src/HOL/hologic.ML
author paulson
Tue Jun 28 15:27:45 2005 +0200 (2005-06-28)
changeset 16587 b34c8aa657a5
parent 15965 f422f8283491
child 16835 2e7d7ec7a268
permissions -rw-r--r--
Constant "If" is now local
     1 (*  Title:      HOL/hologic.ML
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson and Markus Wenzel
     4 
     5 Abstract syntax operations for HOL.
     6 *)
     7 
     8 signature HOLOGIC =
     9 sig
    10   val typeS: sort
    11   val typeT: typ
    12   val read_cterm: Sign.sg -> string -> cterm
    13   val boolN: string
    14   val boolT: typ
    15   val false_const: term
    16   val true_const: term
    17   val not_const: term
    18   val mk_setT: typ -> typ
    19   val dest_setT: typ -> typ
    20   val Trueprop: term
    21   val mk_Trueprop: term -> term
    22   val dest_Trueprop: term -> term
    23   val conj: term
    24   val disj: term
    25   val imp: term
    26   val Not: term
    27   val mk_conj: term * term -> term
    28   val mk_disj: term * term -> term
    29   val mk_imp: term * term -> term
    30   val dest_conj: term -> term list
    31   val dest_disj: term -> term list
    32   val dest_imp: term -> term * term
    33   val dest_not: term -> term
    34   val dest_concls: term -> term list
    35   val eq_const: typ -> term
    36   val all_const: typ -> term
    37   val exists_const: typ -> term
    38   val choice_const: typ -> term
    39   val Collect_const: typ -> term
    40   val mk_eq: term * term -> term
    41   val dest_eq: term -> term * term
    42   val mk_all: string * typ * term -> term
    43   val list_all: (string * typ) list * term -> term
    44   val mk_exists: string * typ * term -> term
    45   val mk_Collect: string * typ * term -> term
    46   val mk_mem: term * term -> term
    47   val dest_mem: term -> term * term
    48   val mk_UNIV: typ -> term
    49   val mk_binop: string -> term * term -> term
    50   val mk_binrel: string -> term * term -> term
    51   val dest_bin: string -> typ -> term -> term * term
    52   val unitT: typ
    53   val is_unitT: typ -> bool
    54   val unit: term
    55   val is_unit: term -> bool
    56   val mk_prodT: typ * typ -> typ
    57   val dest_prodT: typ -> typ * typ
    58   val pair_const: typ -> typ -> term
    59   val mk_prod: term * term -> term
    60   val dest_prod: term -> term * term
    61   val mk_fst: term -> term
    62   val mk_snd: term -> term
    63   val prodT_factors: typ -> typ list
    64   val split_const: typ * typ * typ -> term
    65   val mk_tuple: typ -> term list -> term
    66   val natT: typ
    67   val zero: term
    68   val is_zero: term -> bool
    69   val mk_Suc: term -> term
    70   val dest_Suc: term -> term
    71   val mk_nat: int -> term
    72   val dest_nat: term -> int
    73   val intT: typ
    74   val mk_int: IntInf.int -> term
    75   val realT: typ
    76   val bitT: typ
    77   val B0_const: term
    78   val B1_const: term
    79   val binT: typ
    80   val pls_const: term
    81   val min_const: term
    82   val bit_const: term
    83   val number_of_const: typ -> term
    84   val int_of: int list -> IntInf.int 
    85   val dest_binum: term -> IntInf.int
    86   val mk_bin: IntInf.int -> term
    87   val bin_of : term -> int list
    88   val mk_list: ('a -> term) -> typ -> 'a list -> term
    89   val dest_list: term -> term list
    90 end;
    91 
    92 
    93 structure HOLogic: HOLOGIC =
    94 struct
    95 
    96 (* HOL syntax *)
    97 
    98 val typeS: sort = ["HOL.type"];
    99 val typeT = TypeInfer.anyT typeS;
   100 
   101 fun read_cterm sg s = Thm.read_cterm sg (s, typeT);
   102 
   103 
   104 (* bool and set *)
   105 
   106 val boolN = "bool";
   107 val boolT = Type (boolN, []);
   108 
   109 val true_const =  Const ("True", boolT);
   110 val false_const = Const ("False", boolT);
   111 val not_const = Const ("Not", boolT --> boolT);
   112 
   113 fun mk_setT T = Type ("set", [T]);
   114 
   115 fun dest_setT (Type ("set", [T])) = T
   116   | dest_setT T = raise TYPE ("dest_setT: set type expected", [T], []);
   117 
   118 
   119 (* logic *)
   120 
   121 val Trueprop = Const ("Trueprop", boolT --> propT);
   122 
   123 fun mk_Trueprop P = Trueprop $ P;
   124 
   125 fun dest_Trueprop (Const ("Trueprop", _) $ P) = P
   126   | dest_Trueprop t = raise TERM ("dest_Trueprop", [t]);
   127 
   128 
   129 val conj = Const ("op &", [boolT, boolT] ---> boolT)
   130 and disj = Const ("op |", [boolT, boolT] ---> boolT)
   131 and imp = Const ("op -->", [boolT, boolT] ---> boolT)
   132 and Not = Const ("Not", boolT --> boolT);
   133 
   134 fun mk_conj (t1, t2) = conj $ t1 $ t2
   135 and mk_disj (t1, t2) = disj $ t1 $ t2
   136 and mk_imp (t1, t2) = imp $ t1 $ t2;
   137 
   138 fun dest_conj (Const ("op &", _) $ t $ t') = t :: dest_conj t'
   139   | dest_conj t = [t];
   140 
   141 fun dest_disj (Const ("op |", _) $ t $ t') = t :: dest_disj t'
   142   | dest_disj t = [t];
   143 
   144 fun dest_imp (Const("op -->",_) $ A $ B) = (A, B)
   145   | dest_imp  t = raise TERM ("dest_imp", [t]);
   146 
   147 fun dest_not (Const ("Not", _) $ t) = t
   148   | dest_not t = raise TERM ("dest_not", [t]);
   149 
   150 fun imp_concl_of t = imp_concl_of (#2 (dest_imp t)) handle TERM _ => t;
   151 val dest_concls = map imp_concl_of o dest_conj o dest_Trueprop;
   152 
   153 fun eq_const T = Const ("op =", [T, T] ---> boolT);
   154 fun mk_eq (t, u) = eq_const (fastype_of t) $ t $ u;
   155 
   156 fun dest_eq (Const ("op =", _) $ lhs $ rhs) = (lhs, rhs)
   157   | dest_eq t = raise TERM ("dest_eq", [t])
   158 
   159 fun all_const T = Const ("All", [T --> boolT] ---> boolT);
   160 fun mk_all (x, T, P) = all_const T $ absfree (x, T, P);
   161 fun list_all (vs,x) = foldr (fn ((x, T), P) => all_const T $ Abs (x, T, P)) x vs;
   162 
   163 fun exists_const T = Const ("Ex", [T --> boolT] ---> boolT);
   164 fun mk_exists (x, T, P) = exists_const T $ absfree (x, T, P);
   165 
   166 fun choice_const T = Const("Hilbert_Choice.Eps", (T --> boolT) --> T)
   167 
   168 fun Collect_const T = Const ("Collect", [T --> boolT] ---> mk_setT T);
   169 fun mk_Collect (a, T, t) = Collect_const T $ absfree (a, T, t);
   170 
   171 fun mk_mem (x, A) =
   172   let val setT = fastype_of A in
   173     Const ("op :", [dest_setT setT, setT] ---> boolT) $ x $ A
   174   end;
   175 
   176 fun dest_mem (Const ("op :", _) $ x $ A) = (x, A)
   177   | dest_mem t = raise TERM ("dest_mem", [t]);
   178 
   179 fun mk_UNIV T = Const ("UNIV", mk_setT T);
   180 
   181 
   182 (* binary operations and relations *)
   183 
   184 fun mk_binop c (t, u) =
   185   let val T = fastype_of t in
   186     Const (c, [T, T] ---> T) $ t $ u
   187   end;
   188 
   189 fun mk_binrel c (t, u) =
   190   let val T = fastype_of t in
   191     Const (c, [T, T] ---> boolT) $ t $ u
   192   end;
   193 
   194 (*destruct the application of a binary operator. The dummyT case is a crude
   195   way of handling polymorphic operators.*)
   196 fun dest_bin c T (tm as Const (c', Type ("fun", [T', _])) $ t $ u) =
   197       if c = c' andalso (T=T' orelse T=dummyT) then (t, u)
   198       else raise TERM ("dest_bin " ^ c, [tm])
   199   | dest_bin c _ tm = raise TERM ("dest_bin " ^ c, [tm]);
   200 
   201 
   202 (* unit *)
   203 
   204 val unitT = Type ("Product_Type.unit", []);
   205 
   206 fun is_unitT (Type ("Product_Type.unit", [])) = true
   207   | is_unitT _ = false;
   208 
   209 val unit = Const ("Product_Type.Unity", unitT);
   210 
   211 fun is_unit (Const ("Product_Type.Unity", _)) = true
   212   | is_unit _ = false;
   213 
   214 
   215 (* prod *)
   216 
   217 fun mk_prodT (T1, T2) = Type ("*", [T1, T2]);
   218 
   219 fun dest_prodT (Type ("*", [T1, T2])) = (T1, T2)
   220   | dest_prodT T = raise TYPE ("dest_prodT", [T], []);
   221 
   222 fun pair_const T1 T2 = Const ("Pair", [T1, T2] ---> mk_prodT (T1, T2));
   223 
   224 fun mk_prod (t1, t2) =
   225   let val T1 = fastype_of t1 and T2 = fastype_of t2 in
   226     pair_const T1 T2 $ t1 $ t2
   227   end;
   228 
   229 fun dest_prod (Const ("Pair", _) $ t1 $ t2) = (t1, t2)
   230   | dest_prod t = raise TERM ("dest_prod", [t]);
   231 
   232 fun mk_fst p =
   233   let val pT = fastype_of p in
   234     Const ("fst", pT --> fst (dest_prodT pT)) $ p
   235   end;
   236 
   237 fun mk_snd p =
   238   let val pT = fastype_of p in
   239     Const ("snd", pT --> snd (dest_prodT pT)) $ p
   240   end;
   241 
   242 (*Maps the type T1 * ... * Tn to [T1, ..., Tn], however nested*)
   243 fun prodT_factors (Type ("*", [T1, T2])) = prodT_factors T1 @ prodT_factors T2
   244   | prodT_factors T = [T];
   245 
   246 fun split_const (Ta, Tb, Tc) = 
   247     Const ("split", [[Ta, Tb] ---> Tc, mk_prodT (Ta, Tb)] ---> Tc);
   248 
   249 (*Makes a nested tuple from a list, following the product type structure*)
   250 fun mk_tuple (Type ("*", [T1, T2])) tms = 
   251         mk_prod (mk_tuple T1 tms, 
   252                  mk_tuple T2 (Library.drop (length (prodT_factors T1), tms)))
   253   | mk_tuple T (t::_) = t;
   254 
   255 
   256 
   257 (* proper tuples *)
   258 
   259 local  (*currently unused*)
   260 
   261 fun mk_tupleT Ts = foldr mk_prodT unitT Ts;
   262 
   263 fun dest_tupleT (Type ("Product_Type.unit", [])) = []
   264   | dest_tupleT (Type ("*", [T, U])) = T :: dest_tupleT U
   265   | dest_tupleT T = raise TYPE ("dest_tupleT", [T], []);
   266 
   267 fun mk_tuple ts = foldr mk_prod unit ts;
   268 
   269 fun dest_tuple (Const ("Product_Type.Unity", _)) = []
   270   | dest_tuple (Const ("Pair", _) $ t $ u) = t :: dest_tuple u
   271   | dest_tuple t = raise TERM ("dest_tuple", [t]);
   272 
   273 in val _ = unit end;
   274 
   275 
   276 (* nat *)
   277 
   278 val natT = Type ("nat", []);
   279 
   280 val zero = Const ("0", natT);
   281 
   282 fun is_zero (Const ("0", _)) = true
   283   | is_zero _ = false;
   284 
   285 fun mk_Suc t = Const ("Suc", natT --> natT) $ t;
   286 
   287 fun dest_Suc (Const ("Suc", _) $ t) = t
   288   | dest_Suc t = raise TERM ("dest_Suc", [t]);
   289 
   290 fun mk_nat 0 = zero
   291   | mk_nat n = mk_Suc (mk_nat (n - 1));
   292 
   293 fun dest_nat (Const ("0", _)) = 0
   294   | dest_nat (Const ("Suc", _) $ t) = dest_nat t + 1
   295   | dest_nat t = raise TERM ("dest_nat", [t]);
   296 
   297 
   298 (* binary numerals *)
   299 
   300 val binT = Type ("Numeral.bin", []);
   301 
   302 val bitT = Type ("Numeral.bit", []);
   303 
   304 val B0_const = Const ("Numeral.bit.B0", bitT);
   305 val B1_const =  Const ("Numeral.bit.B1", bitT);
   306 
   307 val pls_const = Const ("Numeral.Pls", binT)
   308 and min_const = Const ("Numeral.Min", binT)
   309 and bit_const = Const ("Numeral.Bit", [binT, bitT] ---> binT);
   310 
   311 fun number_of_const T = Const ("Numeral.number_of", binT --> T);
   312 
   313 fun int_of [] = 0 
   314   | int_of (b :: bs) = IntInf.fromInt b + (2 * int_of bs);
   315 
   316 (*When called from a print translation, the Numeral qualifier will probably have
   317   been removed from Bit, bin.B0, etc.*)
   318 fun dest_bit (Const ("Numeral.bit.B0", _)) = 0
   319   | dest_bit (Const ("Numeral.bit.B1", _)) = 1
   320   | dest_bit (Const ("bit.B0", _)) = 0
   321   | dest_bit (Const ("bit.B1", _)) = 1
   322   | dest_bit t = raise TERM("dest_bit", [t]);
   323 
   324 fun bin_of (Const ("Numeral.Pls", _)) = []
   325   | bin_of (Const ("Numeral.Min", _)) = [~1]
   326   | bin_of (Const ("Numeral.Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
   327   | bin_of (Const ("Bit", _) $ bs $ b) = dest_bit b :: bin_of bs
   328   | bin_of t = raise TERM("bin_of", [t]);
   329 
   330 val dest_binum = int_of o bin_of;
   331 
   332 fun mk_bit 0 = B0_const
   333   | mk_bit 1 = B1_const
   334   | mk_bit _ = sys_error "mk_bit";
   335 
   336 fun mk_bin  n =
   337     let
   338 	fun mk_bit n = if n = 0 then B0_const else B1_const
   339 								 
   340 	fun bin_of n = 
   341 	    if n = 0 then pls_const
   342 	    else if n = ~1 then min_const
   343 	    else 
   344 		let 
   345 		    (*val (q,r) = IntInf.divMod (n, 2): doesn't work in SML 10.0.7, but in newer versions!  FIXME: put this back after new SML released!*)
   346 	            val q = IntInf.div (n, 2)
   347 		    val r = IntInf.mod (n, 2)
   348 		in
   349 		    bit_const $ bin_of q $ mk_bit r
   350 		end
   351     in 
   352 	bin_of n
   353     end
   354 
   355 
   356 (* int *)
   357 
   358 val intT = Type ("IntDef.int", []);
   359 
   360 fun mk_int 0 = Const ("0", intT)
   361   | mk_int 1 = Const ("1", intT)
   362   | mk_int i = number_of_const intT $ mk_bin i;
   363 
   364 
   365 (* real *)
   366 
   367 val realT = Type("RealDef.real", []);
   368 
   369 
   370 (* list *)
   371 
   372 fun mk_list f T [] = Const ("List.list.Nil", Type ("List.list", [T]))
   373   | mk_list f T (x :: xs) = Const ("List.list.Cons",
   374       T --> Type ("List.list", [T]) --> Type ("List.list", [T])) $ f x $
   375         mk_list f T xs;
   376 
   377 fun dest_list (Const ("List.list.Nil", _)) = []
   378   | dest_list (Const ("List.list.Cons", _) $ x $ xs) = x :: dest_list xs
   379   | dest_list t = raise TERM ("dest_list", [t]);
   380 
   381 end;