src/HOL/BNF/Tools/bnf_fp_rec_sugar.ML
author blanchet
Mon Nov 04 14:46:38 2013 +0100 (2013-11-04)
changeset 54243 a596292be9a8
parent 54239 9bd91d5d8a7b
permissions -rw-r--r--
more robust n2m w.r.t. 'let's
blanchet@53303
     1
(*  Title:      HOL/BNF/Tools/bnf_fp_rec_sugar.ML
blanchet@53303
     2
    Author:     Lorenz Panny, TU Muenchen
blanchet@53303
     3
    Copyright   2013
blanchet@53303
     4
blanchet@53303
     5
Recursor and corecursor sugar.
blanchet@53303
     6
*)
blanchet@53303
     7
blanchet@53303
     8
signature BNF_FP_REC_SUGAR =
blanchet@53303
     9
sig
traytel@54013
    10
  val add_primrec: (binding * typ option * mixfix) list ->
traytel@54013
    11
    (Attrib.binding * term) list -> local_theory -> (term list * thm list list) * local_theory
blanchet@53303
    12
  val add_primrec_cmd: (binding * string option * mixfix) list ->
traytel@54013
    13
    (Attrib.binding * string) list -> local_theory -> (term list * thm list list) * local_theory
traytel@54013
    14
  val add_primrec_global: (binding * typ option * mixfix) list ->
traytel@54013
    15
    (Attrib.binding * term) list -> theory -> (term list * thm list list) * theory
traytel@54013
    16
  val add_primrec_overloaded: (string * (string * typ) * bool) list ->
traytel@54013
    17
    (binding * typ option * mixfix) list ->
traytel@54013
    18
    (Attrib.binding * term) list -> theory -> (term list * thm list list) * theory
traytel@54013
    19
  val add_primrec_simple: ((binding * typ) * mixfix) list -> term list ->
traytel@54013
    20
    local_theory -> (string list * (term list * (int list list * thm list list))) * local_theory
blanchet@53753
    21
  val add_primcorecursive_cmd: bool ->
panny@53831
    22
    (binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list ->
panny@53831
    23
    Proof.context -> Proof.state
panny@53822
    24
  val add_primcorec_cmd: bool ->
panny@53831
    25
    (binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list ->
panny@53831
    26
    local_theory -> local_theory
blanchet@53303
    27
end;
blanchet@53303
    28
blanchet@53303
    29
structure BNF_FP_Rec_Sugar : BNF_FP_REC_SUGAR =
blanchet@53303
    30
struct
blanchet@53303
    31
blanchet@53303
    32
open BNF_Util
blanchet@53303
    33
open BNF_FP_Util
blanchet@54243
    34
open BNF_FP_N2M_Sugar
blanchet@53303
    35
open BNF_FP_Rec_Sugar_Util
blanchet@53303
    36
open BNF_FP_Rec_Sugar_Tactics
blanchet@53303
    37
panny@54065
    38
val codeN = "code";
panny@54065
    39
val ctrN = "ctr";
panny@54065
    40
val discN = "disc";
panny@54065
    41
val selN = "sel";
blanchet@53791
    42
blanchet@54145
    43
val nitpicksimp_attrs = @{attributes [nitpick_simp]};
blanchet@53794
    44
val simp_attrs = @{attributes [simp]};
blanchet@54145
    45
val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
blanchet@54145
    46
val code_nitpicksimp_simp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs @ simp_attrs;
blanchet@53794
    47
blanchet@53303
    48
exception Primrec_Error of string * term list;
blanchet@53303
    49
blanchet@53303
    50
fun primrec_error str = raise Primrec_Error (str, []);
blanchet@53303
    51
fun primrec_error_eqn str eqn = raise Primrec_Error (str, [eqn]);
blanchet@53303
    52
fun primrec_error_eqns str eqns = raise Primrec_Error (str, eqns);
blanchet@53303
    53
panny@53358
    54
fun finds eq = fold_map (fn x => List.partition (curry eq x) #>> pair x);
panny@53358
    55
panny@53357
    56
val free_name = try (fn Free (v, _) => v);
panny@53357
    57
val const_name = try (fn Const (v, _) => v);
panny@53358
    58
val undef_const = Const (@{const_name undefined}, dummyT);
panny@53357
    59
panny@53358
    60
fun permute_args n t = list_comb (t, map Bound (0 :: (n downto 1)))
panny@53720
    61
  |> fold (K (Term.abs (Name.uu, dummyT))) (0 upto n);
panny@53401
    62
val abs_tuple = HOLogic.tupled_lambda o HOLogic.mk_tuple;
panny@53654
    63
fun drop_All t = subst_bounds (strip_qnt_vars @{const_name all} t |> map Free |> rev,
panny@53654
    64
  strip_qnt_body @{const_name all} t)
panny@53720
    65
fun abstract vs =
panny@53720
    66
  let fun a n (t $ u) = a n t $ a n u
panny@53720
    67
        | a n (Abs (v, T, b)) = Abs (v, T, a (n + 1) b)
panny@53720
    68
        | a n t = let val idx = find_index (equal t) vs in
panny@53720
    69
            if idx < 0 then t else Bound (n + idx) end
panny@53720
    70
  in a 0 end;
panny@53735
    71
fun mk_prod1 Ts (t, u) = HOLogic.pair_const (fastype_of1 (Ts, t)) (fastype_of1 (Ts, u)) $ t $ u;
panny@53735
    72
fun mk_tuple1 Ts = the_default HOLogic.unit o try (foldr1 (mk_prod1 Ts));
blanchet@53303
    73
blanchet@53794
    74
fun get_indices fixes t = map (fst #>> Binding.name_of #> Free) fixes
blanchet@53794
    75
  |> map_index (fn (i, v) => if exists_subterm (equal v) t then SOME i else NONE)
blanchet@53794
    76
  |> map_filter I;
blanchet@53303
    77
blanchet@53310
    78
blanchet@53310
    79
(* Primrec *)
blanchet@53310
    80
blanchet@53303
    81
type eqn_data = {
blanchet@53303
    82
  fun_name: string,
blanchet@53303
    83
  rec_type: typ,
blanchet@53303
    84
  ctr: term,
blanchet@53303
    85
  ctr_args: term list,
blanchet@53303
    86
  left_args: term list,
blanchet@53303
    87
  right_args: term list,
blanchet@53303
    88
  res_type: typ,
blanchet@53303
    89
  rhs_term: term,
blanchet@53303
    90
  user_eqn: term
blanchet@53303
    91
};
blanchet@53303
    92
blanchet@53303
    93
fun dissect_eqn lthy fun_names eqn' =
blanchet@53303
    94
  let
panny@53654
    95
    val eqn = drop_All eqn' |> HOLogic.dest_Trueprop
panny@53654
    96
      handle TERM _ =>
panny@53654
    97
        primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn';
blanchet@53303
    98
    val (lhs, rhs) = HOLogic.dest_eq eqn
blanchet@53303
    99
        handle TERM _ =>
blanchet@53303
   100
          primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn';
blanchet@53303
   101
    val (fun_name, args) = strip_comb lhs
blanchet@53303
   102
      |>> (fn x => if is_Free x then fst (dest_Free x)
blanchet@53303
   103
          else primrec_error_eqn "malformed function equation (does not start with free)" eqn);
blanchet@53303
   104
    val (left_args, rest) = take_prefix is_Free args;
blanchet@53303
   105
    val (nonfrees, right_args) = take_suffix is_Free rest;
blanchet@53830
   106
    val num_nonfrees = length nonfrees;
blanchet@53830
   107
    val _ = num_nonfrees = 1 orelse if num_nonfrees = 0 then
blanchet@53303
   108
      primrec_error_eqn "constructor pattern missing in left-hand side" eqn else
blanchet@53303
   109
      primrec_error_eqn "more than one non-variable argument in left-hand side" eqn;
blanchet@53303
   110
    val _ = member (op =) fun_names fun_name orelse
blanchet@53303
   111
      primrec_error_eqn "malformed function equation (does not start with function name)" eqn
blanchet@53303
   112
blanchet@53303
   113
    val (ctr, ctr_args) = strip_comb (the_single nonfrees);
blanchet@53303
   114
    val _ = try (num_binder_types o fastype_of) ctr = SOME (length ctr_args) orelse
blanchet@53303
   115
      primrec_error_eqn "partially applied constructor in pattern" eqn;
blanchet@53303
   116
    val _ = let val d = duplicates (op =) (left_args @ ctr_args @ right_args) in null d orelse
blanchet@53303
   117
      primrec_error_eqn ("duplicate variable \"" ^ Syntax.string_of_term lthy (hd d) ^
blanchet@53303
   118
        "\" in left-hand side") eqn end;
blanchet@53303
   119
    val _ = forall is_Free ctr_args orelse
blanchet@53303
   120
      primrec_error_eqn "non-primitive pattern in left-hand side" eqn;
blanchet@53303
   121
    val _ =
blanchet@53303
   122
      let val b = fold_aterms (fn x as Free (v, _) =>
blanchet@53303
   123
        if (not (member (op =) (left_args @ ctr_args @ right_args) x) andalso
blanchet@53303
   124
        not (member (op =) fun_names v) andalso
blanchet@53303
   125
        not (Variable.is_fixed lthy v)) then cons x else I | _ => I) rhs []
blanchet@53303
   126
      in
blanchet@53303
   127
        null b orelse
blanchet@53303
   128
        primrec_error_eqn ("extra variable(s) in right-hand side: " ^
blanchet@53303
   129
          commas (map (Syntax.string_of_term lthy) b)) eqn
blanchet@53303
   130
      end;
blanchet@53303
   131
  in
blanchet@53303
   132
    {fun_name = fun_name,
blanchet@53303
   133
     rec_type = body_type (type_of ctr),
blanchet@53303
   134
     ctr = ctr,
blanchet@53303
   135
     ctr_args = ctr_args,
blanchet@53303
   136
     left_args = left_args,
blanchet@53303
   137
     right_args = right_args,
blanchet@53303
   138
     res_type = map fastype_of (left_args @ right_args) ---> fastype_of rhs,
blanchet@53303
   139
     rhs_term = rhs,
blanchet@53303
   140
     user_eqn = eqn'}
blanchet@53303
   141
  end;
blanchet@53303
   142
panny@53401
   143
fun rewrite_map_arg get_ctr_pos rec_type res_type =
blanchet@53303
   144
  let
panny@53357
   145
    val pT = HOLogic.mk_prodT (rec_type, res_type);
blanchet@53303
   146
panny@53357
   147
    val maybe_suc = Option.map (fn x => x + 1);
panny@53357
   148
    fun subst d (t as Bound d') = t |> d = SOME d' ? curry (op $) (fst_const pT)
panny@53357
   149
      | subst d (Abs (v, T, b)) = Abs (v, if d = SOME ~1 then pT else T, subst (maybe_suc d) b)
panny@53357
   150
      | subst d t =
panny@53358
   151
        let
panny@53358
   152
          val (u, vs) = strip_comb t;
panny@53401
   153
          val ctr_pos = try (get_ctr_pos o the) (free_name u) |> the_default ~1;
panny@53358
   154
        in
panny@53401
   155
          if ctr_pos >= 0 then
panny@53357
   156
            if d = SOME ~1 andalso length vs = ctr_pos then
panny@53357
   157
              list_comb (permute_args ctr_pos (snd_const pT), vs)
panny@53357
   158
            else if length vs > ctr_pos andalso is_some d
panny@53357
   159
                andalso d = try (fn Bound n => n) (nth vs ctr_pos) then
panny@53357
   160
              list_comb (snd_const pT $ nth vs ctr_pos, map (subst d) (nth_drop ctr_pos vs))
blanchet@53303
   161
            else
panny@53357
   162
              primrec_error_eqn ("recursive call not directly applied to constructor argument") t
blanchet@53303
   163
          else
panny@53357
   164
            list_comb (u, map (subst (d |> d = SOME ~1 ? K NONE)) vs)
blanchet@53303
   165
        end
blanchet@53303
   166
  in
panny@53357
   167
    subst (SOME ~1)
blanchet@53303
   168
  end;
blanchet@53303
   169
blanchet@54170
   170
fun subst_rec_calls lthy get_ctr_pos has_call ctr_args mutual_calls nested_calls =
blanchet@53303
   171
  let
blanchet@54169
   172
    fun try_nested_rec bound_Ts y t =
blanchet@54169
   173
      AList.lookup (op =) nested_calls y
blanchet@54169
   174
      |> Option.map (fn y' =>
blanchet@54169
   175
        massage_nested_rec_call lthy has_call (rewrite_map_arg get_ctr_pos) bound_Ts y y' t);
blanchet@54169
   176
blanchet@54166
   177
    fun subst bound_Ts (t as g' $ y) =
blanchet@54170
   178
        let
blanchet@54170
   179
          fun subst_rec () = subst bound_Ts g' $ subst bound_Ts y;
blanchet@54170
   180
          val y_head = head_of y;
blanchet@54170
   181
        in
blanchet@54159
   182
          if not (member (op =) ctr_args y_head) then
blanchet@54170
   183
            subst_rec ()
blanchet@54159
   184
          else
blanchet@54169
   185
            (case try_nested_rec bound_Ts y_head t of
blanchet@54169
   186
              SOME t' => t'
blanchet@54168
   187
            | NONE =>
blanchet@54168
   188
              let val (g, g_args) = strip_comb g' in
blanchet@54168
   189
                (case try (get_ctr_pos o the) (free_name g) of
blanchet@54168
   190
                  SOME ctr_pos =>
blanchet@54168
   191
                  (length g_args >= ctr_pos orelse
blanchet@54168
   192
                   primrec_error_eqn "too few arguments in recursive call" t;
blanchet@54168
   193
                   (case AList.lookup (op =) mutual_calls y of
blanchet@54168
   194
                     SOME y' => list_comb (y', g_args)
blanchet@54170
   195
                   | NONE => subst_rec ()))
blanchet@54170
   196
                | NONE => subst_rec ())
blanchet@54168
   197
              end)
blanchet@54159
   198
        end
blanchet@54166
   199
      | subst bound_Ts (Abs (v, T, b)) = Abs (v, T, subst (T :: bound_Ts) b)
panny@53350
   200
      | subst _ t = t
blanchet@54170
   201
blanchet@54170
   202
    fun subst' t =
blanchet@54170
   203
      if has_call t then
blanchet@54170
   204
        (* FIXME detect this case earlier? *)
blanchet@54170
   205
        primrec_error_eqn "recursive call not directly applied to constructor argument" t
blanchet@54170
   206
      else
blanchet@54170
   207
        try_nested_rec [] (head_of t) t |> the_default t
panny@53350
   208
  in
blanchet@54170
   209
    subst' o subst []
panny@53350
   210
  end;
blanchet@53303
   211
blanchet@54003
   212
fun build_rec_arg lthy (funs_data : eqn_data list list) has_call (ctr_spec : rec_ctr_spec)
blanchet@54003
   213
    (maybe_eqn_data : eqn_data option) =
blanchet@54208
   214
  (case maybe_eqn_data of
blanchet@54208
   215
    NONE => undef_const
blanchet@54208
   216
  | SOME {ctr_args, left_args, right_args, rhs_term = t, ...} =>
blanchet@53303
   217
    let
blanchet@53303
   218
      val calls = #calls ctr_spec;
blanchet@54200
   219
      val n_args = fold (Integer.add o (fn Mutual_Rec _ => 2 | _ => 1)) calls 0;
blanchet@53303
   220
blanchet@53303
   221
      val no_calls' = tag_list 0 calls
blanchet@54200
   222
        |> map_filter (try (apsnd (fn No_Rec p => p | Mutual_Rec (p, _) => p)));
blanchet@54102
   223
      val mutual_calls' = tag_list 0 calls
blanchet@54200
   224
        |> map_filter (try (apsnd (fn Mutual_Rec (_, p) => p)));
blanchet@54102
   225
      val nested_calls' = tag_list 0 calls
blanchet@54200
   226
        |> map_filter (try (apsnd (fn Nested_Rec p => p)));
blanchet@53303
   227
blanchet@53303
   228
      val args = replicate n_args ("", dummyT)
blanchet@53303
   229
        |> Term.rename_wrt_term t
blanchet@53303
   230
        |> map Free
blanchet@54201
   231
        |> fold (fn (ctr_arg_idx, (arg_idx, _)) =>
blanchet@53303
   232
            nth_map arg_idx (K (nth ctr_args ctr_arg_idx)))
blanchet@53303
   233
          no_calls'
blanchet@54200
   234
        |> fold (fn (ctr_arg_idx, (arg_idx, T)) =>
blanchet@54200
   235
            nth_map arg_idx (K (retype_free T (nth ctr_args ctr_arg_idx))))
blanchet@54102
   236
          mutual_calls'
blanchet@54200
   237
        |> fold (fn (ctr_arg_idx, (arg_idx, T)) =>
blanchet@54200
   238
            nth_map arg_idx (K (retype_free T (nth ctr_args ctr_arg_idx))))
blanchet@54102
   239
          nested_calls';
blanchet@53303
   240
panny@53401
   241
      val fun_name_ctr_pos_list =
panny@53401
   242
        map (fn (x :: _) => (#fun_name x, length (#left_args x))) funs_data;
panny@53401
   243
      val get_ctr_pos = try (the o AList.lookup (op =) fun_name_ctr_pos_list) #> the_default ~1;
blanchet@54200
   244
      val mutual_calls = map (apfst (nth ctr_args) o apsnd (nth args o fst)) mutual_calls';
blanchet@54200
   245
      val nested_calls = map (apfst (nth ctr_args) o apsnd (nth args o fst)) nested_calls';
blanchet@53303
   246
    in
panny@53350
   247
      t
blanchet@54102
   248
      |> subst_rec_calls lthy get_ctr_pos has_call ctr_args mutual_calls nested_calls
blanchet@54208
   249
      |> fold_rev lambda (args @ left_args @ right_args)
blanchet@54208
   250
    end);
blanchet@53303
   251
blanchet@54003
   252
fun build_defs lthy bs mxs (funs_data : eqn_data list list) (rec_specs : rec_spec list) has_call =
blanchet@53303
   253
  let
blanchet@53303
   254
    val n_funs = length funs_data;
blanchet@53303
   255
blanchet@53303
   256
    val ctr_spec_eqn_data_list' =
blanchet@53303
   257
      (take n_funs rec_specs |> map #ctr_specs) ~~ funs_data
blanchet@53303
   258
      |> maps (uncurry (finds (fn (x, y) => #ctr x = #ctr y))
blanchet@53303
   259
          ##> (fn x => null x orelse
blanchet@53303
   260
            primrec_error_eqns "excess equations in definition" (map #rhs_term x)) #> fst);
blanchet@53303
   261
    val _ = ctr_spec_eqn_data_list' |> map (fn (_, x) => length x <= 1 orelse
blanchet@53303
   262
      primrec_error_eqns ("multiple equations for constructor") (map #user_eqn x));
blanchet@53303
   263
blanchet@53303
   264
    val ctr_spec_eqn_data_list =
blanchet@53303
   265
      ctr_spec_eqn_data_list' @ (drop n_funs rec_specs |> maps #ctr_specs |> map (rpair []));
blanchet@53303
   266
blanchet@53303
   267
    val recs = take n_funs rec_specs |> map #recx;
blanchet@53303
   268
    val rec_args = ctr_spec_eqn_data_list
blanchet@53303
   269
      |> sort ((op <) o pairself (#offset o fst) |> make_ord)
panny@53358
   270
      |> map (uncurry (build_rec_arg lthy funs_data has_call) o apsnd (try the_single));
blanchet@53303
   271
    val ctr_poss = map (fn x =>
blanchet@53303
   272
      if length (distinct ((op =) o pairself (length o #left_args)) x) <> 1 then
blanchet@53303
   273
        primrec_error ("inconstant constructor pattern position for function " ^
blanchet@53303
   274
          quote (#fun_name (hd x)))
blanchet@53303
   275
      else
blanchet@53303
   276
        hd x |> #left_args |> length) funs_data;
blanchet@53303
   277
  in
blanchet@53303
   278
    (recs, ctr_poss)
blanchet@53303
   279
    |-> map2 (fn recx => fn ctr_pos => list_comb (recx, rec_args) |> permute_args ctr_pos)
blanchet@53303
   280
    |> Syntax.check_terms lthy
blanchet@54155
   281
    |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.conceal (Thm.def_binding b), []), t)))
blanchet@54155
   282
      bs mxs
blanchet@53303
   283
  end;
blanchet@53303
   284
panny@54215
   285
fun find_rec_calls ctxt has_call ({ctr, ctr_args, rhs_term, ...} : eqn_data) =
blanchet@53303
   286
  let
blanchet@54202
   287
    fun find bound_Ts (Abs (_, T, b)) ctr_arg = find (T :: bound_Ts) b ctr_arg
blanchet@54202
   288
      | find bound_Ts (t as _ $ _) ctr_arg =
blanchet@53303
   289
        let
blanchet@54202
   290
          val typof = curry fastype_of1 bound_Ts;
blanchet@53303
   291
          val (f', args') = strip_comb t;
blanchet@54202
   292
          val n = find_index (equal ctr_arg o head_of) args';
blanchet@53303
   293
        in
blanchet@53303
   294
          if n < 0 then
blanchet@54202
   295
            find bound_Ts f' ctr_arg @ maps (fn x => find bound_Ts x ctr_arg) args'
blanchet@53303
   296
          else
blanchet@54202
   297
            let
blanchet@54202
   298
              val (f, args as arg :: _) = chop n args' |>> curry list_comb f'
blanchet@54202
   299
              val (arg_head, arg_args) = Term.strip_comb arg;
blanchet@54202
   300
            in
panny@53358
   301
              if has_call f then
blanchet@54202
   302
                mk_partial_compN (length arg_args) (typof f) (typof arg_head) f ::
blanchet@54202
   303
                maps (fn x => find bound_Ts x ctr_arg) args
blanchet@53303
   304
              else
blanchet@54202
   305
                find bound_Ts f ctr_arg @ maps (fn x => find bound_Ts x ctr_arg) args
blanchet@53303
   306
            end
blanchet@53303
   307
        end
blanchet@54202
   308
      | find _ _ _ = [];
blanchet@53303
   309
  in
panny@54215
   310
    map (find [] rhs_term) ctr_args
panny@54215
   311
    |> (fn [] => NONE | callss => SOME (ctr, callss))
blanchet@53303
   312
  end;
blanchet@53303
   313
traytel@54013
   314
fun prepare_primrec fixes specs lthy =
blanchet@53303
   315
  let
traytel@53352
   316
    val (bs, mxs) = map_split (apfst fst) fixes;
blanchet@53303
   317
    val fun_names = map Binding.name_of bs;
traytel@54013
   318
    val eqns_data = map (dissect_eqn lthy fun_names) specs;
blanchet@53303
   319
    val funs_data = eqns_data
blanchet@53303
   320
      |> partition_eq ((op =) o pairself #fun_name)
blanchet@53303
   321
      |> finds (fn (x, y) => x = #fun_name (hd y)) fun_names |> fst
blanchet@53303
   322
      |> map (fn (x, y) => the_single y handle List.Empty =>
blanchet@53303
   323
          primrec_error ("missing equations for function " ^ quote x));
blanchet@53303
   324
panny@53358
   325
    val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
blanchet@53303
   326
    val arg_Ts = map (#rec_type o hd) funs_data;
blanchet@53303
   327
    val res_Ts = map (#res_type o hd) funs_data;
blanchet@53303
   328
    val callssss = funs_data
blanchet@53303
   329
      |> map (partition_eq ((op =) o pairself #ctr))
blanchet@54202
   330
      |> map (maps (map_filter (find_rec_calls lthy has_call)));
blanchet@53303
   331
blanchet@53830
   332
    val ((n2m, rec_specs, _, induct_thm, induct_thms), lthy') =
blanchet@53794
   333
      rec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;
blanchet@53303
   334
blanchet@53303
   335
    val actual_nn = length funs_data;
blanchet@53303
   336
blanchet@53303
   337
    val _ = let val ctrs = (maps (map #ctr o #ctr_specs) rec_specs) in
blanchet@53303
   338
      map (fn {ctr, user_eqn, ...} => member (op =) ctrs ctr orelse
blanchet@53303
   339
        primrec_error_eqn ("argument " ^ quote (Syntax.string_of_term lthy' ctr) ^
blanchet@53303
   340
          " is not a constructor in left-hand side") user_eqn) eqns_data end;
blanchet@53303
   341
panny@53358
   342
    val defs = build_defs lthy' bs mxs funs_data rec_specs has_call;
blanchet@53303
   343
traytel@54013
   344
    fun prove lthy def_thms' ({ctr_specs, nested_map_idents, nested_map_comps, ...} : rec_spec)
traytel@54013
   345
        (fun_data : eqn_data list) =
blanchet@53303
   346
      let
blanchet@53303
   347
        val def_thms = map (snd o snd) def_thms';
traytel@54013
   348
        val simp_thmss = finds (fn (x, y) => #ctr x = #ctr y) fun_data ctr_specs
blanchet@53303
   349
          |> fst
blanchet@53303
   350
          |> map_filter (try (fn (x, [y]) =>
blanchet@53303
   351
            (#user_eqn x, length (#left_args x) + length (#right_args x), #rec_thm y)))
blanchet@53303
   352
          |> map (fn (user_eqn, num_extra_args, rec_thm) =>
blanchet@53329
   353
            mk_primrec_tac lthy num_extra_args nested_map_idents nested_map_comps def_thms rec_thm
blanchet@54176
   354
            |> K |> Goal.prove lthy [] [] user_eqn
blanchet@54176
   355
            |> Thm.close_derivation);
traytel@54013
   356
        val poss = find_indices (fn (x, y) => #ctr x = #ctr y) fun_data eqns_data;
traytel@54013
   357
      in
traytel@54013
   358
        (poss, simp_thmss)
traytel@54013
   359
      end;
blanchet@53303
   360
traytel@54013
   361
    val notes =
traytel@54013
   362
      (if n2m then map2 (fn name => fn thm =>
traytel@54013
   363
        (name, inductN, [thm], [])) fun_names (take actual_nn induct_thms) else [])
traytel@54013
   364
      |> map (fn (prefix, thmN, thms, attrs) =>
traytel@54013
   365
        ((Binding.qualify true prefix (Binding.name thmN), attrs), [(thms, [])]));
blanchet@53303
   366
blanchet@53303
   367
    val common_name = mk_common_name fun_names;
blanchet@53303
   368
blanchet@53303
   369
    val common_notes =
traytel@54013
   370
      (if n2m then [(inductN, [induct_thm], [])] else [])
blanchet@53303
   371
      |> map (fn (thmN, thms, attrs) =>
blanchet@53303
   372
        ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
blanchet@53303
   373
  in
traytel@54013
   374
    (((fun_names, defs),
traytel@54013
   375
      fn lthy => fn defs =>
traytel@54013
   376
        split_list (map2 (prove lthy defs) (take actual_nn rec_specs) funs_data)),
traytel@54013
   377
      lthy' |> Local_Theory.notes (notes @ common_notes) |> snd)
blanchet@53303
   378
  end;
blanchet@53303
   379
traytel@54013
   380
(* primrec definition *)
traytel@54013
   381
traytel@54013
   382
fun add_primrec_simple fixes ts lthy =
blanchet@53303
   383
  let
traytel@54013
   384
    val (((names, defs), prove), lthy) = prepare_primrec fixes ts lthy
traytel@54013
   385
      handle ERROR str => primrec_error str;
blanchet@53303
   386
  in
traytel@54013
   387
    lthy
traytel@54013
   388
    |> fold_map Local_Theory.define defs
traytel@54013
   389
    |-> (fn defs => `(fn lthy => (names, (map fst defs, prove lthy defs))))
blanchet@53303
   390
  end
blanchet@53303
   391
  handle Primrec_Error (str, eqns) =>
blanchet@53303
   392
    if null eqns
blanchet@53303
   393
    then error ("primrec_new error:\n  " ^ str)
blanchet@53303
   394
    else error ("primrec_new error:\n  " ^ str ^ "\nin\n  " ^
panny@53822
   395
      space_implode "\n  " (map (quote o Syntax.string_of_term lthy) eqns));
blanchet@53303
   396
traytel@54013
   397
local
traytel@54013
   398
traytel@54028
   399
fun gen_primrec prep_spec (raw_fixes : (binding * 'a option * mixfix) list) raw_spec lthy =
traytel@54013
   400
  let
traytel@54013
   401
    val d = duplicates (op =) (map (Binding.name_of o #1) raw_fixes)
traytel@54013
   402
    val _ = null d orelse primrec_error ("duplicate function name(s): " ^ commas d);
traytel@54013
   403
traytel@54013
   404
    val (fixes, specs) = fst (prep_spec raw_fixes raw_spec lthy);
traytel@54013
   405
traytel@54013
   406
    val mk_notes =
traytel@54013
   407
      flat ooo map3 (fn poss => fn prefix => fn thms =>
traytel@54013
   408
        let
traytel@54013
   409
          val (bs, attrss) = map_split (fst o nth specs) poss;
traytel@54013
   410
          val notes =
traytel@54013
   411
            map3 (fn b => fn attrs => fn thm =>
blanchet@54145
   412
              ((Binding.qualify false prefix b, code_nitpicksimp_simp_attrs @ attrs), [([thm], [])]))
traytel@54013
   413
            bs attrss thms;
traytel@54013
   414
        in
traytel@54013
   415
          ((Binding.qualify true prefix (Binding.name simpsN), []), [(thms, [])]) :: notes
traytel@54013
   416
        end);
traytel@54013
   417
  in
traytel@54013
   418
    lthy
traytel@54013
   419
    |> add_primrec_simple fixes (map snd specs)
traytel@54013
   420
    |-> (fn (names, (ts, (posss, simpss))) =>
traytel@54013
   421
      Spec_Rules.add Spec_Rules.Equational (ts, flat simpss)
traytel@54013
   422
      #> Local_Theory.notes (mk_notes posss names simpss)
traytel@54013
   423
      #>> pair ts o map snd)
traytel@54013
   424
  end;
traytel@54013
   425
traytel@54013
   426
in
traytel@54013
   427
traytel@54013
   428
val add_primrec = gen_primrec Specification.check_spec;
traytel@54013
   429
val add_primrec_cmd = gen_primrec Specification.read_spec;
traytel@54013
   430
traytel@54013
   431
end;
traytel@54013
   432
traytel@54013
   433
fun add_primrec_global fixes specs thy =
traytel@54013
   434
  let
traytel@54013
   435
    val lthy = Named_Target.theory_init thy;
traytel@54013
   436
    val ((ts, simps), lthy') = add_primrec fixes specs lthy;
traytel@54013
   437
    val simps' = burrow (Proof_Context.export lthy' lthy) simps;
traytel@54013
   438
  in ((ts, simps'), Local_Theory.exit_global lthy') end;
traytel@54013
   439
traytel@54013
   440
fun add_primrec_overloaded ops fixes specs thy =
traytel@54013
   441
  let
traytel@54013
   442
    val lthy = Overloading.overloading ops thy;
traytel@54013
   443
    val ((ts, simps), lthy') = add_primrec fixes specs lthy;
traytel@54013
   444
    val simps' = burrow (Proof_Context.export lthy' lthy) simps;
traytel@54013
   445
  in ((ts, simps'), Local_Theory.exit_global lthy') end;
traytel@54013
   446
blanchet@53303
   447
blanchet@53303
   448
blanchet@53310
   449
(* Primcorec *)
blanchet@53303
   450
blanchet@54153
   451
type coeqn_data_disc = {
blanchet@53303
   452
  fun_name: string,
panny@53720
   453
  fun_T: typ,
panny@53401
   454
  fun_args: term list,
panny@53720
   455
  ctr: term,
panny@53341
   456
  ctr_no: int, (*###*)
panny@53720
   457
  disc: term,
panny@53654
   458
  prems: term list,
panny@53822
   459
  auto_gen: bool,
panny@54097
   460
  maybe_ctr_rhs: term option,
panny@54097
   461
  maybe_code_rhs: term option,
blanchet@53303
   462
  user_eqn: term
blanchet@53303
   463
};
blanchet@54001
   464
blanchet@54153
   465
type coeqn_data_sel = {
blanchet@53303
   466
  fun_name: string,
panny@53720
   467
  fun_T: typ,
panny@53401
   468
  fun_args: term list,
panny@53341
   469
  ctr: term,
panny@53341
   470
  sel: term,
blanchet@53303
   471
  rhs_term: term,
blanchet@53303
   472
  user_eqn: term
blanchet@53303
   473
};
blanchet@54001
   474
blanchet@54153
   475
datatype coeqn_data =
blanchet@54153
   476
  Disc of coeqn_data_disc |
blanchet@54153
   477
  Sel of coeqn_data_sel;
blanchet@53303
   478
panny@54160
   479
fun dissect_coeqn_disc seq fun_names (basic_ctr_specss : basic_corec_ctr_spec list list)
panny@54160
   480
    maybe_ctr_rhs maybe_code_rhs prems' concl matchedsss =
blanchet@53303
   481
  let
blanchet@53303
   482
    fun find_subterm p = let (* FIXME \<exists>? *)
panny@53401
   483
      fun f (t as u $ v) = if p t then SOME t else merge_options (f u, f v)
blanchet@53303
   484
        | f t = if p t then SOME t else NONE
blanchet@53303
   485
      in f end;
blanchet@53303
   486
panny@53654
   487
    val applied_fun = concl
panny@53654
   488
      |> find_subterm (member ((op =) o apsnd SOME) fun_names o try (fst o dest_Free o head_of))
panny@53654
   489
      |> the
blanchet@54204
   490
      handle Option.Option => primrec_error_eqn "malformed discriminator formula" concl;
panny@53720
   491
    val ((fun_name, fun_T), fun_args) = strip_comb applied_fun |>> dest_Free;
blanchet@54209
   492
    val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name;
blanchet@53303
   493
panny@54160
   494
    val discs = map #disc basic_ctr_specs;
panny@54160
   495
    val ctrs = map #ctr basic_ctr_specs;
panny@53654
   496
    val not_disc = head_of concl = @{term Not};
panny@53401
   497
    val _ = not_disc andalso length ctrs <> 2 andalso
blanchet@54209
   498
      primrec_error_eqn "negated discriminator for a type with \<noteq> 2 constructors" concl;
panny@54160
   499
    val disc' = find_subterm (member (op =) discs o head_of) concl;
blanchet@54209
   500
    val eq_ctr0 = concl |> perhaps (try HOLogic.dest_not) |> try (HOLogic.dest_eq #> snd)
blanchet@53303
   501
        |> (fn SOME t => let val n = find_index (equal t) ctrs in
blanchet@53303
   502
          if n >= 0 then SOME n else NONE end | _ => NONE);
panny@54160
   503
    val _ = is_some disc' orelse is_some eq_ctr0 orelse
panny@53654
   504
      primrec_error_eqn "no discriminator in equation" concl;
blanchet@53303
   505
    val ctr_no' =
panny@54160
   506
      if is_none disc' then the eq_ctr0 else find_index (equal (head_of (the disc'))) discs;
blanchet@53303
   507
    val ctr_no = if not_disc then 1 - ctr_no' else ctr_no';
panny@54160
   508
    val {ctr, disc, ...} = nth basic_ctr_specs ctr_no;
panny@53654
   509
panny@53654
   510
    val catch_all = try (fst o dest_Free o the_single) prems' = SOME Name.uu_;
panny@53720
   511
    val matchedss = AList.lookup (op =) matchedsss fun_name |> the_default [];
panny@53720
   512
    val prems = map (abstract (List.rev fun_args)) prems';
panny@53720
   513
    val real_prems =
blanchet@54067
   514
      (if catch_all orelse seq then maps s_not_conj matchedss else []) @
panny@53654
   515
      (if catch_all then [] else prems);
blanchet@53303
   516
panny@53720
   517
    val matchedsss' = AList.delete (op =) fun_name matchedsss
panny@54065
   518
      |> cons (fun_name, if seq then matchedss @ [prems] else matchedss @ [real_prems]);
blanchet@53303
   519
panny@53654
   520
    val user_eqn =
panny@54097
   521
      (real_prems, concl)
panny@54097
   522
      |>> map HOLogic.mk_Trueprop ||> HOLogic.mk_Trueprop o abstract (List.rev fun_args)
panny@54097
   523
      |> curry Logic.list_all (map dest_Free fun_args) o Logic.list_implies;
blanchet@53303
   524
  in
panny@53341
   525
    (Disc {
blanchet@53303
   526
      fun_name = fun_name,
panny@53720
   527
      fun_T = fun_T,
panny@53401
   528
      fun_args = fun_args,
panny@53720
   529
      ctr = ctr,
blanchet@53303
   530
      ctr_no = ctr_no,
panny@54160
   531
      disc = disc,
panny@53654
   532
      prems = real_prems,
panny@53822
   533
      auto_gen = catch_all,
panny@54097
   534
      maybe_ctr_rhs = maybe_ctr_rhs,
panny@54097
   535
      maybe_code_rhs = maybe_code_rhs,
panny@53654
   536
      user_eqn = user_eqn
panny@53720
   537
    }, matchedsss')
blanchet@53303
   538
  end;
blanchet@53303
   539
blanchet@54209
   540
fun dissect_coeqn_sel fun_names (basic_ctr_specss : basic_corec_ctr_spec list list) eqn'
blanchet@54209
   541
    maybe_of_spec eqn =
blanchet@53303
   542
  let
blanchet@53303
   543
    val (lhs, rhs) = HOLogic.dest_eq eqn
blanchet@53303
   544
      handle TERM _ =>
blanchet@53303
   545
        primrec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn;
blanchet@53303
   546
    val sel = head_of lhs;
panny@53720
   547
    val ((fun_name, fun_T), fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst dest_Free
blanchet@53303
   548
      handle TERM _ =>
blanchet@53303
   549
        primrec_error_eqn "malformed selector argument in left-hand side" eqn;
panny@54160
   550
    val basic_ctr_specs = the (AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name)
blanchet@53303
   551
      handle Option.Option => primrec_error_eqn "malformed selector argument in left-hand side" eqn;
panny@54160
   552
    val {ctr, ...} =
blanchet@54209
   553
      (case maybe_of_spec of
blanchet@54209
   554
        SOME of_spec => the (find_first (equal of_spec o #ctr) basic_ctr_specs)
blanchet@54209
   555
      | NONE => filter (exists (equal sel) o #sels) basic_ctr_specs |> the_single
blanchet@54209
   556
          handle List.Empty => primrec_error_eqn "ambiguous selector - use \"of\"" eqn);
panny@53654
   557
    val user_eqn = drop_All eqn';
blanchet@53303
   558
  in
panny@53341
   559
    Sel {
blanchet@53303
   560
      fun_name = fun_name,
panny@53720
   561
      fun_T = fun_T,
panny@53401
   562
      fun_args = fun_args,
panny@54160
   563
      ctr = ctr,
panny@53341
   564
      sel = sel,
blanchet@53303
   565
      rhs_term = rhs,
panny@53654
   566
      user_eqn = user_eqn
blanchet@53303
   567
    }
blanchet@53303
   568
  end;
blanchet@53303
   569
panny@54160
   570
fun dissect_coeqn_ctr seq fun_names (basic_ctr_specss : basic_corec_ctr_spec list list) eqn'
panny@54160
   571
    maybe_code_rhs prems concl matchedsss =
blanchet@53910
   572
  let
panny@54065
   573
    val (lhs, rhs) = HOLogic.dest_eq concl;
panny@54097
   574
    val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
blanchet@54209
   575
    val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name;
blanchet@54074
   576
    val (ctr, ctr_args) = strip_comb (unfold_let rhs);
panny@54160
   577
    val {disc, sels, ...} = the (find_first (equal ctr o #ctr) basic_ctr_specs)
blanchet@53303
   578
      handle Option.Option => primrec_error_eqn "not a constructor" ctr;
panny@53341
   579
panny@54065
   580
    val disc_concl = betapply (disc, lhs);
panny@54160
   581
    val (maybe_eqn_data_disc, matchedsss') = if length basic_ctr_specs = 1
panny@53720
   582
      then (NONE, matchedsss)
panny@54160
   583
      else apfst SOME (dissect_coeqn_disc seq fun_names basic_ctr_specss
panny@54097
   584
          (SOME (abstract (List.rev fun_args) rhs)) maybe_code_rhs prems disc_concl matchedsss);
blanchet@53303
   585
blanchet@54159
   586
    val sel_concls = sels ~~ ctr_args
blanchet@53303
   587
      |> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg));
blanchet@53303
   588
blanchet@53856
   589
(*
panny@54065
   590
val _ = tracing ("reduced\n    " ^ Syntax.string_of_term @{context} concl ^ "\nto\n    \<cdot> " ^
panny@54065
   591
 (is_some maybe_eqn_data_disc ? K (Syntax.string_of_term @{context} disc_concl ^ "\n    \<cdot> ")) "" ^
panny@54097
   592
 space_implode "\n    \<cdot> " (map (Syntax.string_of_term @{context}) sel_concls) ^
panny@54097
   593
 "\nfor premise(s)\n    \<cdot> " ^
panny@54097
   594
 space_implode "\n    \<cdot> " (map (Syntax.string_of_term @{context}) prems));
blanchet@53856
   595
*)
blanchet@53303
   596
panny@54160
   597
    val eqns_data_sel =
panny@54160
   598
      map (dissect_coeqn_sel fun_names basic_ctr_specss eqn' (SOME ctr)) sel_concls;
blanchet@53303
   599
  in
panny@53720
   600
    (the_list maybe_eqn_data_disc @ eqns_data_sel, matchedsss')
blanchet@53303
   601
  end;
blanchet@53303
   602
panny@54160
   603
fun dissect_coeqn_code lthy has_call fun_names basic_ctr_specss eqn' concl matchedsss =
panny@54065
   604
  let
panny@54065
   605
    val (lhs, (rhs', rhs)) = HOLogic.dest_eq concl ||> `(expand_corec_code_rhs lthy has_call []);
panny@54097
   606
    val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
blanchet@54209
   607
    val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name;
panny@54065
   608
panny@54065
   609
    val cond_ctrs = fold_rev_corec_code_rhs lthy (fn cs => fn ctr => fn _ =>
panny@54160
   610
        if member ((op =) o apsnd #ctr) basic_ctr_specs ctr
panny@54065
   611
        then cons (ctr, cs)
panny@54065
   612
        else primrec_error_eqn "not a constructor" ctr) [] rhs' []
panny@54065
   613
      |> AList.group (op =);
panny@54065
   614
blanchet@54068
   615
    val ctr_premss = (case cond_ctrs of [_] => [[]] | _ => map (s_dnf o snd) cond_ctrs);
panny@54065
   616
    val ctr_concls = cond_ctrs |> map (fn (ctr, _) =>
panny@54065
   617
        binder_types (fastype_of ctr)
panny@54065
   618
        |> map_index (fn (n, T) => massage_corec_code_rhs lthy (fn _ => fn ctr' => fn args =>
panny@54065
   619
          if ctr' = ctr then nth args n else Const (@{const_name undefined}, T)) [] rhs')
panny@54065
   620
        |> curry list_comb ctr
panny@54065
   621
        |> curry HOLogic.mk_eq lhs);
panny@54065
   622
  in
panny@54160
   623
    fold_map2 (dissect_coeqn_ctr false fun_names basic_ctr_specss eqn'
panny@54097
   624
        (SOME (abstract (List.rev fun_args) rhs)))
panny@54097
   625
      ctr_premss ctr_concls matchedsss
panny@54065
   626
  end;
panny@54065
   627
panny@54160
   628
fun dissect_coeqn lthy seq has_call fun_names (basic_ctr_specss : basic_corec_ctr_spec list list)
blanchet@54209
   629
    eqn' maybe_of_spec matchedsss =
blanchet@53303
   630
  let
panny@53654
   631
    val eqn = drop_All eqn'
panny@53654
   632
      handle TERM _ => primrec_error_eqn "malformed function equation" eqn';
panny@54065
   633
    val (prems, concl) = Logic.strip_horn eqn
panny@53341
   634
      |> apfst (map HOLogic.dest_Trueprop) o apsnd HOLogic.dest_Trueprop;
blanchet@53303
   635
panny@54065
   636
    val head = concl
blanchet@53303
   637
      |> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq))
blanchet@53303
   638
      |> head_of;
blanchet@53303
   639
blanchet@54209
   640
    val maybe_rhs = concl |> perhaps (try HOLogic.dest_not) |> try (snd o HOLogic.dest_eq);
blanchet@53303
   641
panny@54160
   642
    val discs = maps (map #disc) basic_ctr_specss;
panny@54160
   643
    val sels = maps (maps #sels) basic_ctr_specss;
panny@54160
   644
    val ctrs = maps (map #ctr) basic_ctr_specss;
blanchet@53303
   645
  in
blanchet@53303
   646
    if member (op =) discs head orelse
blanchet@53303
   647
      is_some maybe_rhs andalso
blanchet@53303
   648
        member (op =) (filter (null o binder_types o fastype_of) ctrs) (the maybe_rhs) then
panny@54160
   649
      dissect_coeqn_disc seq fun_names basic_ctr_specss NONE NONE prems concl matchedsss
blanchet@53303
   650
      |>> single
blanchet@53303
   651
    else if member (op =) sels head then
blanchet@54209
   652
      ([dissect_coeqn_sel fun_names basic_ctr_specss eqn' maybe_of_spec concl], matchedsss)
panny@54065
   653
    else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso
blanchet@54074
   654
      member (op =) ctrs (head_of (unfold_let (the maybe_rhs))) then
panny@54160
   655
      dissect_coeqn_ctr seq fun_names basic_ctr_specss eqn' NONE prems concl matchedsss
panny@54065
   656
    else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso
panny@54065
   657
      null prems then
panny@54160
   658
      dissect_coeqn_code lthy has_call fun_names basic_ctr_specss eqn' concl matchedsss
panny@54065
   659
      |>> flat
blanchet@53303
   660
    else
blanchet@53303
   661
      primrec_error_eqn "malformed function equation" eqn
blanchet@53303
   662
  end;
blanchet@53303
   663
blanchet@54002
   664
fun build_corec_arg_disc (ctr_specs : corec_ctr_spec list)
blanchet@54153
   665
    ({fun_args, ctr_no, prems, ...} : coeqn_data_disc) =
panny@53654
   666
  if is_none (#pred (nth ctr_specs ctr_no)) then I else
blanchet@54068
   667
    s_conjs prems
panny@53654
   668
    |> curry subst_bounds (List.rev fun_args)
panny@53654
   669
    |> HOLogic.tupled_lambda (HOLogic.mk_tuple fun_args)
panny@53654
   670
    |> K |> nth_map (the (#pred (nth ctr_specs ctr_no)));
blanchet@53303
   671
blanchet@54153
   672
fun build_corec_arg_no_call (sel_eqns : coeqn_data_sel list) sel =
panny@53720
   673
  find_first (equal sel o #sel) sel_eqns
panny@53720
   674
  |> try (fn SOME {fun_args, rhs_term, ...} => abs_tuple fun_args rhs_term)
panny@53720
   675
  |> the_default undef_const
panny@53411
   676
  |> K;
panny@53360
   677
blanchet@54153
   678
fun build_corec_args_mutual_call lthy has_call (sel_eqns : coeqn_data_sel list) sel =
blanchet@54208
   679
  (case find_first (equal sel o #sel) sel_eqns of
blanchet@54208
   680
    NONE => (I, I, I)
blanchet@54208
   681
  | SOME {fun_args, rhs_term, ... } =>
panny@53876
   682
    let
panny@54097
   683
      val bound_Ts = List.rev (map fastype_of fun_args);
blanchet@54207
   684
      fun rewrite_stop _ t = if has_call t then @{term False} else @{term True};
blanchet@54207
   685
      fun rewrite_end _ t = if has_call t then undef_const else t;
blanchet@54207
   686
      fun rewrite_cont bound_Ts t =
panny@53899
   687
        if has_call t then mk_tuple1 bound_Ts (snd (strip_comb t)) else undef_const;
blanchet@54102
   688
      fun massage f _ = massage_mutual_corec_call lthy has_call f bound_Ts rhs_term
panny@54097
   689
        |> abs_tuple fun_args;
panny@53876
   690
    in
blanchet@54207
   691
      (massage rewrite_stop, massage rewrite_end, massage rewrite_cont)
blanchet@54208
   692
    end);
panny@53360
   693
blanchet@54153
   694
fun build_corec_arg_nested_call lthy has_call (sel_eqns : coeqn_data_sel list) sel =
blanchet@54208
   695
  (case find_first (equal sel o #sel) sel_eqns of
blanchet@54208
   696
    NONE => I
blanchet@54208
   697
  | SOME {fun_args, rhs_term, ...} =>
panny@53899
   698
    let
panny@54097
   699
      val bound_Ts = List.rev (map fastype_of fun_args);
panny@53899
   700
      fun rewrite bound_Ts U T (Abs (v, V, b)) = Abs (v, V, rewrite (V :: bound_Ts) U T b)
panny@53899
   701
        | rewrite bound_Ts U T (t as _ $ _) =
panny@53899
   702
          let val (u, vs) = strip_comb t in
panny@53899
   703
            if is_Free u andalso has_call u then
panny@53899
   704
              Inr_const U T $ mk_tuple1 bound_Ts vs
panny@54215
   705
            else if const_name u = SOME @{const_name prod_case} then
panny@53899
   706
              map (rewrite bound_Ts U T) vs |> chop 1 |>> HOLogic.mk_split o the_single |> list_comb
panny@53899
   707
            else
panny@53899
   708
              list_comb (rewrite bound_Ts U T u, map (rewrite bound_Ts U T) vs)
panny@53899
   709
          end
panny@53899
   710
        | rewrite _ U T t =
panny@53899
   711
          if is_Free t andalso has_call t then Inr_const U T $ HOLogic.unit else t;
panny@53899
   712
      fun massage t =
panny@54097
   713
        rhs_term
blanchet@54102
   714
        |> massage_nested_corec_call lthy has_call rewrite bound_Ts (range_type (fastype_of t))
panny@53735
   715
        |> abs_tuple fun_args;
panny@53899
   716
    in
panny@53899
   717
      massage
blanchet@54208
   718
    end);
panny@53360
   719
blanchet@54153
   720
fun build_corec_args_sel lthy has_call (all_sel_eqns : coeqn_data_sel list)
blanchet@54002
   721
    (ctr_spec : corec_ctr_spec) =
blanchet@54208
   722
  (case filter (equal (#ctr ctr_spec) o #ctr) all_sel_eqns of
blanchet@54208
   723
    [] => I
blanchet@54208
   724
  | sel_eqns =>
blanchet@54208
   725
    let
blanchet@54208
   726
      val sel_call_list = #sels ctr_spec ~~ #calls ctr_spec;
blanchet@54208
   727
      val no_calls' = map_filter (try (apsnd (fn No_Corec n => n))) sel_call_list;
blanchet@54208
   728
      val mutual_calls' = map_filter (try (apsnd (fn Mutual_Corec n => n))) sel_call_list;
blanchet@54208
   729
      val nested_calls' = map_filter (try (apsnd (fn Nested_Corec n => n))) sel_call_list;
blanchet@54208
   730
    in
blanchet@54208
   731
      I
blanchet@54208
   732
      #> fold (fn (sel, n) => nth_map n (build_corec_arg_no_call sel_eqns sel)) no_calls'
blanchet@54208
   733
      #> fold (fn (sel, (q, g, h)) =>
blanchet@54208
   734
        let val (fq, fg, fh) = build_corec_args_mutual_call lthy has_call sel_eqns sel in
blanchet@54208
   735
          nth_map q fq o nth_map g fg o nth_map h fh end) mutual_calls'
blanchet@54208
   736
      #> fold (fn (sel, n) => nth_map n
blanchet@54208
   737
        (build_corec_arg_nested_call lthy has_call sel_eqns sel)) nested_calls'
blanchet@54208
   738
    end);
blanchet@53303
   739
blanchet@54153
   740
fun build_codefs lthy bs mxs has_call arg_Tss (corec_specs : corec_spec list)
blanchet@54153
   741
    (disc_eqnss : coeqn_data_disc list list) (sel_eqnss : coeqn_data_sel list list) =
panny@53654
   742
  let
panny@54160
   743
    val corecs = map #corec corec_specs;
panny@54160
   744
    val ctr_specss = map #ctr_specs corec_specs;
panny@53360
   745
    val corec_args = hd corecs
panny@53360
   746
      |> fst o split_last o binder_types o fastype_of
panny@53360
   747
      |> map (Const o pair @{const_name undefined})
panny@53720
   748
      |> fold2 (fold o build_corec_arg_disc) ctr_specss disc_eqnss
panny@53360
   749
      |> fold2 (fold o build_corec_args_sel lthy has_call) sel_eqnss ctr_specss;
panny@53735
   750
    fun currys [] t = t
panny@53735
   751
      | currys Ts t = t $ mk_tuple1 (List.rev Ts) (map Bound (length Ts - 1 downto 0))
panny@53735
   752
          |> fold_rev (Term.abs o pair Name.uu) Ts;
panny@53401
   753
blanchet@53856
   754
(*
panny@53360
   755
val _ = tracing ("corecursor arguments:\n    \<cdot> " ^
panny@53411
   756
 space_implode "\n    \<cdot> " (map (Syntax.string_of_term lthy) corec_args));
blanchet@53856
   757
*)
blanchet@53303
   758
panny@53654
   759
    val exclss' =
panny@53720
   760
      disc_eqnss
panny@53822
   761
      |> map (map (fn x => (#fun_args x, #ctr_no x, #prems x, #auto_gen x))
panny@53654
   762
        #> fst o (fn xs => fold_map (fn x => fn ys => ((x, ys), ys @ [x])) xs [])
panny@53654
   763
        #> maps (uncurry (map o pair)
panny@53822
   764
          #> map (fn ((fun_args, c, x, a), (_, c', y, a')) =>
blanchet@54068
   765
              ((c, c', a orelse a'), (x, s_not (s_conjs y)))
panny@53654
   766
            ||> apfst (map HOLogic.mk_Trueprop) o apsnd HOLogic.mk_Trueprop
panny@53654
   767
            ||> Logic.list_implies
panny@53654
   768
            ||> curry Logic.list_all (map dest_Free fun_args))))
blanchet@53303
   769
  in
blanchet@53303
   770
    map (list_comb o rpair corec_args) corecs
blanchet@53303
   771
    |> map2 (fn Ts => fn t => if length Ts = 0 then t $ HOLogic.unit else t) arg_Tss
blanchet@53303
   772
    |> map2 currys arg_Tss
blanchet@53303
   773
    |> Syntax.check_terms lthy
blanchet@54155
   774
    |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.conceal (Thm.def_binding b), []), t)))
blanchet@54155
   775
      bs mxs
panny@53654
   776
    |> rpair exclss'
blanchet@53303
   777
  end;
blanchet@53303
   778
blanchet@54002
   779
fun mk_real_disc_eqns fun_binding arg_Ts ({ctr_specs, ...} : corec_spec)
blanchet@54153
   780
    (sel_eqns : coeqn_data_sel list) (disc_eqns : coeqn_data_disc list) =
panny@53720
   781
  if length disc_eqns <> length ctr_specs - 1 then disc_eqns else
panny@53720
   782
    let
panny@53720
   783
      val n = 0 upto length ctr_specs
panny@53720
   784
        |> the o find_first (fn idx => not (exists (equal idx o #ctr_no) disc_eqns));
panny@53722
   785
      val fun_args = (try (#fun_args o hd) disc_eqns, try (#fun_args o hd) sel_eqns)
panny@53722
   786
        |> the_default (map (curry Free Name.uu) arg_Ts) o merge_options;
panny@53720
   787
      val extra_disc_eqn = {
panny@53720
   788
        fun_name = Binding.name_of fun_binding,
panny@53720
   789
        fun_T = arg_Ts ---> body_type (fastype_of (#ctr (hd ctr_specs))),
panny@53722
   790
        fun_args = fun_args,
panny@53720
   791
        ctr = #ctr (nth ctr_specs n),
panny@53720
   792
        ctr_no = n,
panny@53720
   793
        disc = #disc (nth ctr_specs n),
blanchet@54067
   794
        prems = maps (s_not_conj o #prems) disc_eqns,
panny@53822
   795
        auto_gen = true,
panny@54097
   796
        maybe_ctr_rhs = NONE,
panny@54097
   797
        maybe_code_rhs = NONE,
panny@53720
   798
        user_eqn = undef_const};
panny@53720
   799
    in
panny@53720
   800
      chop n disc_eqns ||> cons extra_disc_eqn |> (op @)
panny@53720
   801
    end;
panny@53720
   802
blanchet@54243
   803
fun find_corec_calls ctxt has_call basic_ctr_specs ({ctr, sel, rhs_term, ...} : coeqn_data_sel) =
panny@54160
   804
  let
panny@54160
   805
    val sel_no = find_first (equal ctr o #ctr) basic_ctr_specs
panny@54160
   806
      |> find_index (equal sel) o #sels o the;
blanchet@54243
   807
    fun find t = if has_call t then snd (fold_rev_corec_call ctxt (K cons) [] t []) else [];
panny@54160
   808
  in
panny@54160
   809
    find rhs_term
panny@54160
   810
    |> K |> nth_map sel_no |> AList.map_entry (op =) ctr
panny@54160
   811
  end;
panny@54160
   812
blanchet@54209
   813
fun add_primcorec_ursive maybe_tac seq fixes specs maybe_of_specs lthy =
blanchet@53303
   814
  let
traytel@53352
   815
    val (bs, mxs) = map_split (apfst fst) fixes;
blanchet@53303
   816
    val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> HOLogic.mk_tupleT) fixes |> split_list;
blanchet@53303
   817
panny@54160
   818
    val fun_names = map Binding.name_of bs;
panny@54160
   819
    val basic_ctr_specss = map (basic_corec_specs_of lthy) res_Ts;
panny@54160
   820
    val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
panny@54160
   821
    val eqns_data =
panny@54160
   822
      fold_map2 (dissect_coeqn lthy seq has_call fun_names basic_ctr_specss) (map snd specs)
blanchet@54209
   823
        maybe_of_specs []
panny@54160
   824
      |> flat o fst;
panny@54160
   825
panny@54160
   826
    val callssss =
panny@54160
   827
      map_filter (try (fn Sel x => x)) eqns_data
panny@54160
   828
      |> partition_eq ((op =) o pairself #fun_name)
panny@54160
   829
      |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
panny@54161
   830
      |> map (flat o snd)
blanchet@54243
   831
      |> map2 (fold o find_corec_calls lthy has_call) basic_ctr_specss
panny@54160
   832
      |> map2 (curry (op |>)) (map (map (fn {ctr, sels, ...} =>
panny@54160
   833
        (ctr, map (K []) sels))) basic_ctr_specss);
panny@54160
   834
panny@54160
   835
(*
panny@54160
   836
val _ = tracing ("callssss = " ^ @{make_string} callssss);
panny@54160
   837
*)
blanchet@53303
   838
blanchet@53830
   839
    val ((n2m, corec_specs', _, coinduct_thm, strong_coinduct_thm, coinduct_thms,
blanchet@53797
   840
          strong_coinduct_thms), lthy') =
blanchet@53794
   841
      corec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;
blanchet@53830
   842
    val actual_nn = length bs;
blanchet@53830
   843
    val corec_specs = take actual_nn corec_specs'; (*###*)
blanchet@54178
   844
    val ctr_specss = map #ctr_specs corec_specs;
blanchet@53303
   845
panny@53720
   846
    val disc_eqnss' = map_filter (try (fn Disc x => x)) eqns_data
panny@53654
   847
      |> partition_eq ((op =) o pairself #fun_name)
panny@53720
   848
      |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
panny@53654
   849
      |> map (sort ((op <) o pairself #ctr_no |> make_ord) o flat o snd);
panny@53720
   850
    val _ = disc_eqnss' |> map (fn x =>
panny@53720
   851
      let val d = duplicates ((op =) o pairself #ctr_no) x in null d orelse
blanchet@54204
   852
        primrec_error_eqns "excess discriminator formula in definition"
panny@53720
   853
          (maps (fn t => filter (equal (#ctr_no t) o #ctr_no) x) d |> map #user_eqn) end);
panny@53654
   854
panny@53654
   855
    val sel_eqnss = map_filter (try (fn Sel x => x)) eqns_data
panny@53654
   856
      |> partition_eq ((op =) o pairself #fun_name)
panny@53720
   857
      |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
panny@53654
   858
      |> map (flat o snd);
panny@53654
   859
panny@53360
   860
    val arg_Tss = map (binder_types o snd o fst) fixes;
panny@53722
   861
    val disc_eqnss = map5 mk_real_disc_eqns bs arg_Tss corec_specs sel_eqnss disc_eqnss';
panny@53654
   862
    val (defs, exclss') =
blanchet@54153
   863
      build_codefs lthy' bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss;
panny@53654
   864
blanchet@53923
   865
    fun excl_tac (c, c', a) =
blanchet@54177
   866
      if a orelse c = c' orelse seq then SOME (K (HEADGOAL (mk_primcorec_assumption_tac lthy [])))
blanchet@54177
   867
      else maybe_tac;
panny@53822
   868
blanchet@53856
   869
(*
panny@53822
   870
val _ = tracing ("exclusiveness properties:\n    \<cdot> " ^
panny@53822
   871
 space_implode "\n    \<cdot> " (maps (map (Syntax.string_of_term lthy o snd)) exclss'));
blanchet@53856
   872
*)
panny@53822
   873
panny@53822
   874
    val exclss'' = exclss' |> map (map (fn (idx, t) =>
blanchet@54177
   875
      (idx, (Option.map (Goal.prove lthy [] [] t #> Thm.close_derivation) (excl_tac idx), t))));
panny@53654
   876
    val taut_thmss = map (map (apsnd (the o fst)) o filter (is_some o fst o snd)) exclss'';
blanchet@54180
   877
    val (goal_idxss, goalss) = exclss''
panny@53654
   878
      |> map (map (apsnd (rpair [] o snd)) o filter (is_none o fst o snd))
panny@53654
   879
      |> split_list o map split_list;
panny@53654
   880
panny@53654
   881
    fun prove thmss' def_thms' lthy =
panny@53654
   882
      let
panny@53654
   883
        val def_thms = map (snd o snd) def_thms';
panny@53654
   884
blanchet@54180
   885
        val exclss' = map (op ~~) (goal_idxss ~~ thmss');
panny@53654
   886
        fun mk_exclsss excls n =
panny@53654
   887
          (excls, map (fn k => replicate k [TrueI] @ replicate (n - k) []) (0 upto n - 1))
panny@53822
   888
          |-> fold (fn ((c, c', _), thm) => nth_map c (nth_map c' (K [thm])));
panny@53654
   889
        val exclssss = (exclss' ~~ taut_thmss |> map (op @), fun_names ~~ corec_specs)
panny@53654
   890
          |-> map2 (fn excls => fn (_, {ctr_specs, ...}) => mk_exclsss excls (length ctr_specs));
panny@53654
   891
blanchet@54002
   892
        fun prove_disc ({ctr_specs, ...} : corec_spec) exclsss
blanchet@54153
   893
            ({fun_name, fun_T, fun_args, ctr_no, prems, ...} : coeqn_data_disc) =
panny@53722
   894
          if Term.aconv_untyped (#disc (nth ctr_specs ctr_no), @{term "\<lambda>x. x = x"}) then [] else
panny@53720
   895
            let
panny@53722
   896
              val {disc_corec, ...} = nth ctr_specs ctr_no;
panny@53720
   897
              val k = 1 + ctr_no;
panny@53720
   898
              val m = length prems;
panny@53720
   899
              val t =
panny@53720
   900
                list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
panny@53720
   901
                |> curry betapply (#disc (nth ctr_specs ctr_no)) (*###*)
panny@53720
   902
                |> HOLogic.mk_Trueprop
panny@53720
   903
                |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
panny@53720
   904
                |> curry Logic.list_all (map dest_Free fun_args);
panny@53720
   905
            in
panny@54097
   906
              if prems = [@{term False}] then [] else
panny@53720
   907
              mk_primcorec_disc_tac lthy def_thms disc_corec k m exclsss
panny@53720
   908
              |> K |> Goal.prove lthy [] [] t
blanchet@54176
   909
              |> Thm.close_derivation
panny@53720
   910
              |> pair (#disc (nth ctr_specs ctr_no))
panny@53720
   911
              |> single
panny@53720
   912
            end;
panny@53720
   913
blanchet@54002
   914
        fun prove_sel ({nested_maps, nested_map_idents, nested_map_comps, ctr_specs, ...}
blanchet@54153
   915
            : corec_spec) (disc_eqns : coeqn_data_disc list) exclsss
blanchet@54153
   916
            ({fun_name, fun_T, fun_args, ctr, sel, rhs_term, ...} : coeqn_data_sel) =
panny@53654
   917
          let
blanchet@53909
   918
            val SOME ctr_spec = find_first (equal ctr o #ctr) ctr_specs;
panny@53720
   919
            val ctr_no = find_index (equal ctr o #ctr) ctr_specs;
blanchet@54067
   920
            val prems = the_default (maps (s_not_conj o #prems) disc_eqns)
panny@53720
   921
                (find_first (equal ctr_no o #ctr_no) disc_eqns |> Option.map #prems);
panny@53720
   922
            val sel_corec = find_index (equal sel) (#sels ctr_spec)
panny@53720
   923
              |> nth (#sel_corecs ctr_spec);
panny@53654
   924
            val k = 1 + ctr_no;
panny@53654
   925
            val m = length prems;
panny@53654
   926
            val t =
panny@53720
   927
              list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
panny@53720
   928
              |> curry betapply sel
panny@53720
   929
              |> rpair (abstract (List.rev fun_args) rhs_term)
panny@53720
   930
              |> HOLogic.mk_Trueprop o HOLogic.mk_eq
panny@53654
   931
              |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
panny@53720
   932
              |> curry Logic.list_all (map dest_Free fun_args);
blanchet@53925
   933
            val (distincts, _, sel_splits, sel_split_asms) = case_thms_of_term lthy [] rhs_term;
panny@53654
   934
          in
blanchet@53918
   935
            mk_primcorec_sel_tac lthy def_thms distincts sel_splits sel_split_asms nested_maps
blanchet@53910
   936
              nested_map_idents nested_map_comps sel_corec k m exclsss
panny@53654
   937
            |> K |> Goal.prove lthy [] [] t
blanchet@54176
   938
            |> Thm.close_derivation
panny@53720
   939
            |> pair sel
panny@53654
   940
          end;
panny@53654
   941
blanchet@54153
   942
        fun prove_ctr disc_alist sel_alist (disc_eqns : coeqn_data_disc list)
blanchet@54153
   943
            (sel_eqns : coeqn_data_sel list) ({ctr, disc, sels, collapse, ...} : corec_ctr_spec) =
panny@54097
   944
          (* don't try to prove theorems when some sel_eqns are missing *)
panny@53720
   945
          if not (exists (equal ctr o #ctr) disc_eqns)
panny@53722
   946
              andalso not (exists (equal ctr o #ctr) sel_eqns)
panny@54097
   947
            orelse
panny@53720
   948
              filter (equal ctr o #ctr) sel_eqns
panny@53720
   949
              |> fst o finds ((op =) o apsnd #sel) sels
panny@53720
   950
              |> exists (null o snd)
panny@53720
   951
          then [] else
panny@53720
   952
            let
panny@54097
   953
              val (fun_name, fun_T, fun_args, prems, maybe_rhs) =
panny@53722
   954
                (find_first (equal ctr o #ctr) disc_eqns, find_first (equal ctr o #ctr) sel_eqns)
panny@54097
   955
                |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #prems x,
panny@54097
   956
                  #maybe_ctr_rhs x))
panny@54097
   957
                ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, [], NONE))
panny@53722
   958
                |> the o merge_options;
panny@53720
   959
              val m = length prems;
panny@54097
   960
              val t = (if is_some maybe_rhs then the maybe_rhs else
panny@54097
   961
                  filter (equal ctr o #ctr) sel_eqns
panny@54097
   962
                  |> fst o finds ((op =) o apsnd #sel) sels
panny@54097
   963
                  |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) #-> abstract)
panny@54097
   964
                  |> curry list_comb ctr)
panny@53720
   965
                |> curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
panny@53720
   966
                  map Bound (length fun_args - 1 downto 0)))
panny@53720
   967
                |> HOLogic.mk_Trueprop
panny@53720
   968
                |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
panny@53720
   969
                |> curry Logic.list_all (map dest_Free fun_args);
blanchet@53791
   970
              val maybe_disc_thm = AList.lookup (op =) disc_alist disc;
blanchet@53791
   971
              val sel_thms = map snd (filter (member (op =) sels o fst) sel_alist);
panny@53720
   972
            in
panny@54097
   973
              if prems = [@{term False}] then [] else
panny@54097
   974
                mk_primcorec_ctr_of_dtr_tac lthy m collapse maybe_disc_thm sel_thms
panny@54097
   975
                |> K |> Goal.prove lthy [] [] t
blanchet@54176
   976
                |> Thm.close_derivation
panny@54097
   977
                |> pair ctr
panny@54097
   978
                |> single
panny@53876
   979
            end;
panny@53720
   980
blanchet@54178
   981
        fun prove_code disc_eqns sel_eqns ctr_alist ctr_specs =
panny@54098
   982
          let
panny@54097
   983
            val (fun_name, fun_T, fun_args, maybe_rhs) =
panny@54097
   984
              (find_first (member (op =) (map #ctr ctr_specs) o #ctr) disc_eqns,
panny@54097
   985
               find_first (member (op =) (map #ctr ctr_specs) o #ctr) sel_eqns)
panny@54097
   986
              |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #maybe_code_rhs x))
panny@54097
   987
              ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, NONE))
panny@54097
   988
              |> the o merge_options;
panny@54097
   989
blanchet@54173
   990
            val bound_Ts = List.rev (map fastype_of fun_args);
blanchet@54173
   991
panny@54120
   992
            val lhs = list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0));
blanchet@54173
   993
            val maybe_rhs_info =
blanchet@54173
   994
              (case maybe_rhs of
blanchet@54173
   995
                SOME rhs =>
blanchet@54173
   996
                let
blanchet@54173
   997
                  val raw_rhs = expand_corec_code_rhs lthy has_call bound_Ts rhs;
blanchet@54173
   998
                  val cond_ctrs =
blanchet@54173
   999
                    fold_rev_corec_code_rhs lthy (K oo (cons oo pair)) bound_Ts raw_rhs [];
blanchet@54173
  1000
                  val ctr_thms = map (the o AList.lookup (op =) ctr_alist o snd) cond_ctrs;
blanchet@54173
  1001
                in SOME (rhs, raw_rhs, ctr_thms) end
blanchet@54173
  1002
              | NONE =>
blanchet@54173
  1003
                let
blanchet@54173
  1004
                  fun prove_code_ctr {ctr, sels, ...} =
blanchet@54173
  1005
                    if not (exists (equal ctr o fst) ctr_alist) then NONE else
blanchet@54173
  1006
                      let
blanchet@54173
  1007
                        val prems = find_first (equal ctr o #ctr) disc_eqns
blanchet@54173
  1008
                          |> Option.map #prems |> the_default [];
blanchet@54173
  1009
                        val t =
blanchet@54173
  1010
                          filter (equal ctr o #ctr) sel_eqns
blanchet@54173
  1011
                          |> fst o finds ((op =) o apsnd #sel) sels
blanchet@54173
  1012
                          |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x))
blanchet@54173
  1013
                            #-> abstract)
blanchet@54173
  1014
                          |> curry list_comb ctr;
blanchet@54173
  1015
                      in
blanchet@54173
  1016
                        SOME (prems, t)
blanchet@54173
  1017
                      end;
blanchet@54173
  1018
                  val maybe_ctr_conds_argss = map prove_code_ctr ctr_specs;
blanchet@54173
  1019
                in
blanchet@54173
  1020
                  if exists is_none maybe_ctr_conds_argss then NONE else
panny@54097
  1021
                    let
blanchet@54173
  1022
                      val rhs = fold_rev (fn SOME (prems, u) => fn t => mk_If (s_conjs prems) u t)
blanchet@54173
  1023
                        maybe_ctr_conds_argss
blanchet@54173
  1024
                        (Const (@{const_name Code.abort}, @{typ String.literal} -->
blanchet@54173
  1025
                            (@{typ unit} --> body_type fun_T) --> body_type fun_T) $
blanchet@54178
  1026
                          HOLogic.mk_literal fun_name $
blanchet@54173
  1027
                          absdummy @{typ unit} (incr_boundvars 1 lhs));
blanchet@54173
  1028
                    in SOME (rhs, rhs, map snd ctr_alist) end
blanchet@54173
  1029
                end);
panny@54097
  1030
          in
blanchet@54173
  1031
            (case maybe_rhs_info of
blanchet@54173
  1032
              NONE => []
blanchet@54173
  1033
            | SOME (rhs, raw_rhs, ctr_thms) =>
panny@54097
  1034
              let
panny@54097
  1035
                val ms = map (Logic.count_prems o prop_of) ctr_thms;
blanchet@54172
  1036
                val (raw_t, t) = (raw_rhs, rhs)
blanchet@54172
  1037
                  |> pairself
blanchet@54172
  1038
                    (curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
blanchet@54172
  1039
                      map Bound (length fun_args - 1 downto 0)))
blanchet@54172
  1040
                    #> HOLogic.mk_Trueprop
blanchet@54172
  1041
                    #> curry Logic.list_all (map dest_Free fun_args));
panny@54098
  1042
                val (distincts, discIs, sel_splits, sel_split_asms) =
blanchet@54172
  1043
                  case_thms_of_term lthy bound_Ts raw_rhs;
panny@54098
  1044
blanchet@54172
  1045
                val raw_code_thm = mk_primcorec_raw_code_of_ctr_tac lthy distincts discIs sel_splits
panny@54097
  1046
                    sel_split_asms ms ctr_thms
blanchet@54176
  1047
                  |> K |> Goal.prove lthy [] [] raw_t
blanchet@54176
  1048
                  |> Thm.close_derivation;
blanchet@54172
  1049
              in
blanchet@54174
  1050
                mk_primcorec_code_of_raw_code_tac lthy distincts sel_splits raw_code_thm
blanchet@54172
  1051
                |> K |> Goal.prove lthy [] [] t
blanchet@54176
  1052
                |> Thm.close_derivation
blanchet@54172
  1053
                |> single
blanchet@54173
  1054
              end)
blanchet@54173
  1055
          end;
panny@54097
  1056
blanchet@53791
  1057
        val disc_alists = map3 (maps oo prove_disc) corec_specs exclssss disc_eqnss;
blanchet@53791
  1058
        val sel_alists = map4 (map ooo prove_sel) corec_specs disc_eqnss exclssss sel_eqnss;
blanchet@53791
  1059
        val disc_thmss = map (map snd) disc_alists;
blanchet@53791
  1060
        val sel_thmss = map (map snd) sel_alists;
panny@54097
  1061
panny@54097
  1062
        val ctr_alists = map5 (maps oooo prove_ctr) disc_alists sel_alists disc_eqnss sel_eqnss
blanchet@54178
  1063
          ctr_specss;
panny@54097
  1064
        val ctr_thmss = map (map snd) ctr_alists;
panny@54097
  1065
blanchet@54178
  1066
        val code_thmss = map4 prove_code disc_eqnss sel_eqnss ctr_alists ctr_specss;
blanchet@53791
  1067
blanchet@54030
  1068
        val simp_thmss = map2 append disc_thmss sel_thmss
blanchet@53795
  1069
blanchet@53797
  1070
        val common_name = mk_common_name fun_names;
blanchet@53797
  1071
blanchet@53791
  1072
        val notes =
blanchet@53830
  1073
          [(coinductN, map (if n2m then single else K []) coinduct_thms, []),
blanchet@54145
  1074
           (codeN, code_thmss, code_nitpicksimp_attrs),
blanchet@53797
  1075
           (ctrN, ctr_thmss, []),
blanchet@53791
  1076
           (discN, disc_thmss, simp_attrs),
blanchet@53795
  1077
           (selN, sel_thmss, simp_attrs),
blanchet@53797
  1078
           (simpsN, simp_thmss, []),
blanchet@53830
  1079
           (strong_coinductN, map (if n2m then single else K []) strong_coinduct_thms, [])]
blanchet@53791
  1080
          |> maps (fn (thmN, thmss, attrs) =>
blanchet@53791
  1081
            map2 (fn fun_name => fn thms =>
blanchet@53791
  1082
                ((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])]))
blanchet@53830
  1083
              fun_names (take actual_nn thmss))
blanchet@53791
  1084
          |> filter_out (null o fst o hd o snd);
blanchet@53797
  1085
blanchet@53797
  1086
        val common_notes =
blanchet@53830
  1087
          [(coinductN, if n2m then [coinduct_thm] else [], []),
blanchet@53830
  1088
           (strong_coinductN, if n2m then [strong_coinduct_thm] else [], [])]
blanchet@53797
  1089
          |> filter_out (null o #2)
blanchet@53797
  1090
          |> map (fn (thmN, thms, attrs) =>
blanchet@53797
  1091
            ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
panny@53654
  1092
      in
blanchet@54030
  1093
        lthy |> Local_Theory.notes (notes @ common_notes) |> snd
panny@53654
  1094
      end;
panny@53822
  1095
panny@53822
  1096
    fun after_qed thmss' = fold_map Local_Theory.define defs #-> prove thmss';
blanchet@53303
  1097
  in
blanchet@54177
  1098
    (goalss, after_qed, lthy')
panny@53822
  1099
  end;
blanchet@53303
  1100
blanchet@54177
  1101
fun add_primcorec_ursive_cmd maybe_tac seq (raw_fixes, raw_specs') lthy =
blanchet@53303
  1102
  let
blanchet@54209
  1103
    val (raw_specs, maybe_of_specs) =
blanchet@54209
  1104
      split_list raw_specs' ||> map (Option.map (Syntax.read_term lthy));
panny@53831
  1105
    val ((fixes, specs), _) = Specification.read_spec raw_fixes raw_specs lthy;
blanchet@53303
  1106
  in
blanchet@54209
  1107
    add_primcorec_ursive maybe_tac seq fixes specs maybe_of_specs lthy
blanchet@53303
  1108
    handle ERROR str => primrec_error str
blanchet@53303
  1109
  end
blanchet@53303
  1110
  handle Primrec_Error (str, eqns) =>
blanchet@53303
  1111
    if null eqns
blanchet@53303
  1112
    then error ("primcorec error:\n  " ^ str)
blanchet@53303
  1113
    else error ("primcorec error:\n  " ^ str ^ "\nin\n  " ^
panny@53822
  1114
      space_implode "\n  " (map (quote o Syntax.string_of_term lthy) eqns));
panny@53822
  1115
blanchet@54177
  1116
val add_primcorecursive_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@54177
  1117
  lthy
blanchet@54177
  1118
  |> Proof.theorem NONE after_qed goalss
blanchet@54177
  1119
  |> Proof.refine (Method.primitive_text I)
blanchet@54177
  1120
  |> Seq.hd) ooo add_primcorec_ursive_cmd NONE;
blanchet@54177
  1121
blanchet@54177
  1122
val add_primcorec_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@54177
  1123
  lthy
blanchet@54177
  1124
  |> after_qed (map (fn [] => []
blanchet@54177
  1125
      | _ => primrec_error "need exclusiveness proofs - use primcorecursive instead of primcorec")
blanchet@54177
  1126
    goalss)) ooo add_primcorec_ursive_cmd (SOME (fn {context = ctxt, ...} => auto_tac ctxt));
blanchet@53303
  1127
blanchet@53303
  1128
end;