(* extends Isabelle/src/Pure/term.ML

    (c) Walther Neuper 1999

 use"Scripts/term_G.sml";

 use"term_G.sml";

 *)

 (*

 > (cterm_of thy) a_term;

 val it = "empty" : cterm        *)

 (*2003 fun match thy t pat =

     (snd (Pattern.match (Sign.tsig_of (sign_of thy)) (pat, t)))

     handle _ => [];

 fn : theory ->

      Term.term -> Term.term -> (Term.indexname * Term.term) list*)

 (*see src/Tools/eqsubst.ML fun clean_match*)

 (*2003 fun matches thy tm pa = if match thy tm pa = [] then false else true;*)

 fun matches thy tm pa = 

     (Pattern.match thy (pa, tm) (Vartab.empty, Vartab.empty); true)

     handle _ => false

 fun atomtyp t = (*see raw_pp_typ*)

   let

     fun ato n (Type (s,[])) = 

       ("\n*** "^indent n^"Type ("^s^",[])")

       | ato n (Type (s,Ts)) =

       ("\n*** "^indent n^"Type ("^s^",["^ atol (n+1) Ts)

       | ato n (TFree (s,sort)) =

       ("\n*** "^indent n^"TFree ("^s^",["^ strs2str' sort)

       | ato n (TVar ((s,i),sort)) =

       ("\n*** "^indent n^"TVar (("^s^","^ 

        string_of_int i ^ strs2str' sort)

     and atol n [] = 

       ("\n*** "^indent n^"]")

       | atol n (T::Ts) = (ato n T ^ atol n Ts)

 (*in print (ato 0 t ^ "\n") end;  TODO TUM10*)

 in writeln(ato 0 t) end;

 (*Prog.Tutorial.p.34*)

 local

    fun pp_pair (x, y) = Pretty.list "(" ")" [x, y]

    fun pp_list xs = Pretty.list "[" "]" xs

    fun pp_str s   = Pretty.str s

    fun pp_qstr s = Pretty.quote (pp_str s)

    fun pp_int i   = pp_str (string_of_int i)

    fun pp_sort S = pp_list (map pp_qstr S)

    fun pp_constr a args = Pretty.block [pp_str a, Pretty.brk 1, args]

 in

 fun raw_pp_typ (TVar ((a, i), S)) =

        pp_constr "TVar" (pp_pair (pp_pair (pp_qstr a, pp_int i), pp_sort S))

    | raw_pp_typ (TFree (a, S)) =

        pp_constr "TFree" (pp_pair (pp_qstr a, pp_sort S))

    | raw_pp_typ (Type (a, tys)) =

        pp_constr "Type" (pp_pair (pp_qstr a, pp_list (map raw_pp_typ tys)))

 end

 (* install

 PolyML.addPrettyPrinter

   (fn _ => fn _ => ml_pretty o Pretty.to_ML o raw_pp_typ);

 de-install

 PolyML.addPrettyPrinter

   (fn _ => fn _ => ml_pretty o Pretty.to_ML o Proof_Display.pp_typ Pure.thy);

 *)

 (*

 > val T = (type_of o term_of o the o (parse thy)) "a::[real,int] => nat";

 > atomtyp T;

 *** Type (fun,[

 ***   Type (RealDef.real,[])

 ***   Type (fun,[

 ***     Type (IntDef.int,[])

 ***     Type (nat,[])

 ***     ]

 ***   ]

 *)

 fun atomt t =

     let fun ato (Const(a,T))     n = 

 	("\n*** "^indent n^"Const ("^a^")")

 	  | ato (Free (a,T))     n =  

 	("\n*** "^indent n^"Free ("^a^", "^")")

 	  | ato (Var ((a,ix),T)) n =

 	("\n*** "^indent n^"Var (("^a^", "^(string_of_int ix)^"), "^")")

 	  | ato (Bound ix)       n = 

 	("\n*** "^indent n^"Bound "^(string_of_int ix))

 	  | ato (Abs(a,T,body))  n = 

 	("\n*** "^indent n^"Abs("^a^",..")^ato body (n+1)

 	  | ato (f$t')           n = (ato f n; ato t' (n+1))

     in writeln("\n*** -------------"^ ato t 0 ^"\n***") end;

 fun term_detail2str t =

     let fun ato (Const (a, T))     n = 

 	    "\n*** "^indent n^"Const ("^a^", "^string_of_typ T^")"

 	  | ato (Free (a, T))     n =  

 	    "\n*** "^indent n^"Free ("^a^", "^string_of_typ T^")"

 	  | ato (Var ((a, ix), T)) n =

 	    "\n*** "^indent n^"Var (("^a^", "^string_of_int ix^"), "^

 	    string_of_typ T^")"

 	  | ato (Bound ix)       n = 

 	    "\n*** "^indent n^"Bound "^string_of_int ix

 	  | ato (Abs(a, T, body))  n = 

 	    "\n*** "^indent n^"Abs ("^a^", "^

 	       (string_of_typ T)^",.."

 	    ^ato body (n + 1)

 	  | ato (f $ t')           n = ato f n^ato t' (n+1)

     in "\n*** "^ato t 0^"\n***" end;

 fun atomty t = (writeln o term_detail2str) t;

 fun term_str thy (Const(s,_)) = s

   | term_str thy (Free(s,_)) = s

   | term_str thy (Var((s,i),_)) = s^(string_of_int i)

   | term_str thy (Bound i) = "B."^(string_of_int i)

   | term_str thy (Abs(s,_,_)) = s

   | term_str thy t = raise error("term_str not for "^term2str t);

 (*.contains the fst argument the second argument (a leave! of term).*)

 fun contains_term (Abs(_,_,body)) t = contains_term body t 

   | contains_term (f $ f') t = 

     contains_term f t orelse contains_term f' t

   | contains_term s t = t = s;

 (*.contains the term a VAR(("*",_),_) ?.*)

 fun contains_Var (Abs(_,_,body)) = contains_Var body

   | contains_Var (f $ f') = contains_Var f orelse contains_Var f'

   | contains_Var (Var _) = true

   | contains_Var _ = false;

 (* contains_Var (str2term "?z = 3") (*true*);

    contains_Var (str2term "z = 3")  (*false*);

    *)

 (*fun int_of_str str =

     let val ss = explode str

 	val str' = case ss of

 	   "("::s => drop_last s | _ => ss

     in case BasisLibrary.Int.fromString (implode str') of

 	     SOME i => SOME i

 	   | NONE => NONE end;*)

 fun int_of_str str =

     let val ss = explode str

 	val str' = case ss of

 	   "("::s => drop_last s | _ => ss

     in (SOME (Thy_Output.integer (implode str'))) handle _ => NONE end;

 (*

 > int_of_str "123";

 val it = SOME 123 : int option

 > int_of_str "(-123)";

 val it = SOME 123 : int option

 > int_of_str "#123";

 val it = NONE : int option

 > int_of_str "-123";

 val it = SOME ~123 : int option

 *)

 fun int_of_str' str = 

     case int_of_str str of

 	SOME i => i

       | NONE => raise TERM ("int_of_string: no int-string",[]);

 val str2int = int_of_str';

 fun is_numeral str = case int_of_str str of

 			 SOME _ => true

 		       | NONE => false;

 val is_no = is_numeral;

 fun is_num (Free (s,_)) = if is_numeral s then true else false

   | is_num _ = false;

 (*>

 > is_num ((term_of o the o (parse thy)) "#1");

 val it = true : bool

 > is_num ((term_of o the o (parse thy)) "#-1");

 val it = true : bool

 > is_num ((term_of o the o (parse thy)) "a123");

 val it = false : bool

 *)

 (*fun int_of_Free (Free (intstr, _)) =

     (case BasisLibrary.Int.fromString intstr of

 	     SOME i => i

 	   | NONE => raise error ("int_of_Free ( "^ intstr ^", _)"))

   | int_of_Free t = raise error ("int_of_Free ( "^ term2str t ^" )");*)

 fun int_of_Free (Free (intstr, _)) = (Thy_Output.integer intstr

     handle _ => raise error ("int_of_Free ( "^ intstr ^", _)"))

   | int_of_Free t = raise error ("int_of_Free ( "^ term2str t ^" )");

 fun vars t =

   let

     fun scan vs (Const(s,T)) = vs

       | scan vs (t as Free(s,T)) = if is_no s then vs else t::vs

       | scan vs (t as Var((s,i),T)) = t::vs

       | scan vs (Bound i) = vs 

       | scan vs (Abs(s,T,t)) = scan vs t

       | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)

   in (distinct o (scan [])) t end;

 fun is_Free (Free _) = true

   | is_Free _ = false;

 fun is_fun_id (Const _) = true

   | is_fun_id (Free _) = true

   | is_fun_id _ = false;

 fun is_f_x (f $ x) = is_fun_id f andalso is_Free x

   | is_f_x _ = false;

 (* is_f_x (str2term "q_0/2 * L * x") (*false*);

    is_f_x (str2term "M_b x") (*true*);

   *)

 fun vars_str t =

   let

     fun scan vs (Const(s,T)) = vs

       | scan vs (t as Free(s,T)) = if is_no s then vs else s::vs

       | scan vs (t as Var((s,i),T)) = (s^"_"^(string_of_int i))::vs

       | scan vs (Bound i) = vs 

       | scan vs (Abs(s,T,t)) = scan vs t

       | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)

   in (distinct o (scan [])) t end;

 fun ids2str t =

   let

     fun scan vs (Const(s,T)) = if is_no s then vs else s::vs

       | scan vs (t as Free(s,T)) = if is_no s then vs else s::vs

       | scan vs (t as Var((s,i),T)) = (s^"_"^(string_of_int i))::vs

       | scan vs (Bound i) = vs 

       | scan vs (Abs(s,T,t)) = scan (s::vs) t

       | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)

   in (distinct o (scan [])) t end;

 fun is_bdv str =

     case explode str of

 	"b"::"d"::"v"::_ => true

       | _ => false;

 fun is_bdv_ (Free (s,_)) = is_bdv s

   | is_bdv_ _ = false;

 fun free2str (Free (s,_)) = s

   | free2str t = raise error ("free2str not for "^ term2str t);

 fun free2int (t as Free (s, _)) = ((str2int s)

     handle _ => raise error ("free2int: "^term_detail2str t))

   | free2int t = raise error ("free2int: "^term_detail2str t);

 (*27.8.01: unused*)

 fun var2free (t as Const(s,T)) = t

   | var2free (t as Free(s,T)) = t

   | var2free (Var((s,i),T)) = Free(s,T)

   | var2free (t as Bound i) = t 

   | var2free (Abs(s,T,t)) = Abs(s,T,var2free t)

   | var2free (t1 $ t2) = (var2free t1) $ (var2free t2);

 (*27.8.01: doesn't find some subterm ???!???*)

 (*2010 Logic.varify !!!*)

 fun free2var (t as Const(s,T)) = t

   | free2var (t as Free(s,T)) = if is_no s then t else Var((s,0),T)

   | free2var (t as Var((s,i),T)) = t

   | free2var (t as Bound i) = t 

   | free2var (Abs(s,T,t)) = Abs(s,T,free2var t)

   | free2var (t1 $ t2) = (free2var t1) $ (free2var t2);

 fun mk_listT T = Type ("List.list", [T]);

 fun list_const T = 

   Const("List.list.Cons", [T, mk_listT T] ---> mk_listT T);

 (*28.8.01: TODO: get type from head of list: 1 arg less!!!*)

 fun list2isalist T [] = Const("List.list.Nil",mk_listT T)

   | list2isalist T (t::ts) = (list_const T) $ t $ (list2isalist T ts);

 (*

 > val tt = (term_of o the o (parse thy)) "R=(R::real)";

 > val TT = type_of tt;

 > val ss = list2isalist TT [tt,tt,tt];

 > (cterm_of thy) ss;

 val it = "[R = R, R = R, R = R]" : cterm  *)

 fun isapair2pair (Const ("Pair",_) $ a $ b) = (a,b)

   | isapair2pair t = 

     raise error ("isapair2pair called with "^term2str t);

 val listType = Type ("List.list",[Type ("bool",[])]);

 fun isalist2list ls =

   let

     fun get es (Const("List.list.Cons",_) $ t $ ls) = get (t::es) ls

       | get es (Const("List.list.Nil",_)) = es

       | get _ t = 

 	raise error ("isalist2list applied to NON-list '"^term2str t^"'")

   in (rev o (get [])) ls end;

 (*      

 > val il = str2term "[a=b,c=d,e=f]";

 > val l = isalist2list il;

 > (writeln o terms2str) l;

 ["a = b","c = d","e = f"]

 > val il = str2term "ss___::bool list";

 > val l = isalist2list il;

 [Free ("ss___", "bool List.list")]

 *)

 (*review Isabelle2009/src/HOL/Tools/hologic.ML*)

 val prop = Type ("prop",[]);     (* ~/Diss.99/Integers-Isa/tools.sml*)

 val bool = Type ("bool",[]);     (* 2002 Integ.int *)

 val Trueprop = Const("Trueprop",bool-->prop);

 fun mk_prop t = Trueprop $ t;

 val true_as_term = Const("True",bool);

 val false_as_term = Const("False",bool);

 val true_as_cterm = cterm_of (theory "HOL") true_as_term;

 val false_as_cterm = cterm_of (theory "HOL") false_as_term;

 infixr 5 -->;                    (*2002 /Pure/term.ML *)

 infixr --->;			 (*2002 /Pure/term.ML *)

 fun S --> T = Type("fun",[S,T]); (*2002 /Pure/term.ML *)

 val op ---> = foldr (op -->);    (*2002 /Pure/term.ML *)

 fun list_implies ([], B) = B : term (*2002 /term.ML *)

   | list_implies (A::AS, B) = Logic.implies $ A $ list_implies(AS,B);

 (** substitution **)

 fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =      (* = thm.ML *)

       match_bvs(s, t, if x="" orelse y="" then al

                                           else (x,y)::al)

   | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))

   | match_bvs(_,_,al) = al;

 fun ren_inst(insts,prop,pat,obj) =              (* = thm.ML *)

   let val ren = match_bvs(pat,obj,[])

       fun renAbs(Abs(x,T,b)) =

             Abs(case assoc_string(ren,x) of NONE => x 

 	  | SOME(y) => y, T, renAbs(b))

         | renAbs(f$t) = renAbs(f) $ renAbs(t)

         | renAbs(t) = t

   in subst_vars insts (if null(ren) then prop else renAbs(prop)) end;

 fun dest_equals' (Const("op =",_) $ t $ u)  =  (t,u)(* logic.ML: Const("=="*)

   | dest_equals' t = raise TERM("dest_equals'", [t]);

 val lhs_ = (fst o dest_equals');

 val rhs_ = (snd o dest_equals');

 fun is_equality (Const("op =",_) $ t $ u)  =  true  (* logic.ML: Const("=="*)

   | is_equality _ = false;

 fun mk_equality (t,u) = (Const("op =",[type_of t,type_of u]--->bool) $ t $ u); 

 fun is_expliceq (Const("op =",_) $ (Free _) $ u)  =  true

   | is_expliceq _ = false;

 fun strip_trueprop (Const("Trueprop",_) $ t) = t

   | strip_trueprop t = t;

 (*  | strip_trueprop t = raise TERM("strip_trueprop", [t]);

 *)

 (*.(A1==>...An==>B) goes to (A1==>...An==>).*)

 fun strip_imp_prems' (Const("==>", T) $ A $ t) = 

     let fun coll_prems As (Const("==>", _) $ A $ t) = 

 	    coll_prems (As $ (Logic.implies $ A)) t

 	  | coll_prems As _ = SOME As

     in coll_prems (Logic.implies $ A) t end

   | strip_imp_prems' _ = NONE;  (* logic.ML: term -> term list*)

 (*

   val thm = real_mult_div_cancel1;

   val prop = (#prop o rep_thm) thm;

   atomt prop;

 *** -------------

 *** Const ( ==>)

 *** . Const ( Trueprop)

 *** . . Const ( Not)

 *** . . . Const ( op =)

 *** . . . . Var ((k, 0), )

 *** . . . . Const ( 0)

 *** . Const ( Trueprop)

 *** . . Const ( op =)                                                          *** .............

   val SOME t = strip_imp_prems' ((#prop o rep_thm) thm);

   atomt t;

 *** -------------

 *** Const ( ==>)

 *** . Const ( Trueprop)

 *** . . Const ( Not)

 *** . . . Const ( op =)

 *** . . . . Var ((k, 0), )

 *** . . . . Const ( 0)

   val thm = real_le_anti_sym;

   val prop = (#prop o rep_thm) thm;

   atomt prop;

 *** -------------

 *** Const ( ==>)

 *** . Const ( Trueprop)

 *** . . Const ( op <=)

 *** . . . Var ((z, 0), )

 *** . . . Var ((w, 0), )

 *** . Const ( ==>)

 *** . . Const ( Trueprop)

 *** . . . Const ( op <=)

 *** . . . . Var ((w, 0), )

 *** . . . . Var ((z, 0), )

 *** . . Const ( Trueprop)

 *** . . . Const ( op =)

 *** .............

   val SOME t = strip_imp_prems' ((#prop o rep_thm) thm);

   atomt t;

 *** -------------

 *** Const ( ==>)

 *** . Const ( Trueprop)

 *** . . Const ( op <=)

 *** . . . Var ((z, 0), )

 *** . . . Var ((w, 0), )

 *** . Const ( ==>)

 *** . . Const ( Trueprop)

 *** . . . Const ( op <=)

 *** . . . . Var ((w, 0), )

 *** . . . . Var ((z, 0), )

 *)

 (*. (A1==>...An==>) (B) goes to (A1==>...An==>B), where B is lowest branch.*)

 fun ins_concl (Const("==>", T) $ A $ t) B = Logic.implies $ A $ (ins_concl t B)

   | ins_concl (Const("==>", T) $ A    ) B = Logic.implies $ A $ B

   | ins_concl t B =  raise TERM("ins_concl", [t, B]);

 (*

   val thm = real_le_anti_sym;

   val prop = (#prop o rep_thm) thm;

   val concl = Logic.strip_imp_concl prop;

   val SOME prems = strip_imp_prems' prop;

   val prop' = ins_concl prems concl;

   prop = prop';

   atomt prop;

   atomt prop';

 *)

 fun vperm (Var _, Var _) = true  (*2002 Pure/thm.ML *)

   | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t)

   | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2)

   | vperm (t, u) = (t = u);

 (*2002 cp from Pure/term.ML --- since 2009 in Pure/old_term.ML*)

 fun mem_term (_, []) = false

   | mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts);

 fun subset_term ([], ys) = true

   | subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys);

 fun eq_set_term (xs, ys) =

     xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs));

 (*a total, irreflexive ordering on index names*)

 fun xless ((a,i), (b,j): indexname) = i<j  orelse  (i=j andalso a<b);

 (*a partial ordering (not reflexive) for atomic terms*)

 fun atless (Const (a,_), Const (b,_))  =  a<b

   | atless (Free (a,_), Free (b,_)) =  a<b

   | atless (Var(v,_), Var(w,_))  =  xless(v,w)

   | atless (Bound i, Bound j)  =   i<j

   | atless _  =  false;

 (*insert atomic term into partially sorted list, suppressing duplicates (?)*)

 fun insert_aterm (t,us) =

   let fun inserta [] = [t]

         | inserta (us as u::us') =

               if atless(t,u) then t::us

               else if t=u then us (*duplicate*)

               else u :: inserta(us')

   in  inserta us  end;

 (*Accumulates the Vars in the term, suppressing duplicates*)

 fun add_term_vars (t, vars: term list) = case t of

     Var   _ => insert_aterm(t,vars)

   | Abs (_,_,body) => add_term_vars(body,vars)

   | f$t =>  add_term_vars (f, add_term_vars(t, vars))

   | _ => vars;

 fun term_vars t = add_term_vars(t,[]);

 fun var_perm (t, u) = (*2002 Pure/thm.ML *)

   vperm (t, u) andalso eq_set_term (term_vars t, term_vars u);

 (*2002 fun decomp_simp, Pure/thm.ML *)

 fun perm lhs rhs = var_perm (lhs, rhs) andalso not (lhs aconv rhs)

     andalso not (is_Var lhs);

 fun str_of_int n = 

   if n < 0 then "-"^((string_of_int o abs) n)

   else string_of_int n;

 (*

 > str_of_int 1;

 val it = "1" : string                                                          > str_of_int ~1;

 val it = "-1" : string

 *)

 fun power b 0 = 1

   | power b n = 

   if n>0 then b*(power b (n-1))

   else raise error ("power "^(str_of_int b)^" "^(str_of_int n));

 (*

 > power 2 3;

 val it = 8 : int

 > power ~2 3;

 val it = ~8 : int

 > power ~3 2;

 val it = 9 : int

 > power 3 ~2;

 *)

 fun gcd 0 b = b

   | gcd a b = if a < b then gcd (b mod a) a

 	      else gcd (a mod b) b;

 fun sign n = if n < 0 then ~1

 	     else if n = 0 then 0 else 1;

 fun sign2 n1 n2 = (sign n1) * (sign n2);

 infix dvd;

 fun d dvd n = n mod d = 0;

 fun divisors n =

   let fun pdiv ds d n = 

     if d=n then d::ds

     else if d dvd n then pdiv (d::ds) d (n div d)

 	 else pdiv ds (d+1) n

   in pdiv [] 2 n end;

 divisors 30;

 divisors 32;

 divisors 60;

 divisors 11;

 fun doubles ds = (* ds is ordered *)

   let fun dbls ds [] = ds

 	| dbls ds [i] = ds

 	| dbls ds (i::i'::is) = if i=i' then dbls (i::ds) is

 				else dbls ds (i'::is)

   in dbls [] ds end;

 (*> doubles [2,3,4];

 val it = [] : int list

 > doubles [2,3,3,5,5,7];

 val it = [5,3] : int list*)

 fun squfact 0 = 0

   | squfact 1 = 1

   | squfact n = foldl op* (1, (doubles o divisors) n);

 (*> squfact 30;

 val it = 1 : int

 > squfact 32;

 val it = 4 : int

 > squfact 60;

 val it = 2 : int

 > squfact 11;

 val it = 1 : int*)

 fun dest_type (Type(T,[])) = T

   | dest_type T = 

     (atomtyp T;

      raise error ("... dest_type: not impl. for this type"));

 fun term_of_num ntyp n = Free (str_of_int n, ntyp);

 fun pairT T1 T2 = Type ("*", [T1, T2]);

 (*> val t = str2term "(1,2)";

 > type_of t = pairT HOLogic.realT HOLogic.realT;

 val it = true : bool

 *)

 fun PairT T1 T2 = ([T1, T2] ---> Type ("*", [T1, T2]));

 (*> val t = str2term "(1,2)";

 > val Const ("Pair",pT) $ _ $ _ = t;

 > pT = PairT HOLogic.realT HOLogic.realT;

 val it = true : bool

 *)

 fun pairt t1 t2 =

     Const ("Pair", PairT (type_of t1) (type_of t2)) $ t1 $ t2;

 (*> val t = str2term "(1,2)";

 > val (t1, t2) = (str2term "1", str2term "2");

 > t = pairt t1 t2;

 val it = true : bool*)

 fun num_of_term (t as Free (s,_)) = 

     (case int_of_str s of

 	 SOME s' => s'

        | NONE => raise error ("num_of_term not for "^ term2str t))

   | num_of_term t = raise error ("num_of_term not for "^term2str t);

 fun mk_factroot op_(*=thy.sqrt*) T fact root = 

   Const ("op *", [T, T] ---> T) $ (term_of_num T fact) $

   (Const (op_, T --> T) $ term_of_num T root);

 (*

 val T =  (type_of o term_of o the) (parse thy "#12::real");

 val t = mk_factroot "SqRoot.sqrt" T 2 3;

 (cterm_of thy) t;

 val it = "#2 * sqrt #3 " : cterm

 *)

 fun var_op_num v op_ optype ntyp n =

   Const (op_, optype) $ v $ 

    Free (str_of_int  n, ntyp);

 fun num_op_var v op_ optype ntyp n =

   Const (op_,optype) $  

    Free (str_of_int n, ntyp) $ v;

 fun num_op_num T1 T2 (op_,Top) n1 n2 = 

   Const (op_,Top) $ 

   Free (str_of_int n1, T1) $ Free (str_of_int n2, T2);

 (*

 > val t = num_op_num "Int" 3 4;

 > atomty t;

 > string_of_cterm ((cterm_of thy) t);

 *)

 fun const_in str (Const _) = false

   | const_in str (Free (s,_)) = if strip_thy s = str then true else false

   | const_in str (Bound _) = false

   | const_in str (Var _) = false

   | const_in str (Abs (_,_,body)) = const_in str body

   | const_in str (f$u) = const_in str f orelse const_in str u;

 (*

 > val t = (term_of o the o (parse thy)) "6 + 5 * sqrt 4 + 3";

 > const_in "sqrt" t;

 val it = true : bool

 > val t = (term_of o the o (parse thy)) "6 + 5 * 4 + 3";

 > const_in "sqrt" t;

 val it = false : bool

 *)

 (*used for calculating built in binary operations in Isabelle2002->Float.ML*)

 (*fun calc "op +"  (n1, n2) = n1+n2

   | calc "op -"  (n1, n2) = n1-n2

   | calc "op *"  (n1, n2) = n1*n2

   | calc "HOL.divide"(n1, n2) = n1 div n2

   | calc "Atools.pow"(n1, n2) = power n1 n2

   | calc op_ _ = raise error ("calc: operator = "^op_^" not defined");-----*)

 fun calc_equ "op <"  (n1, n2) = n1 < n2

   | calc_equ "op <=" (n1, n2) = n1 <= n2

   | calc_equ op_ _ = 

   raise error ("calc_equ: operator = "^op_^" not defined");

 fun sqrt (n:int) = if n < 0 then 0

     (*FIXME ~~~*)  else (trunc o Math.sqrt o Real.fromInt) n;

 fun mk_thmid thmid op_ n1 n2 = 

   thmid ^ (strip_thy n1) ^ "_" ^ (strip_thy n2);

 fun dest_binop_typ (Type("fun",[range,Type("fun",[arg2,arg1])])) =

   (arg1,arg2,range)

   | dest_binop_typ _ = raise error "dest_binop_typ: not binary";

 (* -----

 > val t = (term_of o the o (parse thy)) "#3^#4";

 > val hT = type_of (head_of t);

 > dest_binop_typ hT;

 val it = ("'a","nat","'a") : typ * typ * typ

  ----- *)

 (** transform binary numeralsstrings **)

 (*Makarius 100308, hacked by WN*)

 val numbers_to_string =

   let

     fun dest_num t =

       (case try HOLogic.dest_number t of

         SOME (T, i) =>

           (*if T = @{typ int} orelse T = @{typ real} then WN*)

             SOME (Free (signed_string_of_int i, T))

           (*else NONE  WN*)

       | NONE => NONE);

     fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b)

       | to_str (t as (u1 $ u2)) =

           (case dest_num t of

             SOME t' => t'

           | NONE => to_str u1 $ to_str u2)

       | to_str t = perhaps dest_num t;

   in to_str end

 (*.make uminus uniform: 

    Const ("uminus", _) $ Free ("2", "RealDef.real") --> Free ("-2", _)

 to be used immediately before evaluation of numerals; 

 see Scripts/calculate.sml .*)

 (*2002 fun(*app_num_tr'2 (Const("0",T)) = Free("0",T)

   | app_num_tr'2 (Const("1",T)) = Free("1",T)

   |*)app_num_tr'2 (t as Const("uminus",_) $ Free(s,T)) = 

     (case int_of_str s of SOME i => 

 			  if i > 0 then Free("-"^s,T) else Free(s,T)

 		       | NONE => t)

 (*| app_num_tr'2 (t as Const(s,T)) = t

   | app_num_tr'2 (Const("Numeral.number_of",Type ("fun", [_, T])) $ t) = 

     Free(NumeralSyntax.dest_bin_str t, T)

   | app_num_tr'2 (t as Free(s,T)) = t

   | app_num_tr'2 (t as Var(n,T)) = t

   | app_num_tr'2 (t as Bound i) = t

 *)| app_num_tr'2 (Abs(s,T,body)) = Abs(s,T, app_num_tr'2 body)

   | app_num_tr'2 (t1 $ t2) = (app_num_tr'2 t1) $ (app_num_tr'2 t2)

   | app_num_tr'2 t = t;

 *)

 val uminus_to_string =

     let

 	fun dest_num t =

 	    (case t of

 		 (Const ("HOL.uminus_class.uminus", _) $ Free (s, T)) => 

 		 (case int_of_str s of

 		      SOME i => 

 		      SOME (Free (signed_string_of_int (~1 * i), T))

 		    | NONE => NONE)

 	       | _ => NONE);

 	fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b)

 	  | to_str (t as (u1 $ u2)) =

             (case dest_num t of

 		 SOME t' => t'

                | NONE => to_str u1 $ to_str u2)

 	  | to_str t = perhaps dest_num t;

     in to_str end;

 (*2002 fun num_str thm =

   let 

     val {sign_ref = sign_ref, der = der, maxidx = maxidx,

 	    shyps = shyps, hyps = hyps, (*tpairs = tpairs,*) prop = prop} = 

 	rep_thm_G thm;

     val prop' = app_num_tr'1 prop;

   in assbl_thm sign_ref der maxidx shyps hyps (*tpairs*) prop' end;*)

 fun num_str thm =

   let val (deriv, 

 	   {thy_ref = thy_ref, tags = tags, maxidx = maxidx, shyps = shyps, 

 	    hyps = hyps, tpairs = tpairs, prop = prop}) = rep_thm_G thm

     val prop' = numbers_to_string prop;

   in assbl_thm deriv thy_ref tags maxidx shyps hyps tpairs prop' end;

 fun get_thm' xstring = (*?covers 2009 Thm?!, replaces 2002 fun get_thm :

 val it = fn : theory -> xstring -> Thm.thm*)

     Thm (xstring, 

 	 num_str (ProofContext.get_thm (thy2ctxt' "Isac") xstring)); 

 (** get types of Free and Abs for parse' **)

 (*11.1.00: not used, fix-typed +,*,-,^ instead *)

 val dummyT = Type ("dummy",[]);

 val dummyT = TVar (("DUMMY",0),[]);

 (* assumes only 1 type for numerals 

    and different identifiers for Const, Free and Abs *)

 fun get_types t = 

   let

     fun get ts  (Const(s,T)) = (s,T)::ts

       | get ts  (Free(s,T)) = if is_no s 

 				then ("#",T)::ts else (s,T)::ts

       | get ts  (Var(n,T)) = ts

       | get ts  (Bound i) = ts

       | get ts  (Abs(s,T,body)) = get ((s,T)::ts)  body

       | get ts  (t1 $ t2) = (get ts  t1) @ (get ts  t2)

   in distinct (get [] t) end;

 (*

 val t = (term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)";

 get_types t;

 *)

 (*11.1.00: not used, fix-typed +,*,-,^ instead *)

 fun set_types al (Const(s,T)) = 

     (case assoc (al,s) of

        SOME T' => Const(s,T')

      | NONE => (warning ("set_types: no type for "^s); Const(s,dummyT)))

   | set_types al (Free(s,T)) = 

   if is_no s then

     (case assoc (al,"#") of

       SOME T' => Free(s,T')

     | NONE => (warning ("set_types: no type for numerals"); Free(s,T)))

   else (case assoc (al,s) of

 	       SOME T' => Free(s,T')

 	     | NONE => (warning ("set_types: no type for "^s); Free(s,T)))

   | set_types al (Var(n,T)) = Var(n,T)

   | set_types al (Bound i) = Bound i

   | set_types al (Abs(s,T,body)) = 

 		 (case assoc (al,s) of

 		    SOME T'  => Abs(s,T', set_types al body)

 		  | NONE => (warning ("set_types: no type for "^s);

 			     Abs(s,T, set_types al body)))

   | set_types al (t1 $ t2) = (set_types al t1) $ (set_types al t2);

 (*

 val t = (term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)";

 val al = get_types t;

 val t = (term_of o the o (parse thy)) "x = #0 + #-1 * #-4";

 atomty t;                         (* 'a *)

 val t' = set_types al t;

 atomty t';                        (*real*)

 (cterm_of thy) t';

 val it = "x = #0 + #-1 * #-4" : cterm

 val t = (term_of o the o (parse thy)) 

   "#5 * x + x ^^^ #2 = (#2 + x) ^^^ #2";

 atomty t;

 val t' = set_types al t;

 atomty t';

 (cterm_of thy) t';

 uncaught exception TYPE               (*^^^ is new, NOT in al*)

 *)

 (** from Descript.ML **)

 (** decompose an isa-list to an ML-list 

     i.e. [] belong to the meta-language, too **)

 fun is_list ((Const("List.list.Cons",_)) $ _ $ _) = true

   | is_list _ = false;

 (* val (SOME ct) = parse thy "lll::real list";

 > val ty = (#t o rep_cterm) ct;

 > is_list ty;

 val it = false : bool

 > val (SOME ct) = parse thy "[lll]";

 > val ty = (#t o rep_cterm) ct;

 > is_list ty;

 val it = true : bool *)

 fun mk_Free (s,T) = Free(s,T);

 fun mk_free T s =  Free(s,T);

 (*instantiate let; necessary for ass_up*)

 fun inst_abs thy (Const sT) = Const sT

   | inst_abs thy (Free sT) = Free sT

   | inst_abs thy (Bound n) = Bound n

   | inst_abs thy (Var iT) = Var iT

   | inst_abs thy (Const ("Let",T1) $ e $ (Abs (v,T2,b))) = 

   let val (v',b') = variant_abs (v,T2,b);     (*fun variant_abs: term.ML*)

   in Const ("Let",T1) $ inst_abs thy e $ (Abs (v',T2,inst_abs thy b')) end

   | inst_abs thy (t1 $ t2) = inst_abs thy t1 $ inst_abs thy t2

   | inst_abs thy t = 

     (writeln("inst_abs: unchanged t= "^ term2str t);

      t);

 (*val scr as (Script sc) = Script ((term_of o the o (parse thy))

  "Script Testeq (e_::bool) =                                        \

    \While (contains_root e_) Do                                     \

    \ (let e_ = Try (Repeat (Rewrite rroot_square_inv False e_));    \

    \      e_ = Try (Repeat (Rewrite square_equation_left True e_)) \

    \   in Try (Repeat (Rewrite radd_0 False e_)))                 ");

 ML> atomt sc;

 *** Const ( Script.Testeq)

 *** . Free ( e_, )

 *** . Const ( Script.While)

 *** . . Const ( RatArith.contains'_root)

 *** . . . Free ( e_, )

 *** . . Const ( Let)

 *** . . . Const ( Script.Try)

 *** . . . . Const ( Script.Repeat)

 *** . . . . . Const ( Script.Rewrite)

 *** . . . . . . Free ( rroot_square_inv, )

 *** . . . . . . Const ( False)

 *** . . . . . . Free ( e_, )

 *** . . . Abs( e_,..

 *** . . . . Const ( Let)

 *** . . . . . Const ( Script.Try)

 *** . . . . . . Const ( Script.Repeat)

 *** . . . . . . . Const ( Script.Rewrite)

 *** . . . . . . . . Free ( square_equation_left, )

 *** . . . . . . . . Const ( True)

 *** . . . . . . . . Bound 0                            <-- !!!

 *** . . . . . Abs( e_,..

 *** . . . . . . Const ( Script.Try)

 *** . . . . . . . Const ( Script.Repeat)

 *** . . . . . . . . Const ( Script.Rewrite)

 *** . . . . . . . . . Free ( radd_0, )

 *** . . . . . . . . . Const ( False)

 *** . . . . . . . . . Bound 0                          <-- !!!

 val it = () : unit

 ML> atomt (inst_abs thy sc);

 *** Const ( Script.Testeq)

 *** . Free ( e_, )

 *** . Const ( Script.While)

 *** . . Const ( RatArith.contains'_root)

 *** . . . Free ( e_, )

 *** . . Const ( Let)

 *** . . . Const ( Script.Try)

 *** . . . . Const ( Script.Repeat)

 *** . . . . . Const ( Script.Rewrite)

 *** . . . . . . Free ( rroot_square_inv, )

 *** . . . . . . Const ( False)

 *** . . . . . . Free ( e_, )

 *** . . . Abs( e_,..

 *** . . . . Const ( Let)

 *** . . . . . Const ( Script.Try)

 *** . . . . . . Const ( Script.Repeat)

 *** . . . . . . . Const ( Script.Rewrite)

 *** . . . . . . . . Free ( square_equation_left, )

 *** . . . . . . . . Const ( True)

 *** . . . . . . . . Free ( e_, )                        <-- !!!

 *** . . . . . Abs( e_,..

 *** . . . . . . Const ( Script.Try)

 *** . . . . . . . Const ( Script.Repeat)

 *** . . . . . . . . Const ( Script.Rewrite)

 *** . . . . . . . . . Free ( radd_0, )

 *** . . . . . . . . . Const ( False)

 *** . . . . . . . . . Free ( e_, )                      <-- ZUFALL vor 5.03!!!

 val it = () : unit*)

 fun inst_abs thy (Const sT) = Const sT

   | inst_abs thy (Free sT) = Free sT

   | inst_abs thy (Bound n) = Bound n

   | inst_abs thy (Var iT) = Var iT

   | inst_abs thy (Const ("Let",T1) $ e $ (Abs (v,T2,b))) = 

   let val b' = subst_bound (Free(v,T2),b);

   (*fun variant_abs: term.ML*)

   in Const ("Let",T1) $ inst_abs thy e $ (Abs (v,T2,inst_abs thy b')) end

   | inst_abs thy (t1 $ t2) = inst_abs thy t1 $ inst_abs thy t2

   | inst_abs thy t = 

     (writeln("inst_abs: unchanged t= "^ term2str t);

      t);

 (*val scr =    

    "Script Make_fun_by_explicit (f_::real) (v_::real) (eqs_::bool list) = \

    \ (let h_ = (hd o (filterVar f_)) eqs_;                    \

    \      e_1 = hd (dropWhile (ident h_) eqs_);       \

    \      vs_ = dropWhile (ident f_) (Vars h_);                \

    \      v_1 = hd (dropWhile (ident v_) vs_);                \

    \      (s_1::bool list)=(SubProblem(DiffApp_,[univar,equation],[no_met])\

    \                          [bool_ e_1, real_ v_1])\

    \ in Substitute [(v_1 = (rhs o hd) s_1)] h_)";

 > val ttt = (term_of o the o (parse thy)) scr;

 > writeln(term2str ttt);

 > atomt ttt;

 *** -------------

 *** Const ( DiffApp.Make'_fun'_by'_explicit)

 *** . Free ( f_, )

 *** . Free ( v_, )

 *** . Free ( eqs_, )

 *** . Const ( Let)

 *** . . Const ( Fun.op o)

 *** . . . Const ( List.hd)

 *** . . . Const ( DiffApp.filterVar)

 *** . . . . Free ( f_, )

 *** . . . Free ( eqs_, )

 *** . . Abs( h_,..

 *** . . . Const ( Let)

 *** . . . . Const ( List.hd)

 *** . . . . . Const ( List.dropWhile)

 *** . . . . . . Const ( Atools.ident)

 *** . . . . . . . Bound 0                     <---- Free ( h_, )

 *** . . . . . . Free ( eqs_, )

 *** . . . . Abs( e_1,..

 *** . . . . . Const ( Let)

 *** . . . . . . Const ( List.dropWhile)

 *** . . . . . . . Const ( Atools.ident)

 *** . . . . . . . . Free ( f_, )

 *** . . . . . . . Const ( Tools.Vars)

 *** . . . . . . . . Bound 1                       <---- Free ( h_, )

 *** . . . . . . Abs( vs_,..

 *** . . . . . . . Const ( Let)

 *** . . . . . . . . Const ( List.hd)

 *** . . . . . . . . . Const ( List.dropWhile)

 *** . . . . . . . . . . Const ( Atools.ident)

 *** . . . . . . . . . . . Free ( v_, )

 *** . . . . . . . . . . Bound 0                   <---- Free ( vs_, )

 *** . . . . . . . . Abs( v_1,..

 *** . . . . . . . . . Const ( Let)

 *** . . . . . . . . . . Const ( Script.SubProblem)

 *** . . . . . . . . . . . Const ( Pair)

 *** . . . . . . . . . . . . Free ( DiffApp_, )

 *** . . . . . . . . . . . . Const ( Pair)

 *** . . . . . . . . . . . . . Const ( List.list.Cons)

 *** . . . . . . . . . . . . . . Free ( univar, )

 *** . . . . . . . . . . . . . . Const ( List.list.Cons)

 *** . . . . . . . . . . . . . . . Free ( equation, )

 *** . . . . . . . . . . . . . . . Const ( List.list.Nil)

 *** . . . . . . . . . . . . . Const ( List.list.Cons)

 *** . . . . . . . . . . . . . . Free ( no_met, )

 *** . . . . . . . . . . . . . . Const ( List.list.Nil)

 *** . . . . . . . . . . . Const ( List.list.Cons)

 *** . . . . . . . . . . . . Const ( Script.bool_)

 *** . . . . . . . . . . . . . Bound 2                   <----- Free ( e_1, )

 *** . . . . . . . . . . . . Const ( List.list.Cons)

 *** . . . . . . . . . . . . . Const ( Script.real_)

 *** . . . . . . . . . . . . . . Bound 0                 <----- Free ( v_1, )

 *** . . . . . . . . . . . . . Const ( List.list.Nil)

 *** . . . . . . . . . . Abs( s_1,..

 *** . . . . . . . . . . . Const ( Script.Substitute)

 *** . . . . . . . . . . . . Const ( List.list.Cons)

 *** . . . . . . . . . . . . . Const ( Pair)

 *** . . . . . . . . . . . . . . Bound 1                 <----- Free ( v_1, )

 *** . . . . . . . . . . . . . . Const ( Fun.op o)

 *** . . . . . . . . . . . . . . . Const ( Tools.rhs)

 *** . . . . . . . . . . . . . . . Const ( List.hd)

 *** . . . . . . . . . . . . . . . Bound 0               <----- Free ( s_1, )

 *** . . . . . . . . . . . . . Const ( List.list.Nil)

 *** . . . . . . . . . . . . Bound 4                     <----- Free ( h_, )

 > val ttt' = inst_abs thy ttt;

 > writeln(term2str ttt');

 Script Make_fun_by_explicit f_ v_ eqs_ =  

   ... as above ...

 > atomt ttt';

 *** -------------

 *** Const ( DiffApp.Make'_fun'_by'_explicit)

 *** . Free ( f_, )

 *** . Free ( v_, )

 *** . Free ( eqs_, )

 *** . Const ( Let)

 *** . . Const ( Fun.op o)

 *** . . . Const ( List.hd)

 *** . . . Const ( DiffApp.filterVar)

 *** . . . . Free ( f_, )

 *** . . . Free ( eqs_, )

 *** . . Abs( h_,..

 *** . . . Const ( Let)

 *** . . . . Const ( List.hd)

 *** . . . . . Const ( List.dropWhile)

 *** . . . . . . Const ( Atools.ident)

 *** . . . . . . . Free ( h_, )                <---- Bound 0

 *** . . . . . . Free ( eqs_, )

 *** . . . . Abs( e_1,..

 *** . . . . . Const ( Let)

 *** . . . . . . Const ( List.dropWhile)

 *** . . . . . . . Const ( Atools.ident)

 *** . . . . . . . . Free ( f_, )

 *** . . . . . . . Const ( Tools.Vars)

 *** . . . . . . . . Free ( h_, )                  <---- Bound 1

 *** . . . . . . Abs( vs_,..

 *** . . . . . . . Const ( Let)

 *** . . . . . . . . Const ( List.hd)

 *** . . . . . . . . . Const ( List.dropWhile)

 *** . . . . . . . . . . Const ( Atools.ident)

 *** . . . . . . . . . . . Free ( v_, )

 *** . . . . . . . . . . Free ( vs_, )             <---- Bound 0

 *** . . . . . . . . Abs( v_1,..

 *** . . . . . . . . . Const ( Let)

 *** . . . . . . . . . . Const ( Script.SubProblem)

 *** . . . . . . . . . . . Const ( Pair)

 *** . . . . . . . . . . . . Free ( DiffApp_, )

 *** . . . . . . . . . . . . Const ( Pair)

 *** . . . . . . . . . . . . . Const ( List.list.Cons)

 *** . . . . . . . . . . . . . . Free ( univar, )

 *** . . . . . . . . . . . . . . Const ( List.list.Cons)

 *** . . . . . . . . . . . . . . . Free ( equation, )

 *** . . . . . . . . . . . . . . . Const ( List.list.Nil)

 *** . . . . . . . . . . . . . Const ( List.list.Cons)

 *** . . . . . . . . . . . . . . Free ( no_met, )

 *** . . . . . . . . . . . . . . Const ( List.list.Nil)

 *** . . . . . . . . . . . Const ( List.list.Cons)

 *** . . . . . . . . . . . . Const ( Script.bool_)

 *** . . . . . . . . . . . . . Free ( e_1, )             <----- Bound 2

 *** . . . . . . . . . . . . Const ( List.list.Cons)

 *** . . . . . . . . . . . . . Const ( Script.real_)

 *** . . . . . . . . . . . . . . Free ( v_1, )           <----- Bound 0

 *** . . . . . . . . . . . . . Const ( List.list.Nil)

 *** . . . . . . . . . . Abs( s_1,..

 *** . . . . . . . . . . . Const ( Script.Substitute)

 *** . . . . . . . . . . . . Const ( List.list.Cons)

 *** . . . . . . . . . . . . . Const ( Pair)

 *** . . . . . . . . . . . . . . Free ( v_1, )           <----- Bound 1

 *** . . . . . . . . . . . . . . Const ( Fun.op o)

 *** . . . . . . . . . . . . . . . Const ( Tools.rhs)

 *** . . . . . . . . . . . . . . . Const ( List.hd)

 *** . . . . . . . . . . . . . . . Free ( s_1, )         <----- Bound 0

 *** . . . . . . . . . . . . . Const ( List.list.Nil)

 *** . . . . . . . . . . . . Free ( h_, )                <----- Bound 4

 Note numbering of de Bruijn indexes !

 Script Make_fun_by_explicit f_ v_ eqs_ =

  let h_ = (hd o filterVar f_) eqs_; 

      e_1 = hd (dropWhile (ident h_ BOUND_0) eqs_);

      vs_ = dropWhile (ident f_) (Vars h_ BOUND_1);

      v_1 = hd (dropWhile (ident v_) vs_ BOUND_0);

      s_1 =

        SubProblem (DiffApp_, [univar, equation], [no_met])

         [bool_ e_1 BOUND_2, real_ v_1 BOUND_0]

  in Substitute [(v_1 BOUND_1 = (rhs o hd) s_1 BOUND_0)] h_ BOUND_4

 *)

 fun T_a2real (Type (s, [])) = 

     if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else Type (s, [])

   | T_a2real (Type (s, Ts)) = Type (s, map T_a2real Ts)

   | T_a2real (TFree (s, srt)) = 

     if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else TFree (s, srt)

   | T_a2real (TVar (("DUMMY",_),srt)) = HOLogic.realT;

 (*FIXME .. fixes the type (+see Typefix.thy*)

 fun typ_a2real (Const( s, T)) = (Const( s, T_a2real T)) 

   | typ_a2real (Free( s, T)) = (Free( s, T_a2real T))

   | typ_a2real (Var( n, T)) = (Var( n, T_a2real T))

   | typ_a2real (Bound i) = (Bound i)

   | typ_a2real (Abs(s,T,t)) = Abs(s, T, typ_a2real t)

   | typ_a2real (t1 $ t2) = (typ_a2real t1) $ (typ_a2real t2);

 (*

 ----------------6.8.02---------------------------------------------------

  val str = "1";

  val t = read_cterm (sign_of thy) (str,(TVar(("DUMMY",0),[])));

  atomty (term_of t);

 *** -------------

 *** Const ( 1, 'a)

  val t = (app_num_tr' o term_of) t;

  atomty t;

 *** ------------- 

 *** Const ( 1, 'a)                                                              

  val t = typ_a2real t;

  atomty t;

 *** -------------   

 *** Const ( 1, real)                                                            

  val str = "2";

  val t = read_cterm (sign_of thy) (str,(TVar(("DUMMY",0),[])));

  atomty (term_of t);

 *** -------------

 *** Const ( Numeral.number_of, bin => 'a)

 *** . Const ( Numeral.bin.Bit, [bin, bool] => bin)

 *** . . Const ( Numeral.bin.Bit, [bin, bool] => bin)

 *** . . . Const ( Numeral.bin.Pls, bin)

 *** . . . Const ( True, bool)

 *** . . Const ( False, bool)

  val t = (app_num_tr' o term_of) t;

  atomty t;

 *** -------------

 *** Free ( 2, 'a)

  val t = typ_a2real t;

  atomty t;

 *** -------------

 *** Free ( 2, real)

 ----------------6.8.02---------------------------------------------------

 > val str = "R";

 > val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[]))));

 val t = Free ("R","?DUMMY") : term

 > val t' = typ_a2real t;

 > (cterm_of thy) t';

 val it = "R::RealDef.real" : cterm

 > val str = "R=R";

 > val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[]))));

 > atomty (typ_a2real t);

 *** -------------

 *** Const ( op =, [RealDef.real, RealDef.real] => bool)

 ***   Free ( R, RealDef.real)

 ***   Free ( R, RealDef.real)

 > val t' = typ_a2real t;

 > (cterm_of thy) t';

 val it = "(R::RealDef.real) = R" : cterm

 > val str = "fixed_values [R=R]";

 > val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[]))));

 > val t' = typ_a2real t;

 > (cterm_of thy) t';

 val it = "fixed_values [(R::RealDef.real) = R]" : cterm

 *)

 (*TODO.WN0609: parse should return a term or a string 

 	     (or even more comprehensive datastructure for error-messages)

  i.e. in wrapping with SOME term or NONE the latter is not sufficient*)