src/HOL/Tools/inductive_package.ML
author wenzelm
Fri Feb 02 22:20:09 2001 +0100 (2001-02-02)
changeset 11036 3c30f7b97a50
parent 11005 86f662ba3c3f
child 11358 416ea5c009f5
permissions -rw-r--r--
use hol_simplify;
berghofe@5094
     1
(*  Title:      HOL/Tools/inductive_package.ML
berghofe@5094
     2
    ID:         $Id$
berghofe@5094
     3
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
wenzelm@10735
     4
    Author:     Stefan Berghofer, TU Muenchen
wenzelm@10735
     5
    Author:     Markus Wenzel, TU Muenchen
berghofe@5094
     6
    Copyright   1994  University of Cambridge
wenzelm@9598
     7
                1998  TU Muenchen
berghofe@5094
     8
wenzelm@6424
     9
(Co)Inductive Definition module for HOL.
berghofe@5094
    10
berghofe@5094
    11
Features:
wenzelm@6424
    12
  * least or greatest fixedpoints
wenzelm@6424
    13
  * user-specified product and sum constructions
wenzelm@6424
    14
  * mutually recursive definitions
wenzelm@6424
    15
  * definitions involving arbitrary monotone operators
wenzelm@6424
    16
  * automatically proves introduction and elimination rules
berghofe@5094
    17
wenzelm@6424
    18
The recursive sets must *already* be declared as constants in the
wenzelm@6424
    19
current theory!
berghofe@5094
    20
berghofe@5094
    21
  Introduction rules have the form
wenzelm@8316
    22
  [| ti:M(Sj), ..., P(x), ... |] ==> t: Sk
berghofe@5094
    23
  where M is some monotone operator (usually the identity)
berghofe@5094
    24
  P(x) is any side condition on the free variables
berghofe@5094
    25
  ti, t are any terms
berghofe@5094
    26
  Sj, Sk are two of the sets being defined in mutual recursion
berghofe@5094
    27
wenzelm@6424
    28
Sums are used only for mutual recursion.  Products are used only to
wenzelm@6424
    29
derive "streamlined" induction rules for relations.
berghofe@5094
    30
*)
berghofe@5094
    31
berghofe@5094
    32
signature INDUCTIVE_PACKAGE =
berghofe@5094
    33
sig
wenzelm@6424
    34
  val quiet_mode: bool ref
berghofe@7020
    35
  val unify_consts: Sign.sg -> term list -> term list -> term list * term list
berghofe@10988
    36
  val split_rule_vars: term list -> thm -> thm
berghofe@9116
    37
  val get_inductive: theory -> string -> ({names: string list, coind: bool} *
berghofe@9116
    38
    {defs: thm list, elims: thm list, raw_induct: thm, induct: thm,
berghofe@9116
    39
     intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}) option
wenzelm@6437
    40
  val print_inductives: theory -> unit
berghofe@7710
    41
  val mono_add_global: theory attribute
berghofe@7710
    42
  val mono_del_global: theory attribute
berghofe@7710
    43
  val get_monos: theory -> thm list
wenzelm@10910
    44
  val inductive_forall_name: string
wenzelm@10910
    45
  val inductive_forall_def: thm
wenzelm@10910
    46
  val rulify: thm -> thm
wenzelm@10735
    47
  val inductive_cases: ((bstring * Args.src list) * string list) * Comment.text
wenzelm@10735
    48
    -> theory -> theory
wenzelm@10735
    49
  val inductive_cases_i: ((bstring * theory attribute list) * term list) * Comment.text
wenzelm@10735
    50
    -> theory -> theory
wenzelm@6424
    51
  val add_inductive_i: bool -> bool -> bstring -> bool -> bool -> bool -> term list ->
wenzelm@6521
    52
    theory attribute list -> ((bstring * term) * theory attribute list) list ->
wenzelm@6521
    53
      thm list -> thm list -> theory -> theory *
wenzelm@6424
    54
      {defs: thm list, elims: thm list, raw_induct: thm, induct: thm,
wenzelm@6437
    55
       intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}
wenzelm@6521
    56
  val add_inductive: bool -> bool -> string list -> Args.src list ->
wenzelm@6521
    57
    ((bstring * string) * Args.src list) list -> (xstring * Args.src list) list ->
wenzelm@6521
    58
      (xstring * Args.src list) list -> theory -> theory *
wenzelm@6424
    59
      {defs: thm list, elims: thm list, raw_induct: thm, induct: thm,
wenzelm@6437
    60
       intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}
wenzelm@6437
    61
  val setup: (theory -> theory) list
berghofe@5094
    62
end;
berghofe@5094
    63
wenzelm@6424
    64
structure InductivePackage: INDUCTIVE_PACKAGE =
berghofe@5094
    65
struct
berghofe@5094
    66
wenzelm@9598
    67
wenzelm@10729
    68
(** theory context references **)
wenzelm@10729
    69
wenzelm@10735
    70
val mono_name = "Ord.mono";
wenzelm@10735
    71
val gfp_name = "Gfp.gfp";
wenzelm@10735
    72
val lfp_name = "Lfp.lfp";
wenzelm@10735
    73
val vimage_name = "Inverse_Image.vimage";
wenzelm@10735
    74
val Const _ $ (vimage_f $ _) $ _ = HOLogic.dest_Trueprop (Thm.concl_of vimageD);
wenzelm@10735
    75
wenzelm@10910
    76
val inductive_forall_name = "Inductive.forall";
wenzelm@10910
    77
val inductive_forall_def = thm "forall_def";
wenzelm@10735
    78
val inductive_conj_name = "Inductive.conj";
wenzelm@10729
    79
val inductive_conj_def = thm "conj_def";
wenzelm@10729
    80
val inductive_conj = thms "inductive_conj";
wenzelm@10729
    81
val inductive_atomize = thms "inductive_atomize";
wenzelm@10729
    82
val inductive_rulify1 = thms "inductive_rulify1";
wenzelm@10729
    83
val inductive_rulify2 = thms "inductive_rulify2";
wenzelm@10729
    84
wenzelm@10729
    85
wenzelm@10729
    86
wenzelm@10735
    87
(** theory data **)
berghofe@7710
    88
berghofe@7710
    89
(* data kind 'HOL/inductive' *)
berghofe@7710
    90
berghofe@7710
    91
type inductive_info =
berghofe@7710
    92
  {names: string list, coind: bool} * {defs: thm list, elims: thm list, raw_induct: thm,
berghofe@7710
    93
    induct: thm, intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm};
berghofe@7710
    94
berghofe@7710
    95
structure InductiveArgs =
berghofe@7710
    96
struct
berghofe@7710
    97
  val name = "HOL/inductive";
berghofe@7710
    98
  type T = inductive_info Symtab.table * thm list;
berghofe@7710
    99
berghofe@7710
   100
  val empty = (Symtab.empty, []);
berghofe@7710
   101
  val copy = I;
berghofe@7710
   102
  val prep_ext = I;
berghofe@7710
   103
  fun merge ((tab1, monos1), (tab2, monos2)) = (Symtab.merge (K true) (tab1, tab2),
berghofe@7710
   104
    Library.generic_merge Thm.eq_thm I I monos1 monos2);
berghofe@7710
   105
berghofe@7710
   106
  fun print sg (tab, monos) =
wenzelm@8720
   107
    [Pretty.strs ("(co)inductives:" :: map #1 (Sign.cond_extern_table sg Sign.constK tab)),
wenzelm@10008
   108
     Pretty.big_list "monotonicity rules:" (map (Display.pretty_thm_sg sg) monos)]
wenzelm@8720
   109
    |> Pretty.chunks |> Pretty.writeln;
berghofe@7710
   110
end;
berghofe@7710
   111
berghofe@7710
   112
structure InductiveData = TheoryDataFun(InductiveArgs);
berghofe@7710
   113
val print_inductives = InductiveData.print;
berghofe@7710
   114
berghofe@7710
   115
berghofe@7710
   116
(* get and put data *)
berghofe@7710
   117
berghofe@9116
   118
fun get_inductive thy name = Symtab.lookup (fst (InductiveData.get thy), name);
berghofe@7710
   119
wenzelm@9598
   120
fun the_inductive thy name =
wenzelm@9598
   121
  (case get_inductive thy name of
wenzelm@9598
   122
    None => error ("Unknown (co)inductive set " ^ quote name)
wenzelm@9598
   123
  | Some info => info);
wenzelm@9598
   124
berghofe@7710
   125
fun put_inductives names info thy =
berghofe@7710
   126
  let
berghofe@7710
   127
    fun upd ((tab, monos), name) = (Symtab.update_new ((name, info), tab), monos);
berghofe@7710
   128
    val tab_monos = foldl upd (InductiveData.get thy, names)
berghofe@7710
   129
      handle Symtab.DUP name => error ("Duplicate definition of (co)inductive set " ^ quote name);
berghofe@7710
   130
  in InductiveData.put tab_monos thy end;
berghofe@7710
   131
wenzelm@8277
   132
berghofe@7710
   133
berghofe@7710
   134
(** monotonicity rules **)
berghofe@7710
   135
wenzelm@9831
   136
val get_monos = #2 o InductiveData.get;
wenzelm@9831
   137
fun map_monos f = InductiveData.map (Library.apsnd f);
wenzelm@8277
   138
berghofe@7710
   139
fun mk_mono thm =
berghofe@7710
   140
  let
berghofe@7710
   141
    fun eq2mono thm' = [standard (thm' RS (thm' RS eq_to_mono))] @
berghofe@7710
   142
      (case concl_of thm of
berghofe@7710
   143
          (_ $ (_ $ (Const ("Not", _) $ _) $ _)) => []
berghofe@7710
   144
        | _ => [standard (thm' RS (thm' RS eq_to_mono2))]);
berghofe@7710
   145
    val concl = concl_of thm
berghofe@7710
   146
  in
berghofe@7710
   147
    if Logic.is_equals concl then
berghofe@7710
   148
      eq2mono (thm RS meta_eq_to_obj_eq)
berghofe@7710
   149
    else if can (HOLogic.dest_eq o HOLogic.dest_Trueprop) concl then
berghofe@7710
   150
      eq2mono thm
berghofe@7710
   151
    else [thm]
berghofe@7710
   152
  end;
berghofe@7710
   153
wenzelm@8634
   154
wenzelm@8634
   155
(* attributes *)
berghofe@7710
   156
wenzelm@9831
   157
fun mono_add_global (thy, thm) = (map_monos (Drule.add_rules (mk_mono thm)) thy, thm);
wenzelm@9831
   158
fun mono_del_global (thy, thm) = (map_monos (Drule.del_rules (mk_mono thm)) thy, thm);
berghofe@7710
   159
berghofe@7710
   160
val mono_attr =
wenzelm@8634
   161
 (Attrib.add_del_args mono_add_global mono_del_global,
wenzelm@8634
   162
  Attrib.add_del_args Attrib.undef_local_attribute Attrib.undef_local_attribute);
berghofe@7710
   163
berghofe@7710
   164
wenzelm@7107
   165
wenzelm@10735
   166
(** misc utilities **)
wenzelm@6424
   167
berghofe@5662
   168
val quiet_mode = ref false;
wenzelm@10735
   169
fun message s = if ! quiet_mode then () else writeln s;
wenzelm@10735
   170
fun clean_message s = if ! quick_and_dirty then () else message s;
berghofe@5662
   171
wenzelm@6424
   172
fun coind_prefix true = "co"
wenzelm@6424
   173
  | coind_prefix false = "";
wenzelm@6424
   174
wenzelm@6424
   175
wenzelm@10735
   176
(*the following code ensures that each recursive set always has the
wenzelm@10735
   177
  same type in all introduction rules*)
berghofe@7020
   178
fun unify_consts sign cs intr_ts =
berghofe@7020
   179
  (let
berghofe@7020
   180
    val {tsig, ...} = Sign.rep_sg sign;
berghofe@7020
   181
    val add_term_consts_2 =
berghofe@7020
   182
      foldl_aterms (fn (cs, Const c) => c ins cs | (cs, _) => cs);
berghofe@7020
   183
    fun varify (t, (i, ts)) =
berghofe@7020
   184
      let val t' = map_term_types (incr_tvar (i + 1)) (Type.varify (t, []))
berghofe@7020
   185
      in (maxidx_of_term t', t'::ts) end;
berghofe@7020
   186
    val (i, cs') = foldr varify (cs, (~1, []));
berghofe@7020
   187
    val (i', intr_ts') = foldr varify (intr_ts, (i, []));
berghofe@7020
   188
    val rec_consts = foldl add_term_consts_2 ([], cs');
berghofe@7020
   189
    val intr_consts = foldl add_term_consts_2 ([], intr_ts');
berghofe@7020
   190
    fun unify (env, (cname, cT)) =
berghofe@7020
   191
      let val consts = map snd (filter (fn c => fst c = cname) intr_consts)
berghofe@7020
   192
      in foldl (fn ((env', j'), Tp) => (Type.unify tsig j' env' Tp))
berghofe@7020
   193
          (env, (replicate (length consts) cT) ~~ consts)
berghofe@7020
   194
      end;
berghofe@8410
   195
    val (env, _) = foldl unify ((Vartab.empty, i'), rec_consts);
berghofe@8410
   196
    fun typ_subst_TVars_2 env T = let val T' = typ_subst_TVars_Vartab env T
berghofe@7020
   197
      in if T = T' then T else typ_subst_TVars_2 env T' end;
berghofe@7020
   198
    val subst = fst o Type.freeze_thaw o
berghofe@7020
   199
      (map_term_types (typ_subst_TVars_2 env))
berghofe@7020
   200
berghofe@7020
   201
  in (map subst cs', map subst intr_ts')
berghofe@7020
   202
  end) handle Type.TUNIFY =>
berghofe@7020
   203
    (warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts));
berghofe@7020
   204
berghofe@7020
   205
wenzelm@10735
   206
(*make injections used in mutually recursive definitions*)
berghofe@5094
   207
fun mk_inj cs sumT c x =
berghofe@5094
   208
  let
berghofe@5094
   209
    fun mk_inj' T n i =
berghofe@5094
   210
      if n = 1 then x else
berghofe@5094
   211
      let val n2 = n div 2;
berghofe@5094
   212
          val Type (_, [T1, T2]) = T
berghofe@5094
   213
      in
berghofe@5094
   214
        if i <= n2 then
berghofe@5094
   215
          Const ("Inl", T1 --> T) $ (mk_inj' T1 n2 i)
berghofe@5094
   216
        else
berghofe@5094
   217
          Const ("Inr", T2 --> T) $ (mk_inj' T2 (n - n2) (i - n2))
berghofe@5094
   218
      end
berghofe@5094
   219
  in mk_inj' sumT (length cs) (1 + find_index_eq c cs)
berghofe@5094
   220
  end;
berghofe@5094
   221
wenzelm@10735
   222
(*make "vimage" terms for selecting out components of mutually rec.def*)
berghofe@5094
   223
fun mk_vimage cs sumT t c = if length cs < 2 then t else
berghofe@5094
   224
  let
berghofe@5094
   225
    val cT = HOLogic.dest_setT (fastype_of c);
berghofe@5094
   226
    val vimageT = [cT --> sumT, HOLogic.mk_setT sumT] ---> HOLogic.mk_setT cT
berghofe@5094
   227
  in
berghofe@5094
   228
    Const (vimage_name, vimageT) $
berghofe@5094
   229
      Abs ("y", cT, mk_inj cs sumT c (Bound 0)) $ t
berghofe@5094
   230
  end;
berghofe@5094
   231
berghofe@10988
   232
(** proper splitting **)
berghofe@10988
   233
berghofe@10988
   234
fun prod_factors p (Const ("Pair", _) $ t $ u) =
berghofe@10988
   235
      p :: prod_factors (1::p) t @ prod_factors (2::p) u
berghofe@10988
   236
  | prod_factors p _ = [];
berghofe@10988
   237
berghofe@10988
   238
fun mg_prod_factors ts (fs, t $ u) = if t mem ts then
berghofe@10988
   239
        let val f = prod_factors [] u
berghofe@10988
   240
        in overwrite (fs, (t, f inter if_none (assoc (fs, t)) f)) end
berghofe@10988
   241
      else mg_prod_factors ts (mg_prod_factors ts (fs, t), u)
berghofe@10988
   242
  | mg_prod_factors ts (fs, Abs (_, _, t)) = mg_prod_factors ts (fs, t)
berghofe@10988
   243
  | mg_prod_factors ts (fs, _) = fs;
berghofe@10988
   244
berghofe@10988
   245
fun prodT_factors p ps (T as Type ("*", [T1, T2])) =
berghofe@10988
   246
      if p mem ps then prodT_factors (1::p) ps T1 @ prodT_factors (2::p) ps T2
berghofe@10988
   247
      else [T]
berghofe@10988
   248
  | prodT_factors _ _ T = [T];
berghofe@10988
   249
berghofe@10988
   250
fun ap_split p ps (Type ("*", [T1, T2])) T3 u =
berghofe@10988
   251
      if p mem ps then HOLogic.split_const (T1, T2, T3) $
berghofe@10988
   252
        Abs ("v", T1, ap_split (2::p) ps T2 T3 (ap_split (1::p) ps T1
berghofe@10988
   253
          (prodT_factors (2::p) ps T2 ---> T3) (incr_boundvars 1 u) $ Bound 0))
berghofe@10988
   254
      else u
berghofe@10988
   255
  | ap_split _ _ _ _ u =  u;
berghofe@10988
   256
berghofe@10988
   257
fun mk_tuple p ps (Type ("*", [T1, T2])) (tms as t::_) =
berghofe@10988
   258
      if p mem ps then HOLogic.mk_prod (mk_tuple (1::p) ps T1 tms, 
berghofe@10988
   259
        mk_tuple (2::p) ps T2 (drop (length (prodT_factors (1::p) ps T1), tms)))
berghofe@10988
   260
      else t
berghofe@10988
   261
  | mk_tuple _ _ _ (t::_) = t;
berghofe@10988
   262
berghofe@10988
   263
fun split_rule_var' ((t as Var (v, Type ("fun", [T1, T2])), ps), rl) =
berghofe@10988
   264
      let val T' = prodT_factors [] ps T1 ---> T2
berghofe@10988
   265
          val newt = ap_split [] ps T1 T2 (Var (v, T'))
berghofe@10988
   266
          val cterm = Thm.cterm_of (#sign (rep_thm rl))
berghofe@10988
   267
      in
berghofe@10988
   268
          instantiate ([], [(cterm t, cterm newt)]) rl
berghofe@10988
   269
      end
berghofe@10988
   270
  | split_rule_var' (_, rl) = rl;
berghofe@10988
   271
berghofe@10988
   272
val remove_split = rewrite_rule [split_conv RS eq_reflection];
berghofe@10988
   273
berghofe@10988
   274
fun split_rule_vars vs rl = standard (remove_split (foldr split_rule_var'
berghofe@10988
   275
  (mg_prod_factors vs ([], #prop (rep_thm rl)), rl)));
berghofe@10988
   276
berghofe@10988
   277
fun split_rule vs rl = standard (remove_split (foldr split_rule_var'
berghofe@10988
   278
  (mapfilter (fn (t as Var ((a, _), _)) =>
berghofe@10988
   279
    apsome (pair t) (assoc (vs, a))) (term_vars (#prop (rep_thm rl))), rl)));
wenzelm@6424
   280
wenzelm@6424
   281
wenzelm@10729
   282
(** process rules **)
wenzelm@10729
   283
wenzelm@10729
   284
local
berghofe@5094
   285
wenzelm@10729
   286
fun err_in_rule sg name t msg =
wenzelm@10729
   287
  error (cat_lines ["Ill-formed introduction rule " ^ quote name, Sign.string_of_term sg t, msg]);
wenzelm@10729
   288
wenzelm@10729
   289
fun err_in_prem sg name t p msg =
wenzelm@10729
   290
  error (cat_lines ["Ill-formed premise", Sign.string_of_term sg p,
wenzelm@10729
   291
    "in introduction rule " ^ quote name, Sign.string_of_term sg t, msg]);
berghofe@5094
   292
wenzelm@10729
   293
val bad_concl = "Conclusion of introduction rule must have form \"t : S_i\"";
wenzelm@10729
   294
wenzelm@11036
   295
val atomize_cterm = hol_rewrite_cterm inductive_atomize;
wenzelm@10729
   296
wenzelm@10729
   297
in
berghofe@5094
   298
wenzelm@10729
   299
fun check_rule sg cs ((name, rule), att) =
wenzelm@10729
   300
  let
wenzelm@10729
   301
    val concl = Logic.strip_imp_concl rule;
wenzelm@10729
   302
    val prems = Logic.strip_imp_prems rule;
wenzelm@10729
   303
    val aprems = prems |> map (Thm.term_of o atomize_cterm o Thm.cterm_of sg);
wenzelm@10729
   304
    val arule = Logic.list_implies (aprems, concl);
berghofe@5094
   305
wenzelm@10729
   306
    fun check_prem (prem, aprem) =
wenzelm@10729
   307
      if can HOLogic.dest_Trueprop aprem then ()
wenzelm@10729
   308
      else err_in_prem sg name rule prem "Non-atomic premise";
wenzelm@10729
   309
  in
wenzelm@10729
   310
    (case HOLogic.dest_Trueprop concl of
wenzelm@10729
   311
      (Const ("op :", _) $ t $ u) =>
wenzelm@10729
   312
        if u mem cs then
wenzelm@10729
   313
          if exists (Logic.occs o rpair t) cs then
wenzelm@10729
   314
            err_in_rule sg name rule "Recursion term on left of member symbol"
wenzelm@10729
   315
          else seq check_prem (prems ~~ aprems)
wenzelm@10729
   316
        else err_in_rule sg name rule bad_concl
wenzelm@10729
   317
      | _ => err_in_rule sg name rule bad_concl);
wenzelm@10729
   318
    ((name, arule), att)
wenzelm@10729
   319
  end;
berghofe@5094
   320
wenzelm@10729
   321
val rulify =
wenzelm@10804
   322
  standard o Tactic.norm_hhf o
wenzelm@11036
   323
  hol_simplify inductive_rulify2 o hol_simplify inductive_rulify1 o
wenzelm@11036
   324
  hol_simplify inductive_conj;
wenzelm@10729
   325
wenzelm@10729
   326
end;
wenzelm@10729
   327
berghofe@5094
   328
wenzelm@6424
   329
wenzelm@10735
   330
(** properties of (co)inductive sets **)
berghofe@5094
   331
wenzelm@10735
   332
(* elimination rules *)
berghofe@5094
   333
wenzelm@8375
   334
fun mk_elims cs cTs params intr_ts intr_names =
berghofe@5094
   335
  let
berghofe@5094
   336
    val used = foldr add_term_names (intr_ts, []);
berghofe@5094
   337
    val [aname, pname] = variantlist (["a", "P"], used);
berghofe@5094
   338
    val P = HOLogic.mk_Trueprop (Free (pname, HOLogic.boolT));
berghofe@5094
   339
berghofe@5094
   340
    fun dest_intr r =
berghofe@5094
   341
      let val Const ("op :", _) $ t $ u =
berghofe@5094
   342
        HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   343
      in (u, t, Logic.strip_imp_prems r) end;
berghofe@5094
   344
wenzelm@8380
   345
    val intrs = map dest_intr intr_ts ~~ intr_names;
berghofe@5094
   346
berghofe@5094
   347
    fun mk_elim (c, T) =
berghofe@5094
   348
      let
berghofe@5094
   349
        val a = Free (aname, T);
berghofe@5094
   350
berghofe@5094
   351
        fun mk_elim_prem (_, t, ts) =
berghofe@5094
   352
          list_all_free (map dest_Free ((foldr add_term_frees (t::ts, [])) \\ params),
berghofe@5094
   353
            Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (a, t)) :: ts, P));
wenzelm@8375
   354
        val c_intrs = (filter (equal c o #1 o #1) intrs);
berghofe@5094
   355
      in
wenzelm@8375
   356
        (Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (a, c)) ::
wenzelm@8375
   357
          map mk_elim_prem (map #1 c_intrs), P), map #2 c_intrs)
berghofe@5094
   358
      end
berghofe@5094
   359
  in
berghofe@5094
   360
    map mk_elim (cs ~~ cTs)
berghofe@5094
   361
  end;
wenzelm@9598
   362
wenzelm@6424
   363
wenzelm@10735
   364
(* premises and conclusions of induction rules *)
berghofe@5094
   365
berghofe@5094
   366
fun mk_indrule cs cTs params intr_ts =
berghofe@5094
   367
  let
berghofe@5094
   368
    val used = foldr add_term_names (intr_ts, []);
berghofe@5094
   369
berghofe@5094
   370
    (* predicates for induction rule *)
berghofe@5094
   371
berghofe@5094
   372
    val preds = map Free (variantlist (if length cs < 2 then ["P"] else
berghofe@5094
   373
      map (fn i => "P" ^ string_of_int i) (1 upto length cs), used) ~~
berghofe@5094
   374
        map (fn T => T --> HOLogic.boolT) cTs);
berghofe@5094
   375
berghofe@5094
   376
    (* transform an introduction rule into a premise for induction rule *)
berghofe@5094
   377
berghofe@5094
   378
    fun mk_ind_prem r =
berghofe@5094
   379
      let
berghofe@5094
   380
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
berghofe@5094
   381
berghofe@7710
   382
        val pred_of = curry (Library.gen_assoc (op aconv)) (cs ~~ preds);
berghofe@5094
   383
berghofe@7710
   384
        fun subst (s as ((m as Const ("op :", T)) $ t $ u)) =
berghofe@7710
   385
              (case pred_of u of
berghofe@7710
   386
                  None => (m $ fst (subst t) $ fst (subst u), None)
wenzelm@10735
   387
                | Some P => (HOLogic.mk_binop inductive_conj_name (s, P $ t), Some (s, P $ t)))
berghofe@7710
   388
          | subst s =
berghofe@7710
   389
              (case pred_of s of
berghofe@7710
   390
                  Some P => (HOLogic.mk_binop "op Int"
berghofe@7710
   391
                    (s, HOLogic.Collect_const (HOLogic.dest_setT
berghofe@7710
   392
                      (fastype_of s)) $ P), None)
berghofe@7710
   393
                | None => (case s of
berghofe@7710
   394
                     (t $ u) => (fst (subst t) $ fst (subst u), None)
berghofe@7710
   395
                   | (Abs (a, T, t)) => (Abs (a, T, fst (subst t)), None)
berghofe@7710
   396
                   | _ => (s, None)));
berghofe@7710
   397
berghofe@7710
   398
        fun mk_prem (s, prems) = (case subst s of
berghofe@7710
   399
              (_, Some (t, u)) => t :: u :: prems
berghofe@7710
   400
            | (t, _) => t :: prems);
wenzelm@9598
   401
berghofe@5094
   402
        val Const ("op :", _) $ t $ u =
berghofe@5094
   403
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   404
berghofe@5094
   405
      in list_all_free (frees,
berghofe@7710
   406
           Logic.list_implies (map HOLogic.mk_Trueprop (foldr mk_prem
berghofe@5094
   407
             (map HOLogic.dest_Trueprop (Logic.strip_imp_prems r), [])),
berghofe@7710
   408
               HOLogic.mk_Trueprop (the (pred_of u) $ t)))
berghofe@5094
   409
      end;
berghofe@5094
   410
berghofe@5094
   411
    val ind_prems = map mk_ind_prem intr_ts;
berghofe@10988
   412
    val factors = foldl (mg_prod_factors preds) ([], ind_prems);
berghofe@5094
   413
berghofe@5094
   414
    (* make conclusions for induction rules *)
berghofe@5094
   415
berghofe@5094
   416
    fun mk_ind_concl ((c, P), (ts, x)) =
berghofe@5094
   417
      let val T = HOLogic.dest_setT (fastype_of c);
berghofe@10988
   418
          val ps = if_none (assoc (factors, P)) [];
berghofe@10988
   419
          val Ts = prodT_factors [] ps T;
berghofe@5094
   420
          val (frees, x') = foldr (fn (T', (fs, s)) =>
berghofe@5094
   421
            ((Free (s, T'))::fs, bump_string s)) (Ts, ([], x));
berghofe@10988
   422
          val tuple = mk_tuple [] ps T frees;
berghofe@5094
   423
      in ((HOLogic.mk_binop "op -->"
berghofe@5094
   424
        (HOLogic.mk_mem (tuple, c), P $ tuple))::ts, x')
berghofe@5094
   425
      end;
berghofe@5094
   426
berghofe@7710
   427
    val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@5094
   428
        (fst (foldr mk_ind_concl (cs ~~ preds, ([], "xa")))))
berghofe@5094
   429
berghofe@10988
   430
  in (preds, ind_prems, mutual_ind_concl,
berghofe@10988
   431
    map (apfst (fst o dest_Free)) factors)
berghofe@5094
   432
  end;
berghofe@5094
   433
wenzelm@6424
   434
wenzelm@10735
   435
(* prepare cases and induct rules *)
wenzelm@8316
   436
wenzelm@8316
   437
(*
wenzelm@8316
   438
  transform mutual rule:
wenzelm@8316
   439
    HH ==> (x1:A1 --> P1 x1) & ... & (xn:An --> Pn xn)
wenzelm@8316
   440
  into i-th projection:
wenzelm@8316
   441
    xi:Ai ==> HH ==> Pi xi
wenzelm@8316
   442
*)
wenzelm@8316
   443
wenzelm@8316
   444
fun project_rules [name] rule = [(name, rule)]
wenzelm@8316
   445
  | project_rules names mutual_rule =
wenzelm@8316
   446
      let
wenzelm@8316
   447
        val n = length names;
wenzelm@8316
   448
        fun proj i =
wenzelm@8316
   449
          (if i < n then (fn th => th RS conjunct1) else I)
wenzelm@8316
   450
            (Library.funpow (i - 1) (fn th => th RS conjunct2) mutual_rule)
wenzelm@8316
   451
            RS mp |> Thm.permute_prems 0 ~1 |> Drule.standard;
wenzelm@8316
   452
      in names ~~ map proj (1 upto n) end;
wenzelm@8316
   453
wenzelm@11005
   454
fun add_cases_induct no_elim no_ind names elims induct =
wenzelm@8316
   455
  let
wenzelm@9405
   456
    fun cases_spec (name, elim) thy =
wenzelm@9405
   457
      thy
wenzelm@9405
   458
      |> Theory.add_path (Sign.base_name name)
wenzelm@10279
   459
      |> (#1 o PureThy.add_thms [(("cases", elim), [InductAttrib.cases_set_global name])])
wenzelm@9405
   460
      |> Theory.parent_path;
wenzelm@8375
   461
    val cases_specs = if no_elim then [] else map2 cases_spec (names, elims);
wenzelm@8316
   462
wenzelm@11005
   463
    fun induct_spec (name, th) = #1 o PureThy.add_thms
wenzelm@11005
   464
      [(("", RuleCases.save induct th), [InductAttrib.induct_set_global name])];
wenzelm@8401
   465
    val induct_specs = if no_ind then [] else map induct_spec (project_rules names induct);
wenzelm@9405
   466
  in Library.apply (cases_specs @ induct_specs) end;
wenzelm@8316
   467
wenzelm@8316
   468
wenzelm@8316
   469
wenzelm@10735
   470
(** proofs for (co)inductive sets **)
wenzelm@6424
   471
wenzelm@10735
   472
(* prove monotonicity -- NOT subject to quick_and_dirty! *)
berghofe@5094
   473
berghofe@5094
   474
fun prove_mono setT fp_fun monos thy =
wenzelm@10735
   475
 (message "  Proving monotonicity ...";
wenzelm@10735
   476
  Goals.prove_goalw_cterm []      (*NO SkipProof.prove_goalw_cterm here!*)
wenzelm@10735
   477
    (Thm.cterm_of (Theory.sign_of thy) (HOLogic.mk_Trueprop
berghofe@5094
   478
      (Const (mono_name, (setT --> setT) --> HOLogic.boolT) $ fp_fun)))
wenzelm@10735
   479
    (fn _ => [rtac monoI 1, REPEAT (ares_tac (get_monos thy @ flat (map mk_mono monos)) 1)]));
berghofe@5094
   480
wenzelm@6424
   481
wenzelm@10735
   482
(* prove introduction rules *)
berghofe@5094
   483
berghofe@5094
   484
fun prove_intrs coind mono fp_def intr_ts con_defs rec_sets_defs thy =
berghofe@5094
   485
  let
wenzelm@10735
   486
    val _ = clean_message "  Proving the introduction rules ...";
berghofe@5094
   487
berghofe@5094
   488
    val unfold = standard (mono RS (fp_def RS
nipkow@10186
   489
      (if coind then def_gfp_unfold else def_lfp_unfold)));
berghofe@5094
   490
berghofe@5094
   491
    fun select_disj 1 1 = []
berghofe@5094
   492
      | select_disj _ 1 = [rtac disjI1]
berghofe@5094
   493
      | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
berghofe@5094
   494
wenzelm@10735
   495
    val intrs = map (fn (i, intr) => SkipProof.prove_goalw_cterm thy rec_sets_defs
wenzelm@10735
   496
      (Thm.cterm_of (Theory.sign_of thy) intr) (fn prems =>
berghofe@5094
   497
       [(*insert prems and underlying sets*)
berghofe@5094
   498
       cut_facts_tac prems 1,
berghofe@5094
   499
       stac unfold 1,
berghofe@5094
   500
       REPEAT (resolve_tac [vimageI2, CollectI] 1),
berghofe@5094
   501
       (*Now 1-2 subgoals: the disjunction, perhaps equality.*)
berghofe@5094
   502
       EVERY1 (select_disj (length intr_ts) i),
berghofe@5094
   503
       (*Not ares_tac, since refl must be tried before any equality assumptions;
berghofe@5094
   504
         backtracking may occur if the premises have extra variables!*)
wenzelm@10735
   505
       DEPTH_SOLVE_1 (resolve_tac [refl, exI, conjI] 1 APPEND assume_tac 1),
berghofe@5094
   506
       (*Now solve the equations like Inl 0 = Inl ?b2*)
berghofe@5094
   507
       rewrite_goals_tac con_defs,
wenzelm@10729
   508
       REPEAT (rtac refl 1)])
wenzelm@10729
   509
      |> rulify) (1 upto (length intr_ts) ~~ intr_ts)
berghofe@5094
   510
berghofe@5094
   511
  in (intrs, unfold) end;
berghofe@5094
   512
wenzelm@6424
   513
wenzelm@10735
   514
(* prove elimination rules *)
berghofe@5094
   515
wenzelm@8375
   516
fun prove_elims cs cTs params intr_ts intr_names unfold rec_sets_defs thy =
berghofe@5094
   517
  let
wenzelm@10735
   518
    val _ = clean_message "  Proving the elimination rules ...";
berghofe@5094
   519
berghofe@7710
   520
    val rules1 = [CollectE, disjE, make_elim vimageD, exE];
wenzelm@10735
   521
    val rules2 = [conjE, Inl_neq_Inr, Inr_neq_Inl] @ map make_elim [Inl_inject, Inr_inject];
wenzelm@8375
   522
  in
wenzelm@11005
   523
    mk_elims cs cTs params intr_ts intr_names |> map (fn (t, cases) =>
wenzelm@11005
   524
      SkipProof.prove_goalw_cterm thy rec_sets_defs
wenzelm@11005
   525
        (Thm.cterm_of (Theory.sign_of thy) t) (fn prems =>
wenzelm@11005
   526
          [cut_facts_tac [hd prems] 1,
wenzelm@11005
   527
           dtac (unfold RS subst) 1,
wenzelm@11005
   528
           REPEAT (FIRSTGOAL (eresolve_tac rules1)),
wenzelm@11005
   529
           REPEAT (FIRSTGOAL (eresolve_tac rules2)),
wenzelm@11005
   530
           EVERY (map (fn prem => DEPTH_SOLVE_1 (ares_tac [prem, conjI] 1)) (tl prems))])
wenzelm@11005
   531
        |> rulify
wenzelm@11005
   532
        |> RuleCases.name cases)
wenzelm@8375
   533
  end;
berghofe@5094
   534
wenzelm@6424
   535
wenzelm@10735
   536
(* derivation of simplified elimination rules *)
berghofe@5094
   537
berghofe@5094
   538
(*Applies freeness of the given constructors, which *must* be unfolded by
wenzelm@9598
   539
  the given defs.  Cannot simply use the local con_defs because con_defs=[]
wenzelm@10735
   540
  for inference systems. (??) *)
berghofe@5094
   541
wenzelm@7107
   542
(*cprop should have the form t:Si where Si is an inductive set*)
wenzelm@9598
   543
wenzelm@10735
   544
val mk_cases_err = "mk_cases: proposition not of form \"t : S_i\"";
wenzelm@9598
   545
wenzelm@9598
   546
fun mk_cases_i elims ss cprop =
wenzelm@7107
   547
  let
wenzelm@7107
   548
    val prem = Thm.assume cprop;
wenzelm@9598
   549
    val tac = ALLGOALS (InductMethod.simp_case_tac false ss) THEN prune_params_tac;
wenzelm@9298
   550
    fun mk_elim rl = Drule.standard (Tactic.rule_by_tactic tac (prem RS rl));
wenzelm@7107
   551
  in
wenzelm@7107
   552
    (case get_first (try mk_elim) elims of
wenzelm@7107
   553
      Some r => r
wenzelm@7107
   554
    | None => error (Pretty.string_of (Pretty.block
wenzelm@9598
   555
        [Pretty.str mk_cases_err, Pretty.fbrk, Display.pretty_cterm cprop])))
wenzelm@7107
   556
  end;
wenzelm@7107
   557
paulson@6141
   558
fun mk_cases elims s =
wenzelm@9598
   559
  mk_cases_i elims (simpset()) (Thm.read_cterm (Thm.sign_of_thm (hd elims)) (s, propT));
wenzelm@9598
   560
wenzelm@9598
   561
fun smart_mk_cases thy ss cprop =
wenzelm@9598
   562
  let
wenzelm@9598
   563
    val c = #1 (Term.dest_Const (Term.head_of (#2 (HOLogic.dest_mem (HOLogic.dest_Trueprop
wenzelm@9598
   564
      (Logic.strip_imp_concl (Thm.term_of cprop))))))) handle TERM _ => error mk_cases_err;
wenzelm@9598
   565
    val (_, {elims, ...}) = the_inductive thy c;
wenzelm@9598
   566
  in mk_cases_i elims ss cprop end;
wenzelm@7107
   567
wenzelm@7107
   568
wenzelm@7107
   569
(* inductive_cases(_i) *)
wenzelm@7107
   570
wenzelm@7107
   571
fun gen_inductive_cases prep_att prep_const prep_prop
wenzelm@9598
   572
    (((name, raw_atts), raw_props), comment) thy =
wenzelm@9598
   573
  let
wenzelm@9598
   574
    val ss = Simplifier.simpset_of thy;
wenzelm@9598
   575
    val sign = Theory.sign_of thy;
wenzelm@9598
   576
    val cprops = map (Thm.cterm_of sign o prep_prop (ProofContext.init thy)) raw_props;
wenzelm@9598
   577
    val atts = map (prep_att thy) raw_atts;
wenzelm@9598
   578
    val thms = map (smart_mk_cases thy ss) cprops;
wenzelm@9598
   579
  in thy |> IsarThy.have_theorems_i [(((name, atts), map Thm.no_attributes thms), comment)] end;
berghofe@5094
   580
wenzelm@7107
   581
val inductive_cases =
wenzelm@7107
   582
  gen_inductive_cases Attrib.global_attribute Sign.intern_const ProofContext.read_prop;
wenzelm@7107
   583
wenzelm@7107
   584
val inductive_cases_i = gen_inductive_cases (K I) (K I) ProofContext.cert_prop;
wenzelm@7107
   585
wenzelm@6424
   586
wenzelm@9598
   587
(* mk_cases_meth *)
wenzelm@9598
   588
wenzelm@9598
   589
fun mk_cases_meth (ctxt, raw_props) =
wenzelm@9598
   590
  let
wenzelm@9598
   591
    val thy = ProofContext.theory_of ctxt;
wenzelm@9598
   592
    val ss = Simplifier.get_local_simpset ctxt;
wenzelm@9598
   593
    val cprops = map (Thm.cterm_of (Theory.sign_of thy) o ProofContext.read_prop ctxt) raw_props;
wenzelm@10743
   594
  in Method.erule 0 (map (smart_mk_cases thy ss) cprops) end;
wenzelm@9598
   595
wenzelm@9598
   596
val mk_cases_args = Method.syntax (Scan.lift (Scan.repeat1 Args.name));
wenzelm@9598
   597
wenzelm@9598
   598
wenzelm@10735
   599
(* prove induction rule *)
berghofe@5094
   600
berghofe@5094
   601
fun prove_indrule cs cTs sumT rec_const params intr_ts mono
berghofe@5094
   602
    fp_def rec_sets_defs thy =
berghofe@5094
   603
  let
wenzelm@10735
   604
    val _ = clean_message "  Proving the induction rule ...";
berghofe@5094
   605
wenzelm@6394
   606
    val sign = Theory.sign_of thy;
berghofe@5094
   607
berghofe@7293
   608
    val sum_case_rewrites = (case ThyInfo.lookup_theory "Datatype" of
berghofe@7293
   609
        None => []
berghofe@7293
   610
      | Some thy' => map mk_meta_eq (PureThy.get_thms thy' "sum.cases"));
berghofe@7293
   611
berghofe@10988
   612
    val (preds, ind_prems, mutual_ind_concl, factors) =
berghofe@10988
   613
      mk_indrule cs cTs params intr_ts;
berghofe@5094
   614
berghofe@5094
   615
    (* make predicate for instantiation of abstract induction rule *)
berghofe@5094
   616
berghofe@5094
   617
    fun mk_ind_pred _ [P] = P
berghofe@5094
   618
      | mk_ind_pred T Ps =
berghofe@5094
   619
         let val n = (length Ps) div 2;
berghofe@5094
   620
             val Type (_, [T1, T2]) = T
berghofe@7293
   621
         in Const ("Datatype.sum.sum_case",
berghofe@5094
   622
           [T1 --> HOLogic.boolT, T2 --> HOLogic.boolT, T] ---> HOLogic.boolT) $
berghofe@5094
   623
             mk_ind_pred T1 (take (n, Ps)) $ mk_ind_pred T2 (drop (n, Ps))
berghofe@5094
   624
         end;
berghofe@5094
   625
berghofe@5094
   626
    val ind_pred = mk_ind_pred sumT preds;
berghofe@5094
   627
berghofe@5094
   628
    val ind_concl = HOLogic.mk_Trueprop
berghofe@5094
   629
      (HOLogic.all_const sumT $ Abs ("x", sumT, HOLogic.mk_binop "op -->"
berghofe@5094
   630
        (HOLogic.mk_mem (Bound 0, rec_const), ind_pred $ Bound 0)));
berghofe@5094
   631
berghofe@5094
   632
    (* simplification rules for vimage and Collect *)
berghofe@5094
   633
berghofe@5094
   634
    val vimage_simps = if length cs < 2 then [] else
wenzelm@10735
   635
      map (fn c => SkipProof.prove_goalw_cterm thy [] (Thm.cterm_of sign
berghofe@5094
   636
        (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@5094
   637
          (mk_vimage cs sumT (HOLogic.Collect_const sumT $ ind_pred) c,
berghofe@5094
   638
           HOLogic.Collect_const (HOLogic.dest_setT (fastype_of c)) $
berghofe@5094
   639
             nth_elem (find_index_eq c cs, preds)))))
wenzelm@10735
   640
        (fn _ => [rtac vimage_Collect 1, rewrite_goals_tac sum_case_rewrites, rtac refl 1])) cs;
berghofe@5094
   641
wenzelm@10735
   642
    val induct = SkipProof.prove_goalw_cterm thy [inductive_conj_def] (Thm.cterm_of sign
berghofe@5094
   643
      (Logic.list_implies (ind_prems, ind_concl))) (fn prems =>
berghofe@5094
   644
        [rtac (impI RS allI) 1,
nipkow@10202
   645
         DETERM (etac (mono RS (fp_def RS def_lfp_induct)) 1),
berghofe@7710
   646
         rewrite_goals_tac (map mk_meta_eq (vimage_Int::Int_Collect::vimage_simps)),
berghofe@5094
   647
         fold_goals_tac rec_sets_defs,
berghofe@5094
   648
         (*This CollectE and disjE separates out the introduction rules*)
berghofe@7710
   649
         REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE, exE])),
berghofe@5094
   650
         (*Now break down the individual cases.  No disjE here in case
berghofe@5094
   651
           some premise involves disjunction.*)
berghofe@7710
   652
         REPEAT (FIRSTGOAL (etac conjE ORELSE' hyp_subst_tac)),
berghofe@7293
   653
         rewrite_goals_tac sum_case_rewrites,
berghofe@5094
   654
         EVERY (map (fn prem =>
berghofe@5149
   655
           DEPTH_SOLVE_1 (ares_tac [prem, conjI, refl] 1)) prems)]);
berghofe@5094
   656
wenzelm@10735
   657
    val lemma = SkipProof.prove_goalw_cterm thy rec_sets_defs (Thm.cterm_of sign
berghofe@5094
   658
      (Logic.mk_implies (ind_concl, mutual_ind_concl))) (fn prems =>
berghofe@5094
   659
        [cut_facts_tac prems 1,
berghofe@5094
   660
         REPEAT (EVERY
berghofe@5094
   661
           [REPEAT (resolve_tac [conjI, impI] 1),
berghofe@5094
   662
            TRY (dtac vimageD 1), etac allE 1, dtac mp 1, atac 1,
berghofe@7293
   663
            rewrite_goals_tac sum_case_rewrites,
berghofe@5094
   664
            atac 1])])
berghofe@5094
   665
berghofe@10988
   666
  in standard (split_rule factors (induct RS lemma)) end;
berghofe@5094
   667
wenzelm@6424
   668
wenzelm@6424
   669
wenzelm@10735
   670
(** specification of (co)inductive sets **)
berghofe@5094
   671
wenzelm@10729
   672
fun cond_declare_consts declare_consts cs paramTs cnames =
wenzelm@10729
   673
  if declare_consts then
wenzelm@10729
   674
    Theory.add_consts_i (map (fn (c, n) => (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
wenzelm@10729
   675
  else I;
wenzelm@10729
   676
berghofe@9072
   677
fun mk_ind_def declare_consts alt_name coind cs intr_ts monos con_defs thy
berghofe@9072
   678
      params paramTs cTs cnames =
berghofe@5094
   679
  let
berghofe@5094
   680
    val sumT = fold_bal (fn (T, U) => Type ("+", [T, U])) cTs;
berghofe@5094
   681
    val setT = HOLogic.mk_setT sumT;
berghofe@5094
   682
wenzelm@10735
   683
    val fp_name = if coind then gfp_name else lfp_name;
berghofe@5094
   684
berghofe@5149
   685
    val used = foldr add_term_names (intr_ts, []);
berghofe@5149
   686
    val [sname, xname] = variantlist (["S", "x"], used);
berghofe@5149
   687
berghofe@5094
   688
    (* transform an introduction rule into a conjunction  *)
berghofe@5094
   689
    (*   [| t : ... S_i ... ; ... |] ==> u : S_j          *)
berghofe@5094
   690
    (* is transformed into                                *)
berghofe@5094
   691
    (*   x = Inj_j u & t : ... Inj_i -`` S ... & ...      *)
berghofe@5094
   692
berghofe@5094
   693
    fun transform_rule r =
berghofe@5094
   694
      let
berghofe@5094
   695
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
berghofe@5149
   696
        val subst = subst_free
berghofe@5149
   697
          (cs ~~ (map (mk_vimage cs sumT (Free (sname, setT))) cs));
berghofe@5094
   698
        val Const ("op :", _) $ t $ u =
berghofe@5094
   699
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   700
berghofe@5094
   701
      in foldr (fn ((x, T), P) => HOLogic.mk_exists (x, T, P))
berghofe@7710
   702
        (frees, foldr1 HOLogic.mk_conj
berghofe@5149
   703
          (((HOLogic.eq_const sumT) $ Free (xname, sumT) $ (mk_inj cs sumT u t))::
berghofe@5094
   704
            (map (subst o HOLogic.dest_Trueprop)
berghofe@5094
   705
              (Logic.strip_imp_prems r))))
berghofe@5094
   706
      end
berghofe@5094
   707
berghofe@5094
   708
    (* make a disjunction of all introduction rules *)
berghofe@5094
   709
berghofe@5149
   710
    val fp_fun = absfree (sname, setT, (HOLogic.Collect_const sumT) $
berghofe@7710
   711
      absfree (xname, sumT, foldr1 HOLogic.mk_disj (map transform_rule intr_ts)));
berghofe@5094
   712
berghofe@5094
   713
    (* add definiton of recursive sets to theory *)
berghofe@5094
   714
berghofe@5094
   715
    val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
wenzelm@6394
   716
    val full_rec_name = Sign.full_name (Theory.sign_of thy) rec_name;
berghofe@5094
   717
berghofe@5094
   718
    val rec_const = list_comb
berghofe@5094
   719
      (Const (full_rec_name, paramTs ---> setT), params);
berghofe@5094
   720
berghofe@5094
   721
    val fp_def_term = Logic.mk_equals (rec_const,
wenzelm@10735
   722
      Const (fp_name, (setT --> setT) --> setT) $ fp_fun);
berghofe@5094
   723
berghofe@5094
   724
    val def_terms = fp_def_term :: (if length cs < 2 then [] else
berghofe@5094
   725
      map (fn c => Logic.mk_equals (c, mk_vimage cs sumT rec_const c)) cs);
berghofe@5094
   726
wenzelm@8433
   727
    val (thy', [fp_def :: rec_sets_defs]) =
wenzelm@8433
   728
      thy
wenzelm@10729
   729
      |> cond_declare_consts declare_consts cs paramTs cnames
wenzelm@8433
   730
      |> (if length cs < 2 then I
wenzelm@8433
   731
          else Theory.add_consts_i [(rec_name, paramTs ---> setT, NoSyn)])
wenzelm@8433
   732
      |> Theory.add_path rec_name
wenzelm@9315
   733
      |> PureThy.add_defss_i false [(("defs", def_terms), [])];
berghofe@5094
   734
berghofe@9072
   735
    val mono = prove_mono setT fp_fun monos thy'
berghofe@5094
   736
wenzelm@10735
   737
  in (thy', mono, fp_def, rec_sets_defs, rec_const, sumT) end;
berghofe@5094
   738
berghofe@9072
   739
fun add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs
berghofe@9072
   740
    atts intros monos con_defs thy params paramTs cTs cnames induct_cases =
berghofe@9072
   741
  let
wenzelm@10735
   742
    val _ =
wenzelm@10735
   743
      if verbose then message ("Proofs for " ^ coind_prefix coind ^ "inductive set(s) " ^
wenzelm@10735
   744
        commas_quote cnames) else ();
berghofe@9072
   745
berghofe@9072
   746
    val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
berghofe@9072
   747
wenzelm@9939
   748
    val (thy1, mono, fp_def, rec_sets_defs, rec_const, sumT) =
berghofe@9072
   749
      mk_ind_def declare_consts alt_name coind cs intr_ts monos con_defs thy
berghofe@9072
   750
        params paramTs cTs cnames;
berghofe@9072
   751
berghofe@5094
   752
    val (intrs, unfold) = prove_intrs coind mono fp_def intr_ts con_defs
wenzelm@9939
   753
      rec_sets_defs thy1;
berghofe@5094
   754
    val elims = if no_elim then [] else
wenzelm@9939
   755
      prove_elims cs cTs params intr_ts intr_names unfold rec_sets_defs thy1;
wenzelm@8312
   756
    val raw_induct = if no_ind then Drule.asm_rl else
berghofe@5094
   757
      if coind then standard (rule_by_tactic
oheimb@5553
   758
        (rewrite_tac [mk_meta_eq vimage_Un] THEN
berghofe@5094
   759
          fold_tac rec_sets_defs) (mono RS (fp_def RS def_Collect_coinduct)))
berghofe@5094
   760
      else
berghofe@5094
   761
        prove_indrule cs cTs sumT rec_const params intr_ts mono fp_def
wenzelm@9939
   762
          rec_sets_defs thy1;
berghofe@5108
   763
    val induct = if coind orelse no_ind orelse length cs > 1 then raw_induct
berghofe@5094
   764
      else standard (raw_induct RSN (2, rev_mp));
berghofe@5094
   765
wenzelm@9939
   766
    val (thy2, intrs') =
wenzelm@9939
   767
      thy1 |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts);
wenzelm@10735
   768
    val (thy3, ([intrs'', elims'], [induct'])) =
wenzelm@10735
   769
      thy2
wenzelm@11005
   770
      |> PureThy.add_thmss
wenzelm@11005
   771
        [(("intros", intrs'), atts),
wenzelm@11005
   772
          (("elims", elims), [RuleCases.consumes 1])]
wenzelm@10735
   773
      |>>> PureThy.add_thms
wenzelm@11005
   774
        [((coind_prefix coind ^ "induct", rulify induct),
wenzelm@11005
   775
         [RuleCases.case_names induct_cases,
wenzelm@11005
   776
          RuleCases.consumes 1])]
wenzelm@8433
   777
      |>> Theory.parent_path;
wenzelm@9939
   778
  in (thy3,
wenzelm@10735
   779
    {defs = fp_def :: rec_sets_defs,
berghofe@5094
   780
     mono = mono,
berghofe@5094
   781
     unfold = unfold,
wenzelm@9939
   782
     intrs = intrs'',
wenzelm@7798
   783
     elims = elims',
wenzelm@7798
   784
     mk_cases = mk_cases elims',
wenzelm@10729
   785
     raw_induct = rulify raw_induct,
wenzelm@7798
   786
     induct = induct'})
berghofe@5094
   787
  end;
berghofe@5094
   788
wenzelm@6424
   789
wenzelm@10735
   790
(* external interfaces *)
berghofe@5094
   791
wenzelm@10735
   792
fun try_term f msg sign t =
wenzelm@10735
   793
  (case Library.try f t of
wenzelm@10735
   794
    Some x => x
wenzelm@10735
   795
  | None => error (msg ^ Sign.string_of_term sign t));
berghofe@5094
   796
berghofe@5094
   797
fun add_inductive_i verbose declare_consts alt_name coind no_elim no_ind cs
wenzelm@10729
   798
    atts pre_intros monos con_defs thy =
berghofe@5094
   799
  let
wenzelm@6424
   800
    val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
wenzelm@6394
   801
    val sign = Theory.sign_of thy;
berghofe@5094
   802
berghofe@5094
   803
    (*parameters should agree for all mutually recursive components*)
berghofe@5094
   804
    val (_, params) = strip_comb (hd cs);
wenzelm@10735
   805
    val paramTs = map (try_term (snd o dest_Free) "Parameter in recursive\
berghofe@5094
   806
      \ component is not a free variable: " sign) params;
berghofe@5094
   807
wenzelm@10735
   808
    val cTs = map (try_term (HOLogic.dest_setT o fastype_of)
berghofe@5094
   809
      "Recursive component not of type set: " sign) cs;
berghofe@5094
   810
wenzelm@10735
   811
    val full_cnames = map (try_term (fst o dest_Const o head_of)
berghofe@5094
   812
      "Recursive set not previously declared as constant: " sign) cs;
wenzelm@6437
   813
    val cnames = map Sign.base_name full_cnames;
berghofe@5094
   814
wenzelm@10729
   815
    val save_sign =
wenzelm@10729
   816
      thy |> Theory.copy |> cond_declare_consts declare_consts cs paramTs cnames |> Theory.sign_of;
wenzelm@10729
   817
    val intros = map (check_rule save_sign cs) pre_intros;
wenzelm@8401
   818
    val induct_cases = map (#1 o #1) intros;
wenzelm@6437
   819
wenzelm@9405
   820
    val (thy1, result as {elims, induct, ...}) =
wenzelm@10735
   821
      add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs atts intros monos
wenzelm@8401
   822
        con_defs thy params paramTs cTs cnames induct_cases;
wenzelm@8307
   823
    val thy2 = thy1
wenzelm@8307
   824
      |> put_inductives full_cnames ({names = full_cnames, coind = coind}, result)
wenzelm@11005
   825
      |> add_cases_induct no_elim (no_ind orelse coind) full_cnames elims induct;
wenzelm@6437
   826
  in (thy2, result) end;
berghofe@5094
   827
wenzelm@6521
   828
fun add_inductive verbose coind c_strings srcs intro_srcs raw_monos raw_con_defs thy =
berghofe@5094
   829
  let
wenzelm@6394
   830
    val sign = Theory.sign_of thy;
wenzelm@8100
   831
    val cs = map (term_of o Thm.read_cterm sign o rpair HOLogic.termT) c_strings;
wenzelm@6424
   832
wenzelm@6521
   833
    val atts = map (Attrib.global_attribute thy) srcs;
wenzelm@6424
   834
    val intr_names = map (fst o fst) intro_srcs;
wenzelm@9405
   835
    fun read_rule s = Thm.read_cterm sign (s, propT)
wenzelm@9405
   836
      handle ERROR => error ("The error(s) above occurred for " ^ s);
wenzelm@9405
   837
    val intr_ts = map (Thm.term_of o read_rule o snd o fst) intro_srcs;
wenzelm@6424
   838
    val intr_atts = map (map (Attrib.global_attribute thy) o snd) intro_srcs;
berghofe@7020
   839
    val (cs', intr_ts') = unify_consts sign cs intr_ts;
berghofe@5094
   840
wenzelm@6424
   841
    val ((thy', con_defs), monos) = thy
wenzelm@6424
   842
      |> IsarThy.apply_theorems raw_monos
wenzelm@6424
   843
      |> apfst (IsarThy.apply_theorems raw_con_defs);
wenzelm@6424
   844
  in
berghofe@7020
   845
    add_inductive_i verbose false "" coind false false cs'
berghofe@7020
   846
      atts ((intr_names ~~ intr_ts') ~~ intr_atts) monos con_defs thy'
berghofe@5094
   847
  end;
berghofe@5094
   848
wenzelm@6424
   849
wenzelm@6424
   850
wenzelm@6437
   851
(** package setup **)
wenzelm@6437
   852
wenzelm@6437
   853
(* setup theory *)
wenzelm@6437
   854
wenzelm@8634
   855
val setup =
wenzelm@8634
   856
 [InductiveData.init,
wenzelm@9625
   857
  Method.add_methods [("ind_cases", mk_cases_meth oo mk_cases_args,
wenzelm@9598
   858
    "dynamic case analysis on sets")],
wenzelm@9893
   859
  Attrib.add_attributes [("mono", mono_attr, "declaration of monotonicity rule")]];
wenzelm@6437
   860
wenzelm@6437
   861
wenzelm@6437
   862
(* outer syntax *)
wenzelm@6424
   863
wenzelm@6723
   864
local structure P = OuterParse and K = OuterSyntax.Keyword in
wenzelm@6424
   865
wenzelm@6521
   866
fun mk_ind coind (((sets, (atts, intrs)), monos), con_defs) =
wenzelm@6723
   867
  #1 o add_inductive true coind sets atts (map P.triple_swap intrs) monos con_defs;
wenzelm@6424
   868
wenzelm@6424
   869
fun ind_decl coind =
wenzelm@6729
   870
  (Scan.repeat1 P.term --| P.marg_comment) --
wenzelm@9598
   871
  (P.$$$ "intros" |--
wenzelm@7152
   872
    P.!!! (P.opt_attribs -- Scan.repeat1 (P.opt_thm_name ":" -- P.prop --| P.marg_comment))) --
wenzelm@6729
   873
  Scan.optional (P.$$$ "monos" |-- P.!!! P.xthms1 --| P.marg_comment) [] --
wenzelm@6729
   874
  Scan.optional (P.$$$ "con_defs" |-- P.!!! P.xthms1 --| P.marg_comment) []
wenzelm@6424
   875
  >> (Toplevel.theory o mk_ind coind);
wenzelm@6424
   876
wenzelm@6723
   877
val inductiveP =
wenzelm@6723
   878
  OuterSyntax.command "inductive" "define inductive sets" K.thy_decl (ind_decl false);
wenzelm@6723
   879
wenzelm@6723
   880
val coinductiveP =
wenzelm@6723
   881
  OuterSyntax.command "coinductive" "define coinductive sets" K.thy_decl (ind_decl true);
wenzelm@6424
   882
wenzelm@7107
   883
wenzelm@7107
   884
val ind_cases =
wenzelm@9625
   885
  P.opt_thm_name ":" -- Scan.repeat1 P.prop -- P.marg_comment
wenzelm@7107
   886
  >> (Toplevel.theory o inductive_cases);
wenzelm@7107
   887
wenzelm@7107
   888
val inductive_casesP =
wenzelm@9804
   889
  OuterSyntax.command "inductive_cases"
wenzelm@9598
   890
    "create simplified instances of elimination rules (improper)" K.thy_script ind_cases;
wenzelm@7107
   891
wenzelm@9643
   892
val _ = OuterSyntax.add_keywords ["intros", "monos", "con_defs"];
wenzelm@7107
   893
val _ = OuterSyntax.add_parsers [inductiveP, coinductiveP, inductive_casesP];
wenzelm@6424
   894
berghofe@5094
   895
end;
wenzelm@6424
   896
wenzelm@6424
   897
end;