src/HOL/Tools/hologic.ML
author haftmann
Wed Mar 11 15:56:51 2009 +0100 (2009-03-11)
changeset 30450 7655e6533209
parent 30304 d8e4cd2ac2a1
child 30453 1e7e0d171653
permissions -rw-r--r--
HOLogic.mk_set, HOLogic.dest_set
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
haftmann@30450
    14
  val Trueprop: term
haftmann@30450
    15
  val mk_Trueprop: term -> term
haftmann@30450
    16
  val dest_Trueprop: term -> term
wenzelm@21829
    17
  val true_const: term
paulson@7073
    18
  val false_const: term
clasohm@923
    19
  val mk_setT: typ -> typ
clasohm@923
    20
  val dest_setT: typ -> typ
haftmann@30450
    21
  val Collect_const: typ -> term
haftmann@30450
    22
  val mk_Collect: string * typ * term -> term
haftmann@30450
    23
  val mk_mem: term * term -> term
haftmann@30450
    24
  val dest_mem: term -> term * term
haftmann@30450
    25
  val mk_set: typ -> term list -> term
haftmann@30450
    26
  val dest_set: term -> term list
haftmann@30450
    27
  val mk_UNIV: typ -> term
wenzelm@23555
    28
  val conj_intr: thm -> thm -> thm
wenzelm@23555
    29
  val conj_elim: thm -> thm * thm
wenzelm@23555
    30
  val conj_elims: thm -> thm list
clasohm@923
    31
  val conj: term
clasohm@923
    32
  val disj: term
clasohm@923
    33
  val imp: term
wenzelm@8429
    34
  val Not: term
wenzelm@7690
    35
  val mk_conj: term * term -> term
wenzelm@7690
    36
  val mk_disj: term * term -> term
wenzelm@7690
    37
  val mk_imp: term * term -> term
wenzelm@16835
    38
  val mk_not: term -> term
paulson@15151
    39
  val dest_conj: term -> term list
paulson@15945
    40
  val dest_disj: term -> term list
paulson@24958
    41
  val disjuncts: term -> term list
wenzelm@4571
    42
  val dest_imp: term -> term * term
paulson@15151
    43
  val dest_not: term -> term
clasohm@923
    44
  val eq_const: typ -> term
wenzelm@21829
    45
  val mk_eq: term * term -> term
wenzelm@21829
    46
  val dest_eq: term -> term * term
clasohm@923
    47
  val all_const: typ -> term
wenzelm@21829
    48
  val mk_all: string * typ * term -> term
wenzelm@21829
    49
  val list_all: (string * typ) list * term -> term
clasohm@923
    50
  val exists_const: typ -> term
wenzelm@21829
    51
  val mk_exists: string * typ * term -> term
paulson@15945
    52
  val choice_const: typ -> term
wenzelm@21829
    53
  val class_eq: string
wenzelm@2510
    54
  val mk_binop: string -> term * term -> term
wenzelm@2510
    55
  val mk_binrel: string -> term * term -> term
wenzelm@2510
    56
  val dest_bin: string -> typ -> term -> term * term
wenzelm@4571
    57
  val unitT: typ
wenzelm@9362
    58
  val is_unitT: typ -> bool
wenzelm@4571
    59
  val unit: term
wenzelm@4571
    60
  val is_unit: term -> bool
wenzelm@4571
    61
  val mk_prodT: typ * typ -> typ
wenzelm@4571
    62
  val dest_prodT: typ -> typ * typ
berghofe@14048
    63
  val pair_const: typ -> typ -> term
wenzelm@4571
    64
  val mk_prod: term * term -> term
wenzelm@4571
    65
  val dest_prod: term -> term * term
wenzelm@4571
    66
  val mk_fst: term -> term
wenzelm@4571
    67
  val mk_snd: term -> term
wenzelm@21829
    68
  val split_const: typ * typ * typ -> term
wenzelm@18285
    69
  val mk_split: term -> term
berghofe@5096
    70
  val prodT_factors: typ -> typ list
berghofe@5096
    71
  val mk_tuple: typ -> term list -> term
berghofe@23745
    72
  val dest_tuple: term -> term list
berghofe@23745
    73
  val ap_split: typ -> typ -> term -> term
berghofe@23745
    74
  val prod_factors: term -> int list list
berghofe@23745
    75
  val dest_tuple': int list list -> term -> term list
berghofe@23745
    76
  val prodT_factors': int list list -> typ -> typ list
berghofe@23745
    77
  val ap_split': int list list -> typ -> typ -> term -> term
berghofe@23745
    78
  val mk_tuple': int list list -> typ -> term list -> term
berghofe@23745
    79
  val mk_tupleT: int list list -> typ list -> typ
berghofe@23745
    80
  val strip_split: term -> term * typ list * int list list
wenzelm@5207
    81
  val natT: typ
wenzelm@5207
    82
  val zero: term
wenzelm@5207
    83
  val is_zero: term -> bool
wenzelm@5207
    84
  val mk_Suc: term -> term
wenzelm@5207
    85
  val dest_Suc: term -> term
haftmann@21621
    86
  val Suc_zero: term
wenzelm@24630
    87
  val mk_nat: int -> term
wenzelm@24630
    88
  val dest_nat: term -> int
haftmann@22994
    89
  val class_size: string
haftmann@22994
    90
  val size_const: typ -> term
haftmann@26036
    91
  val indexT: typ
wenzelm@21829
    92
  val intT: typ
paulson@7073
    93
  val pls_const: term
paulson@7073
    94
  val min_const: term
huffman@26086
    95
  val bit0_const: term
huffman@26086
    96
  val bit1_const: term
huffman@26086
    97
  val mk_bit: int -> term
huffman@26086
    98
  val dest_bit: term -> int
wenzelm@24630
    99
  val mk_numeral: int -> term
wenzelm@24630
   100
  val dest_numeral: term -> int
wenzelm@21829
   101
  val number_of_const: typ -> term
wenzelm@23269
   102
  val add_numerals: term -> (term * typ) list -> (term * typ) list
wenzelm@24630
   103
  val mk_number: typ -> int -> term
wenzelm@24630
   104
  val dest_number: term -> typ * int
wenzelm@21778
   105
  val realT: typ
wenzelm@21755
   106
  val nibbleT: typ
wenzelm@21755
   107
  val mk_nibble: int -> term
wenzelm@21755
   108
  val dest_nibble: term -> int
wenzelm@21755
   109
  val charT: typ
wenzelm@21755
   110
  val mk_char: int -> term
wenzelm@21755
   111
  val dest_char: term -> int
wenzelm@21829
   112
  val listT: typ -> typ
berghofe@25887
   113
  val nil_const: typ -> term
berghofe@25887
   114
  val cons_const: typ -> term
wenzelm@21829
   115
  val mk_list: typ -> term list -> term
wenzelm@21829
   116
  val dest_list: term -> term list
wenzelm@21778
   117
  val stringT: typ
haftmann@21820
   118
  val mk_string: string -> term
haftmann@21820
   119
  val dest_string: term -> string
clasohm@923
   120
end;
clasohm@923
   121
clasohm@923
   122
structure HOLogic: HOLOGIC =
clasohm@923
   123
struct
clasohm@923
   124
wenzelm@12338
   125
(* HOL syntax *)
clasohm@923
   126
wenzelm@12338
   127
val typeS: sort = ["HOL.type"];
wenzelm@12338
   128
val typeT = TypeInfer.anyT typeS;
wenzelm@12338
   129
clasohm@923
   130
wenzelm@2510
   131
(* bool and set *)
clasohm@923
   132
wenzelm@8275
   133
val boolN = "bool";
wenzelm@8275
   134
val boolT = Type (boolN, []);
clasohm@923
   135
wenzelm@9856
   136
val true_const =  Const ("True", boolT);
wenzelm@9856
   137
val false_const = Const ("False", boolT);
paulson@7073
   138
berghofe@26804
   139
fun mk_setT T = T --> boolT;
clasohm@923
   140
berghofe@26804
   141
fun dest_setT (Type ("fun", [T, Type ("bool", [])])) = T
wenzelm@3794
   142
  | dest_setT T = raise TYPE ("dest_setT: set type expected", [T], []);
clasohm@923
   143
haftmann@30450
   144
fun mk_set T ts =
haftmann@30450
   145
  let
haftmann@30450
   146
    val sT = mk_setT T;
haftmann@30450
   147
    val empty = Const ("Orderings.bot", sT);
haftmann@30450
   148
    fun insert t u = Const ("insert", T --> sT --> sT) $ t $ u;
haftmann@30450
   149
  in fold_rev insert ts empty end;
haftmann@30450
   150
haftmann@30450
   151
fun mk_UNIV T = Const ("Set.UNIV", mk_setT T);
haftmann@30450
   152
haftmann@30450
   153
fun dest_set (Const ("Orderings.bot", _)) = []
haftmann@30450
   154
  | dest_set (Const ("insert", _) $ t $ u) = t :: dest_set u
haftmann@30450
   155
  | dest_set t = raise TERM ("dest_set", [t]);
haftmann@30450
   156
haftmann@30450
   157
fun Collect_const T = Const ("Collect", (T --> boolT) --> mk_setT T);
haftmann@30450
   158
fun mk_Collect (a, T, t) = Collect_const T $ absfree (a, T, t);
haftmann@30450
   159
haftmann@30450
   160
fun mk_mem (x, A) =
haftmann@30450
   161
  let val setT = fastype_of A in
haftmann@30450
   162
    Const ("op :", dest_setT setT --> setT --> boolT) $ x $ A
haftmann@30450
   163
  end;
haftmann@30450
   164
haftmann@30450
   165
fun dest_mem (Const ("op :", _) $ x $ A) = (x, A)
haftmann@30450
   166
  | dest_mem t = raise TERM ("dest_mem", [t]);
haftmann@30450
   167
wenzelm@8275
   168
paulson@7073
   169
(* logic *)
clasohm@923
   170
clasohm@923
   171
val Trueprop = Const ("Trueprop", boolT --> propT);
clasohm@923
   172
clasohm@923
   173
fun mk_Trueprop P = Trueprop $ P;
clasohm@923
   174
clasohm@923
   175
fun dest_Trueprop (Const ("Trueprop", _) $ P) = P
wenzelm@3794
   176
  | dest_Trueprop t = raise TERM ("dest_Trueprop", [t]);
clasohm@923
   177
wenzelm@23555
   178
fun conj_intr thP thQ =
wenzelm@23555
   179
  let
wenzelm@23576
   180
    val (P, Q) = pairself (ObjectLogic.dest_judgment o Thm.cprop_of) (thP, thQ)
wenzelm@23555
   181
      handle CTERM (msg, _) => raise THM (msg, 0, [thP, thQ]);
wenzelm@23555
   182
    val inst = Thm.instantiate ([], [(@{cpat "?P::bool"}, P), (@{cpat "?Q::bool"}, Q)]);
wenzelm@23555
   183
  in Drule.implies_elim_list (inst @{thm conjI}) [thP, thQ] end;
clasohm@923
   184
wenzelm@23555
   185
fun conj_elim thPQ =
wenzelm@23555
   186
  let
wenzelm@23576
   187
    val (P, Q) = Thm.dest_binop (ObjectLogic.dest_judgment (Thm.cprop_of thPQ))
wenzelm@23555
   188
      handle CTERM (msg, _) => raise THM (msg, 0, [thPQ]);
wenzelm@23555
   189
    val inst = Thm.instantiate ([], [(@{cpat "?P::bool"}, P), (@{cpat "?Q::bool"}, Q)]);
wenzelm@23555
   190
    val thP = Thm.implies_elim (inst @{thm conjunct1}) thPQ;
wenzelm@23555
   191
    val thQ = Thm.implies_elim (inst @{thm conjunct2}) thPQ;
wenzelm@23555
   192
  in (thP, thQ) end;
wenzelm@23555
   193
wenzelm@23555
   194
fun conj_elims th =
wenzelm@23555
   195
  let val (th1, th2) = conj_elim th
wenzelm@23555
   196
  in conj_elims th1 @ conj_elims th2 end handle THM _ => [th];
wenzelm@23555
   197
wenzelm@23555
   198
val conj = @{term "op &"}
wenzelm@23555
   199
and disj = @{term "op |"}
wenzelm@23555
   200
and imp = @{term "op -->"}
wenzelm@23555
   201
and Not = @{term "Not"};
clasohm@923
   202
wenzelm@7690
   203
fun mk_conj (t1, t2) = conj $ t1 $ t2
wenzelm@7690
   204
and mk_disj (t1, t2) = disj $ t1 $ t2
wenzelm@16835
   205
and mk_imp (t1, t2) = imp $ t1 $ t2
wenzelm@16835
   206
and mk_not t = Not $ t;
wenzelm@7690
   207
paulson@15151
   208
fun dest_conj (Const ("op &", _) $ t $ t') = t :: dest_conj t'
paulson@15151
   209
  | dest_conj t = [t];
paulson@15151
   210
paulson@15945
   211
fun dest_disj (Const ("op |", _) $ t $ t') = t :: dest_disj t'
paulson@15945
   212
  | dest_disj t = [t];
paulson@15945
   213
paulson@24958
   214
(*Like dest_disj, but flattens disjunctions however nested*)
paulson@24958
   215
fun disjuncts_aux (Const ("op |", _) $ t $ t') disjs = disjuncts_aux t (disjuncts_aux t' disjs)
paulson@24958
   216
  | disjuncts_aux t disjs = t::disjs;
paulson@24958
   217
paulson@24958
   218
fun disjuncts t = disjuncts_aux t [];
paulson@24958
   219
paulson@4466
   220
fun dest_imp (Const("op -->",_) $ A $ B) = (A, B)
paulson@4466
   221
  | dest_imp  t = raise TERM ("dest_imp", [t]);
paulson@4466
   222
paulson@15151
   223
fun dest_not (Const ("Not", _) $ t) = t
paulson@15151
   224
  | dest_not t = raise TERM ("dest_not", [t]);
wenzelm@8302
   225
clasohm@923
   226
fun eq_const T = Const ("op =", [T, T] ---> boolT);
clasohm@923
   227
fun mk_eq (t, u) = eq_const (fastype_of t) $ t $ u;
clasohm@923
   228
paulson@6031
   229
fun dest_eq (Const ("op =", _) $ lhs $ rhs) = (lhs, rhs)
paulson@6031
   230
  | dest_eq t = raise TERM ("dest_eq", [t])
paulson@6031
   231
clasohm@923
   232
fun all_const T = Const ("All", [T --> boolT] ---> boolT);
clasohm@923
   233
fun mk_all (x, T, P) = all_const T $ absfree (x, T, P);
wenzelm@21173
   234
fun list_all (xs, t) = fold_rev (fn (x, T) => fn P => all_const T $ Abs (x, T, P)) xs t;
clasohm@923
   235
clasohm@923
   236
fun exists_const T = Const ("Ex", [T --> boolT] ---> boolT);
clasohm@923
   237
fun mk_exists (x, T, P) = exists_const T $ absfree (x, T, P);
clasohm@923
   238
wenzelm@21755
   239
fun choice_const T = Const("Hilbert_Choice.Eps", (T --> boolT) --> T);
paulson@15945
   240
haftmann@23247
   241
val class_eq = "HOL.eq";
haftmann@21045
   242
clasohm@923
   243
ballarin@13743
   244
(* binary operations and relations *)
wenzelm@2510
   245
wenzelm@2510
   246
fun mk_binop c (t, u) =
wenzelm@2510
   247
  let val T = fastype_of t in
wenzelm@2510
   248
    Const (c, [T, T] ---> T) $ t $ u
wenzelm@2510
   249
  end;
wenzelm@2510
   250
wenzelm@2510
   251
fun mk_binrel c (t, u) =
wenzelm@2510
   252
  let val T = fastype_of t in
wenzelm@2510
   253
    Const (c, [T, T] ---> boolT) $ t $ u
wenzelm@2510
   254
  end;
wenzelm@2510
   255
paulson@14387
   256
(*destruct the application of a binary operator. The dummyT case is a crude
paulson@14387
   257
  way of handling polymorphic operators.*)
wenzelm@2510
   258
fun dest_bin c T (tm as Const (c', Type ("fun", [T', _])) $ t $ u) =
paulson@14387
   259
      if c = c' andalso (T=T' orelse T=dummyT) then (t, u)
wenzelm@3794
   260
      else raise TERM ("dest_bin " ^ c, [tm])
wenzelm@3794
   261
  | dest_bin c _ tm = raise TERM ("dest_bin " ^ c, [tm]);
wenzelm@2510
   262
wenzelm@2510
   263
wenzelm@4571
   264
(* unit *)
wenzelm@4571
   265
wenzelm@11604
   266
val unitT = Type ("Product_Type.unit", []);
wenzelm@4571
   267
wenzelm@11604
   268
fun is_unitT (Type ("Product_Type.unit", [])) = true
wenzelm@9362
   269
  | is_unitT _ = false;
wenzelm@9362
   270
wenzelm@11604
   271
val unit = Const ("Product_Type.Unity", unitT);
wenzelm@4571
   272
wenzelm@11604
   273
fun is_unit (Const ("Product_Type.Unity", _)) = true
wenzelm@4571
   274
  | is_unit _ = false;
wenzelm@4571
   275
wenzelm@4571
   276
wenzelm@4571
   277
(* prod *)
wenzelm@4571
   278
wenzelm@4571
   279
fun mk_prodT (T1, T2) = Type ("*", [T1, T2]);
wenzelm@4571
   280
wenzelm@4571
   281
fun dest_prodT (Type ("*", [T1, T2])) = (T1, T2)
wenzelm@4571
   282
  | dest_prodT T = raise TYPE ("dest_prodT", [T], []);
wenzelm@4571
   283
berghofe@14048
   284
fun pair_const T1 T2 = Const ("Pair", [T1, T2] ---> mk_prodT (T1, T2));
berghofe@14048
   285
wenzelm@4571
   286
fun mk_prod (t1, t2) =
wenzelm@4571
   287
  let val T1 = fastype_of t1 and T2 = fastype_of t2 in
berghofe@14048
   288
    pair_const T1 T2 $ t1 $ t2
wenzelm@4571
   289
  end;
wenzelm@4571
   290
wenzelm@4571
   291
fun dest_prod (Const ("Pair", _) $ t1 $ t2) = (t1, t2)
wenzelm@4571
   292
  | dest_prod t = raise TERM ("dest_prod", [t]);
wenzelm@4571
   293
wenzelm@4571
   294
fun mk_fst p =
wenzelm@4571
   295
  let val pT = fastype_of p in
wenzelm@4571
   296
    Const ("fst", pT --> fst (dest_prodT pT)) $ p
wenzelm@4571
   297
  end;
wenzelm@4571
   298
wenzelm@4571
   299
fun mk_snd p =
wenzelm@4571
   300
  let val pT = fastype_of p in
wenzelm@4571
   301
    Const ("snd", pT --> snd (dest_prodT pT)) $ p
wenzelm@4571
   302
  end;
wenzelm@4571
   303
wenzelm@18285
   304
fun split_const (A, B, C) =
wenzelm@18285
   305
  Const ("split", (A --> B --> C) --> mk_prodT (A, B) --> C);
wenzelm@18285
   306
wenzelm@18285
   307
fun mk_split t =
wenzelm@18285
   308
  (case Term.fastype_of t of
wenzelm@18285
   309
    T as (Type ("fun", [A, Type ("fun", [B, C])])) =>
wenzelm@18285
   310
      Const ("split", T --> mk_prodT (A, B) --> C) $ t
wenzelm@18285
   311
  | _ => raise TERM ("mk_split: bad body type", [t]));
wenzelm@18285
   312
berghofe@5096
   313
(*Maps the type T1 * ... * Tn to [T1, ..., Tn], however nested*)
berghofe@5096
   314
fun prodT_factors (Type ("*", [T1, T2])) = prodT_factors T1 @ prodT_factors T2
berghofe@5096
   315
  | prodT_factors T = [T];
berghofe@5096
   316
berghofe@5096
   317
(*Makes a nested tuple from a list, following the product type structure*)
wenzelm@16971
   318
fun mk_tuple (Type ("*", [T1, T2])) tms =
wenzelm@16971
   319
        mk_prod (mk_tuple T1 tms,
skalberg@15570
   320
                 mk_tuple T2 (Library.drop (length (prodT_factors T1), tms)))
berghofe@5096
   321
  | mk_tuple T (t::_) = t;
wenzelm@4571
   322
berghofe@23745
   323
fun dest_tuple (Const ("Pair", _) $ t $ u) = dest_tuple t @ dest_tuple u
berghofe@23745
   324
  | dest_tuple t = [t];
berghofe@23745
   325
berghofe@23745
   326
(*In ap_split S T u, term u expects separate arguments for the factors of S,
berghofe@23745
   327
  with result type T.  The call creates a new term expecting one argument
berghofe@23745
   328
  of type S.*)
berghofe@23745
   329
fun ap_split T T3 u =
berghofe@23745
   330
  let
berghofe@23745
   331
    fun ap (T :: Ts) =
berghofe@23745
   332
          (case T of
berghofe@23745
   333
             Type ("*", [T1, T2]) =>
berghofe@23745
   334
               split_const (T1, T2, Ts ---> T3) $ ap (T1 :: T2 :: Ts)
berghofe@23745
   335
           | _ => Abs ("x", T, ap Ts))
berghofe@23745
   336
      | ap [] =
berghofe@23745
   337
          let val k = length (prodT_factors T)
berghofe@23745
   338
          in list_comb (incr_boundvars k u, map Bound (k - 1 downto 0)) end
berghofe@23745
   339
  in ap [T] end;
berghofe@23745
   340
berghofe@23745
   341
wenzelm@25172
   342
(* operations on tuples with specific arities *)
wenzelm@25172
   343
(*
wenzelm@25172
   344
  an "arity" of a tuple is a list of lists of integers
wenzelm@25172
   345
  ("factors"), denoting paths to subterms that are pairs
wenzelm@25172
   346
*)
berghofe@23745
   347
berghofe@23745
   348
fun prod_err s = raise TERM (s ^ ": inconsistent use of products", []);
berghofe@23745
   349
berghofe@23745
   350
fun prod_factors t =
berghofe@23745
   351
  let
berghofe@23745
   352
    fun factors p (Const ("Pair", _) $ t $ u) =
berghofe@23745
   353
          p :: factors (1::p) t @ factors (2::p) u
berghofe@23745
   354
      | factors p _ = []
berghofe@23745
   355
  in factors [] t end;
berghofe@23745
   356
berghofe@23745
   357
fun dest_tuple' ps =
berghofe@23745
   358
  let
berghofe@23745
   359
    fun dest p t = if p mem ps then (case t of
berghofe@23745
   360
        Const ("Pair", _) $ t $ u =>
berghofe@23745
   361
          dest (1::p) t @ dest (2::p) u
berghofe@23745
   362
      | _ => prod_err "dest_tuple'") else [t]
berghofe@23745
   363
  in dest [] end;
berghofe@23745
   364
berghofe@23745
   365
fun prodT_factors' ps =
berghofe@23745
   366
  let
berghofe@23745
   367
    fun factors p T = if p mem ps then (case T of
berghofe@23745
   368
        Type ("*", [T1, T2]) =>
berghofe@23745
   369
          factors (1::p) T1 @ factors (2::p) T2
berghofe@23745
   370
      | _ => prod_err "prodT_factors'") else [T]
berghofe@23745
   371
  in factors [] end;
berghofe@23745
   372
berghofe@23745
   373
(*In ap_split' ps S T u, term u expects separate arguments for the factors of S,
berghofe@23745
   374
  with result type T.  The call creates a new term expecting one argument
berghofe@23745
   375
  of type S.*)
berghofe@23745
   376
fun ap_split' ps T T3 u =
berghofe@23745
   377
  let
berghofe@23745
   378
    fun ap ((p, T) :: pTs) =
berghofe@23745
   379
          if p mem ps then (case T of
berghofe@23745
   380
              Type ("*", [T1, T2]) =>
berghofe@23745
   381
                split_const (T1, T2, map snd pTs ---> T3) $
berghofe@23745
   382
                  ap ((1::p, T1) :: (2::p, T2) :: pTs)
berghofe@23745
   383
            | _ => prod_err "ap_split'")
berghofe@23745
   384
          else Abs ("x", T, ap pTs)
berghofe@23745
   385
      | ap [] =
berghofe@23745
   386
          let val k = length ps
berghofe@23745
   387
          in list_comb (incr_boundvars (k + 1) u, map Bound (k downto 0)) end
berghofe@23745
   388
  in ap [([], T)] end;
berghofe@23745
   389
berghofe@23745
   390
fun mk_tuple' ps =
berghofe@23745
   391
  let
berghofe@23745
   392
    fun mk p T ts =
berghofe@23745
   393
      if p mem ps then (case T of
berghofe@23745
   394
          Type ("*", [T1, T2]) =>
berghofe@23745
   395
            let
berghofe@23745
   396
              val (t, ts') = mk (1::p) T1 ts;
berghofe@23745
   397
              val (u, ts'') = mk (2::p) T2 ts'
berghofe@23745
   398
            in (pair_const T1 T2 $ t $ u, ts'') end
berghofe@23745
   399
        | _ => prod_err "mk_tuple'")
berghofe@23745
   400
      else (hd ts, tl ts)
berghofe@23745
   401
  in fst oo mk [] end;
berghofe@23745
   402
berghofe@23745
   403
fun mk_tupleT ps =
berghofe@23745
   404
  let
berghofe@23745
   405
    fun mk p Ts =
berghofe@23745
   406
      if p mem ps then
berghofe@23745
   407
        let
berghofe@23745
   408
          val (T, Ts') = mk (1::p) Ts;
berghofe@23745
   409
          val (U, Ts'') = mk (2::p) Ts'
berghofe@23745
   410
        in (mk_prodT (T, U), Ts'') end
berghofe@23745
   411
      else (hd Ts, tl Ts)
berghofe@23745
   412
  in fst o mk [] end;
berghofe@23745
   413
berghofe@23745
   414
fun strip_split t =
berghofe@23745
   415
  let
berghofe@23745
   416
    fun strip [] qs Ts t = (t, Ts, qs)
berghofe@23745
   417
      | strip (p :: ps) qs Ts (Const ("split", _) $ t) =
berghofe@23745
   418
          strip ((1 :: p) :: (2 :: p) :: ps) (p :: qs) Ts t
berghofe@23745
   419
      | strip (p :: ps) qs Ts (Abs (s, T, t)) = strip ps qs (T :: Ts) t
berghofe@23745
   420
      | strip (p :: ps) qs Ts t = strip ps qs
berghofe@23745
   421
          (hd (binder_types (fastype_of1 (Ts, t))) :: Ts)
berghofe@23745
   422
          (incr_boundvars 1 t $ Bound 0)
berghofe@23745
   423
  in strip [[]] [] [] t end;
berghofe@23745
   424
wenzelm@5207
   425
wenzelm@5207
   426
(* nat *)
wenzelm@5207
   427
wenzelm@5207
   428
val natT = Type ("nat", []);
wenzelm@5207
   429
haftmann@22994
   430
val zero = Const ("HOL.zero_class.zero", natT);
wenzelm@5207
   431
haftmann@22994
   432
fun is_zero (Const ("HOL.zero_class.zero", _)) = true
wenzelm@5207
   433
  | is_zero _ = false;
wenzelm@5207
   434
wenzelm@5207
   435
fun mk_Suc t = Const ("Suc", natT --> natT) $ t;
wenzelm@5207
   436
wenzelm@5207
   437
fun dest_Suc (Const ("Suc", _) $ t) = t
wenzelm@5207
   438
  | dest_Suc t = raise TERM ("dest_Suc", [t]);
wenzelm@5207
   439
haftmann@21621
   440
val Suc_zero = mk_Suc zero;
haftmann@21621
   441
wenzelm@24630
   442
fun mk_nat n =
haftmann@22994
   443
  let
haftmann@22994
   444
    fun mk 0 = zero
wenzelm@23297
   445
      | mk n = mk_Suc (mk (n - 1));
wenzelm@23576
   446
  in if n < 0 then raise TERM ("mk_nat: negative number", []) else mk n end;
wenzelm@5207
   447
wenzelm@24630
   448
fun dest_nat (Const ("HOL.zero_class.zero", _)) = 0
wenzelm@23297
   449
  | dest_nat (Const ("Suc", _) $ t) = dest_nat t + 1
wenzelm@5207
   450
  | dest_nat t = raise TERM ("dest_nat", [t]);
wenzelm@5207
   451
haftmann@22994
   452
val class_size = "Nat.size";
haftmann@22994
   453
haftmann@22994
   454
fun size_const T = Const ("Nat.size_class.size", T --> natT);
haftmann@22994
   455
wenzelm@5207
   456
haftmann@26036
   457
(* index *)
haftmann@26036
   458
haftmann@26036
   459
val indexT = Type ("Code_Index.index", []);
haftmann@26036
   460
haftmann@26036
   461
wenzelm@21778
   462
(* binary numerals and int -- non-unique representation due to leading zeros/ones! *)
wenzelm@21778
   463
haftmann@25919
   464
val intT = Type ("Int.int", []);
wenzelm@21778
   465
haftmann@25919
   466
val pls_const = Const ("Int.Pls", intT)
haftmann@25919
   467
and min_const = Const ("Int.Min", intT)
huffman@26086
   468
and bit0_const = Const ("Int.Bit0", intT --> intT)
huffman@26086
   469
and bit1_const = Const ("Int.Bit1", intT --> intT);
huffman@26086
   470
huffman@26086
   471
fun mk_bit 0 = bit0_const
huffman@26086
   472
  | mk_bit 1 = bit1_const
huffman@26086
   473
  | mk_bit _ = raise TERM ("mk_bit", []);
huffman@26086
   474
huffman@26086
   475
fun dest_bit (Const ("Int.Bit0", _)) = 0
huffman@26086
   476
  | dest_bit (Const ("Int.Bit1", _)) = 1
huffman@26086
   477
  | dest_bit t = raise TERM ("dest_bit", [t]);
paulson@8768
   478
wenzelm@21829
   479
fun mk_numeral 0 = pls_const
wenzelm@21829
   480
  | mk_numeral ~1 = min_const
wenzelm@21829
   481
  | mk_numeral i =
wenzelm@24630
   482
      let val (q, r) = Integer.div_mod i 2;
huffman@26086
   483
      in mk_bit r $ mk_numeral q end;
berghofe@13755
   484
haftmann@25919
   485
fun dest_numeral (Const ("Int.Pls", _)) = 0
haftmann@25919
   486
  | dest_numeral (Const ("Int.Min", _)) = ~1
huffman@26086
   487
  | dest_numeral (Const ("Int.Bit0", _) $ bs) = 2 * dest_numeral bs
huffman@26086
   488
  | dest_numeral (Const ("Int.Bit1", _) $ bs) = 2 * dest_numeral bs + 1
wenzelm@21829
   489
  | dest_numeral t = raise TERM ("dest_numeral", [t]);
berghofe@13755
   490
haftmann@25919
   491
fun number_of_const T = Const ("Int.number_class.number_of", intT --> T);
haftmann@21820
   492
haftmann@25919
   493
fun add_numerals (Const ("Int.number_class.number_of", Type (_, [_, T])) $ t) = cons (t, T)
wenzelm@23269
   494
  | add_numerals (t $ u) = add_numerals t #> add_numerals u
wenzelm@23269
   495
  | add_numerals (Abs (_, _, t)) = add_numerals t
wenzelm@23269
   496
  | add_numerals _ = I;
haftmann@22391
   497
haftmann@22994
   498
fun mk_number T 0 = Const ("HOL.zero_class.zero", T)
haftmann@22994
   499
  | mk_number T 1 = Const ("HOL.one_class.one", T)
haftmann@21820
   500
  | mk_number T i = number_of_const T $ mk_numeral i;
haftmann@21820
   501
haftmann@22994
   502
fun dest_number (Const ("HOL.zero_class.zero", T)) = (T, 0)
haftmann@22994
   503
  | dest_number (Const ("HOL.one_class.one", T)) = (T, 1)
haftmann@25919
   504
  | dest_number (Const ("Int.number_class.number_of", Type ("fun", [_, T])) $ t) =
haftmann@22994
   505
      (T, dest_numeral t)
haftmann@21820
   506
  | dest_number t = raise TERM ("dest_number", [t]);
berghofe@13755
   507
wenzelm@21829
   508
berghofe@13755
   509
(* real *)
berghofe@13755
   510
wenzelm@16971
   511
val realT = Type ("RealDef.real", []);
berghofe@13755
   512
berghofe@13755
   513
wenzelm@21755
   514
(* nibble *)
wenzelm@21755
   515
wenzelm@21755
   516
val nibbleT = Type ("List.nibble", []);
berghofe@13755
   517
wenzelm@21755
   518
fun mk_nibble n =
wenzelm@21755
   519
  let val s =
wenzelm@21755
   520
    if 0 <= n andalso n <= 9 then chr (n + ord "0")
wenzelm@21755
   521
    else if 10 <= n andalso n <= 15 then chr (n + ord "A" - 10)
wenzelm@21755
   522
    else raise TERM ("mk_nibble", [])
wenzelm@21755
   523
  in Const ("List.nibble.Nibble" ^ s, nibbleT) end;
nipkow@17083
   524
wenzelm@21755
   525
fun dest_nibble t =
wenzelm@21755
   526
  let fun err () = raise TERM ("dest_nibble", [t]) in
wenzelm@21755
   527
    (case try (unprefix "List.nibble.Nibble" o fst o Term.dest_Const) t of
wenzelm@21755
   528
      NONE => err ()
wenzelm@21755
   529
    | SOME c =>
wenzelm@21755
   530
        if size c <> 1 then err ()
wenzelm@21755
   531
        else if "0" <= c andalso c <= "9" then ord c - ord "0"
wenzelm@21755
   532
        else if "A" <= c andalso c <= "F" then ord c - ord "A" + 10
wenzelm@21755
   533
        else err ())
wenzelm@21755
   534
  end;
berghofe@15062
   535
haftmann@21455
   536
haftmann@21455
   537
(* char *)
haftmann@21455
   538
haftmann@21455
   539
val charT = Type ("List.char", []);
haftmann@21455
   540
wenzelm@21755
   541
fun mk_char n =
wenzelm@21755
   542
  if 0 <= n andalso n <= 255 then
wenzelm@21755
   543
    Const ("List.char.Char", nibbleT --> nibbleT --> charT) $
wenzelm@21755
   544
      mk_nibble (n div 16) $ mk_nibble (n mod 16)
wenzelm@21755
   545
  else raise TERM ("mk_char", []);
haftmann@21455
   546
wenzelm@21755
   547
fun dest_char (Const ("List.char.Char", _) $ t $ u) =
wenzelm@21755
   548
      dest_nibble t * 16 + dest_nibble u
wenzelm@21755
   549
  | dest_char t = raise TERM ("dest_char", [t]);
haftmann@21455
   550
wenzelm@21755
   551
wenzelm@21755
   552
(* list *)
haftmann@21455
   553
wenzelm@21755
   554
fun listT T = Type ("List.list", [T]);
haftmann@21455
   555
berghofe@25887
   556
fun nil_const T = Const ("List.list.Nil", listT T);
berghofe@25887
   557
berghofe@25887
   558
fun cons_const T =
berghofe@25887
   559
  let val lT = listT T
berghofe@25887
   560
  in Const ("List.list.Cons", T --> lT --> lT) end;
berghofe@25887
   561
wenzelm@21755
   562
fun mk_list T ts =
haftmann@21455
   563
  let
wenzelm@21755
   564
    val lT = listT T;
wenzelm@21755
   565
    val Nil = Const ("List.list.Nil", lT);
wenzelm@21755
   566
    fun Cons t u = Const ("List.list.Cons", T --> lT --> lT) $ t $ u;
wenzelm@21755
   567
  in fold_rev Cons ts Nil end;
wenzelm@21755
   568
wenzelm@21755
   569
fun dest_list (Const ("List.list.Nil", _)) = []
wenzelm@21755
   570
  | dest_list (Const ("List.list.Cons", _) $ t $ u) = t :: dest_list u
wenzelm@21755
   571
  | dest_list t = raise TERM ("dest_list", [t]);
haftmann@21455
   572
haftmann@21455
   573
haftmann@21455
   574
(* string *)
haftmann@21455
   575
haftmann@21820
   576
val stringT = Type ("List.string", []);
haftmann@21455
   577
wenzelm@21755
   578
val mk_string = mk_list charT o map (mk_char o ord) o explode;
wenzelm@21755
   579
val dest_string = implode o map (chr o dest_char) o dest_list;
haftmann@21455
   580
clasohm@923
   581
end;