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