src/HOL/hologic.ML
author wenzelm
Tue Sep 05 18:48:22 2000 +0200 (2000-09-05)
changeset 9856 c34d3c94298c
parent 9473 7d13a5ace928
child 10384 a499b9ce2ffe
permissions -rw-r--r--
added not_const;
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
clasohm@923
    10
  val termC: class
clasohm@923
    11
  val termS: sort
wenzelm@8100
    12
  val termT: typ
wenzelm@8275
    13
  val boolN: string
clasohm@923
    14
  val boolT: typ
paulson@7073
    15
  val false_const: term
paulson@7073
    16
  val true_const: term
wenzelm@9856
    17
  val not_const: term
clasohm@923
    18
  val mk_setT: typ -> typ
clasohm@923
    19
  val dest_setT: typ -> typ
clasohm@923
    20
  val mk_Trueprop: term -> term
wenzelm@9473
    21
  val atomic_Trueprop: string -> term
clasohm@923
    22
  val dest_Trueprop: term -> term
clasohm@923
    23
  val conj: term
clasohm@923
    24
  val disj: term
clasohm@923
    25
  val imp: term
wenzelm@8429
    26
  val Not: term
wenzelm@7690
    27
  val mk_conj: term * term -> term
wenzelm@7690
    28
  val mk_disj: term * term -> term
wenzelm@7690
    29
  val mk_imp: term * term -> term
wenzelm@4571
    30
  val dest_imp: term -> term * term
wenzelm@8302
    31
  val dest_conj: term -> term list
clasohm@923
    32
  val eq_const: typ -> term
clasohm@923
    33
  val all_const: typ -> term
clasohm@923
    34
  val exists_const: typ -> term
clasohm@923
    35
  val Collect_const: typ -> term
clasohm@923
    36
  val mk_eq: term * term -> term
paulson@6031
    37
  val dest_eq: term -> term * term
clasohm@923
    38
  val mk_all: string * typ * term -> term
clasohm@923
    39
  val mk_exists: string * typ * term -> term
clasohm@923
    40
  val mk_Collect: string * typ * term -> term
clasohm@923
    41
  val mk_mem: term * term -> term
wenzelm@6380
    42
  val dest_mem: term -> term * term
wenzelm@2510
    43
  val mk_binop: string -> term * term -> term
wenzelm@2510
    44
  val mk_binrel: string -> term * term -> term
wenzelm@2510
    45
  val dest_bin: string -> typ -> term -> term * term
wenzelm@4571
    46
  val unitT: typ
wenzelm@9362
    47
  val is_unitT: typ -> bool
wenzelm@4571
    48
  val unit: term
wenzelm@4571
    49
  val is_unit: term -> bool
wenzelm@4571
    50
  val mk_prodT: typ * typ -> typ
wenzelm@4571
    51
  val dest_prodT: typ -> typ * typ
wenzelm@4571
    52
  val mk_prod: term * term -> term
wenzelm@4571
    53
  val dest_prod: term -> term * term
wenzelm@4571
    54
  val mk_fst: term -> term
wenzelm@4571
    55
  val mk_snd: term -> term
berghofe@5096
    56
  val prodT_factors: typ -> typ list
berghofe@5096
    57
  val split_const: typ * typ * typ -> term
berghofe@5096
    58
  val mk_tuple: typ -> term list -> term
wenzelm@5207
    59
  val natT: typ
wenzelm@5207
    60
  val zero: term
wenzelm@5207
    61
  val is_zero: term -> bool
wenzelm@5207
    62
  val mk_Suc: term -> term
wenzelm@5207
    63
  val dest_Suc: term -> term
wenzelm@5207
    64
  val mk_nat: int -> term
wenzelm@5207
    65
  val dest_nat: term -> int
paulson@7073
    66
  val intT: typ
paulson@7163
    67
  val realT: typ
paulson@7073
    68
  val binT: typ
paulson@7073
    69
  val pls_const: term
paulson@7073
    70
  val min_const: term
paulson@7073
    71
  val bit_const: term
paulson@8768
    72
  val number_of_const: typ -> term
nipkow@7548
    73
  val int_of: int list -> int
nipkow@7548
    74
  val dest_binum: term -> int
clasohm@923
    75
end;
clasohm@923
    76
wenzelm@2510
    77
clasohm@923
    78
structure HOLogic: HOLOGIC =
clasohm@923
    79
struct
clasohm@923
    80
wenzelm@2510
    81
(* basics *)
clasohm@923
    82
clasohm@923
    83
val termC: class = "term";
clasohm@923
    84
val termS: sort = [termC];
wenzelm@8100
    85
val termT = TypeInfer.anyT termS;
clasohm@923
    86
clasohm@923
    87
wenzelm@2510
    88
(* bool and set *)
clasohm@923
    89
wenzelm@8275
    90
val boolN = "bool";
wenzelm@8275
    91
val boolT = Type (boolN, []);
clasohm@923
    92
wenzelm@9856
    93
val true_const =  Const ("True", boolT);
wenzelm@9856
    94
val false_const = Const ("False", boolT);
wenzelm@9856
    95
val not_const = Const ("Not", boolT --> boolT);
paulson@7073
    96
clasohm@923
    97
fun mk_setT T = Type ("set", [T]);
clasohm@923
    98
clasohm@923
    99
fun dest_setT (Type ("set", [T])) = T
wenzelm@3794
   100
  | dest_setT T = raise TYPE ("dest_setT: set type expected", [T], []);
clasohm@923
   101
wenzelm@8275
   102
paulson@7073
   103
(* logic *)
clasohm@923
   104
clasohm@923
   105
val Trueprop = Const ("Trueprop", boolT --> propT);
clasohm@923
   106
clasohm@923
   107
fun mk_Trueprop P = Trueprop $ P;
clasohm@923
   108
wenzelm@9473
   109
fun atomic_Trueprop x = mk_Trueprop (Free (x, boolT));
wenzelm@9473
   110
clasohm@923
   111
fun dest_Trueprop (Const ("Trueprop", _) $ P) = P
wenzelm@3794
   112
  | dest_Trueprop t = raise TERM ("dest_Trueprop", [t]);
clasohm@923
   113
clasohm@923
   114
clasohm@923
   115
val conj = Const ("op &", [boolT, boolT] ---> boolT)
clasohm@923
   116
and disj = Const ("op |", [boolT, boolT] ---> boolT)
wenzelm@8429
   117
and imp = Const ("op -->", [boolT, boolT] ---> boolT)
wenzelm@8429
   118
and Not = Const ("Not", boolT --> boolT);
clasohm@923
   119
wenzelm@7690
   120
fun mk_conj (t1, t2) = conj $ t1 $ t2
wenzelm@7690
   121
and mk_disj (t1, t2) = disj $ t1 $ t2
wenzelm@7690
   122
and mk_imp (t1, t2) = imp $ t1 $ t2;
wenzelm@7690
   123
paulson@4466
   124
fun dest_imp (Const("op -->",_) $ A $ B) = (A, B)
paulson@4466
   125
  | dest_imp  t = raise TERM ("dest_imp", [t]);
paulson@4466
   126
wenzelm@8302
   127
fun dest_conj (Const ("op &", _) $ t $ t') = t :: dest_conj t'
wenzelm@8302
   128
  | dest_conj t = [t];
wenzelm@8302
   129
clasohm@923
   130
fun eq_const T = Const ("op =", [T, T] ---> boolT);
clasohm@923
   131
fun mk_eq (t, u) = eq_const (fastype_of t) $ t $ u;
clasohm@923
   132
paulson@6031
   133
fun dest_eq (Const ("op =", _) $ lhs $ rhs) = (lhs, rhs)
paulson@6031
   134
  | dest_eq t = raise TERM ("dest_eq", [t])
paulson@6031
   135
clasohm@923
   136
fun all_const T = Const ("All", [T --> boolT] ---> boolT);
clasohm@923
   137
fun mk_all (x, T, P) = all_const T $ absfree (x, T, P);
clasohm@923
   138
clasohm@923
   139
fun exists_const T = Const ("Ex", [T --> boolT] ---> boolT);
clasohm@923
   140
fun mk_exists (x, T, P) = exists_const T $ absfree (x, T, P);
clasohm@923
   141
clasohm@923
   142
fun Collect_const T = Const ("Collect", [T --> boolT] ---> mk_setT T);
clasohm@923
   143
fun mk_Collect (a, T, t) = Collect_const T $ absfree (a, T, t);
clasohm@923
   144
clasohm@923
   145
fun mk_mem (x, A) =
clasohm@923
   146
  let val setT = fastype_of A in
clasohm@923
   147
    Const ("op :", [dest_setT setT, setT] ---> boolT) $ x $ A
clasohm@923
   148
  end;
clasohm@923
   149
wenzelm@6380
   150
fun dest_mem (Const ("op :", _) $ x $ A) = (x, A)
wenzelm@6380
   151
  | dest_mem t = raise TERM ("dest_mem", [t]);
wenzelm@6380
   152
clasohm@923
   153
wenzelm@2510
   154
(* binary oprations and relations *)
wenzelm@2510
   155
wenzelm@2510
   156
fun mk_binop c (t, u) =
wenzelm@2510
   157
  let val T = fastype_of t in
wenzelm@2510
   158
    Const (c, [T, T] ---> T) $ t $ u
wenzelm@2510
   159
  end;
wenzelm@2510
   160
wenzelm@2510
   161
fun mk_binrel c (t, u) =
wenzelm@2510
   162
  let val T = fastype_of t in
wenzelm@2510
   163
    Const (c, [T, T] ---> boolT) $ t $ u
wenzelm@2510
   164
  end;
wenzelm@2510
   165
wenzelm@2510
   166
fun dest_bin c T (tm as Const (c', Type ("fun", [T', _])) $ t $ u) =
wenzelm@2510
   167
      if c = c' andalso T = T' then (t, u)
wenzelm@3794
   168
      else raise TERM ("dest_bin " ^ c, [tm])
wenzelm@3794
   169
  | dest_bin c _ tm = raise TERM ("dest_bin " ^ c, [tm]);
wenzelm@2510
   170
wenzelm@2510
   171
wenzelm@4571
   172
(* unit *)
wenzelm@4571
   173
wenzelm@4571
   174
val unitT = Type ("unit", []);
wenzelm@4571
   175
wenzelm@9362
   176
fun is_unitT (Type ("unit", [])) = true
wenzelm@9362
   177
  | is_unitT _ = false;
wenzelm@9362
   178
wenzelm@4571
   179
val unit = Const ("()", unitT);
wenzelm@4571
   180
wenzelm@4571
   181
fun is_unit (Const ("()", _)) = true
wenzelm@4571
   182
  | is_unit _ = false;
wenzelm@4571
   183
wenzelm@4571
   184
wenzelm@4571
   185
(* prod *)
wenzelm@4571
   186
wenzelm@4571
   187
fun mk_prodT (T1, T2) = Type ("*", [T1, T2]);
wenzelm@4571
   188
wenzelm@4571
   189
fun dest_prodT (Type ("*", [T1, T2])) = (T1, T2)
wenzelm@4571
   190
  | dest_prodT T = raise TYPE ("dest_prodT", [T], []);
wenzelm@4571
   191
wenzelm@4571
   192
fun mk_prod (t1, t2) =
wenzelm@4571
   193
  let val T1 = fastype_of t1 and T2 = fastype_of t2 in
wenzelm@4571
   194
    Const ("Pair", [T1, T2] ---> mk_prodT (T1, T2)) $ t1 $ t2
wenzelm@4571
   195
  end;
wenzelm@4571
   196
wenzelm@4571
   197
fun dest_prod (Const ("Pair", _) $ t1 $ t2) = (t1, t2)
wenzelm@4571
   198
  | dest_prod t = raise TERM ("dest_prod", [t]);
wenzelm@4571
   199
wenzelm@4571
   200
fun mk_fst p =
wenzelm@4571
   201
  let val pT = fastype_of p in
wenzelm@4571
   202
    Const ("fst", pT --> fst (dest_prodT pT)) $ p
wenzelm@4571
   203
  end;
wenzelm@4571
   204
wenzelm@4571
   205
fun mk_snd p =
wenzelm@4571
   206
  let val pT = fastype_of p in
wenzelm@4571
   207
    Const ("snd", pT --> snd (dest_prodT pT)) $ p
wenzelm@4571
   208
  end;
wenzelm@4571
   209
berghofe@5096
   210
(*Maps the type T1 * ... * Tn to [T1, ..., Tn], however nested*)
berghofe@5096
   211
fun prodT_factors (Type ("*", [T1, T2])) = prodT_factors T1 @ prodT_factors T2
berghofe@5096
   212
  | prodT_factors T = [T];
berghofe@5096
   213
berghofe@5096
   214
fun split_const (Ta, Tb, Tc) = 
berghofe@5096
   215
    Const ("split", [[Ta, Tb] ---> Tc, mk_prodT (Ta, Tb)] ---> Tc);
berghofe@5096
   216
berghofe@5096
   217
(*Makes a nested tuple from a list, following the product type structure*)
berghofe@5096
   218
fun mk_tuple (Type ("*", [T1, T2])) tms = 
berghofe@5096
   219
        mk_prod (mk_tuple T1 tms, 
berghofe@5096
   220
                 mk_tuple T2 (drop (length (prodT_factors T1), tms)))
berghofe@5096
   221
  | mk_tuple T (t::_) = t;
wenzelm@4571
   222
wenzelm@5207
   223
wenzelm@5207
   224
wenzelm@9362
   225
(* proper tuples *)
wenzelm@9362
   226
wenzelm@9362
   227
local  (*currently unused*)
wenzelm@9362
   228
wenzelm@9362
   229
fun mk_tupleT Ts = foldr mk_prodT (Ts, unitT);
wenzelm@9362
   230
wenzelm@9362
   231
fun dest_tupleT (Type ("unit", [])) = []
wenzelm@9362
   232
  | dest_tupleT (Type ("*", [T, U])) = T :: dest_tupleT U
wenzelm@9362
   233
  | dest_tupleT T = raise TYPE ("dest_tupleT", [T], []);
wenzelm@9362
   234
wenzelm@9362
   235
fun mk_tuple ts = foldr mk_prod (ts, unit);
wenzelm@9362
   236
wenzelm@9362
   237
fun dest_tuple (Const ("()", _)) = []
wenzelm@9362
   238
  | dest_tuple (Const ("Pair", _) $ t $ u) = t :: dest_tuple u
wenzelm@9362
   239
  | dest_tuple t = raise TERM ("dest_tuple", [t]);
wenzelm@9362
   240
wenzelm@9362
   241
in val _ = unit end;
wenzelm@9362
   242
wenzelm@9362
   243
wenzelm@5207
   244
(* nat *)
wenzelm@5207
   245
wenzelm@5207
   246
val natT = Type ("nat", []);
wenzelm@5207
   247
wenzelm@5207
   248
val zero = Const ("0", natT);
wenzelm@5207
   249
wenzelm@5207
   250
fun is_zero (Const ("0", _)) = true
wenzelm@5207
   251
  | is_zero _ = false;
wenzelm@5207
   252
wenzelm@5207
   253
fun mk_Suc t = Const ("Suc", natT --> natT) $ t;
wenzelm@5207
   254
wenzelm@5207
   255
fun dest_Suc (Const ("Suc", _) $ t) = t
wenzelm@5207
   256
  | dest_Suc t = raise TERM ("dest_Suc", [t]);
wenzelm@5207
   257
wenzelm@5207
   258
fun mk_nat 0 = zero
wenzelm@5207
   259
  | mk_nat n = mk_Suc (mk_nat (n - 1));
wenzelm@5207
   260
wenzelm@5207
   261
fun dest_nat (Const ("0", _)) = 0
wenzelm@5207
   262
  | dest_nat (Const ("Suc", _) $ t) = dest_nat t + 1
wenzelm@5207
   263
  | dest_nat t = raise TERM ("dest_nat", [t]);
wenzelm@5207
   264
wenzelm@5207
   265
paulson@7073
   266
val intT = Type ("IntDef.int", []);
paulson@7073
   267
paulson@7163
   268
val realT = Type("RealDef.real",[]);
paulson@7163
   269
paulson@7073
   270
paulson@7073
   271
(* binary numerals *)
paulson@7073
   272
paulson@7073
   273
val binT = Type ("Numeral.bin", []);
paulson@7073
   274
paulson@7073
   275
val pls_const =  Const ("Numeral.bin.Pls", binT)
paulson@7073
   276
and min_const = Const ("Numeral.bin.Min", binT)
paulson@8768
   277
and bit_const = Const ("Numeral.bin.Bit", [binT, boolT] ---> binT);
paulson@8768
   278
paulson@8768
   279
fun number_of_const T = Const ("Numeral.number_of", binT --> T);
paulson@8739
   280
paulson@7073
   281
nipkow@7548
   282
fun int_of [] = 0
nipkow@7548
   283
  | int_of (b :: bs) = b + 2 * int_of bs;
nipkow@7548
   284
nipkow@7548
   285
fun dest_bit (Const ("False", _)) = 0
nipkow@7548
   286
  | dest_bit (Const ("True", _)) = 1
nipkow@7548
   287
  | dest_bit t = raise TERM("dest_bit", [t]);
nipkow@7548
   288
nipkow@7548
   289
fun bin_of (Const ("Numeral.bin.Pls", _)) = []
nipkow@7548
   290
  | bin_of (Const ("Numeral.bin.Min", _)) = [~1]
nipkow@7548
   291
  | bin_of (Const ("Numeral.bin.Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
nipkow@7548
   292
  | bin_of t = raise TERM("bin_of", [t]);
nipkow@7548
   293
nipkow@7548
   294
val dest_binum = int_of o bin_of;
nipkow@7548
   295
clasohm@923
   296
end;