src/HOL/Tools/datatype_aux.ML
author wenzelm
Wed Mar 01 20:48:57 2000 +0100 (2000-03-01)
changeset 8324 df7dccddc3de
parent 8305 93aa21ec5494
child 8404 4b39358f9810
permissions -rw-r--r--
tuned;
berghofe@5177
     1
(*  Title:      HOL/Tools/datatype_aux.ML
berghofe@5177
     2
    ID:         $Id$
berghofe@5177
     3
    Author:     Stefan Berghofer
berghofe@5177
     4
    Copyright   1998  TU Muenchen
berghofe@5177
     5
berghofe@5177
     6
Auxiliary functions for defining datatypes
berghofe@5177
     7
*)
berghofe@5177
     8
berghofe@5177
     9
signature DATATYPE_AUX =
berghofe@5177
    10
sig
berghofe@5661
    11
  val quiet_mode : bool ref
berghofe@5661
    12
  val message : string -> unit
berghofe@5661
    13
  
berghofe@5177
    14
  val foldl1 : ('a * 'a -> 'a) -> 'a list -> 'a
berghofe@5177
    15
berghofe@5661
    16
  val add_path : bool -> string -> theory -> theory
berghofe@5661
    17
  val parent_path : bool -> theory -> theory
berghofe@5661
    18
berghofe@5177
    19
  val store_thmss : string -> string list -> thm list list -> theory -> theory
berghofe@5177
    20
  val store_thms : string -> string list -> thm list -> theory -> theory
berghofe@5177
    21
berghofe@5177
    22
  val split_conj_thm : thm -> thm list
berghofe@5177
    23
  val mk_conj : term list -> term
berghofe@5177
    24
  val mk_disj : term list -> term
berghofe@5177
    25
berghofe@5177
    26
  val indtac : thm -> int -> tactic
berghofe@5177
    27
  val exh_tac : (string -> thm) -> int -> tactic
berghofe@5177
    28
berghofe@7015
    29
  datatype simproc_dist = QuickAndDirty
berghofe@7015
    30
                        | FewConstrs of thm list
berghofe@7015
    31
                        | ManyConstrs of thm * simpset;
berghofe@7015
    32
berghofe@5177
    33
  datatype dtyp =
berghofe@5177
    34
      DtTFree of string
berghofe@5177
    35
    | DtType of string * (dtyp list)
berghofe@5177
    36
    | DtRec of int;
berghofe@5177
    37
berghofe@5177
    38
  type datatype_info
berghofe@5177
    39
berghofe@7015
    40
  exception Datatype
berghofe@5177
    41
  val dtyp_of_typ : (string * string list) list -> typ -> dtyp
berghofe@5177
    42
  val mk_Free : string -> typ -> int -> term
berghofe@5177
    43
  val is_rec_type : dtyp -> bool
berghofe@5177
    44
  val typ_of_dtyp : (int * (string * dtyp list *
berghofe@5177
    45
    (string * dtyp list) list)) list -> (string * sort) list -> dtyp -> typ
berghofe@5177
    46
  val dest_DtTFree : dtyp -> string
berghofe@5177
    47
  val dest_DtRec : dtyp -> int
berghofe@5177
    48
  val dest_TFree : typ -> string
berghofe@5177
    49
  val get_nonrec_types : (int * (string * dtyp list *
berghofe@5177
    50
    (string * dtyp list) list)) list -> (string * sort) list -> typ list
berghofe@7015
    51
  val get_branching_types : (int * (string * dtyp list *
berghofe@7015
    52
    (string * dtyp list) list)) list -> (string * sort) list -> typ list
berghofe@5177
    53
  val get_rec_types : (int * (string * dtyp list *
berghofe@5177
    54
    (string * dtyp list) list)) list -> (string * sort) list -> typ list
berghofe@5177
    55
  val check_nonempty : (int * (string * dtyp list *
berghofe@5177
    56
    (string * dtyp list) list)) list list -> unit
berghofe@5177
    57
  val unfold_datatypes : 
berghofe@7015
    58
    Sign.sg -> (int * (string * dtyp list * (string * dtyp list) list)) list ->
berghofe@7015
    59
      (string * sort) list -> datatype_info Symtab.table ->
berghofe@7015
    60
        (int * (string * dtyp list * (string * dtyp list) list)) list -> int ->
berghofe@5177
    61
          (int * (string * dtyp list *
berghofe@5177
    62
            (string * dtyp list) list)) list list * int
berghofe@5177
    63
end;
berghofe@5177
    64
berghofe@5177
    65
structure DatatypeAux : DATATYPE_AUX =
berghofe@5177
    66
struct
berghofe@5177
    67
berghofe@5661
    68
val quiet_mode = ref false;
berghofe@5661
    69
fun message s = if !quiet_mode then () else writeln s;
berghofe@5661
    70
berghofe@5177
    71
(* FIXME: move to library ? *)
berghofe@5177
    72
fun foldl1 f (x::xs) = foldl f (x, xs);
berghofe@5177
    73
berghofe@5661
    74
fun add_path flat_names s = if flat_names then I else Theory.add_path s;
berghofe@5661
    75
fun parent_path flat_names = if flat_names then I else Theory.parent_path;
berghofe@5661
    76
berghofe@5177
    77
(* store theorems in theory *)
berghofe@5177
    78
berghofe@5177
    79
fun store_thmss label tnames thmss thy =
berghofe@5177
    80
  foldr (fn ((tname, thms), thy') => thy' |>
berghofe@5661
    81
    Theory.add_path tname |>
wenzelm@6092
    82
    PureThy.add_thmss [((label, thms), [])] |>
berghofe@5661
    83
    Theory.parent_path)
berghofe@5661
    84
      (tnames ~~ thmss, thy);
berghofe@5177
    85
berghofe@5177
    86
fun store_thms label tnames thms thy =
berghofe@5177
    87
  foldr (fn ((tname, thm), thy') => thy' |>
berghofe@5661
    88
    Theory.add_path tname |>
wenzelm@6092
    89
    PureThy.add_thms [((label, thm), [])] |>
berghofe@5661
    90
    Theory.parent_path)
berghofe@5661
    91
      (tnames ~~ thms, thy);
berghofe@5177
    92
berghofe@5177
    93
(* split theorem thm_1 & ... & thm_n into n theorems *)
berghofe@5177
    94
berghofe@5177
    95
fun split_conj_thm th =
berghofe@7015
    96
  ((th RS conjunct1)::(split_conj_thm (th RS conjunct2))) handle THM _ => [th];
berghofe@5177
    97
berghofe@5177
    98
val mk_conj = foldr1 (HOLogic.mk_binop "op &");
berghofe@5177
    99
val mk_disj = foldr1 (HOLogic.mk_binop "op |");
berghofe@5177
   100
berghofe@5177
   101
berghofe@5177
   102
(* instantiate induction rule *)
berghofe@5177
   103
berghofe@5177
   104
fun indtac indrule i st =
berghofe@5177
   105
  let
wenzelm@8305
   106
    val ts = HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule));
wenzelm@8305
   107
    val ts' = HOLogic.dest_conj (HOLogic.dest_Trueprop
berghofe@5177
   108
      (Logic.strip_imp_concl (nth_elem (i - 1, prems_of st))));
berghofe@5177
   109
    val getP = if can HOLogic.dest_imp (hd ts) then
berghofe@5177
   110
      (apfst Some) o HOLogic.dest_imp else pair None;
berghofe@5177
   111
    fun abstr (t1, t2) = (case t1 of
berghofe@5177
   112
        None => let val [Free (s, T)] = add_term_frees (t2, [])
berghofe@5177
   113
          in absfree (s, T, t2) end
berghofe@5177
   114
      | Some (_ $ t' $ _) => Abs ("x", fastype_of t', abstract_over (t', t2)))
wenzelm@6394
   115
    val cert = cterm_of (Thm.sign_of_thm st);
berghofe@5177
   116
    val Ps = map (cert o head_of o snd o getP) ts;
berghofe@5177
   117
    val indrule' = cterm_instantiate (Ps ~~
berghofe@5177
   118
      (map (cert o abstr o getP) ts')) indrule
berghofe@5177
   119
  in
berghofe@5177
   120
    rtac indrule' i st
berghofe@5177
   121
  end;
berghofe@5177
   122
berghofe@5177
   123
(* perform exhaustive case analysis on last parameter of subgoal i *)
berghofe@5177
   124
berghofe@5177
   125
fun exh_tac exh_thm_of i state =
berghofe@5177
   126
  let
wenzelm@6394
   127
    val sg = Thm.sign_of_thm state;
berghofe@5177
   128
    val prem = nth_elem (i - 1, prems_of state);
berghofe@5177
   129
    val params = Logic.strip_params prem;
berghofe@5177
   130
    val (_, Type (tname, _)) = hd (rev params);
berghofe@5177
   131
    val exhaustion = lift_rule (state, i) (exh_thm_of tname);
berghofe@5177
   132
    val prem' = hd (prems_of exhaustion);
berghofe@5177
   133
    val _ $ (_ $ lhs $ _) = hd (rev (Logic.strip_assums_hyp prem'));
berghofe@5177
   134
    val exhaustion' = cterm_instantiate [(cterm_of sg (head_of lhs),
berghofe@5177
   135
      cterm_of sg (foldr (fn ((_, T), t) => Abs ("z", T, t))
berghofe@5177
   136
        (params, Bound 0)))] exhaustion
berghofe@5177
   137
  in compose_tac (false, exhaustion', nprems_of exhaustion) i state
berghofe@5177
   138
  end;
berghofe@5177
   139
berghofe@7015
   140
(* handling of distinctness theorems *)
berghofe@7015
   141
berghofe@7015
   142
datatype simproc_dist = QuickAndDirty
berghofe@7015
   143
                      | FewConstrs of thm list
berghofe@7015
   144
                      | ManyConstrs of thm * simpset;
berghofe@7015
   145
berghofe@5177
   146
(********************** Internal description of datatypes *********************)
berghofe@5177
   147
berghofe@5177
   148
datatype dtyp =
berghofe@5177
   149
    DtTFree of string
berghofe@5177
   150
  | DtType of string * (dtyp list)
berghofe@5177
   151
  | DtRec of int;
berghofe@5177
   152
berghofe@5177
   153
(* information about datatypes *)
berghofe@5177
   154
berghofe@5177
   155
type datatype_info =
berghofe@5177
   156
  {index : int,
wenzelm@8324
   157
   descr : (int * (string * dtyp list * (string * dtyp list) list)) list,
berghofe@5177
   158
   rec_names : string list,
berghofe@5177
   159
   rec_rewrites : thm list,
berghofe@5177
   160
   case_name : string,
berghofe@5177
   161
   case_rewrites : thm list,
berghofe@5177
   162
   induction : thm,
berghofe@5177
   163
   exhaustion : thm,
berghofe@7015
   164
   distinct : simproc_dist,
berghofe@5177
   165
   inject : thm list,
berghofe@5177
   166
   nchotomy : thm,
berghofe@5177
   167
   case_cong : thm};
berghofe@5177
   168
berghofe@5177
   169
fun mk_Free s T i = Free (s ^ (string_of_int i), T);
berghofe@5177
   170
berghofe@5177
   171
fun subst_DtTFree _ substs (T as (DtTFree name)) =
berghofe@5177
   172
      (case assoc (substs, name) of
berghofe@5177
   173
         None => T
berghofe@5177
   174
       | Some U => U)
berghofe@5177
   175
  | subst_DtTFree i substs (DtType (name, ts)) =
berghofe@5177
   176
      DtType (name, map (subst_DtTFree i substs) ts)
berghofe@5177
   177
  | subst_DtTFree i _ (DtRec j) = DtRec (i + j);
berghofe@5177
   178
berghofe@7015
   179
exception Datatype;
berghofe@7015
   180
berghofe@7015
   181
fun dest_DtTFree (DtTFree a) = a
berghofe@7015
   182
  | dest_DtTFree _ = raise Datatype;
berghofe@7015
   183
berghofe@7015
   184
fun dest_DtRec (DtRec i) = i
berghofe@7015
   185
  | dest_DtRec _ = raise Datatype;
berghofe@5177
   186
berghofe@5177
   187
fun is_rec_type (DtType (_, dts)) = exists is_rec_type dts
berghofe@5177
   188
  | is_rec_type (DtRec _) = true
berghofe@5177
   189
  | is_rec_type _ = false;
berghofe@5177
   190
berghofe@5177
   191
fun dest_TFree (TFree (n, _)) = n;
berghofe@5177
   192
berghofe@5177
   193
fun dtyp_of_typ _ (TFree (n, _)) = DtTFree n
berghofe@5177
   194
  | dtyp_of_typ _ (TVar _) = error "Illegal schematic type variable(s)"
berghofe@5177
   195
  | dtyp_of_typ new_dts (Type (tname, Ts)) =
berghofe@5177
   196
      (case assoc (new_dts, tname) of
berghofe@5177
   197
         None => DtType (tname, map (dtyp_of_typ new_dts) Ts)
berghofe@5177
   198
       | Some vs => if map (try dest_TFree) Ts = map Some vs then
berghofe@5177
   199
             DtRec (find_index (curry op = tname o fst) new_dts)
berghofe@5177
   200
           else error ("Illegal occurence of recursive type " ^ tname));
berghofe@5177
   201
berghofe@5177
   202
fun typ_of_dtyp descr sorts (DtTFree a) = TFree (a, the (assoc (sorts, a)))
berghofe@5177
   203
  | typ_of_dtyp descr sorts (DtRec i) =
berghofe@5177
   204
      let val (s, ds, _) = the (assoc (descr, i))
berghofe@5177
   205
      in Type (s, map (typ_of_dtyp descr sorts) ds) end
berghofe@5177
   206
  | typ_of_dtyp descr sorts (DtType (s, ds)) =
berghofe@5177
   207
      Type (s, map (typ_of_dtyp descr sorts) ds);
berghofe@5177
   208
berghofe@5177
   209
(* find all non-recursive types in datatype description *)
berghofe@5177
   210
berghofe@5177
   211
fun get_nonrec_types descr sorts =
berghofe@5177
   212
  let fun add (Ts, T as DtTFree _) = T ins Ts
berghofe@7015
   213
        | add (Ts, T as DtType ("fun", [_, DtRec _])) = Ts
berghofe@5177
   214
        | add (Ts, T as DtType _) = T ins Ts
berghofe@5177
   215
        | add (Ts, _) = Ts
berghofe@5177
   216
  in map (typ_of_dtyp descr sorts) (foldl (fn (Ts, (_, (_, _, constrs))) =>
berghofe@5177
   217
    foldl (fn (Ts', (_, cargs)) =>
berghofe@5177
   218
      foldl add (Ts', cargs)) (Ts, constrs)) ([], descr))
berghofe@5177
   219
  end;
berghofe@5177
   220
berghofe@5177
   221
(* get all recursive types in datatype description *)
berghofe@5177
   222
berghofe@5177
   223
fun get_rec_types descr sorts = map (fn (_ , (s, ds, _)) =>
berghofe@5177
   224
  Type (s, map (typ_of_dtyp descr sorts) ds)) descr;
berghofe@5177
   225
berghofe@7015
   226
(* get all branching types *)
berghofe@7015
   227
berghofe@7015
   228
fun get_branching_types descr sorts = 
berghofe@7015
   229
  let fun add (Ts, DtType ("fun", [T, DtRec _])) = T ins Ts
berghofe@7015
   230
        | add (Ts, _) = Ts
berghofe@7015
   231
  in map (typ_of_dtyp descr sorts) (foldl (fn (Ts, (_, (_, _, constrs))) =>
berghofe@7015
   232
    foldl (fn (Ts', (_, cargs)) =>
berghofe@7015
   233
      foldl add (Ts', cargs)) (Ts, constrs)) ([], descr))
berghofe@7015
   234
  end;
berghofe@7015
   235
berghofe@5177
   236
(* nonemptiness check for datatypes *)
berghofe@5177
   237
berghofe@5177
   238
fun check_nonempty descr =
berghofe@5177
   239
  let
berghofe@5177
   240
    val descr' = flat descr;
berghofe@5177
   241
    fun is_nonempty_dt is i =
berghofe@5177
   242
      let
berghofe@5177
   243
        val (_, _, constrs) = the (assoc (descr', i));
berghofe@5177
   244
        fun arg_nonempty (DtRec i) = if i mem is then false
berghofe@5177
   245
              else is_nonempty_dt (i::is) i
berghofe@7015
   246
          | arg_nonempty (DtType ("fun", [_, T])) = arg_nonempty T
berghofe@5177
   247
          | arg_nonempty _ = true;
berghofe@5177
   248
      in exists ((forall arg_nonempty) o snd) constrs
berghofe@5177
   249
      end
berghofe@5177
   250
  in assert_all (fn (i, _) => is_nonempty_dt [i] i) (hd descr)
berghofe@5177
   251
    (fn (_, (s, _, _)) => "Nonemptiness check failed for datatype " ^ s)
berghofe@5177
   252
  end;
berghofe@5177
   253
berghofe@5177
   254
(* unfold a list of mutually recursive datatype specifications *)
berghofe@5177
   255
(* all types of the form DtType (dt_name, [..., DtRec _, ...]) *)
berghofe@5177
   256
(* need to be unfolded                                         *)
berghofe@5177
   257
berghofe@7015
   258
fun unfold_datatypes sign orig_descr sorts (dt_info : datatype_info Symtab.table) descr i =
berghofe@5177
   259
  let
berghofe@7015
   260
    fun typ_error T msg = error ("Non-admissible type expression\n" ^
berghofe@7015
   261
      Sign.string_of_typ sign (typ_of_dtyp (orig_descr @ descr) sorts T) ^ "\n" ^ msg);
berghofe@7015
   262
berghofe@7015
   263
    fun get_dt_descr T i tname dts =
berghofe@5177
   264
      (case Symtab.lookup (dt_info, tname) of
berghofe@7015
   265
         None => typ_error T (tname ^ " is not a datatype - can't use it in\
berghofe@7015
   266
           \ nested recursion")
berghofe@5177
   267
       | (Some {index, descr, ...}) =>
berghofe@5177
   268
           let val (_, vars, _) = the (assoc (descr, index));
berghofe@7015
   269
               val subst = ((map dest_DtTFree vars) ~~ dts) handle LIST _ =>
berghofe@7015
   270
                 typ_error T ("Type constructor " ^ tname ^ " used with wrong\
berghofe@5177
   271
                  \ number of arguments")
berghofe@5177
   272
           in (i + index, map (fn (j, (tn, args, cs)) => (i + j,
berghofe@5177
   273
             (tn, map (subst_DtTFree i subst) args,
berghofe@5177
   274
              map (apsnd (map (subst_DtTFree i subst))) cs))) descr)
berghofe@5177
   275
           end);
berghofe@5177
   276
berghofe@5177
   277
    (* unfold a single constructor argument *)
berghofe@5177
   278
berghofe@5177
   279
    fun unfold_arg ((i, Ts, descrs), T as (DtType (tname, dts))) =
berghofe@5177
   280
          if is_rec_type T then
berghofe@7015
   281
            if tname = "fun" then
berghofe@7015
   282
              if is_rec_type (hd dts) then
berghofe@7015
   283
                typ_error T "Non-strictly positive recursive occurrence of type"
berghofe@7015
   284
              else
berghofe@7015
   285
                (case hd (tl dts) of
berghofe@7015
   286
                   DtType ("fun", _) => typ_error T "Curried function types not allowed"
berghofe@7015
   287
                 | T' => let val (i', [T''], descrs') = unfold_arg ((i, [], descrs), T')
berghofe@7015
   288
                         in (i', Ts @ [DtType (tname, [hd dts, T''])], descrs') end)
berghofe@7015
   289
            else
berghofe@7015
   290
              let val (index, descr) = get_dt_descr T i tname dts;
berghofe@7015
   291
                  val (descr', i') = unfold_datatypes sign orig_descr sorts dt_info descr (i + length descr)
berghofe@7015
   292
              in (i', Ts @ [DtRec index], descrs @ descr') end
berghofe@5177
   293
          else (i, Ts @ [T], descrs)
berghofe@5177
   294
      | unfold_arg ((i, Ts, descrs), T) = (i, Ts @ [T], descrs);
berghofe@5177
   295
berghofe@5177
   296
    (* unfold a constructor *)
berghofe@5177
   297
berghofe@5177
   298
    fun unfold_constr ((i, constrs, descrs), (cname, cargs)) =
berghofe@5177
   299
      let val (i', cargs', descrs') = foldl unfold_arg ((i, [], descrs), cargs)
berghofe@5177
   300
      in (i', constrs @ [(cname, cargs')], descrs') end;
berghofe@5177
   301
berghofe@5177
   302
    (* unfold a single datatype *)
berghofe@5177
   303
berghofe@5177
   304
    fun unfold_datatype ((i, dtypes, descrs), (j, (tname, tvars, constrs))) =
berghofe@5177
   305
      let val (i', constrs', descrs') =
berghofe@5177
   306
        foldl unfold_constr ((i, [], descrs), constrs)
berghofe@5177
   307
      in (i', dtypes @ [(j, (tname, tvars, constrs'))], descrs')
berghofe@5177
   308
      end;
berghofe@5177
   309
berghofe@5177
   310
    val (i', descr', descrs) = foldl unfold_datatype ((i, [],[]), descr);
berghofe@5177
   311
berghofe@5177
   312
  in (descr' :: descrs, i') end;
berghofe@5177
   313
berghofe@5177
   314
end;