src/HOL/Tools/hologic.ML
author wenzelm
Thu May 27 17:41:27 2010 +0200 (2010-05-27)
changeset 37145 01aa36932739
parent 36692 54b64d4ad524
child 37387 3581483cca6c
permissions -rw-r--r--
renamed structure TypeInfer to Type_Infer, keeping the old name as legacy alias for some time;
     1 (*  Title:      HOL/hologic.ML
     2     Author:     Lawrence C Paulson and Markus Wenzel
     3 
     4 Abstract syntax operations for HOL.
     5 *)
     6 
     7 signature HOLOGIC =
     8 sig
     9   val typeS: sort
    10   val typeT: typ
    11   val boolN: string
    12   val boolT: typ
    13   val Trueprop: term
    14   val mk_Trueprop: term -> term
    15   val dest_Trueprop: term -> term
    16   val true_const: term
    17   val false_const: term
    18   val mk_setT: typ -> typ
    19   val dest_setT: typ -> typ
    20   val Collect_const: typ -> term
    21   val mk_Collect: string * typ * term -> term
    22   val mk_mem: term * term -> term
    23   val dest_mem: term -> term * term
    24   val mk_set: typ -> term list -> term
    25   val dest_set: term -> term list
    26   val mk_UNIV: typ -> term
    27   val conj_intr: thm -> thm -> thm
    28   val conj_elim: thm -> thm * thm
    29   val conj_elims: thm -> thm list
    30   val conj: term
    31   val disj: term
    32   val imp: term
    33   val Not: term
    34   val mk_conj: term * term -> term
    35   val mk_disj: term * term -> term
    36   val mk_imp: term * term -> term
    37   val mk_not: term -> term
    38   val dest_conj: term -> term list
    39   val dest_disj: term -> term list
    40   val disjuncts: term -> term list
    41   val dest_imp: term -> term * term
    42   val dest_not: term -> term
    43   val eq_const: typ -> term
    44   val mk_eq: term * term -> term
    45   val dest_eq: term -> term * term
    46   val all_const: typ -> term
    47   val mk_all: string * typ * term -> term
    48   val list_all: (string * typ) list * term -> term
    49   val exists_const: typ -> term
    50   val mk_exists: string * typ * term -> term
    51   val choice_const: typ -> term
    52   val class_eq: string
    53   val mk_binop: string -> term * term -> term
    54   val mk_binrel: string -> term * term -> term
    55   val dest_bin: string -> typ -> term -> term * term
    56   val unitT: typ
    57   val is_unitT: typ -> bool
    58   val unit: term
    59   val is_unit: term -> bool
    60   val mk_prodT: typ * typ -> typ
    61   val dest_prodT: typ -> typ * typ
    62   val pair_const: typ -> typ -> term
    63   val mk_prod: term * term -> term
    64   val dest_prod: term -> term * term
    65   val mk_fst: term -> term
    66   val mk_snd: term -> term
    67   val split_const: typ * typ * typ -> term
    68   val mk_split: term -> term
    69   val flatten_tupleT: typ -> typ list
    70   val mk_tupleT: typ list -> typ
    71   val strip_tupleT: typ -> typ list
    72   val mk_tuple: term list -> term
    73   val strip_tuple: term -> term list
    74   val mk_ptupleT: int list list -> typ list -> typ
    75   val strip_ptupleT: int list list -> typ -> typ list
    76   val flat_tupleT_paths: typ -> int list list
    77   val mk_ptuple: int list list -> typ -> term list -> term
    78   val strip_ptuple: int list list -> term -> term list
    79   val flat_tuple_paths: term -> int list list
    80   val mk_psplits: int list list -> typ -> typ -> term -> term
    81   val strip_psplits: term -> term * typ list * int list list
    82   val natT: typ
    83   val zero: term
    84   val is_zero: term -> bool
    85   val mk_Suc: term -> term
    86   val dest_Suc: term -> term
    87   val Suc_zero: term
    88   val mk_nat: int -> term
    89   val dest_nat: term -> int
    90   val class_size: string
    91   val size_const: typ -> term
    92   val code_numeralT: typ
    93   val intT: typ
    94   val pls_const: term
    95   val min_const: term
    96   val bit0_const: term
    97   val bit1_const: term
    98   val mk_bit: int -> term
    99   val dest_bit: term -> int
   100   val mk_numeral: int -> term
   101   val dest_numeral: term -> int
   102   val number_of_const: typ -> term
   103   val add_numerals: term -> (term * typ) list -> (term * typ) list
   104   val mk_number: typ -> int -> term
   105   val dest_number: term -> typ * int
   106   val realT: typ
   107   val nibbleT: typ
   108   val mk_nibble: int -> term
   109   val dest_nibble: term -> int
   110   val charT: typ
   111   val mk_char: int -> term
   112   val dest_char: term -> int
   113   val listT: typ -> typ
   114   val nil_const: typ -> term
   115   val cons_const: typ -> term
   116   val mk_list: typ -> term list -> term
   117   val dest_list: term -> term list
   118   val stringT: typ
   119   val mk_string: string -> term
   120   val dest_string: term -> string
   121   val literalT: typ
   122   val mk_literal: string -> term
   123   val dest_literal: term -> string
   124   val mk_typerep: typ -> term
   125   val termT: typ
   126   val term_of_const: typ -> term
   127   val mk_term_of: typ -> term -> term
   128   val reflect_term: term -> term
   129   val mk_valtermify_app: string -> (string * typ) list -> typ -> term
   130   val mk_return: typ -> typ -> term -> term
   131   val mk_ST: ((term * typ) * (string * typ) option)  list -> term -> typ -> typ option * typ -> term
   132   val mk_random: typ -> term -> term
   133 end;
   134 
   135 structure HOLogic: HOLOGIC =
   136 struct
   137 
   138 (* HOL syntax *)
   139 
   140 val typeS: sort = ["HOL.type"];
   141 val typeT = Type_Infer.anyT typeS;
   142 
   143 
   144 (* bool and set *)
   145 
   146 val boolN = "bool";
   147 val boolT = Type (boolN, []);
   148 
   149 val true_const =  Const ("True", boolT);
   150 val false_const = Const ("False", boolT);
   151 
   152 fun mk_setT T = T --> boolT;
   153 
   154 fun dest_setT (Type ("fun", [T, Type ("bool", [])])) = T
   155   | dest_setT T = raise TYPE ("dest_setT: set type expected", [T], []);
   156 
   157 fun mk_set T ts =
   158   let
   159     val sT = mk_setT T;
   160     val empty = Const ("Orderings.bot_class.bot", sT);
   161     fun insert t u = Const ("Set.insert", T --> sT --> sT) $ t $ u;
   162   in fold_rev insert ts empty end;
   163 
   164 fun mk_UNIV T = Const ("Orderings.top_class.top", mk_setT T);
   165 
   166 fun dest_set (Const ("Orderings.bot_class.bot", _)) = []
   167   | dest_set (Const ("Set.insert", _) $ t $ u) = t :: dest_set u
   168   | dest_set t = raise TERM ("dest_set", [t]);
   169 
   170 fun Collect_const T = Const ("Collect", (T --> boolT) --> mk_setT T);
   171 fun mk_Collect (a, T, t) = Collect_const T $ absfree (a, T, t);
   172 
   173 fun mk_mem (x, A) =
   174   let val setT = fastype_of A in
   175     Const ("op :", dest_setT setT --> setT --> boolT) $ x $ A
   176   end;
   177 
   178 fun dest_mem (Const ("op :", _) $ x $ A) = (x, A)
   179   | dest_mem t = raise TERM ("dest_mem", [t]);
   180 
   181 
   182 (* logic *)
   183 
   184 val Trueprop = Const ("Trueprop", boolT --> propT);
   185 
   186 fun mk_Trueprop P = Trueprop $ P;
   187 
   188 fun dest_Trueprop (Const ("Trueprop", _) $ P) = P
   189   | dest_Trueprop t = raise TERM ("dest_Trueprop", [t]);
   190 
   191 fun conj_intr thP thQ =
   192   let
   193     val (P, Q) = pairself (Object_Logic.dest_judgment o Thm.cprop_of) (thP, thQ)
   194       handle CTERM (msg, _) => raise THM (msg, 0, [thP, thQ]);
   195     val inst = Thm.instantiate ([], [(@{cpat "?P::bool"}, P), (@{cpat "?Q::bool"}, Q)]);
   196   in Drule.implies_elim_list (inst @{thm conjI}) [thP, thQ] end;
   197 
   198 fun conj_elim thPQ =
   199   let
   200     val (P, Q) = Thm.dest_binop (Object_Logic.dest_judgment (Thm.cprop_of thPQ))
   201       handle CTERM (msg, _) => raise THM (msg, 0, [thPQ]);
   202     val inst = Thm.instantiate ([], [(@{cpat "?P::bool"}, P), (@{cpat "?Q::bool"}, Q)]);
   203     val thP = Thm.implies_elim (inst @{thm conjunct1}) thPQ;
   204     val thQ = Thm.implies_elim (inst @{thm conjunct2}) thPQ;
   205   in (thP, thQ) end;
   206 
   207 fun conj_elims th =
   208   let val (th1, th2) = conj_elim th
   209   in conj_elims th1 @ conj_elims th2 end handle THM _ => [th];
   210 
   211 val conj = @{term "op &"}
   212 and disj = @{term "op |"}
   213 and imp = @{term "op -->"}
   214 and Not = @{term "Not"};
   215 
   216 fun mk_conj (t1, t2) = conj $ t1 $ t2
   217 and mk_disj (t1, t2) = disj $ t1 $ t2
   218 and mk_imp (t1, t2) = imp $ t1 $ t2
   219 and mk_not t = Not $ t;
   220 
   221 fun dest_conj (Const ("op &", _) $ t $ t') = t :: dest_conj t'
   222   | dest_conj t = [t];
   223 
   224 fun dest_disj (Const ("op |", _) $ t $ t') = t :: dest_disj t'
   225   | dest_disj t = [t];
   226 
   227 (*Like dest_disj, but flattens disjunctions however nested*)
   228 fun disjuncts_aux (Const ("op |", _) $ t $ t') disjs = disjuncts_aux t (disjuncts_aux t' disjs)
   229   | disjuncts_aux t disjs = t::disjs;
   230 
   231 fun disjuncts t = disjuncts_aux t [];
   232 
   233 fun dest_imp (Const("op -->",_) $ A $ B) = (A, B)
   234   | dest_imp  t = raise TERM ("dest_imp", [t]);
   235 
   236 fun dest_not (Const ("Not", _) $ t) = t
   237   | dest_not t = raise TERM ("dest_not", [t]);
   238 
   239 fun eq_const T = Const ("op =", [T, T] ---> boolT);
   240 fun mk_eq (t, u) = eq_const (fastype_of t) $ t $ u;
   241 
   242 fun dest_eq (Const ("op =", _) $ lhs $ rhs) = (lhs, rhs)
   243   | dest_eq t = raise TERM ("dest_eq", [t])
   244 
   245 fun all_const T = Const ("All", [T --> boolT] ---> boolT);
   246 fun mk_all (x, T, P) = all_const T $ absfree (x, T, P);
   247 fun list_all (xs, t) = fold_rev (fn (x, T) => fn P => all_const T $ Abs (x, T, P)) xs t;
   248 
   249 fun exists_const T = Const ("Ex", [T --> boolT] ---> boolT);
   250 fun mk_exists (x, T, P) = exists_const T $ absfree (x, T, P);
   251 
   252 fun choice_const T = Const("Hilbert_Choice.Eps", (T --> boolT) --> T);
   253 
   254 val class_eq = "HOL.eq";
   255 
   256 
   257 (* binary operations and relations *)
   258 
   259 fun mk_binop c (t, u) =
   260   let val T = fastype_of t in
   261     Const (c, [T, T] ---> T) $ t $ u
   262   end;
   263 
   264 fun mk_binrel c (t, u) =
   265   let val T = fastype_of t in
   266     Const (c, [T, T] ---> boolT) $ t $ u
   267   end;
   268 
   269 (*destruct the application of a binary operator. The dummyT case is a crude
   270   way of handling polymorphic operators.*)
   271 fun dest_bin c T (tm as Const (c', Type ("fun", [T', _])) $ t $ u) =
   272       if c = c' andalso (T=T' orelse T=dummyT) then (t, u)
   273       else raise TERM ("dest_bin " ^ c, [tm])
   274   | dest_bin c _ tm = raise TERM ("dest_bin " ^ c, [tm]);
   275 
   276 
   277 (* unit *)
   278 
   279 val unitT = Type ("Product_Type.unit", []);
   280 
   281 fun is_unitT (Type ("Product_Type.unit", [])) = true
   282   | is_unitT _ = false;
   283 
   284 val unit = Const ("Product_Type.Unity", unitT);
   285 
   286 fun is_unit (Const ("Product_Type.Unity", _)) = true
   287   | is_unit _ = false;
   288 
   289 
   290 (* prod *)
   291 
   292 fun mk_prodT (T1, T2) = Type ("*", [T1, T2]);
   293 
   294 fun dest_prodT (Type ("*", [T1, T2])) = (T1, T2)
   295   | dest_prodT T = raise TYPE ("dest_prodT", [T], []);
   296 
   297 fun pair_const T1 T2 = Const ("Pair", [T1, T2] ---> mk_prodT (T1, T2));
   298 
   299 fun mk_prod (t1, t2) =
   300   let val T1 = fastype_of t1 and T2 = fastype_of t2 in
   301     pair_const T1 T2 $ t1 $ t2
   302   end;
   303 
   304 fun dest_prod (Const ("Pair", _) $ t1 $ t2) = (t1, t2)
   305   | dest_prod t = raise TERM ("dest_prod", [t]);
   306 
   307 fun mk_fst p =
   308   let val pT = fastype_of p in
   309     Const ("fst", pT --> fst (dest_prodT pT)) $ p
   310   end;
   311 
   312 fun mk_snd p =
   313   let val pT = fastype_of p in
   314     Const ("snd", pT --> snd (dest_prodT pT)) $ p
   315   end;
   316 
   317 fun split_const (A, B, C) =
   318   Const ("split", (A --> B --> C) --> mk_prodT (A, B) --> C);
   319 
   320 fun mk_split t =
   321   (case Term.fastype_of t of
   322     T as (Type ("fun", [A, Type ("fun", [B, C])])) =>
   323       Const ("split", T --> mk_prodT (A, B) --> C) $ t
   324   | _ => raise TERM ("mk_split: bad body type", [t]));
   325 
   326 (*Maps the type T1 * ... * Tn to [T1, ..., Tn], however nested*)
   327 fun flatten_tupleT (Type ("*", [T1, T2])) = flatten_tupleT T1 @ flatten_tupleT T2
   328   | flatten_tupleT T = [T];
   329 
   330 
   331 (* tuples with right-fold structure *)
   332 
   333 fun mk_tupleT [] = unitT
   334   | mk_tupleT Ts = foldr1 mk_prodT Ts;
   335 
   336 fun strip_tupleT (Type ("Product_Type.unit", [])) = []
   337   | strip_tupleT (Type ("*", [T1, T2])) = T1 :: strip_tupleT T2
   338   | strip_tupleT T = [T];
   339 
   340 fun mk_tuple [] = unit
   341   | mk_tuple ts = foldr1 mk_prod ts;
   342 
   343 fun strip_tuple (Const ("Product_Type.Unity", _)) = []
   344   | strip_tuple (Const ("Pair", _) $ t1 $ t2) = t1 :: strip_tuple t2
   345   | strip_tuple t = [t];
   346 
   347 
   348 (* tuples with specific arities
   349 
   350    an "arity" of a tuple is a list of lists of integers,
   351    denoting paths to subterms that are pairs
   352 *)
   353 
   354 fun ptuple_err s = raise TERM (s ^ ": inconsistent use of nested products", []);
   355 
   356 fun mk_ptupleT ps =
   357   let
   358     fun mk p Ts =
   359       if member (op =) ps p then
   360         let
   361           val (T, Ts') = mk (1::p) Ts;
   362           val (U, Ts'') = mk (2::p) Ts'
   363         in (mk_prodT (T, U), Ts'') end
   364       else (hd Ts, tl Ts)
   365   in fst o mk [] end;
   366 
   367 fun strip_ptupleT ps =
   368   let
   369     fun factors p T = if member (op =) ps p then (case T of
   370         Type ("*", [T1, T2]) =>
   371           factors (1::p) T1 @ factors (2::p) T2
   372       | _ => ptuple_err "strip_ptupleT") else [T]
   373   in factors [] end;
   374 
   375 val flat_tupleT_paths =
   376   let
   377     fun factors p (Type ("*", [T1, T2])) =
   378           p :: factors (1::p) T1 @ factors (2::p) T2
   379       | factors p _ = []
   380   in factors [] end;
   381 
   382 fun mk_ptuple ps =
   383   let
   384     fun mk p T ts =
   385       if member (op =) ps p then (case T of
   386           Type ("*", [T1, T2]) =>
   387             let
   388               val (t, ts') = mk (1::p) T1 ts;
   389               val (u, ts'') = mk (2::p) T2 ts'
   390             in (pair_const T1 T2 $ t $ u, ts'') end
   391         | _ => ptuple_err "mk_ptuple")
   392       else (hd ts, tl ts)
   393   in fst oo mk [] end;
   394 
   395 fun strip_ptuple ps =
   396   let
   397     fun dest p t = if member (op =) ps p then (case t of
   398         Const ("Pair", _) $ t $ u =>
   399           dest (1::p) t @ dest (2::p) u
   400       | _ => ptuple_err "strip_ptuple") else [t]
   401   in dest [] end;
   402 
   403 val flat_tuple_paths =
   404   let
   405     fun factors p (Const ("Pair", _) $ t $ u) =
   406           p :: factors (1::p) t @ factors (2::p) u
   407       | factors p _ = []
   408   in factors [] end;
   409 
   410 (*In mk_psplits ps S T u, term u expects separate arguments for the factors of S,
   411   with result type T.  The call creates a new term expecting one argument
   412   of type S.*)
   413 fun mk_psplits ps T T3 u =
   414   let
   415     fun ap ((p, T) :: pTs) =
   416           if member (op =) ps p then (case T of
   417               Type ("*", [T1, T2]) =>
   418                 split_const (T1, T2, map snd pTs ---> T3) $
   419                   ap ((1::p, T1) :: (2::p, T2) :: pTs)
   420             | _ => ptuple_err "mk_psplits")
   421           else Abs ("x", T, ap pTs)
   422       | ap [] =
   423           let val k = length ps
   424           in list_comb (incr_boundvars (k + 1) u, map Bound (k downto 0)) end
   425   in ap [([], T)] end;
   426 
   427 val strip_psplits =
   428   let
   429     fun strip [] qs Ts t = (t, rev Ts, qs)
   430       | strip (p :: ps) qs Ts (Const ("split", _) $ t) =
   431           strip ((1 :: p) :: (2 :: p) :: ps) (p :: qs) Ts t
   432       | strip (p :: ps) qs Ts (Abs (s, T, t)) = strip ps qs (T :: Ts) t
   433       | strip (p :: ps) qs Ts t = strip ps qs
   434           (hd (binder_types (fastype_of1 (Ts, t))) :: Ts)
   435           (incr_boundvars 1 t $ Bound 0)
   436   in strip [[]] [] [] end;
   437 
   438 
   439 (* nat *)
   440 
   441 val natT = Type ("nat", []);
   442 
   443 val zero = Const ("Groups.zero_class.zero", natT);
   444 
   445 fun is_zero (Const ("Groups.zero_class.zero", _)) = true
   446   | is_zero _ = false;
   447 
   448 fun mk_Suc t = Const ("Suc", natT --> natT) $ t;
   449 
   450 fun dest_Suc (Const ("Suc", _) $ t) = t
   451   | dest_Suc t = raise TERM ("dest_Suc", [t]);
   452 
   453 val Suc_zero = mk_Suc zero;
   454 
   455 fun mk_nat n =
   456   let
   457     fun mk 0 = zero
   458       | mk n = mk_Suc (mk (n - 1));
   459   in if n < 0 then raise TERM ("mk_nat: negative number", []) else mk n end;
   460 
   461 fun dest_nat (Const ("Groups.zero_class.zero", _)) = 0
   462   | dest_nat (Const ("Suc", _) $ t) = dest_nat t + 1
   463   | dest_nat t = raise TERM ("dest_nat", [t]);
   464 
   465 val class_size = "Nat.size";
   466 
   467 fun size_const T = Const ("Nat.size_class.size", T --> natT);
   468 
   469 
   470 (* code numeral *)
   471 
   472 val code_numeralT = Type ("Code_Numeral.code_numeral", []);
   473 
   474 
   475 (* binary numerals and int -- non-unique representation due to leading zeros/ones! *)
   476 
   477 val intT = Type ("Int.int", []);
   478 
   479 val pls_const = Const ("Int.Pls", intT)
   480 and min_const = Const ("Int.Min", intT)
   481 and bit0_const = Const ("Int.Bit0", intT --> intT)
   482 and bit1_const = Const ("Int.Bit1", intT --> intT);
   483 
   484 fun mk_bit 0 = bit0_const
   485   | mk_bit 1 = bit1_const
   486   | mk_bit _ = raise TERM ("mk_bit", []);
   487 
   488 fun dest_bit (Const ("Int.Bit0", _)) = 0
   489   | dest_bit (Const ("Int.Bit1", _)) = 1
   490   | dest_bit t = raise TERM ("dest_bit", [t]);
   491 
   492 fun mk_numeral 0 = pls_const
   493   | mk_numeral ~1 = min_const
   494   | mk_numeral i =
   495       let val (q, r) = Integer.div_mod i 2;
   496       in mk_bit r $ mk_numeral q end;
   497 
   498 fun dest_numeral (Const ("Int.Pls", _)) = 0
   499   | dest_numeral (Const ("Int.Min", _)) = ~1
   500   | dest_numeral (Const ("Int.Bit0", _) $ bs) = 2 * dest_numeral bs
   501   | dest_numeral (Const ("Int.Bit1", _) $ bs) = 2 * dest_numeral bs + 1
   502   | dest_numeral t = raise TERM ("dest_numeral", [t]);
   503 
   504 fun number_of_const T = Const ("Int.number_class.number_of", intT --> T);
   505 
   506 fun add_numerals (Const ("Int.number_class.number_of", Type (_, [_, T])) $ t) = cons (t, T)
   507   | add_numerals (t $ u) = add_numerals t #> add_numerals u
   508   | add_numerals (Abs (_, _, t)) = add_numerals t
   509   | add_numerals _ = I;
   510 
   511 fun mk_number T 0 = Const ("Groups.zero_class.zero", T)
   512   | mk_number T 1 = Const ("Groups.one_class.one", T)
   513   | mk_number T i = number_of_const T $ mk_numeral i;
   514 
   515 fun dest_number (Const ("Groups.zero_class.zero", T)) = (T, 0)
   516   | dest_number (Const ("Groups.one_class.one", T)) = (T, 1)
   517   | dest_number (Const ("Int.number_class.number_of", Type ("fun", [_, T])) $ t) =
   518       (T, dest_numeral t)
   519   | dest_number t = raise TERM ("dest_number", [t]);
   520 
   521 
   522 (* real *)
   523 
   524 val realT = Type ("RealDef.real", []);
   525 
   526 
   527 (* list *)
   528 
   529 fun listT T = Type ("List.list", [T]);
   530 
   531 fun nil_const T = Const ("List.list.Nil", listT T);
   532 
   533 fun cons_const T =
   534   let val lT = listT T
   535   in Const ("List.list.Cons", T --> lT --> lT) end;
   536 
   537 fun mk_list T ts =
   538   let
   539     val lT = listT T;
   540     val Nil = Const ("List.list.Nil", lT);
   541     fun Cons t u = Const ("List.list.Cons", T --> lT --> lT) $ t $ u;
   542   in fold_rev Cons ts Nil end;
   543 
   544 fun dest_list (Const ("List.list.Nil", _)) = []
   545   | dest_list (Const ("List.list.Cons", _) $ t $ u) = t :: dest_list u
   546   | dest_list t = raise TERM ("dest_list", [t]);
   547 
   548 
   549 (* nibble *)
   550 
   551 val nibbleT = Type ("String.nibble", []);
   552 
   553 fun mk_nibble n =
   554   let val s =
   555     if 0 <= n andalso n <= 9 then chr (n + ord "0")
   556     else if 10 <= n andalso n <= 15 then chr (n + ord "A" - 10)
   557     else raise TERM ("mk_nibble", [])
   558   in Const ("String.nibble.Nibble" ^ s, nibbleT) end;
   559 
   560 fun dest_nibble t =
   561   let fun err () = raise TERM ("dest_nibble", [t]) in
   562     (case try (unprefix "String.nibble.Nibble" o fst o Term.dest_Const) t of
   563       NONE => err ()
   564     | SOME c =>
   565         if size c <> 1 then err ()
   566         else if "0" <= c andalso c <= "9" then ord c - ord "0"
   567         else if "A" <= c andalso c <= "F" then ord c - ord "A" + 10
   568         else err ())
   569   end;
   570 
   571 
   572 (* char *)
   573 
   574 val charT = Type ("String.char", []);
   575 
   576 fun mk_char n =
   577   if 0 <= n andalso n <= 255 then
   578     Const ("String.char.Char", nibbleT --> nibbleT --> charT) $
   579       mk_nibble (n div 16) $ mk_nibble (n mod 16)
   580   else raise TERM ("mk_char", []);
   581 
   582 fun dest_char (Const ("String.char.Char", _) $ t $ u) =
   583       dest_nibble t * 16 + dest_nibble u
   584   | dest_char t = raise TERM ("dest_char", [t]);
   585 
   586 
   587 (* string *)
   588 
   589 val stringT = listT charT;
   590 
   591 val mk_string = mk_list charT o map (mk_char o ord) o explode;
   592 val dest_string = implode o map (chr o dest_char) o dest_list;
   593 
   594 
   595 (* literal *)
   596 
   597 val literalT = Type ("String.literal", []);
   598 
   599 fun mk_literal s = Const ("String.literal.STR", stringT --> literalT)
   600       $ mk_string s;
   601 fun dest_literal (Const ("String.literal.STR", _) $ t) =
   602       dest_string t
   603   | dest_literal t = raise TERM ("dest_literal", [t]);
   604 
   605 
   606 (* typerep and term *)
   607 
   608 val typerepT = Type ("Typerep.typerep", []);
   609 
   610 fun mk_typerep (Type (tyco, Ts)) = Const ("Typerep.typerep.Typerep",
   611       literalT --> listT typerepT --> typerepT) $ mk_literal tyco
   612         $ mk_list typerepT (map mk_typerep Ts)
   613   | mk_typerep (T as TFree _) = Const ("Typerep.typerep_class.typerep",
   614       Term.itselfT T --> typerepT) $ Logic.mk_type T;
   615 
   616 val termT = Type ("Code_Evaluation.term", []);
   617 
   618 fun term_of_const T = Const ("Code_Evaluation.term_of_class.term_of", T --> termT);
   619 
   620 fun mk_term_of T t = term_of_const T $ t;
   621 
   622 fun reflect_term (Const (c, T)) =
   623       Const ("Code_Evaluation.Const", literalT --> typerepT --> termT)
   624         $ mk_literal c $ mk_typerep T
   625   | reflect_term (t1 $ t2) =
   626       Const ("Code_Evaluation.App", termT --> termT --> termT)
   627         $ reflect_term t1 $ reflect_term t2
   628   | reflect_term (Abs (v, _, t)) = Abs (v, termT, reflect_term t)
   629   | reflect_term t = t;
   630 
   631 fun mk_valtermify_app c vs T =
   632   let
   633     fun termifyT T = mk_prodT (T, unitT --> termT);
   634     fun valapp T T' = Const ("Code_Evaluation.valapp",
   635       termifyT (T --> T') --> termifyT T --> termifyT T');
   636     fun mk_fTs [] _ = []
   637       | mk_fTs (_ :: Ts) T = (Ts ---> T) :: mk_fTs Ts T;
   638     val Ts = map snd vs;
   639     val t = Const (c, Ts ---> T);
   640     val tt = mk_prod (t, Abs ("u", unitT, reflect_term t));
   641     fun app (fT, (v, T)) t = valapp T fT $ t $ Free (v, termifyT T);
   642   in fold app (mk_fTs Ts T ~~ vs) tt end;
   643 
   644 
   645 (* open state monads *)
   646 
   647 fun mk_return T U x = pair_const T U $ x;
   648 
   649 fun mk_ST clauses t U (someT, V) =
   650   let
   651     val R = case someT of SOME T => mk_prodT (T, V) | NONE => V
   652     fun mk_clause ((t, U), SOME (v, T)) (t', U') =
   653           (Const ("Product_Type.scomp", (U --> mk_prodT (T, U')) --> (T --> U' --> R) --> U --> R)
   654             $ t $ lambda (Free (v, T)) t', U)
   655       | mk_clause ((t, U), NONE) (t', U') =
   656           (Const ("Product_Type.fcomp", (U --> U') --> (U' --> R) --> U --> R)
   657             $ t $ t', U)
   658   in fold_rev mk_clause clauses (t, U) |> fst end;
   659 
   660 val code_numeralT = Type ("Code_Numeral.code_numeral", []);
   661 val random_seedT = mk_prodT (code_numeralT, code_numeralT);
   662 
   663 fun mk_random T t = Const ("Quickcheck.random_class.random", code_numeralT
   664   --> random_seedT --> mk_prodT (mk_prodT (T, unitT --> termT), random_seedT)) $ t;
   665 
   666 end;