.cert_prop;
```
```   469
```
```   470
```
```   471 fun ind_cases src = Method.syntax (Scan.lift (Scan.repeat1 Args.name --
```
```   472     Scan.optional (Args.\$\$\$ "for" |-- Scan.repeat1 Args.name) [])) src
```
```   473   #> (fn ((raw_props, fixes), ctxt) =>
```
```   474     let
```
```   475       val (_, ctxt') = Variable.add_fixes fixes ctxt;
```
```   476       val props = map (ProofContext.read_prop ctxt') raw_props;
```
```   477       val ctxt'' = fold Variable.declare_term props ctxt';
```
```   478       val rules = ProofContext.export ctxt'' ctxt (map (mk_cases ctxt'') props)
```
```   479     in Method.erule 0 rules end);
```
```   480
```
```   481
```
```   482
```
```   483 (* prove induction rule *)
```
```   484
```
```   485 fun prove_indrule cs argTs bs xs rec_const params intr_ts mono
```
```   486     fp_def rec_preds_defs ctxt =
```
```   487   let
```
```   488     val _ = clean_message "  Proving the induction rule ...";
```
```   489     val thy = ProofContext.theory_of ctxt;
```
```   490
```
```   491     (* predicates for induction rule *)
```
```   492
```
```   493     val (pnames, ctxt') = ctxt |>
```
```   494       Variable.add_fixes (map (fst o dest_Free) params) |> snd |>
```
```   495       Variable.variant_fixes (mk_names "P" (length cs));
```
```   496     val preds = map Free (pnames ~~
```
```   497       map (fn c => List.drop (binder_types (fastype_of c), length params) --->
```
```   498         HOLogic.boolT) cs);
```
```   499
```
```   500     (* transform an introduction rule into a premise for induction rule *)
```
```   501
```
```   502     fun mk_ind_prem r =
```
```   503       let
```
```   504         fun subst s = (case dest_predicate cs params s of
```
```   505             SOME (_, i, ys, (_, Ts)) =>
```
```   506               let
```
```   507                 val k = length Ts;
```
```   508                 val bs = map Bound (k - 1 downto 0);
```
```   509                 val P = list_comb (List.nth (preds, i),
```
```   510                   map (incr_boundvars k) ys @ bs);
```
```   511                 val Q = list_abs (mk_names "x" k ~~ Ts,
```
```   512                   HOLogic.mk_binop inductive_conj_name
```
```   513                     (list_comb (incr_boundvars k s, bs), P))
```
```   514               in (Q, case Ts of [] => SOME (s, P) | _ => NONE) end
```
```   515           | NONE => (case s of
```
```   516               (t \$ u) => (fst (subst t) \$ fst (subst u), NONE)
```
```   517             | (Abs (a, T, t)) => (Abs (a, T, fst (subst t)), NONE)
```
```   518             | _ => (s, NONE)));
```
```   519
```
```   520         fun mk_prem (s, prems) = (case subst s of
```
```   521               (_, SOME (t, u)) => t :: u :: prems
```
```   522             | (t, _) => t :: prems);
```
```   523
```
```   524         val SOME (_, i, ys, _) = dest_predicate cs params
```
```   525           (HOLogic.dest_Trueprop (Logic.strip_assums_concl r))
```
```   526
```
```   527       in list_all_free (Logic.strip_params r,
```
```   528         Logic.list_implies (map HOLogic.mk_Trueprop (foldr mk_prem
```
```   529           [] (map HOLogic.dest_Trueprop (Logic.strip_assums_hyp r))),
```
```   530             HOLogic.mk_Trueprop (list_comb (List.nth (preds, i), ys))))
```
```   531       end;
```
```   532
```
```   533     val ind_prems = map mk_ind_prem intr_ts;
```
```   534
```
```   535
```
```   536     (* make conclusions for induction rules *)
```
```   537
```
```   538     val Tss = map (binder_types o fastype_of) preds;
```
```   539     val (xnames, ctxt'') =
```
```   540       Variable.variant_fixes (mk_names "x" (length (flat Tss))) ctxt';
```
```   541     val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
```
```   542         (map (fn (((xnames, Ts), c), P) =>
```
```   543            let val frees = map Free (xnames ~~ Ts)
```
```   544            in HOLogic.mk_imp
```
```   545              (list_comb (c, params @ frees), list_comb (P, frees))
```
```   546            end) (unflat Tss xnames ~~ Tss ~~ cs ~~ preds)));
```
```   547
```
```   548
```
```   549     (* make predicate for instantiation of abstract induction rule *)
```
```   550
```
```   551     val ind_pred = fold_rev lambda (bs @ xs) (foldr1 HOLogic.mk_conj
```
```   552       (map_index (fn (i, P) => foldr HOLogic.mk_imp
```
```   553          (list_comb (P, make_args' argTs xs (binder_types (fastype_of P))))
```
```   554          (make_bool_args HOLogic.mk_not I bs i)) preds));
```
```   555
```
```   556     val ind_concl = HOLogic.mk_Trueprop
```
```   557       (HOLogic.mk_binrel "HOL.ord_class.less_eq" (rec_const, ind_pred));
```
```   558
```
```   559     val raw_fp_induct = (mono RS (fp_def RS def_lfp_induct));
```
```   560
```
```   561     val induct = SkipProof.prove ctxt'' [] ind_prems ind_concl
```
```   562       (fn {prems, ...} => EVERY
```
```   563         [rewrite_goals_tac [inductive_conj_def],
```
```   564          DETERM (rtac raw_fp_induct 1),
```
```   565          REPEAT (resolve_tac [le_funI, le_boolI] 1),
```
```   566          rewrite_goals_tac (inf_fun_eq :: inf_bool_eq :: simp_thms'),
```
```   567          (*This disjE separates out the introduction rules*)
```
```   568          REPEAT (FIRSTGOAL (eresolve_tac [disjE, exE, FalseE])),
```
```   569          (*Now break down the individual cases.  No disjE here in case
```
```   570            some premise involves disjunction.*)
```
```   571          REPEAT (FIRSTGOAL (etac conjE ORELSE' bound_hyp_subst_tac)),
```
```   572          REPEAT (FIRSTGOAL
```
```   573            (resolve_tac [conjI, impI] ORELSE' (etac notE THEN' atac))),
```
```   574          EVERY (map (fn prem => DEPTH_SOLVE_1 (ares_tac [rewrite_rule
```
```   575              (inductive_conj_def :: rec_preds_defs @ simp_thms') prem,
```
```   576            conjI, refl] 1)) prems)]);
```
```   577
```
```   578     val lemma = SkipProof.prove ctxt'' [] []
```
```   579       (Logic.mk_implies (ind_concl, mutual_ind_concl)) (fn _ => EVERY
```
```   580         [rewrite_goals_tac rec_preds_defs,
```
```   581          REPEAT (EVERY
```
```   582            [REPEAT (resolve_tac [conjI, impI] 1),
```
```   583             REPEAT (eresolve_tac [le_funE, le_boolE] 1),
```
```   584             atac 1,
```
```   585             rewrite_goals_tac simp_thms',
```
```   586             atac 1])])
```
```   587
```
```   588   in singleton (ProofContext.export ctxt'' ctxt) (induct RS lemma) end;
```
```   589
```
```   590
```
```   591
```
```   592 (** specification of (co)inductive predicates **)
```
```   593
```
```   594 fun mk_ind_def alt_name coind cs intr_ts monos
```
```   595       params cnames_syn ctxt =
```
```   596   let
```
```   597     val fp_name = if coind then gfp_name else lfp_name;
```
```   598
```
```   599     val argTs = fold (fn c => fn Ts => Ts @
```
```   600       (List.drop (binder_types (fastype_of c), length params) \\ Ts)) cs [];
```
```   601     val k = log 2 1 (length cs);
```
```   602     val predT = replicate k HOLogic.boolT ---> argTs ---> HOLogic.boolT;
```
```   603     val p :: xs = map Free (Variable.variant_frees ctxt intr_ts
```
```   604       (("p", predT) :: (mk_names "x" (length argTs) ~~ argTs)));
```
```   605     val bs = map Free (Variable.variant_frees ctxt (p :: xs @ intr_ts)
```
```   606       (map (rpair HOLogic.boolT) (mk_names "b" k)));
```
```   607
```
```   608     fun subst t = (case dest_predicate cs params t of
```
```   609         SOME (_, i, ts, (Ts, Us)) =>
```
```   610           let
```
```   611             val l = length Us;
```
```   612             val zs = map Bound (l - 1 downto 0)
```
```   613           in
```
```   614             list_abs (map (pair "z") Us, list_comb (p,
```
```   615               make_bool_args' bs i @ make_args argTs
```
```   616                 ((map (incr_boundvars l) ts ~~ Ts) @ (zs ~~ Us))))
```
```   617           end
```
```   618       | NONE => (case t of
```
```   619           t1 \$ t2 => subst t1 \$ subst t2
```
```   620         | Abs (x, T, u) => Abs (x, T, subst u)
```
```   621         | _ => t));
```
```   622
```
```   623     (* transform an introduction rule into a conjunction  *)
```
```   624     (*   [| p_i t; ... |] ==> p_j u                       *)
```
```   625     (* is transformed into                                *)
```
```   626     (*   b_j & x_j = u & p b_j t & ...                    *)
```
```   627
```
```   628     fun transform_rule r =
```
```   629       let
```
```   630         val SOME (_, i, ts, (Ts, _)) = dest_predicate cs params
```
```   631           (HOLogic.dest_Trueprop (Logic.strip_assums_concl r));
```
```   632         val ps = make_bool_args HOLogic.mk_not I bs i @
```
```   633           map HOLogic.mk_eq (make_args' argTs xs Ts ~~ ts) @
```
```   634           map (subst o HOLogic.dest_Trueprop)
```
```   635             (Logic.strip_assums_hyp r)
```
```   636       in foldr (fn ((x, T), P) => HOLogic.exists_const T \$ (Abs (x, T, P)))
```
```   637         (if null ps then HOLogic.true_const else foldr1 HOLogic.mk_conj ps)
```
```   638         (Logic.strip_params r)
```
```   639       end
```
```   640
```
```   641     (* make a disjunction of all introduction rules *)
```
```   642
```
```   643     val fp_fun = fold_rev lambda (p :: bs @ xs)
```
```   644       (if null intr_ts then HOLogic.false_const
```
```   645        else foldr1 HOLogic.mk_disj (map transform_rule intr_ts));
```
```   646
```
```   647     (* add definiton of recursive predicates to theory *)
```
```   648
```
```   649     val rec_name = if alt_name = "" then
```
```   650       space_implode "_" (map fst cnames_syn) else alt_name;
```
```   651
```
```   652     val ((rec_const, (_, fp_def)), ctxt') = ctxt |>
```
```   653       LocalTheory.def Thm.internalK
```
```   654         ((rec_name, case cnames_syn of [(_, syn)] => syn | _ => NoSyn),
```
```   655          (("", []), fold_rev lambda params
```
```   656            (Const (fp_name, (predT --> predT) --> predT) \$ fp_fun)));
```
```   657     val fp_def' = Simplifier.rewrite (HOL_basic_ss addsimps [fp_def])
```
```   658       (cterm_of (ProofContext.theory_of ctxt') (list_comb (rec_const, params)));
```
```   659     val specs = if length cs < 2 then [] else
```
```   660       map_index (fn (i, (name_mx, c)) =>
```
```   661         let
```
```   662           val Ts = List.drop (binder_types (fastype_of c), length params);
```
```   663           val xs = map Free (Variable.variant_frees ctxt intr_ts
```
```   664             (mk_names "x" (length Ts) ~~ Ts))
```
```   665         in
```
```   666           (name_mx, (("", []), fold_rev lambda (params @ xs)
```
```   667             (list_comb (rec_const, params @ make_bool_args' bs i @
```
```   668               make_args argTs (xs ~~ Ts)))))
```
```   669         end) (cnames_syn ~~ cs);
```
```   670     val (consts_defs, ctxt'') = LocalTheory.defs Thm.internalK specs ctxt';
```
```   671     val preds = (case cs of [_] => [rec_const] | _ => map #1 consts_defs);
```
```   672
```
```   673     val mono = prove_mono predT fp_fun monos ctxt''
```
```   674
```
```   675   in (ctxt'', rec_name, mono, fp_def', map (#2 o #2) consts_defs,
```
```   676     list_comb (rec_const, params), preds, argTs, bs, xs)
```
```   677   end;
```
```   678
```
```   679 fun declare_rules rec_name coind no_ind cnames intrs intr_names intr_atts
```
```   680       elims raw_induct ctxt =
```
```   681   let
```
```   682     val ind_case_names = RuleCases.case_names intr_names;
```
```   683     val induct =
```
```   684       if coind then
```
```   685         (raw_induct, [RuleCases.case_names [rec_name],
```
```   686           RuleCases.case_conclusion (rec_name, intr_names),
```
```   687           RuleCases.consumes 1, InductAttrib.coinduct_set (hd cnames)])
```
```   688       else if no_ind orelse length cnames > 1 then
```
```   689         (raw_induct, [ind_case_names, RuleCases.consumes 0])
```
```   690       else (raw_induct RSN (2, rev_mp), [ind_case_names, RuleCases.consumes 1]);
```
```   691
```
```   692     val (intrs', ctxt1) =
```
```   693       ctxt |>
```
```   694       note_theorems
```
```   695         (map (NameSpace.qualified rec_name) intr_names ~~
```
```   696          intr_atts ~~ map (fn th => [([th],
```
```   697            [Attrib.internal (K (ContextRules.intro_query NONE))])]) intrs) |>>
```
```   698       map (hd o snd); (* FIXME? *)
```
```   699     val (((_, elims'), (_, [induct'])), ctxt2) =
```
```   700       ctxt1 |>
```
```   701       note_theorem ((NameSpace.qualified rec_name "intros", []), intrs') ||>>
```
```   702       fold_map (fn (name, (elim, cases)) =>
```
```   703         note_theorem ((NameSpace.qualified (Sign.base_name name) "cases",
```
```   704           [Attrib.internal (K (RuleCases.case_names cases)),
```
```   705            Attrib.internal (K (RuleCases.consumes 1)),
```
```   706            Attrib.internal (K (InductAttrib.cases_set name)),
```
```   707            Attrib.internal (K (ContextRules.elim_query NONE))]), [elim]) #>
```
```   708         apfst (hd o snd)) (if null elims then [] else cnames ~~ elims) ||>>
```
```   709       note_theorem ((NameSpace.qualified rec_name (coind_prefix coind ^ "induct"),
```
```   710         map (Attrib.internal o K) (#2 induct)), [rulify (#1 induct)]);
```
```   711
```
```   712     val ctxt3 = if no_ind orelse coind then ctxt2 else
```
```   713       let val inducts = cnames ~~ ProjectRule.projects ctxt2 (1 upto length cnames) induct'
```
```   714       in
```
```   715         ctxt2 |>
```
```   716         note_theorems [((NameSpace.qualified rec_name "inducts", []),
```
```   717           inducts |> map (fn (name, th) => ([th],
```
```   718             [Attrib.internal (K ind_case_names),
```
```   719              Attrib.internal (K (RuleCases.consumes 1)),
```
```   720              Attrib.internal (K (InductAttrib.induct_set name))])))] |> snd
```
```   721       end
```
```   722   in (intrs', elims', induct', ctxt3) end;
```
```   723
```
```   724 type add_ind_def = bool -> bstring -> bool -> bool -> bool ->
```
```   725   term list -> ((string * Attrib.src list) * term) list -> thm list ->
```
```   726   term list -> (string * mixfix) list ->
```
```   727   local_theory -> inductive_result * local_theory
```
```   728
```
```   729 fun add_ind_def verbose alt_name coind no_elim no_ind cs
```
```   730     intros monos params cnames_syn ctxt =
```
```   731   let
```
```   732     val _ =
```
```   733       if verbose then message ("Proofs for " ^ coind_prefix coind ^ "inductive predicate(s) " ^
```
```   734         commas_quote (map fst cnames_syn)) else ();
```
```   735
```
```   736     val cnames = map (Sign.full_name (ProofContext.theory_of ctxt) o #1) cnames_syn;  (* FIXME *)
```
```   737     val ((intr_names, intr_atts), intr_ts) =
```
```   738       apfst split_list (split_list (map (check_rule ctxt cs params) intros));
```
```   739
```
```   740     val (ctxt1, rec_name, mono, fp_def, rec_preds_defs, rec_const, preds,
```
```   741       argTs, bs, xs) = mk_ind_def alt_name coind cs intr_ts
```
```   742         monos params cnames_syn ctxt;
```
```   743
```
```   744     val (intrs, unfold) = prove_intrs coind mono fp_def (length bs + length xs)
```
```   745       params intr_ts rec_preds_defs ctxt1;
```
```   746     val elims = if no_elim then [] else
```
```   747       prove_elims cs params intr_ts intr_names unfold rec_preds_defs ctxt1;
```
```   748     val raw_induct = zero_var_indexes
```
```   749       (if no_ind then Drule.asm_rl else
```
```   750        if coind then
```
```   751          singleton (ProofContext.export
```
```   752            (snd (Variable.add_fixes (map (fst o dest_Free) params) ctxt1)) ctxt1)
```
```   753            (rotate_prems ~1 (ObjectLogic.rulify (rule_by_tactic
```
```   754              (rewrite_tac [le_fun_def, le_bool_def, sup_fun_eq, sup_bool_eq] THEN
```
```   755                fold_tac rec_preds_defs) (mono RS (fp_def RS def_coinduct)))))
```
```   756        else
```
```   757          prove_indrule cs argTs bs xs rec_const params intr_ts mono fp_def
```
```   758            rec_preds_defs ctxt1);
```
```   759
```
```   760     val (intrs', elims', induct, ctxt2) = declare_rules rec_name coind no_ind
```
```   761       cnames intrs intr_names intr_atts elims raw_induct ctxt1;
```
```   762
```
```   763     val names = map #1 cnames_syn;
```
```   764     val result =
```
```   765       {preds = preds,
```
```   766        intrs = intrs',
```
```   767        elims = elims',
```
```   768        raw_induct = rulify raw_induct,
```
```   769        induct = induct};
```
```   770
```
```   771     val ctxt3 = ctxt2
```
```   772       |> Context.proof_map (put_inductives names ({names = names, coind = coind}, result))
```
```   773       |> LocalTheory.declaration (fn phi =>
```
```   774         let
```
```   775           val names' = map (LocalTheory.target_name ctxt2 o Morphism.name phi) names;
```
```   776           val result' = morph_result phi result;
```
```   777         in put_inductives names' ({names = names', coind = coind}, result') end);
```
```   778   in (result, ctxt3) end;
```
```   779
```
```   780
```
```   781 (* external interfaces *)
```
```   782
```
```   783 fun gen_add_inductive_i mk_def verbose alt_name coind no_elim no_ind
```
```   784     cnames_syn pnames pre_intros monos ctxt =
```
```   785   let
```
```   786     val thy = ProofContext.theory_of ctxt;
```
```   787     val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
```
```   788
```
```   789     val frees = fold (Term.add_frees o snd) pre_intros [];
```
```   790     fun type_of s = (case AList.lookup op = frees s of
```
```   791       NONE => error ("No such variable: " ^ s) | SOME T => T);
```
```   792
```
```   793     fun is_abbrev ((name, atts), t) =
```
```   794       can (Logic.strip_assums_concl #> Logic.dest_equals) t andalso
```
```   795       (name = "" andalso null atts orelse
```
```   796        error "Abbreviations may not have names or attributes");
```
```   797
```
```   798     fun expand_atom tab (t as Free xT) =
```
```   799           the_default t (AList.lookup op = tab xT)
```
```   800       | expand_atom tab t = t;
```
```   801     fun expand [] r = r
```
```   802       | expand tab r = Envir.beta_norm (Term.map_aterms (expand_atom tab) r);
```
```   803
```
```   804     val (_, ctxt') = Variable.add_fixes (map #1 cnames_syn) ctxt;
```
```   805
```
```   806     fun prep_abbrevs [] abbrevs' abbrevs'' = (rev abbrevs', rev abbrevs'')
```
```   807       | prep_abbrevs ((_, abbrev) :: abbrevs) abbrevs' abbrevs'' =
```
```   808           let val ((s, T), t) =
```
```   809             LocalDefs.abs_def (snd (LocalDefs.cert_def ctxt' abbrev))
```
```   810           in case find_first (equal s o #1) cnames_syn of
```
```   811               NONE => error ("Head of abbreviation " ^ quote s ^ " undeclared")
```
```   812             | SOME (_, _, mx) => prep_abbrevs abbrevs
```
```   813                 (((s, T), expand abbrevs' t) :: abbrevs')
```
```   814                 (((s, mx), expand abbrevs' t) :: abbrevs'') (* FIXME: do not expand *)
```
```   815           end;
```
```   816
```
```   817     val (abbrevs, pre_intros') = List.partition is_abbrev pre_intros;
```
```   818     val (abbrevs', abbrevs'') = prep_abbrevs abbrevs [] [];
```
```   819     val _ = (case gen_inter (op = o apsnd fst)
```
```   820       (fold (Term.add_frees o snd) abbrevs' [], abbrevs') of
```
```   821         [] => ()
```
```   822       | xs => error ("Bad abbreviation(s): " ^ commas (map fst xs)));
```
```   823
```
```   824     val params = map
```
```   825       (fn (s, SOME T) => Free (s, T) | (s, NONE) => Free (s, type_of s)) pnames;
```
```   826     val cnames_syn' = filter_out (fn (s, _, _) =>
```
```   827       exists (equal s o fst o fst) abbrevs') cnames_syn;
```
```   828     val cs = map
```
```   829       (fn (s, SOME T, _) => Free (s, T) | (s, NONE, _) => Free (s, type_of s)) cnames_syn';
```
```   830     val cnames_syn'' = map (fn (s, _, mx) => (s, mx)) cnames_syn';
```
```   831
```
```   832     fun close_rule (x, r) = (x, list_all_free (rev (fold_aterms
```
```   833       (fn t as Free (v as (s, _)) =>
```
```   834             if Variable.is_fixed ctxt s orelse member op = cs t orelse
```
```   835               member op = params t then I else insert op = v
```
```   836         | _ => I) r []), r));
```
```   837
```
```   838     val intros = map (apsnd (expand abbrevs') #> close_rule) pre_intros';
```
```   839   in
```
```   840     ctxt |>
```
```   841     mk_def verbose alt_name coind no_elim no_ind cs intros monos
```
```   842       params cnames_syn'' ||>
```
```   843     fold (snd oo LocalTheory.abbrev Syntax.default_mode) abbrevs''
```
```   844   end;
```
```   845
```
```   846 fun gen_add_inductive mk_def verbose coind cnames_syn pnames_syn intro_srcs raw_monos ctxt =
```
```   847   let
```
```   848     val (_, ctxt') = Specification.read_specification (cnames_syn @ pnames_syn) [] ctxt;
```
```   849     val intrs = map (fn ((name, att), s) => apsnd hd (hd (snd (fst
```
```   850       (Specification.read_specification [] [((name, att), [s])] ctxt'))))
```
```   851       handle ERROR msg =>
```
```   852         cat_error msg ("The error(s) above occurred for\n" ^
```
```   853           (if name = "" then "" else name ^ ": ") ^ s)) intro_srcs;
```
```   854     val pnames = map (fn (s, _, _) =>
```
```   855       (s, SOME (ProofContext.infer_type ctxt' s))) pnames_syn;
```
```   856     val cnames_syn' = map (fn (s, _, mx) =>
```
```   857       (s, SOME (ProofContext.infer_type ctxt' s), mx)) cnames_syn;
```
```   858     val (monos, ctxt'') = LocalTheory.theory_result (IsarCmd.apply_theorems raw_monos) ctxt;
```
```   859   in
```
```   860     gen_add_inductive_i mk_def verbose "" coind false false cnames_syn' pnames intrs monos ctxt''
```
```   861   end;
```
```   862
```
```   863 val add_inductive_i = gen_add_inductive_i add_ind_def;
```
```   864 val add_inductive = gen_add_inductive add_ind_def;
```
```   865
```
```   866 fun add_inductive_global verbose alt_name coind no_elim no_ind cnames_syn pnames pre_intros monos =
```
```   867   TheoryTarget.init NONE #>
```
```   868   add_inductive_i verbose alt_name coind no_elim no_ind cnames_syn pnames pre_intros monos #>
```
```   869   (fn (_, lthy) =>
```
```   870     (#2 (the_inductive (LocalTheory.target_of lthy)
```
```   871       (LocalTheory.target_name lthy (#1 (hd cnames_syn)))),
```
```   872     ProofContext.theory_of (LocalTheory.exit lthy)));
```
```   873
```
```   874
```
```   875 (* read off arities of inductive predicates from raw induction rule *)
```
```   876 fun arities_of induct =
```
```   877   map (fn (_ \$ t \$ u) =>
```
```   878       (fst (dest_Const (head_of t)), length (snd (strip_comb u))))
```
```   879     (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
```
```   880
```
```   881 (* read off parameters of inductive predicate from raw induction rule *)
```
```   882 fun params_of induct =
```
```   883   let
```
```   884     val (_ \$ t \$ u :: _) =
```
```   885       HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct));
```
```   886     val (_, ts) = strip_comb t;
```
```   887     val (_, us) = strip_comb u
```
```   888   in
```
```   889     List.take (ts, length ts - length us)
```
```   890   end;
```
```   891
```
```   892 val pname_of_intr =
```
```   893   concl_of #> HOLogic.dest_Trueprop #> head_of #> dest_Const #> fst;
```
```   894
```
```   895 (* partition introduction rules according to predicate name *)
```
```   896 fun partition_rules induct intros =
```
```   897   fold_rev (fn r => AList.map_entry op = (pname_of_intr r) (cons r)) intros
```
```   898     (map (rpair [] o fst) (arities_of induct));
```
```   899
```
```   900 fun unpartition_rules intros xs =
```
```   901   fold_map (fn r => AList.map_entry_yield op = (pname_of_intr r)
```
```   902     (fn x :: xs => (x, xs)) #>> the) intros xs |> fst;
```
```   903
```
```   904 (* infer order of variables in intro rules from order of quantifiers in elim rule *)
```
```   905 fun infer_intro_vars elim arity intros =
```
```   906   let
```
```   907     val thy = theory_of_thm elim;
```
```   908     val _ :: cases = prems_of elim;
```
```   909     val used = map (fst o fst) (Term.add_vars (prop_of elim) []);
```
```   910     fun mtch (t, u) =
```
```   911       let
```
```   912         val params = Logic.strip_params t;
```
```   913         val vars = map (Var o apfst (rpair 0))
```
```   914           (Name.variant_list used (map fst params) ~~ map snd params);
```
```   915         val ts = map (curry subst_bounds (rev vars))
```
```   916           (List.drop (Logic.strip_assums_hyp t, arity));
```
```   917         val us = Logic.strip_imp_prems u;
```
```   918         val tab = fold (Pattern.first_order_match thy) (ts ~~ us)
```
```   919           (Vartab.empty, Vartab.empty);
```
```   920       in
```
```   921         map (Envir.subst_vars tab) vars
```
```   922       end
```
```   923   in
```
```   924     map (mtch o apsnd prop_of) (cases ~~ intros)
```
```   925   end;
```
```   926
```
```   927
```
```   928 (** package setup **)
```
```   929
```
```   930 (* setup theory *)
```
```   931
```
```   932 val setup =
```
```   933   Method.add_methods [("ind_cases", ind_cases,
```
```   934     "dynamic case analysis on predicates")] #>
```
```   935   Attrib.add_attributes [("mono", Attrib.add_del_args mono_add mono_del,
```
```   936     "declaration of monotonicity rule")];
```
```   937
```
```   938
```
```   939 (* outer syntax *)
```
```   940
```
```   941 local structure P = OuterParse and K = OuterKeyword in
```
```   942
```
```   943 (* FIXME tmp *)
```
```   944 fun flatten_specification specs = specs |> maps
```
```   945   (fn (a, (concl, [])) => concl |> map
```
```   946         (fn ((b, atts), [B]) =>
```
```   947               if a = "" then ((b, atts), B)
```
```   948               else if b = "" then ((a, atts), B)
```
```   949               else error ("Illegal nested case names " ^ quote (NameSpace.append a b))
```
```   950           | ((b, _), _) => error ("Illegal simultaneous specification " ^ quote b))
```
```   951     | (a, _) => error ("Illegal local specification parameters for " ^ quote a));
```
```   952
```
```   953 fun gen_ind_decl mk_def coind =
```
```   954   P.opt_target --
```
```   955   P.fixes -- P.for_fixes --
```
```   956   Scan.optional (P.\$\$\$ "where" |-- P.!!! SpecParse.specification) [] --
```
```   957   Scan.optional (P.\$\$\$ "monos" |-- P.!!! SpecParse.xthms1) []
```
```   958   >> (fn ((((loc, preds), params), specs), monos) =>
```
```   959     Toplevel.local_theory loc
```
```   960       (fn lthy => lthy |> gen_add_inductive mk_def true coind preds params
```
```   961          (flatten_specification specs) monos |> snd));
```
```   962
```
```   963 val ind_decl = gen_ind_decl add_ind_def;
```
```   964
```
```   965 val inductiveP =
```
```   966   OuterSyntax.command "inductive" "define inductive predicates" K.thy_decl (ind_decl false);
```
```   967
```
```   968 val coinductiveP =
```
```   969   OuterSyntax.command "coinductive" "define coinductive predicates" K.thy_decl (ind_decl true);
```
```   970
```
```   971
```
```   972 val inductive_casesP =
```
```   973   OuterSyntax.command "inductive_cases"
```
```   974     "create simplified instances of elimination rules (improper)" K.thy_script
```
```   975     (P.opt_target -- P.and_list1 SpecParse.spec
```
```   976       >> (fn (loc, specs) => Toplevel.local_theory loc (snd o inductive_cases specs)));
```
```   977
```
```   978 val _ = OuterSyntax.add_keywords ["monos"];
```
```   979 val _ = OuterSyntax.add_parsers [inductiveP, coinductiveP, inductive_casesP];
```
```   980
```
```   981 end;
```
```   982
```
```   983 end;
```