src/HOL/hologic.ML
author obua
Tue Mar 08 16:02:52 2005 +0100 (2005-03-08)
changeset 15595 dc8a41c7cefc
parent 15574 b1d1b5bfc464
child 15620 8ccdc8bc66a2
permissions -rw-r--r--
fix integer overflow in numeral syntax for SML NJ.
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@12338
    12
  val read_cterm: Sign.sg -> string -> cterm
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
clasohm@923
    21
  val dest_Trueprop: term -> term
clasohm@923
    22
  val conj: term
clasohm@923
    23
  val disj: term
clasohm@923
    24
  val imp: term
wenzelm@8429
    25
  val Not: term
wenzelm@7690
    26
  val mk_conj: term * term -> term
wenzelm@7690
    27
  val mk_disj: term * term -> term
wenzelm@7690
    28
  val mk_imp: term * term -> term
paulson@15151
    29
  val dest_conj: term -> term list
wenzelm@4571
    30
  val dest_imp: term -> term * term
paulson@15151
    31
  val dest_not: term -> term
wenzelm@11683
    32
  val dest_concls: term -> term list
clasohm@923
    33
  val eq_const: typ -> term
clasohm@923
    34
  val all_const: typ -> term
clasohm@923
    35
  val exists_const: typ -> term
clasohm@923
    36
  val Collect_const: typ -> term
clasohm@923
    37
  val mk_eq: term * term -> term
paulson@6031
    38
  val dest_eq: term -> term * term
clasohm@923
    39
  val mk_all: string * typ * term -> term
berghofe@13640
    40
  val list_all: (string * typ) list * term -> term
clasohm@923
    41
  val mk_exists: string * typ * term -> term
clasohm@923
    42
  val mk_Collect: string * typ * term -> term
clasohm@923
    43
  val mk_mem: term * term -> term
wenzelm@6380
    44
  val dest_mem: term -> term * term
wenzelm@11818
    45
  val mk_UNIV: typ -> term
wenzelm@2510
    46
  val mk_binop: string -> term * term -> term
wenzelm@2510
    47
  val mk_binrel: string -> term * term -> term
wenzelm@2510
    48
  val dest_bin: string -> typ -> term -> term * term
wenzelm@4571
    49
  val unitT: typ
wenzelm@9362
    50
  val is_unitT: typ -> bool
wenzelm@4571
    51
  val unit: term
wenzelm@4571
    52
  val is_unit: term -> bool
wenzelm@4571
    53
  val mk_prodT: typ * typ -> typ
wenzelm@4571
    54
  val dest_prodT: typ -> typ * typ
berghofe@14048
    55
  val pair_const: typ -> typ -> term
wenzelm@4571
    56
  val mk_prod: term * term -> term
wenzelm@4571
    57
  val dest_prod: term -> term * term
wenzelm@4571
    58
  val mk_fst: term -> term
wenzelm@4571
    59
  val mk_snd: term -> term
berghofe@5096
    60
  val prodT_factors: typ -> typ list
berghofe@5096
    61
  val split_const: typ * typ * typ -> term
berghofe@5096
    62
  val mk_tuple: typ -> term list -> term
wenzelm@5207
    63
  val natT: typ
wenzelm@5207
    64
  val zero: term
wenzelm@5207
    65
  val is_zero: term -> bool
wenzelm@5207
    66
  val mk_Suc: term -> term
wenzelm@5207
    67
  val dest_Suc: term -> term
wenzelm@5207
    68
  val mk_nat: int -> term
wenzelm@5207
    69
  val dest_nat: term -> int
paulson@7073
    70
  val intT: typ
berghofe@13755
    71
  val mk_int: int -> term
paulson@7163
    72
  val realT: typ
paulson@7073
    73
  val binT: typ
paulson@7073
    74
  val pls_const: term
paulson@7073
    75
  val min_const: term
paulson@7073
    76
  val bit_const: term
paulson@8768
    77
  val number_of_const: typ -> term
nipkow@7548
    78
  val int_of: int list -> int
obua@15595
    79
  val intinf_of: int list -> IntInf.int
nipkow@7548
    80
  val dest_binum: term -> int
berghofe@13755
    81
  val mk_bin: int -> term
obua@15595
    82
  val mk_bin_from_intinf: IntInf.int -> term
berghofe@13755
    83
  val mk_list: ('a -> term) -> typ -> 'a list -> term
berghofe@15062
    84
  val dest_list: term -> term list
clasohm@923
    85
end;
clasohm@923
    86
wenzelm@2510
    87
clasohm@923
    88
structure HOLogic: HOLOGIC =
clasohm@923
    89
struct
clasohm@923
    90
wenzelm@12338
    91
(* HOL syntax *)
clasohm@923
    92
wenzelm@12338
    93
val typeS: sort = ["HOL.type"];
wenzelm@12338
    94
val typeT = TypeInfer.anyT typeS;
wenzelm@12338
    95
wenzelm@12338
    96
fun read_cterm sg s = Thm.read_cterm sg (s, typeT);
clasohm@923
    97
clasohm@923
    98
wenzelm@2510
    99
(* bool and set *)
clasohm@923
   100
wenzelm@8275
   101
val boolN = "bool";
wenzelm@8275
   102
val boolT = Type (boolN, []);
clasohm@923
   103
wenzelm@9856
   104
val true_const =  Const ("True", boolT);
wenzelm@9856
   105
val false_const = Const ("False", boolT);
wenzelm@9856
   106
val not_const = Const ("Not", boolT --> boolT);
paulson@7073
   107
clasohm@923
   108
fun mk_setT T = Type ("set", [T]);
clasohm@923
   109
clasohm@923
   110
fun dest_setT (Type ("set", [T])) = T
wenzelm@3794
   111
  | dest_setT T = raise TYPE ("dest_setT: set type expected", [T], []);
clasohm@923
   112
wenzelm@8275
   113
paulson@7073
   114
(* logic *)
clasohm@923
   115
clasohm@923
   116
val Trueprop = Const ("Trueprop", boolT --> propT);
clasohm@923
   117
clasohm@923
   118
fun mk_Trueprop P = Trueprop $ P;
clasohm@923
   119
clasohm@923
   120
fun dest_Trueprop (Const ("Trueprop", _) $ P) = P
wenzelm@3794
   121
  | dest_Trueprop t = raise TERM ("dest_Trueprop", [t]);
clasohm@923
   122
clasohm@923
   123
clasohm@923
   124
val conj = Const ("op &", [boolT, boolT] ---> boolT)
clasohm@923
   125
and disj = Const ("op |", [boolT, boolT] ---> boolT)
wenzelm@8429
   126
and imp = Const ("op -->", [boolT, boolT] ---> boolT)
wenzelm@8429
   127
and Not = Const ("Not", boolT --> boolT);
clasohm@923
   128
wenzelm@7690
   129
fun mk_conj (t1, t2) = conj $ t1 $ t2
wenzelm@7690
   130
and mk_disj (t1, t2) = disj $ t1 $ t2
wenzelm@7690
   131
and mk_imp (t1, t2) = imp $ t1 $ t2;
wenzelm@7690
   132
paulson@15151
   133
fun dest_conj (Const ("op &", _) $ t $ t') = t :: dest_conj t'
paulson@15151
   134
  | dest_conj t = [t];
paulson@15151
   135
paulson@4466
   136
fun dest_imp (Const("op -->",_) $ A $ B) = (A, B)
paulson@4466
   137
  | dest_imp  t = raise TERM ("dest_imp", [t]);
paulson@4466
   138
paulson@15151
   139
fun dest_not (Const ("Not", _) $ t) = t
paulson@15151
   140
  | dest_not t = raise TERM ("dest_not", [t]);
wenzelm@8302
   141
wenzelm@11683
   142
fun imp_concl_of t = imp_concl_of (#2 (dest_imp t)) handle TERM _ => t;
wenzelm@11683
   143
val dest_concls = map imp_concl_of o dest_conj o dest_Trueprop;
wenzelm@11683
   144
clasohm@923
   145
fun eq_const T = Const ("op =", [T, T] ---> boolT);
clasohm@923
   146
fun mk_eq (t, u) = eq_const (fastype_of t) $ t $ u;
clasohm@923
   147
paulson@6031
   148
fun dest_eq (Const ("op =", _) $ lhs $ rhs) = (lhs, rhs)
paulson@6031
   149
  | dest_eq t = raise TERM ("dest_eq", [t])
paulson@6031
   150
clasohm@923
   151
fun all_const T = Const ("All", [T --> boolT] ---> boolT);
clasohm@923
   152
fun mk_all (x, T, P) = all_const T $ absfree (x, T, P);
skalberg@15574
   153
fun list_all (vs,x) = foldr (fn ((x, T), P) => all_const T $ Abs (x, T, P)) x vs;
clasohm@923
   154
clasohm@923
   155
fun exists_const T = Const ("Ex", [T --> boolT] ---> boolT);
clasohm@923
   156
fun mk_exists (x, T, P) = exists_const T $ absfree (x, T, P);
clasohm@923
   157
clasohm@923
   158
fun Collect_const T = Const ("Collect", [T --> boolT] ---> mk_setT T);
clasohm@923
   159
fun mk_Collect (a, T, t) = Collect_const T $ absfree (a, T, t);
clasohm@923
   160
clasohm@923
   161
fun mk_mem (x, A) =
clasohm@923
   162
  let val setT = fastype_of A in
clasohm@923
   163
    Const ("op :", [dest_setT setT, setT] ---> boolT) $ x $ A
clasohm@923
   164
  end;
clasohm@923
   165
wenzelm@6380
   166
fun dest_mem (Const ("op :", _) $ x $ A) = (x, A)
wenzelm@6380
   167
  | dest_mem t = raise TERM ("dest_mem", [t]);
wenzelm@6380
   168
wenzelm@11818
   169
fun mk_UNIV T = Const ("UNIV", mk_setT T);
wenzelm@11818
   170
clasohm@923
   171
ballarin@13743
   172
(* binary operations and relations *)
wenzelm@2510
   173
wenzelm@2510
   174
fun mk_binop c (t, u) =
wenzelm@2510
   175
  let val T = fastype_of t in
wenzelm@2510
   176
    Const (c, [T, T] ---> T) $ t $ u
wenzelm@2510
   177
  end;
wenzelm@2510
   178
wenzelm@2510
   179
fun mk_binrel c (t, u) =
wenzelm@2510
   180
  let val T = fastype_of t in
wenzelm@2510
   181
    Const (c, [T, T] ---> boolT) $ t $ u
wenzelm@2510
   182
  end;
wenzelm@2510
   183
paulson@14387
   184
(*destruct the application of a binary operator. The dummyT case is a crude
paulson@14387
   185
  way of handling polymorphic operators.*)
wenzelm@2510
   186
fun dest_bin c T (tm as Const (c', Type ("fun", [T', _])) $ t $ u) =
paulson@14387
   187
      if c = c' andalso (T=T' orelse T=dummyT) then (t, u)
wenzelm@3794
   188
      else raise TERM ("dest_bin " ^ c, [tm])
wenzelm@3794
   189
  | dest_bin c _ tm = raise TERM ("dest_bin " ^ c, [tm]);
wenzelm@2510
   190
wenzelm@2510
   191
wenzelm@4571
   192
(* unit *)
wenzelm@4571
   193
wenzelm@11604
   194
val unitT = Type ("Product_Type.unit", []);
wenzelm@4571
   195
wenzelm@11604
   196
fun is_unitT (Type ("Product_Type.unit", [])) = true
wenzelm@9362
   197
  | is_unitT _ = false;
wenzelm@9362
   198
wenzelm@11604
   199
val unit = Const ("Product_Type.Unity", unitT);
wenzelm@4571
   200
wenzelm@11604
   201
fun is_unit (Const ("Product_Type.Unity", _)) = true
wenzelm@4571
   202
  | is_unit _ = false;
wenzelm@4571
   203
wenzelm@4571
   204
wenzelm@4571
   205
(* prod *)
wenzelm@4571
   206
wenzelm@4571
   207
fun mk_prodT (T1, T2) = Type ("*", [T1, T2]);
wenzelm@4571
   208
wenzelm@4571
   209
fun dest_prodT (Type ("*", [T1, T2])) = (T1, T2)
wenzelm@4571
   210
  | dest_prodT T = raise TYPE ("dest_prodT", [T], []);
wenzelm@4571
   211
berghofe@14048
   212
fun pair_const T1 T2 = Const ("Pair", [T1, T2] ---> mk_prodT (T1, T2));
berghofe@14048
   213
wenzelm@4571
   214
fun mk_prod (t1, t2) =
wenzelm@4571
   215
  let val T1 = fastype_of t1 and T2 = fastype_of t2 in
berghofe@14048
   216
    pair_const T1 T2 $ t1 $ t2
wenzelm@4571
   217
  end;
wenzelm@4571
   218
wenzelm@4571
   219
fun dest_prod (Const ("Pair", _) $ t1 $ t2) = (t1, t2)
wenzelm@4571
   220
  | dest_prod t = raise TERM ("dest_prod", [t]);
wenzelm@4571
   221
wenzelm@4571
   222
fun mk_fst p =
wenzelm@4571
   223
  let val pT = fastype_of p in
wenzelm@4571
   224
    Const ("fst", pT --> fst (dest_prodT pT)) $ p
wenzelm@4571
   225
  end;
wenzelm@4571
   226
wenzelm@4571
   227
fun mk_snd p =
wenzelm@4571
   228
  let val pT = fastype_of p in
wenzelm@4571
   229
    Const ("snd", pT --> snd (dest_prodT pT)) $ p
wenzelm@4571
   230
  end;
wenzelm@4571
   231
berghofe@5096
   232
(*Maps the type T1 * ... * Tn to [T1, ..., Tn], however nested*)
berghofe@5096
   233
fun prodT_factors (Type ("*", [T1, T2])) = prodT_factors T1 @ prodT_factors T2
berghofe@5096
   234
  | prodT_factors T = [T];
berghofe@5096
   235
berghofe@5096
   236
fun split_const (Ta, Tb, Tc) = 
berghofe@5096
   237
    Const ("split", [[Ta, Tb] ---> Tc, mk_prodT (Ta, Tb)] ---> Tc);
berghofe@5096
   238
berghofe@5096
   239
(*Makes a nested tuple from a list, following the product type structure*)
berghofe@5096
   240
fun mk_tuple (Type ("*", [T1, T2])) tms = 
berghofe@5096
   241
        mk_prod (mk_tuple T1 tms, 
skalberg@15570
   242
                 mk_tuple T2 (Library.drop (length (prodT_factors T1), tms)))
berghofe@5096
   243
  | mk_tuple T (t::_) = t;
wenzelm@4571
   244
wenzelm@5207
   245
wenzelm@5207
   246
wenzelm@9362
   247
(* proper tuples *)
wenzelm@9362
   248
wenzelm@9362
   249
local  (*currently unused*)
wenzelm@9362
   250
skalberg@15574
   251
fun mk_tupleT Ts = foldr mk_prodT unitT Ts;
wenzelm@9362
   252
wenzelm@11604
   253
fun dest_tupleT (Type ("Product_Type.unit", [])) = []
wenzelm@9362
   254
  | dest_tupleT (Type ("*", [T, U])) = T :: dest_tupleT U
wenzelm@9362
   255
  | dest_tupleT T = raise TYPE ("dest_tupleT", [T], []);
wenzelm@9362
   256
skalberg@15574
   257
fun mk_tuple ts = foldr mk_prod unit ts;
wenzelm@9362
   258
wenzelm@11604
   259
fun dest_tuple (Const ("Product_Type.Unity", _)) = []
wenzelm@9362
   260
  | dest_tuple (Const ("Pair", _) $ t $ u) = t :: dest_tuple u
wenzelm@9362
   261
  | dest_tuple t = raise TERM ("dest_tuple", [t]);
wenzelm@9362
   262
wenzelm@9362
   263
in val _ = unit end;
wenzelm@9362
   264
wenzelm@9362
   265
wenzelm@5207
   266
(* nat *)
wenzelm@5207
   267
wenzelm@5207
   268
val natT = Type ("nat", []);
wenzelm@5207
   269
wenzelm@5207
   270
val zero = Const ("0", natT);
wenzelm@5207
   271
wenzelm@5207
   272
fun is_zero (Const ("0", _)) = true
wenzelm@5207
   273
  | is_zero _ = false;
wenzelm@5207
   274
wenzelm@5207
   275
fun mk_Suc t = Const ("Suc", natT --> natT) $ t;
wenzelm@5207
   276
wenzelm@5207
   277
fun dest_Suc (Const ("Suc", _) $ t) = t
wenzelm@5207
   278
  | dest_Suc t = raise TERM ("dest_Suc", [t]);
wenzelm@5207
   279
wenzelm@5207
   280
fun mk_nat 0 = zero
wenzelm@5207
   281
  | mk_nat n = mk_Suc (mk_nat (n - 1));
wenzelm@5207
   282
wenzelm@5207
   283
fun dest_nat (Const ("0", _)) = 0
wenzelm@5207
   284
  | dest_nat (Const ("Suc", _) $ t) = dest_nat t + 1
wenzelm@5207
   285
  | dest_nat t = raise TERM ("dest_nat", [t]);
wenzelm@5207
   286
wenzelm@5207
   287
paulson@7073
   288
(* binary numerals *)
paulson@7073
   289
paulson@7073
   290
val binT = Type ("Numeral.bin", []);
paulson@7073
   291
paulson@15013
   292
val pls_const = Const ("Numeral.Pls", binT)
paulson@15013
   293
and min_const = Const ("Numeral.Min", binT)
paulson@15013
   294
and bit_const = Const ("Numeral.Bit", [binT, boolT] ---> binT);
paulson@8768
   295
paulson@8768
   296
fun number_of_const T = Const ("Numeral.number_of", binT --> T);
paulson@8739
   297
paulson@7073
   298
nipkow@7548
   299
fun int_of [] = 0
nipkow@7548
   300
  | int_of (b :: bs) = b + 2 * int_of bs;
nipkow@7548
   301
obua@15595
   302
fun intinf_of [] = IntInf.fromInt 0
obua@15595
   303
  | intinf_of (b :: bs) = IntInf.+ (IntInf.fromInt b, IntInf.*(IntInf.fromInt 2, intinf_of bs));
obua@15595
   304
nipkow@7548
   305
fun dest_bit (Const ("False", _)) = 0
nipkow@7548
   306
  | dest_bit (Const ("True", _)) = 1
nipkow@7548
   307
  | dest_bit t = raise TERM("dest_bit", [t]);
nipkow@7548
   308
paulson@15013
   309
fun bin_of (Const ("Numeral.Pls", _)) = []
paulson@15013
   310
  | bin_of (Const ("Numeral.Min", _)) = [~1]
paulson@15013
   311
  | bin_of (Const ("Numeral.Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
nipkow@7548
   312
  | bin_of t = raise TERM("bin_of", [t]);
nipkow@7548
   313
nipkow@7548
   314
val dest_binum = int_of o bin_of;
nipkow@7548
   315
nipkow@10693
   316
fun mk_bit 0 = false_const
nipkow@10693
   317
  | mk_bit 1 = true_const
nipkow@10693
   318
  | mk_bit _ = sys_error "mk_bit";
nipkow@10693
   319
nipkow@10693
   320
fun mk_bin n =
nipkow@10693
   321
  let
nipkow@10693
   322
    fun bin_of 0  = []
nipkow@10693
   323
      | bin_of ~1 = [~1]
nipkow@10693
   324
      | bin_of n  = (n mod 2) :: bin_of (n div 2);
nipkow@10693
   325
nipkow@10693
   326
    fun term_of []   = pls_const
nipkow@10693
   327
      | term_of [~1] = min_const
nipkow@10693
   328
      | term_of (b :: bs) = bit_const $ term_of bs $ mk_bit b;
nipkow@10693
   329
    in term_of (bin_of n) end;
nipkow@10693
   330
obua@15595
   331
fun mk_bin_from_intinf  n =
obua@15595
   332
    let
obua@15595
   333
	val zero = IntInf.fromInt 0
obua@15595
   334
	val minus_one = IntInf.fromInt ~1
obua@15595
   335
	val two = IntInf.fromInt 2
obua@15595
   336
obua@15595
   337
	fun mk_bit n = if n = zero then false_const else true_const
obua@15595
   338
								 
obua@15595
   339
	fun bin_of n = 
obua@15595
   340
	    if n = zero then pls_const
obua@15595
   341
	    else if n = minus_one then min_const
obua@15595
   342
	    else 
obua@15595
   343
		let 
obua@15595
   344
		    (*val (q,r) = IntInf.divMod (n, two): doesn't work in SML 10.0.7, but in newer versions!*)
obua@15595
   345
	            val q = IntInf.div (n, two)
obua@15595
   346
		    val r = IntInf.mod (n, two)
obua@15595
   347
		in
obua@15595
   348
		    bit_const $ bin_of q $ mk_bit r
obua@15595
   349
		end
obua@15595
   350
    in 
obua@15595
   351
	bin_of n
obua@15595
   352
    end
berghofe@13755
   353
berghofe@13755
   354
(* int *)
berghofe@13755
   355
berghofe@13755
   356
val intT = Type ("IntDef.int", []);
berghofe@13755
   357
berghofe@14103
   358
fun mk_int 0 = Const ("0", intT)
berghofe@14103
   359
  | mk_int 1 = Const ("1", intT)
berghofe@14103
   360
  | mk_int i = number_of_const intT $ mk_bin i;
berghofe@13755
   361
berghofe@13755
   362
berghofe@13755
   363
(* real *)
berghofe@13755
   364
berghofe@13755
   365
val realT = Type("RealDef.real", []);
berghofe@13755
   366
berghofe@13755
   367
berghofe@13755
   368
(* list *)
berghofe@13755
   369
berghofe@13755
   370
fun mk_list f T [] = Const ("List.list.Nil", Type ("List.list", [T]))
berghofe@13755
   371
  | mk_list f T (x :: xs) = Const ("List.list.Cons",
berghofe@13755
   372
      T --> Type ("List.list", [T]) --> Type ("List.list", [T])) $ f x $
berghofe@13755
   373
        mk_list f T xs;
berghofe@13755
   374
berghofe@15062
   375
fun dest_list (Const ("List.list.Nil", _)) = []
berghofe@15062
   376
  | dest_list (Const ("List.list.Cons", _) $ x $ xs) = x :: dest_list xs
berghofe@15062
   377
  | dest_list t = raise TERM ("dest_list", [t]);
berghofe@15062
   378
clasohm@923
   379
end;