wneuper/isa: src/Pure/isac/Scripts/term

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

     2    (c) Walther Neuper 1999

     4 use"Scripts/term_G.sml";

     5 use"term_G.sml";

     6 *)

     8 (*

     9 > cterm_of (sign_of thy) a_term;

    10 val it = "empty" : cterm        *)

    12 (*1003 fun match thy t pat =

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

    14     handle _ => [];

    15 fn : Theory.theory ->

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

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

    18 (*1003 fun matches thy tm pa = if match thy tm pa = [] then false else true;*)

    19 fun matches thy tm pa =

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

    21     handle _ => false

    23 fun atomtyp t = (*see raw_pp_typ*)

    24   let

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

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

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

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

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

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

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

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

    35        string_of_int i ^ strs2str' sort)

    36     and atol n [] =

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

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

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

    40 in writeln(ato 0 t) end;

    42 (*Prog.Tutorial.p.34*)

    43 local

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

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

    46    fun pp_str s   = Pretty.str s

    47    fun pp_qstr s = Pretty.quote (pp_str s)

    48    fun pp_int i   = pp_str (string_of_int i)

    49    fun pp_sort S = pp_list (map pp_qstr S)

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

    51 in

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

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

    54    | raw_pp_typ (TFree (a, S)) =

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

    56    | raw_pp_typ (Type (a, tys)) =

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

    58 end

    59 (* install

    60 PolyML.addPrettyPrinter

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

    62 de-install

    63 PolyML.addPrettyPrinter

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

    65 *)

    67 (*

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

    69 > atomtyp T;

    70 *** Type (fun,[

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

    72 ***   Type (fun,[

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

    74 ***     Type (nat,[])

    75 ***     ]

    76 ***   ]

    77 *)

    79 fun atomt t =

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

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

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

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

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

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

    86 	  | ato (Bound ix)       n =

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

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

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

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

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

    93 fun term_detail2str t =

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

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

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

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

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

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

   100 	    string_of_typ T^")"

   101 	  | ato (Bound ix)       n =

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

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

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

   105 	       (string_of_typ T)^",.."

   106 	    ^ato body (n + 1)

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

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

   109 fun atomty t = (writeln o term_detail2str) t;

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

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

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

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

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

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

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

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

   120   | contains_term (f $ f') t =

   121     contains_term f t orelse contains_term f' t

   122   | contains_term s t = t = s;

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

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

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

   126   | contains_Var (Var _) = true

   127   | contains_Var _ = false;

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

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

   130    *)

   132 (*fun int_of_str str =

   133     let val ss = explode str

   134 	val str' = case ss of

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

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

   137 	     SOME i => SOME i

   138 	   | NONE => NONE end;*)

   139 fun int_of_str str =

   140     let val ss = explode str

   141 	val str' = case ss of

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

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

   144 (*

   145 > int_of_str "123";

   146 val it = SOME 123 : int option                                                 > int_of_str "(-123)";

   147 val it = SOME 123 : int option                                                 > int_of_str "#123";

   148 val it = NONE : int option                                                     > int_of_str "-123";

   149 val it = SOME ~123 : int option                                                *)

   150 fun int_of_str' str =

   151     case int_of_str str of

   152 	SOME i => i

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

   154 val str2int = int_of_str';

   156 fun is_numeral str = case int_of_str str of

   157 			 SOME _ => true

   158 		       | NONE => false;

   159 val is_no = is_numeral;

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

   161   | is_num _ = false;

   162 (*>

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

   164 val it = true : bool

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

   166 val it = true : bool

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

   168 val it = false : bool

   169 *)

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

   172     (case BasisLibrary.Int.fromString intstr of

   173 	     SOME i => i

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

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

   176 fun int_of_Free (Free (intstr, _)) = (ThyOutput.integer intstr

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

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

   180 fun vars t =

   181   let

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

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

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

   185       | scan vs (Bound i) = vs

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

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

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

   190 fun is_Free (Free _) = true

   191   | is_Free _ = false;

   192 fun is_fun_id (Const _) = true

   193   | is_fun_id (Free _) = true

   194   | is_fun_id _ = false;

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

   196   | is_f_x _ = false;

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

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

   199   *)

   200 fun vars_str t =

   201   let

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

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

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

   205       | scan vs (Bound i) = vs

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

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

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

   210 fun ids2str t =

   211   let

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

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

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

   215       | scan vs (Bound i) = vs

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

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

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

   219 fun is_bdv str =

   220     case explode str of

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

   222       | _ => false;

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

   224   | is_bdv_ _ = false;

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

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

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

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

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

   232 (*27.8.01: unused*)

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

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

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

   236   | var2free (t as Bound i) = t

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

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

   240 (*27.8.01: doesn't find some subterm ???!???*)

   241 (*2010 Logic.varify !!!*)

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

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

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

   245   | free2var (t as Bound i) = t

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

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

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

   251 fun list_const T =

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

   253 (*28.8.01: TODO: get type from head of list: 1 arg less!!!*)

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

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

   256 (*

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

   258 > val TT = type_of tt;

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

   260 > cterm_of (sign_of thy) ss;

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

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

   264   | isapair2pair t =

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

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

   268 fun isalist2list ls =

   269   let

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

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

   272       | get _ t =

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

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

   275 (*

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

   277 > val l = isalist2list il;

   278 > (writeln o terms2str) l;

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

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

   282 > val l = isalist2list il;

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

   284 *)

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

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

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

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

   291 fun mk_prop t = Trueprop $ t;

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

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

   294 val true_as_cterm = cterm_of HOL true_as_term;

   295 val false_as_cterm = cterm_of HOL false_as_term;

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

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

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

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

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

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

   306 (** substitution **)

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

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

   310                                           else (x,y)::al)

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

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

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

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

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

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

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

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

   319         | renAbs(t) = t

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

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

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

   329 val lhs_ = (fst o dest_equals');

   330 val rhs_ = (snd o dest_equals');

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

   333   | is_equality _ = false;

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

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

   336   | is_expliceq _ = false;

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

   338   | strip_trueprop t = t;

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

   340 *)

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

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

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

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

   346 	  | coll_prems As _ = SOME As

   347     in coll_prems (Logic.implies $ A) t end

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

   349 (*

   350   val thm = real_mult_div_cancel1;

   351   val prop = (#prop o rep_thm) thm;

   352   atomt prop;

   353 *** -------------

   354 *** Const ( ==>)

   355 *** . Const ( Trueprop)

   356 *** . . Const ( Not)

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

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

   359 *** . . . . Const ( 0)

   360 *** . Const ( Trueprop)

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

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

   363   atomt t;

   364 *** -------------

   365 *** Const ( ==>)

   366 *** . Const ( Trueprop)

   367 *** . . Const ( Not)

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

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

   370 *** . . . . Const ( 0)

   372   val thm = real_le_anti_sym;

   373   val prop = (#prop o rep_thm) thm;

   374   atomt prop;

   375 *** -------------

   376 *** Const ( ==>)

   377 *** . Const ( Trueprop)

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

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

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

   381 *** . Const ( ==>)

   382 *** . . Const ( Trueprop)

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

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

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

   386 *** . . Const ( Trueprop)

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

   388 *** .............

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

   390   atomt t;

   391 *** -------------

   392 *** Const ( ==>)

   393 *** . Const ( Trueprop)

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

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

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

   397 *** . Const ( ==>)

   398 *** . . Const ( Trueprop)

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

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

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

   402 *)

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

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

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

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

   408 (*

   409   val thm = real_le_anti_sym;

   410   val prop = (#prop o rep_thm) thm;

   411   val concl = Logic.strip_imp_concl prop;

   412   val SOME prems = strip_imp_prems' prop;

   413   val prop' = ins_concl prems concl;

   414   prop = prop';

   415   atomt prop;

   416   atomt prop';

   417 *)

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

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

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

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

   425 (*2002 cp from Pure/term.ML --- since 2009 in Pure/old_term.ML*)

   426 fun mem_term (_, []) = false

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

   428 fun subset_term ([], ys) = true

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

   430 fun eq_set_term (xs, ys) =

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

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

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

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

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

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

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

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

   439   | atless _  =  false;

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

   441 fun insert_aterm (t,us) =

   442   let fun inserta [] = [t]

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

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

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

   446               else u :: inserta(us')

   447   in  inserta us  end;

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

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

   451     Var   _ => insert_aterm(t,vars)

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

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

   454   | _ => vars;

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

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

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

   461 (*2002 fun decomp_simp, Pure/thm.ML *)

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

   463     andalso not (is_Var lhs);

   466 fun str_of_int n =

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

   468   else string_of_int n;

   469 (*

   470 > str_of_int 1;

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

   472 val it = "-1" : string

   473 *)

   476 fun power b 0 = 1

   477   | power b n =

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

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

   480 (*

   481 > power 2 3;

   482 val it = 8 : int

   483 > power ~2 3;

   484 val it = ~8 : int

   485 > power ~3 2;

   486 val it = 9 : int

   487 > power 3 ~2;

   488 *)

   489 fun gcd 0 b = b

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

   491 	      else gcd (a mod b) b;

   492 fun sign n = if n < 0 then ~1

   493 	     else if n = 0 then 0 else 1;

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

   496 infix dvd;

   497 fun d dvd n = n mod d = 0;

   499 fun divisors n =

   500   let fun pdiv ds d n =

   501     if d=n then d::ds

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

   503 	 else pdiv ds (d+1) n

   504   in pdiv [] 2 n end;

   506 divisors 30;

   507 divisors 32;

   508 divisors 60;

   509 divisors 11;

   511 fun doubles ds = (* ds is ordered *)

   512   let fun dbls ds [] = ds

   513 	| dbls ds [i] = ds

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

   515 				else dbls ds (i'::is)

   516   in dbls [] ds end;

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

   518 val it = [] : int list

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

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

   522 fun squfact 0 = 0

   523   | squfact 1 = 1

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

   525 (*> squfact 30;

   526 val it = 1 : int

   527 > squfact 32;

   528 val it = 4 : int

   529 > squfact 60;

   530 val it = 2 : int

   531 > squfact 11;

   532 val it = 1 : int*)

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

   536   | dest_type T =

   537     (atomtyp T;

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

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

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

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

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

   545 val it = true : bool

   546 *)

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

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

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

   550 > pT = PairT HOLogic.realT HOLogic.realT;

   551 val it = true : bool

   552 *)

   553 fun pairt t1 t2 =

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

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

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

   557 > t = pairt t1 t2;

   558 val it = true : bool*)

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

   562     (case int_of_str s of

   563 	 SOME s' => s'

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

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

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

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

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

   570 (*

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

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

   573 cterm_of (sign_of thy) t;

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

   575 *)

   576 fun var_op_num v op_ optype ntyp n =

   577   Const (op_, optype) $ v $

   578    Free (str_of_int  n, ntyp);

   580 fun num_op_var v op_ optype ntyp n =

   581   Const (op_,optype) $

   582    Free (str_of_int n, ntyp) $ v;

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

   585   Const (op_,Top) $

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

   587 (*

   588 > val t = num_op_num "Int" 3 4;

   589 > atomty t;

   590 > string_of_cterm (cterm_of (sign_of thy) t);

   591 *)

   593 fun const_in str (Const _) = false

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

   595   | const_in str (Bound _) = false

   596   | const_in str (Var _) = false

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

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

   599 (*

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

   601 > const_in "sqrt" t;

   602 val it = true : bool

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

   604 > const_in "sqrt" t;

   605 val it = false : bool

   606 *)

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

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

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

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

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

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

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

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

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

   617   | calc_equ op_ _ =

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

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

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

   622 fun mk_thmid thmid op_ n1 n2 =

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

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

   626   (arg1,arg2,range)

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

   628 (* -----

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

   630 > val hT = type_of (head_of t);

   631 > dest_binop_typ hT;

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

   633  ----- *)

   636 (** transform binary numeralsstrings **)

   637 (*Makarius 100308, hacked by WN*)

   638 val numbers_to_string =

   639   let

   640     fun dest_num t =

   641       (case try HOLogic.dest_number t of

   642         SOME (T, i) =>

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

   644             SOME (Free (signed_string_of_int i, T))

   645           (*else NONE  WN*)

   646       | NONE => NONE);

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

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

   650           (case dest_num t of

   651             SOME t' => t'

   652           | NONE => to_str u1 $ to_str u2)

   653       | to_str t = perhaps dest_num t;

   654   in to_str end

   656 (*.make uminus uniform:

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

   658 to be used immediately before evaluation of numerals;

   659 see Scripts/calculate.sml .*)

   660 (*2002 fun(*app_num_tr'2 (Const("0",T)) = Free("0",T)

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

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

   663     (case int_of_str s of Some i =>

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

   665 		       | None => t)

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

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

   668     Free(NumeralSyntax.dest_bin_str t, T)

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

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

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

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

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

   674   | app_num_tr'2 t = t;

   675 *)

   676 val uminus_to_string =

   677     let

   678 	fun dest_num t =

   679 	    (case t of

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

   681 		 (case int_of_str s of

   682 		      SOME i =>

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

   684 		    | NONE => NONE)

   685 	       | _ => NONE);

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

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

   689             (case dest_num t of

   690 		 SOME t' => t'

   691                | NONE => to_str u1 $ to_str u2)

   692 	  | to_str t = perhaps dest_num t;

   693     in to_str end;

   696 (*2002 fun num_str thm =

   697   let

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

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

   700 	rep_thm_G thm;

   701     val prop' = app_num_tr'1 prop;

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

   703 fun num_str thm =

   704   let val (deriv,

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

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

   707     val prop' = numbers_to_string prop;

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

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

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

   712     Thm (xstring,

   713 	 num_str (ProofContext.get_thm (ctxt_Isac"") xstring));

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

   716 (*11.1.00: not used, fix-typed +,*,-,^ instead *)

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

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

   721 (* assumes only 1 type for numerals

   722    and different identifiers for Const, Free and Abs *)

   723 fun get_types t =

   724   let

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

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

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

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

   729       | get ts  (Bound i) = ts

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

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

   732   in distinct (get [] t) end;

   733 (*

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

   735 get_types t;

   736 *)

   738 (*11.1.00: not used, fix-typed +,*,-,^ instead *)

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

   740     (case assoc (al,s) of

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

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

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

   744   if is_no s then

   745     (case assoc (al,"#") of

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

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

   748   else (case assoc (al,s) of

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

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

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

   752   | set_types al (Bound i) = Bound i

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

   754 		 (case assoc (al,s) of

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

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

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

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

   759 (*

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

   761 val al = get_types t;

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

   764 atomty t;                         (* 'a *)

   765 val t' = set_types al t;

   766 atomty t';                        (*real*)

   767 cterm_of (sign_of thy) t';

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

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

   771   "#5 * x + x ^^^ #2 = (#2 + x) ^^^ #2";

   772 atomty t;

   773 val t' = set_types al t;

   774 atomty t';

   775 cterm_of (sign_of thy) t';

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

   777 *)

   780 (** from Descript.ML **)

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

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

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

   786   | is_list _ = false;

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

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

   789 > is_list ty;

   790 val it = false : bool

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

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

   793 > is_list ty;

   794 val it = true : bool *)

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

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

   801 (*instantiate let; necessary for ass_up*)

   802 fun inst_abs thy (Const sT) = Const sT

   803   | inst_abs thy (Free sT) = Free sT

   804   | inst_abs thy (Bound n) = Bound n

   805   | inst_abs thy (Var iT) = Var iT

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

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

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

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

   810   | inst_abs thy t =

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

   812      t);

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

   814  "Script Testeq (e_::bool) =                                        \

   815    \While (contains_root e_) Do                                     \

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

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

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

   819 ML> atomt sc;

   820 *** Const ( Script.Testeq)

   821 *** . Free ( e_, )

   822 *** . Const ( Script.While)

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

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

   825 *** . . Const ( Let)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   847 val it = () : unit

   848 ML> atomt (inst_abs thy sc);

   849 *** Const ( Script.Testeq)

   850 *** . Free ( e_, )

   851 *** . Const ( Script.While)

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

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

   854 *** . . Const ( Let)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   876 val it = () : unit*)

   881 fun inst_abs thy (Const sT) = Const sT

   882   | inst_abs thy (Free sT) = Free sT

   883   | inst_abs thy (Bound n) = Bound n

   884   | inst_abs thy (Var iT) = Var iT

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

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

   887   (*fun variant_abs: term.ML*)

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

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

   890   | inst_abs thy t =

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

   892      t);

   893 (*val scr =

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

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

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

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

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

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

   900    \                          [bool_ e_1, real_ v_1])\

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

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

   903 > writeln(term2str ttt);

   904 > atomt ttt;

   905 *** -------------

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

   907 *** . Free ( f_, )

   908 *** . Free ( v_, )

   909 *** . Free ( eqs_, )

   910 *** . Const ( Let)

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

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

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

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

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

   916 *** . . Abs( h_,..

   917 *** . . . Const ( Let)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   970 > val ttt' = inst_abs thy ttt;

   971 > writeln(term2str ttt');

   972 Script Make_fun_by_explicit f_ v_ eqs_ =

   973   ... as above ...

   974 > atomt ttt';

   975 *** -------------

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

   977 *** . Free ( f_, )

   978 *** . Free ( v_, )

   979 *** . Free ( eqs_, )

   980 *** . Const ( Let)

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

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

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

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

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

   986 *** . . Abs( h_,..

   987 *** . . . Const ( Let)

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

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

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

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

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

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

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

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

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

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

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

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

  1000 *** . . . . . . Abs( vs_,..

  1001 *** . . . . . . . Const ( Let)

  1002 *** . . . . . . . . Const ( List.hd)

  1003 *** . . . . . . . . . Const ( List.dropWhile)

  1004 *** . . . . . . . . . . Const ( Atools.ident)

  1005 *** . . . . . . . . . . . Free ( v_, )

  1006 *** . . . . . . . . . . Free ( vs_, )             <---- Bound 0

  1007 *** . . . . . . . . Abs( v_1,..

  1008 *** . . . . . . . . . Const ( Let)

  1009 *** . . . . . . . . . . Const ( Script.SubProblem)

  1010 *** . . . . . . . . . . . Const ( Pair)

  1011 *** . . . . . . . . . . . . Free ( DiffApp_, )

  1012 *** . . . . . . . . . . . . Const ( Pair)

  1013 *** . . . . . . . . . . . . . Const ( List.list.Cons)

  1014 *** . . . . . . . . . . . . . . Free ( univar, )

  1015 *** . . . . . . . . . . . . . . Const ( List.list.Cons)

  1016 *** . . . . . . . . . . . . . . . Free ( equation, )

  1017 *** . . . . . . . . . . . . . . . Const ( List.list.Nil)

  1018 *** . . . . . . . . . . . . . Const ( List.list.Cons)

  1019 *** . . . . . . . . . . . . . . Free ( no_met, )

  1020 *** . . . . . . . . . . . . . . Const ( List.list.Nil)

  1021 *** . . . . . . . . . . . Const ( List.list.Cons)

  1022 *** . . . . . . . . . . . . Const ( Script.bool_)

  1023 *** . . . . . . . . . . . . . Free ( e_1, )             <----- Bound 2

  1024 *** . . . . . . . . . . . . Const ( List.list.Cons)

  1025 *** . . . . . . . . . . . . . Const ( Script.real_)

  1026 *** . . . . . . . . . . . . . . Free ( v_1, )           <----- Bound 0

  1027 *** . . . . . . . . . . . . . Const ( List.list.Nil)

  1028 *** . . . . . . . . . . Abs( s_1,..

  1029 *** . . . . . . . . . . . Const ( Script.Substitute)

  1030 *** . . . . . . . . . . . . Const ( List.list.Cons)

  1031 *** . . . . . . . . . . . . . Const ( Pair)

  1032 *** . . . . . . . . . . . . . . Free ( v_1, )           <----- Bound 1

  1033 *** . . . . . . . . . . . . . . Const ( Fun.op o)

  1034 *** . . . . . . . . . . . . . . . Const ( Tools.rhs)

  1035 *** . . . . . . . . . . . . . . . Const ( List.hd)

  1036 *** . . . . . . . . . . . . . . . Free ( s_1, )         <----- Bound 0

  1037 *** . . . . . . . . . . . . . Const ( List.list.Nil)

  1038 *** . . . . . . . . . . . . Free ( h_, )                <----- Bound 4

  1040 Note numbering of de Bruijn indexes !

  1042 Script Make_fun_by_explicit f_ v_ eqs_ =

  1043  let h_ = (hd o filterVar f_) eqs_;

  1044      e_1 = hd (dropWhile (ident h_ BOUND_0) eqs_);

  1045      vs_ = dropWhile (ident f_) (Vars h_ BOUND_1);

  1046      v_1 = hd (dropWhile (ident v_) vs_ BOUND_0);

  1047      s_1 =

  1048        SubProblem (DiffApp_, [univar, equation], [no_met])

  1049         [bool_ e_1 BOUND_2, real_ v_1 BOUND_0]

  1050  in Substitute [(v_1 BOUND_1 = (rhs o hd) s_1 BOUND_0)] h_ BOUND_4

  1051 *)

  1054 fun T_a2real (Type (s, [])) =

  1055     if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else Type (s, [])

  1056   | T_a2real (Type (s, Ts)) = Type (s, map T_a2real Ts)

  1057   | T_a2real (TFree (s, srt)) =

  1058     if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else TFree (s, srt)

  1059   | T_a2real (TVar (("DUMMY",_),srt)) = HOLogic.realT;

  1061 (*FIXME .. fixes the type (+see Typefix.thy*)

  1062 fun typ_a2real (Const( s, T)) = (Const( s, T_a2real T))

  1063   | typ_a2real (Free( s, T)) = (Free( s, T_a2real T))

  1064   | typ_a2real (Var( n, T)) = (Var( n, T_a2real T))

  1065   | typ_a2real (Bound i) = (Bound i)

  1066   | typ_a2real (Abs(s,T,t)) = Abs(s, T, typ_a2real t)

  1067   | typ_a2real (t1 $ t2) = (typ_a2real t1) $ (typ_a2real t2);

  1068 (*

  1069 ----------------6.8.02---------------------------------------------------

  1070  val str = "1";

  1071  val t = read_cterm (sign_of thy) (str,(TVar(("DUMMY",0),[])));

  1072  atomty (term_of t);

  1073 *** -------------

  1074 *** Const ( 1, 'a)

  1075  val t = (app_num_tr' o term_of) t;

  1076  atomty t;

  1077 *** -------------

  1078 *** Const ( 1, 'a)

  1079  val t = typ_a2real t;

  1080  atomty t;

  1081 *** -------------

  1082 *** Const ( 1, real)

  1084  val str = "2";

  1085  val t = read_cterm (sign_of thy) (str,(TVar(("DUMMY",0),[])));

  1086  atomty (term_of t);

  1087 *** -------------

  1088 *** Const ( Numeral.number_of, bin => 'a)

  1089 *** . Const ( Numeral.bin.Bit, [bin, bool] => bin)

  1090 *** . . Const ( Numeral.bin.Bit, [bin, bool] => bin)

  1091 *** . . . Const ( Numeral.bin.Pls, bin)

  1092 *** . . . Const ( True, bool)

  1093 *** . . Const ( False, bool)

  1094  val t = (app_num_tr' o term_of) t;

  1095  atomty t;

  1096 *** -------------

  1097 *** Free ( 2, 'a)

  1098  val t = typ_a2real t;

  1099  atomty t;

  1100 *** -------------

  1101 *** Free ( 2, real)

  1102 ----------------6.8.02---------------------------------------------------

  1105 > val str = "R";

  1106 > val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[]))));

  1107 val t = Free ("R","?DUMMY") : term

  1108 > val t' = typ_a2real t;

  1109 > cterm_of (sign_of thy) t';

  1110 val it = "R::RealDef.real" : cterm

  1112 > val str = "R=R";

  1113 > val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[]))));

  1114 > atomty (typ_a2real t);

  1115 *** -------------

  1116 *** Const ( op =, [RealDef.real, RealDef.real] => bool)

  1117 ***   Free ( R, RealDef.real)

  1118 ***   Free ( R, RealDef.real)

  1119 > val t' = typ_a2real t;

  1120 > cterm_of (sign_of thy) t';

  1121 val it = "(R::RealDef.real) = R" : cterm

  1123 > val str = "fixed_values [R=R]";

  1124 > val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[]))));

  1125 > val t' = typ_a2real t;

  1126 > cterm_of (sign_of thy) t';

  1127 val it = "fixed_values [(R::RealDef.real) = R]" : cterm

  1128 *)

  1130 (*TODO.WN0609: parse should return a term or a string

  1131 	     (or even more comprehensive datastructure for error-messages)

  1132  i.e. in wrapping with SOME term or NONE the latter is not sufficient*)

  1133 (*2002 fun parseold thy str =

  1134   (let

  1135      val sgn = sign_of thy;

  1136      val t = ((*typ_a2real o*) app_num_tr'1 o term_of)

  1137        (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));

  1138    in SOME (cterm_of sgn t) end)

  1139      handle _ => NONE;*)

  1143 fun parseold thy str =

  1144   (let val t = ((*typ_a2real o*) numbers_to_string)

  1145 		   (Syntax.read_term_global thy str)

  1146    in SOME (cterm_of thy t) end)

  1147     handle _ => NONE;

  1148 (*2002 fun parseN thy str =

  1149   (let

  1150      val sgn = sign_of thy;

  1151      val t = ((*typ_a2real o app_num_tr'1 o*) term_of)

  1152        (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));

  1153    in SOME (cterm_of sgn t) end)

  1154      handle _ => NONE;*)

  1155 fun parseN thy str =

  1156   (let val t = (*(typ_a2real o numbers_to_string)*)

  1157 	   (Syntax.read_term_global thy str)

  1158    in SOME (cterm_of thy t) end)

  1159     handle _ => NONE;

  1160 (*2002 fun parse thy str =

  1161   (let

  1162      val sgn = sign_of thy;

  1163      val t = (typ_a2real o app_num_tr'1 o term_of)

  1164        (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));

  1165    in SOME (cterm_of sgn t) end) (*FIXXXXME 10.8.02: return term !!!*)

  1166      handle _ => NONE;*)

  1167 (*2010 fun parse thy str =

  1168   (let val t = (typ_a2real o app_num_tr'1) (Syntax.read_term_global thy str)

  1169    in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*)

  1170      handle _ => NONE;*)

  1171 fun parse thy str =

  1172   (let val t = (typ_a2real o numbers_to_string)

  1173 		   (Syntax.read_term_global thy str)

  1174    in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*)

  1175      handle _ => NONE;

  1177 (* 10.8.02: for this reason we still have ^^^--------------------

  1178  val thy = SqRoot.thy;

  1179  val str = "(1::real) ^ (2::nat)";

  1180  val sgn = sign_of thy;

  1181  val ct = (read_cterm sgn (str,(TVar(("DUMMY",0),[])))) handle e =>print_exn e;

  1182 (*1*)"(1::real) ^ 2";

  1183  atomty (term_of ct);

  1184 *** -------------

  1185 *** Const ( Nat.power, [real, nat] => real)

  1186 *** . Const ( 1, real)

  1187 *** . Const ( Numeral.number_of, bin => nat)

  1188 *** . . Const ( Numeral.bin.Bit, [bin, bool] => bin)

  1189 *** . . . Const ( Numeral.bin.Bit, [bin, bool] => bin)

  1190 *** . . . . Const ( Numeral.bin.Pls, bin)

  1191 *** . . . . Const ( True, bool)

  1192 *** . . . Const ( False, bool)

  1193  val t = ((app_num_tr' o term_of)

  1194 	 (read_cterm sgn (str,(TVar(("DUMMY",0),[])))))handle e => print_exn e;

  1195  val ct = (cterm_of sgn t) handle e => print_exn e;

  1196 (*2*)"(1::real) ^ (2::nat)";

  1197  atomty (term_of ct);

  1198 *** -------------

  1199 *** Const ( Nat.power, [real, nat] => real)

  1200 *** . Free ( 1, real)

  1201 *** . Free ( 2, nat)                                                            (*1*) Const("2",_) (*2*) Free("2",_)

  1204  val str = "(2::real) ^ (2::nat)";

  1205  val t = (read_cterm sgn (str,(TVar(("DUMMY",0),[])))) handle e => print_exn e;

  1206 val t = "(2::real) ^ 2" : cterm

  1207  val t = ((app_num_tr' o term_of)

  1208 	 (read_cterm sgn (str,(TVar(("DUMMY",0),[])))))handle e => print_exn e;

  1209  val ct = (cterm_of sgn t) handle e => print_exn e;

  1210 Variable "2" has two distinct types

  1211 real

  1212 nat

  1213 uncaught exception TYPE

  1214   raised at: sign.ML:672.26-673.56

  1215              goals.ML:1100.61

  1218  val str = "(3::real) ^ (2::nat)";

  1219  val t = (read_cterm sgn (str,(TVar(("DUMMY",0),[])))) handle e => print_exn e;

  1220 val t = "(3::real) ^ 2" : cterm

  1221  val t = ((app_num_tr' o term_of)

  1222 	 (read_cterm sgn (str,(TVar(("DUMMY",0),[])))))handle e => print_exn e;

  1223  val ct = (cterm_of sgn t) handle e => print_exn e;

  1224 val ct = "(3::real) ^ (2::nat)" : cterm

  1227 Conclusion: The type inference allows different types

  1228             for one and the same  Numeral.number_of

  1229         BUT the type inference doesn't allow

  1230 	    Free ( 2, real) and Free ( 2, nat) within one term

  1231 ---------------       ~~~~                ~~~                  *)

  1232 (*

  1233 > val (SOME ct) = parse thy "(-#5)^^^#3";

  1234 > atomty (term_of ct);

  1235 *** -------------

  1236 *** Const ( Nat.op ^, ['a, nat] => 'a)

  1237 ***   Const ( uminus, 'a => 'a)

  1238 ***     Free ( #5, 'a)

  1239 ***   Free ( #3, nat)

  1240 > val (SOME ct) = parse thy "R=R";

  1241 > atomty (term_of ct);

  1242 *** -------------

  1243 *** Const ( op =, [real, real] => bool)

  1244 ***   Free ( R, real)

  1245 ***   Free ( R, real)

  1247 THIS IS THE OUTPUT FOR VERSION (3) above at typ_a2real !!!!!

  1248 *** -------------

  1249 *** Const ( op =, [RealDef.real, RealDef.real] => bool)

  1250 ***   Free ( R, RealDef.real)

  1251 ***   Free ( R, RealDef.real)                  *)

  1253 (*version for testing local to theories*)

  1254 fun str2t thy str = (term_of o the o (parse thy )) str;

  1256 fun str2term str = (term_of o the o (parse (assoc_thy "Isac.thy"))) str;

  1257 fun str2termN str = (term_of o the o (parseN (assoc_thy "Isac.thy"))) str;

  1258 fun strs2terms ss = map str2term ss;

  1260 (*+ makes a substitution from the output of Pattern.match +*)

  1261 (*fun mk_subs ((id, _):indexname, t:term) = (Free (id,type_of t), t);*)

  1262 fun mk_subs (subs: ((string * int) * (Term.typ * Term.term)) list) =

  1263 let fun mk_sub ((id, _), (ty, tm)) = (Free (id, ty), tm) in

  1264 map mk_sub subs end;

  1266 val atomthm = atomt o #prop o rep_thm;

  1268 (*.instantiate #prop thm with bound variables (as Free).*)

  1269 fun inst_bdv [] t = t : term

  1270   | inst_bdv (instl: (term*term) list) t =

  1271       let fun subst (v as Var((s,_),T)) =

  1272 	      (case explode s of

  1273 		   "b"::"d"::"v"::_ =>

  1274 		   if_none (assoc(instl,Free(s,T))) (Free(s,T))

  1275 		 | _ => v)

  1276             | subst (Abs(a,T,body)) = Abs(a, T, subst body)

  1277             | subst (f$t') = subst f $ subst t'

  1278             | subst t = if_none (assoc(instl,t)) t

  1279       in  subst t  end;

  1282 (*WN050829 caution: is_atom (str2term"q_0/2 * L * x") = true !!!

  1283   use length (vars term) = 1 instead*)

  1284 fun is_atom (Const ("Float.Float",_) $ _) = true

  1285   | is_atom (Const ("ComplexI.I'_'_",_)) = true

  1286   | is_atom (Const ("op *",_) $ t $ Const ("ComplexI.I'_'_",_)) = is_atom t

  1287   | is_atom (Const ("op +",_) $ t1 $ Const ("ComplexI.I'_'_",_)) = is_atom t1

  1288   | is_atom (Const ("op +",_) $ t1 $

  1289 		   (Const ("op *",_) $ t2 $ Const ("ComplexI.I'_'_",_))) =

  1290     is_atom t1 andalso is_atom t2

  1291   | is_atom (Const _) = true

  1292   | is_atom (Free _) = true

  1293   | is_atom (Var _) = true

  1294   | is_atom _ = false;

  1295 (* val t = str2term "q_0/2 * L * x";

  1298 *)

  1299 (*val t = str2term "Float ((1,2),(0,0))";

  1300 > is_atom t;

  1301 val it = true : bool

  1302 > val t = str2term "Float ((1,2),(0,0)) * I__";

  1303 > is_atom t;

  1304 val it = true : bool

  1305 > val t = str2term "Float ((1,2),(0,0)) + Float ((3,4),(0,0)) * I__";

  1306 > is_atom t;

  1307 val it = true : bool

  1308 > val t = str2term "1 + 2*I__";

  1309 > val Const ("op +",_) $ t1 $ (Const ("op *",_) $ t2 $ Const ("ComplexI.I'_'_",_)) = t;

  1310 *)

  1312 (*.adaption from Isabelle/src/Pure/term.ML; reports if ALL Free's

  1313    have found a substitution (required for evaluating the preconditions

  1314    of _incomplete_ models).*)

  1315 fun subst_atomic_all [] t = (false, (*TODO may be 'true' for some terms ?*)

  1316 			     t : term)

  1317   | subst_atomic_all (instl: (term*term) list) t =

  1318       let fun subst (Abs(a,T,body)) =

  1319 	      let val (all, body') = subst body

  1320 	      in (all, Abs(a, T, body')) end

  1321             | subst (f$tt) =

  1322 	      let val (all1, f') = subst f

  1323 		  val (all2, tt') = subst tt

  1324 	      in (all1 andalso all2, f' $ tt') end

  1325             | subst (t as Free _) =

  1326 	      if is_num t then (true, t) (*numerals cannot be subst*)

  1327 	      else (case assoc(instl,t) of

  1328 					 SOME t' => (true, t')

  1329 				       | NONE => (false, t))

  1330             | subst t = (true, if_none (assoc(instl,t)) t)

  1331       in  subst t  end;

  1333 (*.add two terms with a type given.*)

  1334 fun mk_add t1 t2 =

  1335     let val T1 = type_of t1

  1336 	val T2 = type_of t2

  1337     in if T1 <> T2 then raise TYPE ("mk_add gets ",[T1, T2],[t1,t2])

  1338        else (Const ("op +", [T1, T2] ---> T1) $ t1 $ t2)

  1339     end;

author	Walther Neuper <neuper@ist.tugraz.at>
	Wed, 21 Jul 2010 13:53:39 +0200
branch	isac-from-Isabelle2009-2
changeset 37871	875b6efa7ced
child 37876	902c99093693
permissions	-rw-r--r--