src/HOL/hologic.ML
author haftmann
Wed Sep 26 20:27:55 2007 +0200 (2007-09-26)
changeset 24728 e2b3a1065676
parent 24630 351a308ab58d
child 24958 ff15f76741bd
permissions -rw-r--r--
moved Finite_Set before Datatype
clasohm@923
     1
(*  Title:      HOL/hologic.ML
clasohm@923
     2
    ID:         $Id$
clasohm@923
     3
    Author:     Lawrence C Paulson and Markus Wenzel
clasohm@923
     4
clasohm@923
     5
Abstract syntax operations for HOL.
clasohm@923
     6
*)
clasohm@923
     7
clasohm@923
     8
signature HOLOGIC =
clasohm@923
     9
sig
wenzelm@12338
    10
  val typeS: sort
wenzelm@12338
    11
  val typeT: typ
wenzelm@8275
    12
  val boolN: string
clasohm@923
    13
  val boolT: typ
wenzelm@21829
    14
  val true_const: term
paulson@7073
    15
  val false_const: term
clasohm@923
    16
  val mk_setT: typ -> typ
clasohm@923
    17
  val dest_setT: typ -> typ
paulson@15965
    18
  val Trueprop: term
clasohm@923
    19
  val mk_Trueprop: term -> term
clasohm@923
    20
  val dest_Trueprop: term -> term
wenzelm@23555
    21
  val conj_intr: thm -> thm -> thm
wenzelm@23555
    22
  val conj_elim: thm -> thm * thm
wenzelm@23555
    23
  val conj_elims: thm -> thm list
clasohm@923
    24
  val conj: term
clasohm@923
    25
  val disj: term
clasohm@923
    26
  val imp: term
wenzelm@8429
    27
  val Not: term
wenzelm@7690
    28
  val mk_conj: term * term -> term
wenzelm@7690
    29
  val mk_disj: term * term -> term
wenzelm@7690
    30
  val mk_imp: term * term -> term
wenzelm@16835
    31
  val mk_not: term -> term
paulson@15151
    32
  val dest_conj: term -> term list
paulson@15945
    33
  val dest_disj: term -> term list
wenzelm@4571
    34
  val dest_imp: term -> term * term
paulson@15151
    35
  val dest_not: term -> term
wenzelm@11683
    36
  val dest_concls: term -> term list
clasohm@923
    37
  val eq_const: typ -> term
wenzelm@21829
    38
  val mk_eq: term * term -> term
wenzelm@21829
    39
  val dest_eq: term -> term * term
clasohm@923
    40
  val all_const: typ -> term
wenzelm@21829
    41
  val mk_all: string * typ * term -> term
wenzelm@21829
    42
  val list_all: (string * typ) list * term -> term
clasohm@923
    43
  val exists_const: typ -> term
wenzelm@21829
    44
  val mk_exists: string * typ * term -> term
paulson@15945
    45
  val choice_const: typ -> term
clasohm@923
    46
  val Collect_const: typ -> term
clasohm@923
    47
  val mk_Collect: string * typ * term -> term
wenzelm@21829
    48
  val class_eq: string
clasohm@923
    49
  val mk_mem: term * term -> term
wenzelm@6380
    50
  val dest_mem: term -> term * term
wenzelm@11818
    51
  val mk_UNIV: typ -> term
wenzelm@2510
    52
  val mk_binop: string -> term * term -> term
wenzelm@2510
    53
  val mk_binrel: string -> term * term -> term
wenzelm@2510
    54
  val dest_bin: string -> typ -> term -> term * term
wenzelm@4571
    55
  val unitT: typ
wenzelm@9362
    56
  val is_unitT: typ -> bool
wenzelm@4571
    57
  val unit: term
wenzelm@4571
    58
  val is_unit: term -> bool
wenzelm@4571
    59
  val mk_prodT: typ * typ -> typ
wenzelm@4571
    60
  val dest_prodT: typ -> typ * typ
berghofe@14048
    61
  val pair_const: typ -> typ -> term
wenzelm@4571
    62
  val mk_prod: term * term -> term
wenzelm@4571
    63
  val dest_prod: term -> term * term
wenzelm@4571
    64
  val mk_fst: term -> term
wenzelm@4571
    65
  val mk_snd: term -> term
wenzelm@21829
    66
  val split_const: typ * typ * typ -> term
wenzelm@18285
    67
  val mk_split: term -> term
berghofe@5096
    68
  val prodT_factors: typ -> typ list
berghofe@5096
    69
  val mk_tuple: typ -> term list -> term
berghofe@23745
    70
  val dest_tuple: term -> term list
berghofe@23745
    71
  val ap_split: typ -> typ -> term -> term
berghofe@23745
    72
  val prod_factors: term -> int list list
berghofe@23745
    73
  val dest_tuple': int list list -> term -> term list
berghofe@23745
    74
  val prodT_factors': int list list -> typ -> typ list
berghofe@23745
    75
  val ap_split': int list list -> typ -> typ -> term -> term
berghofe@23745
    76
  val mk_tuple': int list list -> typ -> term list -> term
berghofe@23745
    77
  val mk_tupleT: int list list -> typ list -> typ
berghofe@23745
    78
  val strip_split: term -> term * typ list * int list list
wenzelm@5207
    79
  val natT: typ
wenzelm@5207
    80
  val zero: term
wenzelm@5207
    81
  val is_zero: term -> bool
wenzelm@5207
    82
  val mk_Suc: term -> term
wenzelm@5207
    83
  val dest_Suc: term -> term
haftmann@21621
    84
  val Suc_zero: term
wenzelm@24630
    85
  val mk_nat: int -> term
wenzelm@24630
    86
  val dest_nat: term -> int
haftmann@22994
    87
  val class_size: string
haftmann@22994
    88
  val size_const: typ -> term
paulson@15620
    89
  val bitT: typ
paulson@15620
    90
  val B0_const: term
paulson@15620
    91
  val B1_const: term
wenzelm@21778
    92
  val mk_bit: int -> term
wenzelm@21778
    93
  val dest_bit: term -> int
wenzelm@21829
    94
  val intT: typ
paulson@7073
    95
  val pls_const: term
paulson@7073
    96
  val min_const: term
paulson@7073
    97
  val bit_const: term
wenzelm@24630
    98
  val mk_numeral: int -> term
wenzelm@24630
    99
  val dest_numeral: term -> int
wenzelm@21829
   100
  val number_of_const: typ -> term
wenzelm@23269
   101
  val add_numerals: term -> (term * typ) list -> (term * typ) list
wenzelm@24630
   102
  val mk_number: typ -> int -> term
wenzelm@24630
   103
  val dest_number: term -> typ * int
wenzelm@21778
   104
  val realT: typ
wenzelm@21755
   105
  val nibbleT: typ
wenzelm@21755
   106
  val mk_nibble: int -> term
wenzelm@21755
   107
  val dest_nibble: term -> int
wenzelm@21755
   108
  val charT: typ
wenzelm@21755
   109
  val mk_char: int -> term
wenzelm@21755
   110
  val dest_char: term -> int
wenzelm@21829
   111
  val listT: typ -> typ
wenzelm@21829
   112
  val mk_list: typ -> term list -> term
wenzelm@21829
   113
  val dest_list: term -> term list
wenzelm@21778
   114
  val stringT: typ
haftmann@21820
   115
  val mk_string: string -> term
haftmann@21820
   116
  val dest_string: term -> string
clasohm@923
   117
end;
clasohm@923
   118
clasohm@923
   119
structure HOLogic: HOLOGIC =
clasohm@923
   120
struct
clasohm@923
   121
wenzelm@12338
   122
(* HOL syntax *)
clasohm@923
   123
wenzelm@12338
   124
val typeS: sort = ["HOL.type"];
wenzelm@12338
   125
val typeT = TypeInfer.anyT typeS;
wenzelm@12338
   126
clasohm@923
   127
wenzelm@2510
   128
(* bool and set *)
clasohm@923
   129
wenzelm@8275
   130
val boolN = "bool";
wenzelm@8275
   131
val boolT = Type (boolN, []);
clasohm@923
   132
wenzelm@9856
   133
val true_const =  Const ("True", boolT);
wenzelm@9856
   134
val false_const = Const ("False", boolT);
paulson@7073
   135
clasohm@923
   136
fun mk_setT T = Type ("set", [T]);
clasohm@923
   137
clasohm@923
   138
fun dest_setT (Type ("set", [T])) = T
wenzelm@3794
   139
  | dest_setT T = raise TYPE ("dest_setT: set type expected", [T], []);
clasohm@923
   140
wenzelm@8275
   141
paulson@7073
   142
(* logic *)
clasohm@923
   143
clasohm@923
   144
val Trueprop = Const ("Trueprop", boolT --> propT);
clasohm@923
   145
clasohm@923
   146
fun mk_Trueprop P = Trueprop $ P;
clasohm@923
   147
clasohm@923
   148
fun dest_Trueprop (Const ("Trueprop", _) $ P) = P
wenzelm@3794
   149
  | dest_Trueprop t = raise TERM ("dest_Trueprop", [t]);
clasohm@923
   150
wenzelm@23555
   151
fun conj_intr thP thQ =
wenzelm@23555
   152
  let
wenzelm@23576
   153
    val (P, Q) = pairself (ObjectLogic.dest_judgment o Thm.cprop_of) (thP, thQ)
wenzelm@23555
   154
      handle CTERM (msg, _) => raise THM (msg, 0, [thP, thQ]);
wenzelm@23555
   155
    val inst = Thm.instantiate ([], [(@{cpat "?P::bool"}, P), (@{cpat "?Q::bool"}, Q)]);
wenzelm@23555
   156
  in Drule.implies_elim_list (inst @{thm conjI}) [thP, thQ] end;
clasohm@923
   157
wenzelm@23555
   158
fun conj_elim thPQ =
wenzelm@23555
   159
  let
wenzelm@23576
   160
    val (P, Q) = Thm.dest_binop (ObjectLogic.dest_judgment (Thm.cprop_of thPQ))
wenzelm@23555
   161
      handle CTERM (msg, _) => raise THM (msg, 0, [thPQ]);
wenzelm@23555
   162
    val inst = Thm.instantiate ([], [(@{cpat "?P::bool"}, P), (@{cpat "?Q::bool"}, Q)]);
wenzelm@23555
   163
    val thP = Thm.implies_elim (inst @{thm conjunct1}) thPQ;
wenzelm@23555
   164
    val thQ = Thm.implies_elim (inst @{thm conjunct2}) thPQ;
wenzelm@23555
   165
  in (thP, thQ) end;
wenzelm@23555
   166
wenzelm@23555
   167
fun conj_elims th =
wenzelm@23555
   168
  let val (th1, th2) = conj_elim th
wenzelm@23555
   169
  in conj_elims th1 @ conj_elims th2 end handle THM _ => [th];
wenzelm@23555
   170
wenzelm@23555
   171
val conj = @{term "op &"}
wenzelm@23555
   172
and disj = @{term "op |"}
wenzelm@23555
   173
and imp = @{term "op -->"}
wenzelm@23555
   174
and Not = @{term "Not"};
clasohm@923
   175
wenzelm@7690
   176
fun mk_conj (t1, t2) = conj $ t1 $ t2
wenzelm@7690
   177
and mk_disj (t1, t2) = disj $ t1 $ t2
wenzelm@16835
   178
and mk_imp (t1, t2) = imp $ t1 $ t2
wenzelm@16835
   179
and mk_not t = Not $ t;
wenzelm@7690
   180
paulson@15151
   181
fun dest_conj (Const ("op &", _) $ t $ t') = t :: dest_conj t'
paulson@15151
   182
  | dest_conj t = [t];
paulson@15151
   183
paulson@15945
   184
fun dest_disj (Const ("op |", _) $ t $ t') = t :: dest_disj t'
paulson@15945
   185
  | dest_disj t = [t];
paulson@15945
   186
paulson@4466
   187
fun dest_imp (Const("op -->",_) $ A $ B) = (A, B)
paulson@4466
   188
  | dest_imp  t = raise TERM ("dest_imp", [t]);
paulson@4466
   189
paulson@15151
   190
fun dest_not (Const ("Not", _) $ t) = t
paulson@15151
   191
  | dest_not t = raise TERM ("dest_not", [t]);
wenzelm@8302
   192
wenzelm@11683
   193
fun imp_concl_of t = imp_concl_of (#2 (dest_imp t)) handle TERM _ => t;
wenzelm@11683
   194
val dest_concls = map imp_concl_of o dest_conj o dest_Trueprop;
wenzelm@11683
   195
clasohm@923
   196
fun eq_const T = Const ("op =", [T, T] ---> boolT);
clasohm@923
   197
fun mk_eq (t, u) = eq_const (fastype_of t) $ t $ u;
clasohm@923
   198
paulson@6031
   199
fun dest_eq (Const ("op =", _) $ lhs $ rhs) = (lhs, rhs)
paulson@6031
   200
  | dest_eq t = raise TERM ("dest_eq", [t])
paulson@6031
   201
clasohm@923
   202
fun all_const T = Const ("All", [T --> boolT] ---> boolT);
clasohm@923
   203
fun mk_all (x, T, P) = all_const T $ absfree (x, T, P);
wenzelm@21173
   204
fun list_all (xs, t) = fold_rev (fn (x, T) => fn P => all_const T $ Abs (x, T, P)) xs t;
clasohm@923
   205
clasohm@923
   206
fun exists_const T = Const ("Ex", [T --> boolT] ---> boolT);
clasohm@923
   207
fun mk_exists (x, T, P) = exists_const T $ absfree (x, T, P);
clasohm@923
   208
wenzelm@21755
   209
fun choice_const T = Const("Hilbert_Choice.Eps", (T --> boolT) --> T);
paulson@15945
   210
clasohm@923
   211
fun Collect_const T = Const ("Collect", [T --> boolT] ---> mk_setT T);
clasohm@923
   212
fun mk_Collect (a, T, t) = Collect_const T $ absfree (a, T, t);
clasohm@923
   213
haftmann@23247
   214
val class_eq = "HOL.eq";
haftmann@21045
   215
clasohm@923
   216
fun mk_mem (x, A) =
clasohm@923
   217
  let val setT = fastype_of A in
clasohm@923
   218
    Const ("op :", [dest_setT setT, setT] ---> boolT) $ x $ A
clasohm@923
   219
  end;
clasohm@923
   220
wenzelm@6380
   221
fun dest_mem (Const ("op :", _) $ x $ A) = (x, A)
wenzelm@6380
   222
  | dest_mem t = raise TERM ("dest_mem", [t]);
wenzelm@6380
   223
wenzelm@11818
   224
fun mk_UNIV T = Const ("UNIV", mk_setT T);
wenzelm@11818
   225
clasohm@923
   226
ballarin@13743
   227
(* binary operations and relations *)
wenzelm@2510
   228
wenzelm@2510
   229
fun mk_binop c (t, u) =
wenzelm@2510
   230
  let val T = fastype_of t in
wenzelm@2510
   231
    Const (c, [T, T] ---> T) $ t $ u
wenzelm@2510
   232
  end;
wenzelm@2510
   233
wenzelm@2510
   234
fun mk_binrel c (t, u) =
wenzelm@2510
   235
  let val T = fastype_of t in
wenzelm@2510
   236
    Const (c, [T, T] ---> boolT) $ t $ u
wenzelm@2510
   237
  end;
wenzelm@2510
   238
paulson@14387
   239
(*destruct the application of a binary operator. The dummyT case is a crude
paulson@14387
   240
  way of handling polymorphic operators.*)
wenzelm@2510
   241
fun dest_bin c T (tm as Const (c', Type ("fun", [T', _])) $ t $ u) =
paulson@14387
   242
      if c = c' andalso (T=T' orelse T=dummyT) then (t, u)
wenzelm@3794
   243
      else raise TERM ("dest_bin " ^ c, [tm])
wenzelm@3794
   244
  | dest_bin c _ tm = raise TERM ("dest_bin " ^ c, [tm]);
wenzelm@2510
   245
wenzelm@2510
   246
wenzelm@4571
   247
(* unit *)
wenzelm@4571
   248
wenzelm@11604
   249
val unitT = Type ("Product_Type.unit", []);
wenzelm@4571
   250
wenzelm@11604
   251
fun is_unitT (Type ("Product_Type.unit", [])) = true
wenzelm@9362
   252
  | is_unitT _ = false;
wenzelm@9362
   253
wenzelm@11604
   254
val unit = Const ("Product_Type.Unity", unitT);
wenzelm@4571
   255
wenzelm@11604
   256
fun is_unit (Const ("Product_Type.Unity", _)) = true
wenzelm@4571
   257
  | is_unit _ = false;
wenzelm@4571
   258
wenzelm@4571
   259
wenzelm@4571
   260
(* prod *)
wenzelm@4571
   261
wenzelm@4571
   262
fun mk_prodT (T1, T2) = Type ("*", [T1, T2]);
wenzelm@4571
   263
wenzelm@4571
   264
fun dest_prodT (Type ("*", [T1, T2])) = (T1, T2)
wenzelm@4571
   265
  | dest_prodT T = raise TYPE ("dest_prodT", [T], []);
wenzelm@4571
   266
berghofe@14048
   267
fun pair_const T1 T2 = Const ("Pair", [T1, T2] ---> mk_prodT (T1, T2));
berghofe@14048
   268
wenzelm@4571
   269
fun mk_prod (t1, t2) =
wenzelm@4571
   270
  let val T1 = fastype_of t1 and T2 = fastype_of t2 in
berghofe@14048
   271
    pair_const T1 T2 $ t1 $ t2
wenzelm@4571
   272
  end;
wenzelm@4571
   273
wenzelm@4571
   274
fun dest_prod (Const ("Pair", _) $ t1 $ t2) = (t1, t2)
wenzelm@4571
   275
  | dest_prod t = raise TERM ("dest_prod", [t]);
wenzelm@4571
   276
wenzelm@4571
   277
fun mk_fst p =
wenzelm@4571
   278
  let val pT = fastype_of p in
wenzelm@4571
   279
    Const ("fst", pT --> fst (dest_prodT pT)) $ p
wenzelm@4571
   280
  end;
wenzelm@4571
   281
wenzelm@4571
   282
fun mk_snd p =
wenzelm@4571
   283
  let val pT = fastype_of p in
wenzelm@4571
   284
    Const ("snd", pT --> snd (dest_prodT pT)) $ p
wenzelm@4571
   285
  end;
wenzelm@4571
   286
wenzelm@18285
   287
fun split_const (A, B, C) =
wenzelm@18285
   288
  Const ("split", (A --> B --> C) --> mk_prodT (A, B) --> C);
wenzelm@18285
   289
wenzelm@18285
   290
fun mk_split t =
wenzelm@18285
   291
  (case Term.fastype_of t of
wenzelm@18285
   292
    T as (Type ("fun", [A, Type ("fun", [B, C])])) =>
wenzelm@18285
   293
      Const ("split", T --> mk_prodT (A, B) --> C) $ t
wenzelm@18285
   294
  | _ => raise TERM ("mk_split: bad body type", [t]));
wenzelm@18285
   295
berghofe@5096
   296
(*Maps the type T1 * ... * Tn to [T1, ..., Tn], however nested*)
berghofe@5096
   297
fun prodT_factors (Type ("*", [T1, T2])) = prodT_factors T1 @ prodT_factors T2
berghofe@5096
   298
  | prodT_factors T = [T];
berghofe@5096
   299
berghofe@5096
   300
(*Makes a nested tuple from a list, following the product type structure*)
wenzelm@16971
   301
fun mk_tuple (Type ("*", [T1, T2])) tms =
wenzelm@16971
   302
        mk_prod (mk_tuple T1 tms,
skalberg@15570
   303
                 mk_tuple T2 (Library.drop (length (prodT_factors T1), tms)))
berghofe@5096
   304
  | mk_tuple T (t::_) = t;
wenzelm@4571
   305
berghofe@23745
   306
fun dest_tuple (Const ("Pair", _) $ t $ u) = dest_tuple t @ dest_tuple u
berghofe@23745
   307
  | dest_tuple t = [t];
berghofe@23745
   308
berghofe@23745
   309
(*In ap_split S T u, term u expects separate arguments for the factors of S,
berghofe@23745
   310
  with result type T.  The call creates a new term expecting one argument
berghofe@23745
   311
  of type S.*)
berghofe@23745
   312
fun ap_split T T3 u =
berghofe@23745
   313
  let
berghofe@23745
   314
    fun ap (T :: Ts) =
berghofe@23745
   315
          (case T of
berghofe@23745
   316
             Type ("*", [T1, T2]) =>
berghofe@23745
   317
               split_const (T1, T2, Ts ---> T3) $ ap (T1 :: T2 :: Ts)
berghofe@23745
   318
           | _ => Abs ("x", T, ap Ts))
berghofe@23745
   319
      | ap [] =
berghofe@23745
   320
          let val k = length (prodT_factors T)
berghofe@23745
   321
          in list_comb (incr_boundvars k u, map Bound (k - 1 downto 0)) end
berghofe@23745
   322
  in ap [T] end;
berghofe@23745
   323
berghofe@23745
   324
berghofe@23745
   325
(***********************************************************)
berghofe@23745
   326
(*       operations on tuples with specific arities        *)
berghofe@23745
   327
(*                                                         *)
berghofe@23745
   328
(* an "arity" of a tuple is a list of lists of integers    *)
berghofe@23745
   329
(* ("factors"), denoting paths to subterms that are pairs  *)
berghofe@23745
   330
(***********************************************************)
berghofe@23745
   331
berghofe@23745
   332
fun prod_err s = raise TERM (s ^ ": inconsistent use of products", []);
berghofe@23745
   333
berghofe@23745
   334
fun prod_factors t =
berghofe@23745
   335
  let
berghofe@23745
   336
    fun factors p (Const ("Pair", _) $ t $ u) =
berghofe@23745
   337
          p :: factors (1::p) t @ factors (2::p) u
berghofe@23745
   338
      | factors p _ = []
berghofe@23745
   339
  in factors [] t end;
berghofe@23745
   340
berghofe@23745
   341
fun dest_tuple' ps =
berghofe@23745
   342
  let
berghofe@23745
   343
    fun dest p t = if p mem ps then (case t of
berghofe@23745
   344
        Const ("Pair", _) $ t $ u =>
berghofe@23745
   345
          dest (1::p) t @ dest (2::p) u
berghofe@23745
   346
      | _ => prod_err "dest_tuple'") else [t]
berghofe@23745
   347
  in dest [] end;
berghofe@23745
   348
berghofe@23745
   349
fun prodT_factors' ps =
berghofe@23745
   350
  let
berghofe@23745
   351
    fun factors p T = if p mem ps then (case T of
berghofe@23745
   352
        Type ("*", [T1, T2]) =>
berghofe@23745
   353
          factors (1::p) T1 @ factors (2::p) T2
berghofe@23745
   354
      | _ => prod_err "prodT_factors'") else [T]
berghofe@23745
   355
  in factors [] end;
berghofe@23745
   356
berghofe@23745
   357
(*In ap_split' ps S T u, term u expects separate arguments for the factors of S,
berghofe@23745
   358
  with result type T.  The call creates a new term expecting one argument
berghofe@23745
   359
  of type S.*)
berghofe@23745
   360
fun ap_split' ps T T3 u =
berghofe@23745
   361
  let
berghofe@23745
   362
    fun ap ((p, T) :: pTs) =
berghofe@23745
   363
          if p mem ps then (case T of
berghofe@23745
   364
              Type ("*", [T1, T2]) =>
berghofe@23745
   365
                split_const (T1, T2, map snd pTs ---> T3) $
berghofe@23745
   366
                  ap ((1::p, T1) :: (2::p, T2) :: pTs)
berghofe@23745
   367
            | _ => prod_err "ap_split'")
berghofe@23745
   368
          else Abs ("x", T, ap pTs)
berghofe@23745
   369
      | ap [] =
berghofe@23745
   370
          let val k = length ps
berghofe@23745
   371
          in list_comb (incr_boundvars (k + 1) u, map Bound (k downto 0)) end
berghofe@23745
   372
  in ap [([], T)] end;
berghofe@23745
   373
berghofe@23745
   374
fun mk_tuple' ps =
berghofe@23745
   375
  let
berghofe@23745
   376
    fun mk p T ts =
berghofe@23745
   377
      if p mem ps then (case T of
berghofe@23745
   378
          Type ("*", [T1, T2]) =>
berghofe@23745
   379
            let
berghofe@23745
   380
              val (t, ts') = mk (1::p) T1 ts;
berghofe@23745
   381
              val (u, ts'') = mk (2::p) T2 ts'
berghofe@23745
   382
            in (pair_const T1 T2 $ t $ u, ts'') end
berghofe@23745
   383
        | _ => prod_err "mk_tuple'")
berghofe@23745
   384
      else (hd ts, tl ts)
berghofe@23745
   385
  in fst oo mk [] end;
berghofe@23745
   386
berghofe@23745
   387
fun mk_tupleT ps =
berghofe@23745
   388
  let
berghofe@23745
   389
    fun mk p Ts =
berghofe@23745
   390
      if p mem ps then
berghofe@23745
   391
        let
berghofe@23745
   392
          val (T, Ts') = mk (1::p) Ts;
berghofe@23745
   393
          val (U, Ts'') = mk (2::p) Ts'
berghofe@23745
   394
        in (mk_prodT (T, U), Ts'') end
berghofe@23745
   395
      else (hd Ts, tl Ts)
berghofe@23745
   396
  in fst o mk [] end;
berghofe@23745
   397
berghofe@23745
   398
fun strip_split t =
berghofe@23745
   399
  let
berghofe@23745
   400
    fun strip [] qs Ts t = (t, Ts, qs)
berghofe@23745
   401
      | strip (p :: ps) qs Ts (Const ("split", _) $ t) =
berghofe@23745
   402
          strip ((1 :: p) :: (2 :: p) :: ps) (p :: qs) Ts t
berghofe@23745
   403
      | strip (p :: ps) qs Ts (Abs (s, T, t)) = strip ps qs (T :: Ts) t
berghofe@23745
   404
      | strip (p :: ps) qs Ts t = strip ps qs
berghofe@23745
   405
          (hd (binder_types (fastype_of1 (Ts, t))) :: Ts)
berghofe@23745
   406
          (incr_boundvars 1 t $ Bound 0)
berghofe@23745
   407
  in strip [[]] [] [] t end;
berghofe@23745
   408
wenzelm@5207
   409
wenzelm@5207
   410
(* nat *)
wenzelm@5207
   411
wenzelm@5207
   412
val natT = Type ("nat", []);
wenzelm@5207
   413
haftmann@22994
   414
val zero = Const ("HOL.zero_class.zero", natT);
wenzelm@5207
   415
haftmann@22994
   416
fun is_zero (Const ("HOL.zero_class.zero", _)) = true
wenzelm@5207
   417
  | is_zero _ = false;
wenzelm@5207
   418
wenzelm@5207
   419
fun mk_Suc t = Const ("Suc", natT --> natT) $ t;
wenzelm@5207
   420
wenzelm@5207
   421
fun dest_Suc (Const ("Suc", _) $ t) = t
wenzelm@5207
   422
  | dest_Suc t = raise TERM ("dest_Suc", [t]);
wenzelm@5207
   423
haftmann@21621
   424
val Suc_zero = mk_Suc zero;
haftmann@21621
   425
wenzelm@24630
   426
fun mk_nat n =
haftmann@22994
   427
  let
haftmann@22994
   428
    fun mk 0 = zero
wenzelm@23297
   429
      | mk n = mk_Suc (mk (n - 1));
wenzelm@23576
   430
  in if n < 0 then raise TERM ("mk_nat: negative number", []) else mk n end;
wenzelm@5207
   431
wenzelm@24630
   432
fun dest_nat (Const ("HOL.zero_class.zero", _)) = 0
wenzelm@23297
   433
  | dest_nat (Const ("Suc", _) $ t) = dest_nat t + 1
wenzelm@5207
   434
  | dest_nat t = raise TERM ("dest_nat", [t]);
wenzelm@5207
   435
haftmann@22994
   436
val class_size = "Nat.size";
haftmann@22994
   437
haftmann@22994
   438
fun size_const T = Const ("Nat.size_class.size", T --> natT);
haftmann@22994
   439
wenzelm@5207
   440
wenzelm@21778
   441
(* bit *)
paulson@7073
   442
paulson@15620
   443
val bitT = Type ("Numeral.bit", []);
paulson@15620
   444
paulson@15620
   445
val B0_const = Const ("Numeral.bit.B0", bitT);
paulson@15620
   446
val B1_const =  Const ("Numeral.bit.B1", bitT);
paulson@15620
   447
wenzelm@21778
   448
fun mk_bit 0 = B0_const
wenzelm@21778
   449
  | mk_bit 1 = B1_const
wenzelm@21778
   450
  | mk_bit _ = raise TERM ("mk_bit", []);
wenzelm@21778
   451
wenzelm@21778
   452
fun dest_bit (Const ("Numeral.bit.B0", _)) = 0
wenzelm@21778
   453
  | dest_bit (Const ("Numeral.bit.B1", _)) = 1
wenzelm@21778
   454
  | dest_bit t = raise TERM ("dest_bit", [t]);
wenzelm@21778
   455
wenzelm@21778
   456
wenzelm@21778
   457
(* binary numerals and int -- non-unique representation due to leading zeros/ones! *)
wenzelm@21778
   458
wenzelm@21778
   459
val intT = Type ("IntDef.int", []);
wenzelm@21778
   460
haftmann@20485
   461
val pls_const = Const ("Numeral.Pls", intT)
haftmann@20485
   462
and min_const = Const ("Numeral.Min", intT)
haftmann@23247
   463
and bit_const = Const ("Numeral.Bit", intT --> bitT --> intT);
paulson@8768
   464
wenzelm@21829
   465
fun mk_numeral 0 = pls_const
wenzelm@21829
   466
  | mk_numeral ~1 = min_const
wenzelm@21829
   467
  | mk_numeral i =
wenzelm@24630
   468
      let val (q, r) = Integer.div_mod i 2;
wenzelm@24630
   469
      in bit_const $ mk_numeral q $ mk_bit r end;
berghofe@13755
   470
wenzelm@21829
   471
fun dest_numeral (Const ("Numeral.Pls", _)) = 0
wenzelm@21829
   472
  | dest_numeral (Const ("Numeral.Min", _)) = ~1
wenzelm@24630
   473
  | dest_numeral (Const ("Numeral.Bit", _) $ bs $ b) = 2 * dest_numeral bs + dest_bit b
wenzelm@21829
   474
  | dest_numeral t = raise TERM ("dest_numeral", [t]);
berghofe@13755
   475
haftmann@22994
   476
fun number_of_const T = Const ("Numeral.number_class.number_of", intT --> T);
haftmann@21820
   477
wenzelm@23269
   478
fun add_numerals (Const ("Numeral.number_class.number_of", Type (_, [_, T])) $ t) = cons (t, T)
wenzelm@23269
   479
  | add_numerals (t $ u) = add_numerals t #> add_numerals u
wenzelm@23269
   480
  | add_numerals (Abs (_, _, t)) = add_numerals t
wenzelm@23269
   481
  | add_numerals _ = I;
haftmann@22391
   482
haftmann@22994
   483
fun mk_number T 0 = Const ("HOL.zero_class.zero", T)
haftmann@22994
   484
  | mk_number T 1 = Const ("HOL.one_class.one", T)
haftmann@21820
   485
  | mk_number T i = number_of_const T $ mk_numeral i;
haftmann@21820
   486
haftmann@22994
   487
fun dest_number (Const ("HOL.zero_class.zero", T)) = (T, 0)
haftmann@22994
   488
  | dest_number (Const ("HOL.one_class.one", T)) = (T, 1)
haftmann@22994
   489
  | dest_number (Const ("Numeral.number_class.number_of", Type ("fun", [_, T])) $ t) =
haftmann@22994
   490
      (T, dest_numeral t)
haftmann@21820
   491
  | dest_number t = raise TERM ("dest_number", [t]);
berghofe@13755
   492
wenzelm@21829
   493
berghofe@13755
   494
(* real *)
berghofe@13755
   495
wenzelm@16971
   496
val realT = Type ("RealDef.real", []);
berghofe@13755
   497
berghofe@13755
   498
wenzelm@21755
   499
(* nibble *)
wenzelm@21755
   500
wenzelm@21755
   501
val nibbleT = Type ("List.nibble", []);
berghofe@13755
   502
wenzelm@21755
   503
fun mk_nibble n =
wenzelm@21755
   504
  let val s =
wenzelm@21755
   505
    if 0 <= n andalso n <= 9 then chr (n + ord "0")
wenzelm@21755
   506
    else if 10 <= n andalso n <= 15 then chr (n + ord "A" - 10)
wenzelm@21755
   507
    else raise TERM ("mk_nibble", [])
wenzelm@21755
   508
  in Const ("List.nibble.Nibble" ^ s, nibbleT) end;
nipkow@17083
   509
wenzelm@21755
   510
fun dest_nibble t =
wenzelm@21755
   511
  let fun err () = raise TERM ("dest_nibble", [t]) in
wenzelm@21755
   512
    (case try (unprefix "List.nibble.Nibble" o fst o Term.dest_Const) t of
wenzelm@21755
   513
      NONE => err ()
wenzelm@21755
   514
    | SOME c =>
wenzelm@21755
   515
        if size c <> 1 then err ()
wenzelm@21755
   516
        else if "0" <= c andalso c <= "9" then ord c - ord "0"
wenzelm@21755
   517
        else if "A" <= c andalso c <= "F" then ord c - ord "A" + 10
wenzelm@21755
   518
        else err ())
wenzelm@21755
   519
  end;
berghofe@15062
   520
haftmann@21455
   521
haftmann@21455
   522
(* char *)
haftmann@21455
   523
haftmann@21455
   524
val charT = Type ("List.char", []);
haftmann@21455
   525
wenzelm@21755
   526
fun mk_char n =
wenzelm@21755
   527
  if 0 <= n andalso n <= 255 then
wenzelm@21755
   528
    Const ("List.char.Char", nibbleT --> nibbleT --> charT) $
wenzelm@21755
   529
      mk_nibble (n div 16) $ mk_nibble (n mod 16)
wenzelm@21755
   530
  else raise TERM ("mk_char", []);
haftmann@21455
   531
wenzelm@21755
   532
fun dest_char (Const ("List.char.Char", _) $ t $ u) =
wenzelm@21755
   533
      dest_nibble t * 16 + dest_nibble u
wenzelm@21755
   534
  | dest_char t = raise TERM ("dest_char", [t]);
haftmann@21455
   535
wenzelm@21755
   536
wenzelm@21755
   537
(* list *)
haftmann@21455
   538
wenzelm@21755
   539
fun listT T = Type ("List.list", [T]);
haftmann@21455
   540
wenzelm@21755
   541
fun mk_list T ts =
haftmann@21455
   542
  let
wenzelm@21755
   543
    val lT = listT T;
wenzelm@21755
   544
    val Nil = Const ("List.list.Nil", lT);
wenzelm@21755
   545
    fun Cons t u = Const ("List.list.Cons", T --> lT --> lT) $ t $ u;
wenzelm@21755
   546
  in fold_rev Cons ts Nil end;
wenzelm@21755
   547
wenzelm@21755
   548
fun dest_list (Const ("List.list.Nil", _)) = []
wenzelm@21755
   549
  | dest_list (Const ("List.list.Cons", _) $ t $ u) = t :: dest_list u
wenzelm@21755
   550
  | dest_list t = raise TERM ("dest_list", [t]);
haftmann@21455
   551
haftmann@21455
   552
haftmann@21455
   553
(* string *)
haftmann@21455
   554
haftmann@21820
   555
val stringT = Type ("List.string", []);
haftmann@21455
   556
wenzelm@21755
   557
val mk_string = mk_list charT o map (mk_char o ord) o explode;
wenzelm@21755
   558
val dest_string = implode o map (chr o dest_char) o dest_list;
haftmann@21455
   559
clasohm@923
   560
end;