wneuper/isa: src/Tools/isac/ProgLang/termC.sml@2c8de368c64c

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

     2    Author: Walther Neuper 1999, Mathias Lehnfeld

     3    (c) due to copyright terms

     4 *)

     6 (*

     7 > (cterm_of thy) a_term;

     8 val it = "empty" : cterm        *)

    10 (*2003 fun match thy t pat =

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

    12     handle _ => [];

    13 fn : theory ->

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

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

    16 (*2003 fun matches thy tm pa = if match thy tm pa = [] then false else true;*)

    17 fun matches thy tm pa =

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

    19     handle _ => false

    21 fun atomtyp t = (*WN10 see raw_pp_typ*)

    22   let

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

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

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

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

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

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

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

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

    33        string_of_int i ^ strs2str' sort)

    34     and atol n [] =

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

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

    37 in tracing (ato 0 t ^ "\n") end;

    38 (*

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

    40 > atomtyp T;

    41 *** Type (fun,[

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

    43 ***   Type (fun,[

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

    45 ***     Type (nat,[])

    46 ***     ]

    47 ***   ]

    48 *)

    50 (*Prog.Tutorial.p.34, Makarius 1005 does the above like this..*)

    51 local

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

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

    54    fun pp_str s   = Pretty.str s

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

    56    fun pp_int i   = pp_str (string_of_int i)

    57    fun pp_sort S = pp_list (map pp_qstr S)

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

    59 in

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

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

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

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

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

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

    66 end

    67 (* install

    68 PolyML.addPrettyPrinter

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

    70 de-install

    71 PolyML.addPrettyPrinter

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

    73 *)

    75 local

    76   fun ato (Const (a, _)) n =

    77 	           "\n*** " ^ indent n ^ "Const (" ^ a ^ ", _)"

    78 	  | ato (Free (a, _)) n =

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

    80 	  | ato (Var ((a, i), _)) n =

    81 	           "\n*** " ^ indent n ^ "Var (" ^ a ^ ", " ^

    82                                                string_of_int i ^ "), _)"

    83 	  | ato (Bound i) n =

    84 	           "\n*** " ^ indent n ^ "Bound " ^ string_of_int i

    85 	  | ato (Abs (a, _, body)) n =

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

    87 	  | ato (f $ t) n = (ato f n ^ ato t (n + 1))

    88 in

    89 fun atomw t = writeln ("\n*** -------------" ^ ato t 0 ^ "\n***");

    90 fun atomt t = tracing ("\n*** -------------" ^ ato t 0 ^ "\n***");

    91 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, i), T)) n =

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

   100 	    string_of_typ T ^ ")"

   101 	  | ato (Bound i) n =

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

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

   104 	    "\n*** " ^ indent n ^ "Abs (" ^ a ^ ", " ^ string_of_typ T ^ ",.."

   105 	    ^ ato body (n + 1)

   106 	  | ato (f $ t) n = ato f n ^ ato t (n + 1)

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

   108 fun atomwy t = (writeln o term_detail2str) t;

   109 fun atomty t = (tracing 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 = 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 = Symbol.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 = Symbol.explode str

   141 	val str' = case ss of

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

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

   144 (*

   145 > int_of_str "123";

   146 val it = SOME 123 : int option

   147 > int_of_str "(-123)";

   148 val it = SOME 123 : int option

   149 > int_of_str "#123";

   150 val it = NONE : int option

   151 > int_of_str "-123";

   152 val it = SOME ~123 : int option

   153 *)

   154 fun int_of_str' str =

   155     case int_of_str str of

   156 	SOME i => i

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

   158 val str2int = int_of_str';

   160 fun is_numeral str = case int_of_str str of

   161 			 SOME _ => true

   162 		       | NONE => false;

   163 val is_no = is_numeral;

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

   165   | is_num _ = false;

   166 (*>

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

   168 val it = true : bool

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

   170 val it = true : bool

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

   172 val it = false : bool

   173 *)

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

   176     (case BasisLibrary.Int.fromString intstr of

   177 	     SOME i => i

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

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

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

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

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

   184 fun vars t =

   185   let

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

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

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

   189       | scan vs (Bound i) = vs

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

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

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

   194 fun is_Free (Free _) = true

   195   | is_Free _ = false;

   196 fun is_fun_id (Const _) = true

   197   | is_fun_id (Free _) = true

   198   | is_fun_id _ = false;

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

   200   | is_f_x _ = false;

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

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

   203   *)

   204 fun vars_str t =

   205   let

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

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

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

   209       | scan vs (Bound i) = vs

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

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

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

   214 fun ids2str t =

   215   let

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

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

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

   219       | scan vs (Bound i) = vs

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

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

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

   223 fun is_bdv str =

   224     case Symbol.explode str of

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

   226       | _ => false;

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

   228   | is_bdv_ _ = false;

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

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

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

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

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

   236 (*compare Logic.unvarify_global, which rejects Free*)

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

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

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

   240   | var2free (t as Bound i) = t

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

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

   244 (*27.8.01: doesn't find some subterm ???!???*)

   245 (*2010 free2var -> Logic.varify, but take care of 'Free ("1",_)'*)

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

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

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

   249   | free2var (t as Bound i) = t

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

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

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

   255 fun list_const T =

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

   257 (*28.8.01: TODO: get type from head of list: 1 arg less!!!*)

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

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

   260 (*

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

   262 > val TT = type_of tt;

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

   264 > (cterm_of thy) ss;

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

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

   268   | isapair2pair t =

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

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

   272 fun isalist2list ls =

   273   let

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

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

   276       | get _ t =

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

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

   279 (*

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

   281 > val l = isalist2list il;

   282 > (tracing o terms2str) l;

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

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

   286 > val l = isalist2list il;

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

   288 *)

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

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

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

   293 val Trueprop = HOLogic.Trueprop;

   294 fun mk_prop t = HOLogic.mk_Trueprop t;

   295 val true_as_term = HOLogic.true_const;

   296 val false_as_term = HOLogic.false_const;

   297 val true_as_cterm = cterm_of (Thy_Info.get_theory "HOL") true_as_term;

   298 val false_as_cterm = cterm_of (Thy_Info.get_theory "HOL") false_as_term;

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

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

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

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

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

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

   308 (** substitution **)

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

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

   312                                           else (x,y)::al)

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

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

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

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

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

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

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

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

   321         | renAbs(t) = t

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

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

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

   331 val lhs_ = (fst o dest_equals');

   332 val rhs_ = (snd o dest_equals');

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

   335   | is_equality _ = false;

   336 fun mk_equality (t,u) = (Const("HOL.eq",[type_of t,type_of u]--->bool) $ t $ u);

   337 fun is_expliceq (Const("HOL.eq",_) $ (Free _) $ u)  =  true

   338   | is_expliceq _ = false;

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

   340   | strip_trueprop t = t;

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

   342 *)

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

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

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

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

   348 	  | coll_prems As _ = SOME As

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

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

   351 (*

   352   val thm = real_mult_div_cancel1;

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

   354   atomt prop;

   355 *** -------------

   356 *** Const ( ==>)

   357 *** . Const ( Trueprop)

   358 *** . . Const ( Not)

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

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

   361 *** . . . . Const ( 0)

   362 *** . Const ( Trueprop)

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

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

   365   atomt t;

   366 *** -------------

   367 *** Const ( ==>)

   368 *** . Const ( Trueprop)

   369 *** . . Const ( Not)

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

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

   372 *** . . . . Const ( 0)

   374   val thm = real_le_anti_sym;

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

   376   atomt prop;

   377 *** -------------

   378 *** Const ( ==>)

   379 *** . Const ( Trueprop)

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

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

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

   383 *** . Const ( ==>)

   384 *** . . Const ( Trueprop)

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

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

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

   388 *** . . Const ( Trueprop)

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

   390 *** .............

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

   392   atomt t;

   393 *** -------------

   394 *** Const ( ==>)

   395 *** . Const ( Trueprop)

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

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

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

   399 *** . Const ( ==>)

   400 *** . . Const ( Trueprop)

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

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

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

   404 *)

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

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

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

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

   410 (*

   411   val thm = real_le_anti_sym;

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

   413   val concl = Logic.strip_imp_concl prop;

   414   val SOME prems = strip_imp_prems' prop;

   415   val prop' = ins_concl prems concl;

   416   prop = prop';

   417   atomt prop;

   418   atomt prop';

   419 *)

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

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

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

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

   427 (*2002 cp from Pure/term.ML --- since 2009 in Pure/old_term.ML*)

   428 fun mem_term (_, []) = false

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

   430 fun subset_term ([], ys) = true

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

   432 fun eq_set_term (xs, ys) =

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

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

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

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

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

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

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

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

   441   | atless _  =  false;

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

   443 fun insert_aterm (t,us) =

   444   let fun inserta [] = [t]

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

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

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

   448               else u :: inserta(us')

   449   in  inserta us  end;

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

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

   453     Var   _ => insert_aterm(t,vars)

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

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

   456   | _ => vars;

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

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

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

   463 (*2002 fun decomp_simp, Pure/thm.ML *)

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

   465     andalso not (is_Var lhs);

   468 fun str_of_int n =

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

   470   else string_of_int n;

   471 (*

   472 > str_of_int 1;

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

   474 val it = "-1" : string

   475 *)

   478 fun power b 0 = 1

   479   | power b n =

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

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

   482 (*

   483 > power 2 3;

   484 val it = 8 : int

   485 > power ~2 3;

   486 val it = ~8 : int

   487 > power ~3 2;

   488 val it = 9 : int

   489 > power 3 ~2;

   490 *)

   491 fun gcd 0 b = b

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

   493 	      else gcd (a mod b) b;

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

   495 	     else if n = 0 then 0 else 1;

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

   498 infix dvd;

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

   501 fun divisors n =

   502   let fun pdiv ds d n =

   503     if d=n then d::ds

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

   505 	 else pdiv ds (d+1) n

   506   in pdiv [] 2 n end;

   508 divisors 30;

   509 divisors 32;

   510 divisors 60;

   511 divisors 11;

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

   514   let fun dbls ds [] = ds

   515 	| dbls ds [i] = ds

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

   517 				else dbls ds (i'::is)

   518   in dbls [] ds end;

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

   520 val it = [] : int list

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

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

   524 fun squfact 0 = 0

   525   | squfact 1 = 1

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

   527 (*> squfact 30;

   528 val it = 1 : int

   529 > squfact 32;

   530 val it = 4 : int

   531 > squfact 60;

   532 val it = 2 : int

   533 > squfact 11;

   534 val it = 1 : int*)

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

   538   | dest_type T =

   539     (atomtyp T;

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

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

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

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

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

   547 val it = true : bool

   548 *)

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

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

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

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

   553 val it = true : bool

   554 *)

   555 fun pairt t1 t2 =

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

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

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

   559 > t = pairt t1 t2;

   560 val it = true : bool*)

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

   564     (case int_of_str s of

   565 	 SOME s' => s'

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

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

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

   570   Const ("Groups.times_class.times", [T, T] ---> T) $ (term_of_num T fact) $

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

   572 (*

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

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

   575 (cterm_of thy) t;

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

   577 *)

   578 fun var_op_num v op_ optype ntyp n =

   579   Const (op_, optype) $ v $

   580    Free (str_of_int  n, ntyp);

   582 fun num_op_var v op_ optype ntyp n =

   583   Const (op_,optype) $

   584    Free (str_of_int n, ntyp) $ v;

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

   587   Const (op_,Top) $

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

   589 (*

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

   591 > atomty t;

   592 > string_of_cterm ((cterm_of thy) t);

   593 *)

   597 fun const_in str (Const _) = false

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

   599   | const_in str (Bound _) = false

   600   | const_in str (Var _) = false

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

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

   603 (*

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

   605 > const_in "sqrt" t;

   606 val it = true : bool

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

   608 > const_in "sqrt" t;

   609 val it = false : bool

   610 *)

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

   613 (*fun calc "Groups.plus_class.plus"  (n1, n2) = n1+n2

   614   | calc "Groups.minus_class.minus"  (n1, n2) = n1-n2

   615   | calc "Groups.times_class.times"  (n1, n2) = n1*n2

   616   | calc "Rings.inverse_class.divide"(n1, n2) = n1 div n2

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

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

   619 fun calc_equ "less"  (n1, n2) = n1 < n2

   620   | calc_equ "less_eq" (n1, n2) = n1 <= n2

   621   | calc_equ op_ _ =

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

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

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

   626 fun mk_thmid thmid op_ n1 n2 =

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

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

   630   (arg1,arg2,range)

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

   632 (* -----

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

   634 > val hT = type_of (head_of t);

   635 > dest_binop_typ hT;

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

   637  ----- *)

   640 (** transform binary numeralsstrings **)

   641 (*Makarius 100308, hacked by WN*)

   642 val numbers_to_string =

   643   let

   644     fun dest_num t =

   645       (case try HOLogic.dest_number t of

   646         SOME (T, i) =>

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

   648             SOME (Free (signed_string_of_int i, T))

   649           (*else NONE  WN*)

   650       | NONE => NONE);

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

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

   654           (case dest_num t of

   655             SOME t' => t'

   656           | NONE => to_str u1 $ to_str u2)

   657       | to_str t = perhaps dest_num t;

   658   in to_str end

   660 (*.make uminus uniform:

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

   662 to be used immediately before evaluation of numerals;

   663 see Scripts/calculate.sml .*)

   664 (*2002 fun(*app_num_tr'2 (Const("0",T)) = Free("0",T)

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

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

   667     (case int_of_str s of SOME i =>

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

   669 		       | NONE => t)

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

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

   672     Free(NumeralSyntax.dest_bin_str t, T)

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

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

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

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

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

   678   | app_num_tr'2 t = t;

   679 *)

   680 val uminus_to_string =

   681     let

   682 	fun dest_num t =

   683 	    (case t of

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

   685 		 (case int_of_str s of

   686 		      SOME i =>

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

   688 		    | NONE => NONE)

   689 	       | _ => NONE);

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

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

   693             (case dest_num t of

   694 		 SOME t' => t'

   695                | NONE => to_str u1 $ to_str u2)

   696 	  | to_str t = perhaps dest_num t;

   697     in to_str end;

   700 (*2002 fun num_str thm =

   701   let

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

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

   704 	rep_thm_G thm;

   705     val prop' = app_num_tr'1 prop;

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

   707 fun num_str thm =

   708   let val (deriv,

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

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

   711     val prop' = numbers_to_string prop;

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

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

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

   716     Thm (xstring,

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

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

   720 (*11.1.00: not used, fix-typed +,*,-,^ instead *)

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

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

   725 (* assumes only 1 type for numerals

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

   727 fun get_types t =

   728   let

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

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

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

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

   733       | get ts  (Bound i) = ts

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

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

   736   in distinct (get [] t) end;

   737 (*

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

   739 get_types t;

   740 *)

   742 (*11.1.00: not used, fix-typed +,*,-,^ instead *)

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

   744     (case assoc (al,s) of

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

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

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

   748   if is_no s then

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

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

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

   752   else (case assoc (al,s) of

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

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

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

   756   | set_types al (Bound i) = Bound i

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

   758 		 (case assoc (al,s) of

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

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

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

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

   763 (*

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

   765 val al = get_types t;

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

   768 atomty t;                         (* 'a *)

   769 val t' = set_types al t;

   770 atomty t';                        (*real*)

   771 (cterm_of thy) t';

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

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

   775   "#5 * x + x ^^^ #2 = (#2 + x) ^^^ #2";

   776 atomty t;

   777 val t' = set_types al t;

   778 atomty t';

   779 (cterm_of thy) t';

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

   781 *)

   784 (** from Descript.ML **)

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

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

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

   790   | is_list _ = false;

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

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

   793 > is_list ty;

   794 val it = false : bool

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

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

   797 > is_list ty;

   798 val it = true : bool *)

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

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

   805 (*Special case: one argument cp from Isabelle2002/src/Pure/term.ML*)

   806 fun subst_bound (arg, t) : term = (*WN100908 neglects 'raise Same.SAME'*)

   807   let fun subst (t as Bound i, lev) =

   808             if i<lev then  t    (*var is locally bound*)

   809             else  if i=lev then incr_boundvars lev arg

   810                            else Bound(i-1)  (*loose: change it*)

   811         | subst (Abs(a,T,body), lev) = Abs(a, T,  subst(body,lev+1))

   812         | subst (f$t, lev) =  subst(f,lev)  $  subst(t,lev)

   813         | subst (t,lev) = t

   814   in  subst (t,0)  end;

   816 (*instantiate let; necessary for ass_up*)

   817 fun inst_abs thy (Const sT) = Const sT  (*TODO.WN100907 drop thy*)

   818   | inst_abs thy (Free sT) = Free sT

   819   | inst_abs thy (Bound n) = Bound n

   820   | inst_abs thy (Var iT) = Var iT

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

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

   823     (*fun variant_abs: term.ML*)

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

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

   826   | inst_abs thy t = t;

   827 (*val scr =

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

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

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

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

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

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

   834    \                          [BOOL e_1, REAL v_1])\

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

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

   837 > tracing(term2str ttt);

   838 > atomt ttt;

   839 *** -------------

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

   841 *** . Free ( f_, )

   842 *** . Free ( v_, )

   843 *** . Free ( eqs_, )

   844 *** . Const ( Let)

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

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

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

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

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

   850 *** . . Abs( h_,..

   851 *** . . . Const ( Let)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   886 *** . . . . . . . . . . . . Const ( Script.BOOL)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   904 > val ttt' = inst_abs thy ttt;

   905 > tracing(term2str ttt');

   906 Script Make_fun_by_explicit f_ v_ eqs_ =

   907   ... as above ...

   908 > atomt ttt';

   909 *** -------------

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

   911 *** . Free ( f_, )

   912 *** . Free ( v_, )

   913 *** . Free ( eqs_, )

   914 *** . Const ( Let)

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

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

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

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

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

   920 *** . . Abs( h_,..

   921 *** . . . Const ( Let)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   956 *** . . . . . . . . . . . . Const ( Script.BOOL)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   974 Note numbering of de Bruijn indexes !

   976 Script Make_fun_by_explicit f_ v_ eqs_ =

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

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

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

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

   981      s_1 =

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

   983         [BOOL e_1 BOUND_2, REAL v_1 BOUND_0]

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

   985 *)

   987 (* for parse and parse_patt: fix all types to real *)

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

   989     if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT

   990     else Type (s, [])

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

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

   993     if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT

   994     else TFree (s, srt)

   995   | T_a2real (TVar ((s, i), srt)) =

   996     if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT

   997     else TVar ((s, i), srt)

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

  1000 (*FIXME .. fixes the type (+see Typefix.thy*)

  1001 fun typ_a2real (Const( s, T)) = (Const( s, T_a2real T))

  1002   | typ_a2real (Free( s, T)) = (Free( s, T_a2real T))

  1003   | typ_a2real (Var( n, T)) = (Var( n, T_a2real T))

  1004   | typ_a2real (Bound i) = (Bound i)

  1005   | typ_a2real (Abs(s,T,t)) = Abs(s, T, typ_a2real t)

  1006   | typ_a2real (t1 $ t2) = (typ_a2real t1) $ (typ_a2real t2);

  1009 (* before 2002 *)

  1010 fun parseold thy str =

  1011   (let val t = ((*typ_a2real o*) numbers_to_string)

  1012 		   (Syntax.read_term_global thy str)

  1013    in SOME (cterm_of thy t) end)

  1014     handle _ => NONE;

  1015 (*2002 fun parseN thy str =

  1016   (let

  1017      val sgn = sign_of thy;

  1018      val t = ((*typ_a2real o app_num_tr'1 o*) term_of)

  1019        (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));

  1020    in SOME (cterm_of sgn t) end)

  1021      handle _ => NONE;*)

  1022 fun parseN thy str =

  1023   (let val t = (*(typ_a2real o numbers_to_string)*)

  1024 	   (Syntax.read_term_global thy str)

  1025    in SOME (cterm_of thy t) end)

  1026     handle _ => NONE;

  1027 (*2002 fun parse thy str =

  1028   (let

  1029      val sgn = sign_of thy;

  1030      val t = (typ_a2real o app_num_tr'1 o term_of)

  1031        (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));

  1032    in SOME (cterm_of sgn t) end) (*FIXXXXME 10.8.02: return term !!!*)

  1033      handle _ => NONE;*)

  1034 (*2010 fun parse thy str =

  1035   (let val t = (typ_a2real o app_num_tr'1) (Syntax.read_term_global thy str)

  1036    in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*)

  1037      handle _ => NONE;*)

  1038 fun parse thy str =

  1039   (let val t = (typ_a2real o numbers_to_string)

  1040 		   (Syntax.read_term_global thy str)

  1041    in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*)

  1042      handle _ => NONE;

  1043 (*

  1044 > val (SOME ct) = parse thy "(-#5)^^^#3";

  1045 > atomty (term_of ct);

  1046 *** -------------

  1047 *** Const ( Nat.op ^, ['a, nat] => 'a)

  1048 ***   Const ( uminus, 'a => 'a)

  1049 ***     Free ( #5, 'a)

  1050 ***   Free ( #3, nat)

  1051 > val (SOME ct) = parse thy "R=R";

  1052 > atomty (term_of ct);

  1053 *** -------------

  1054 *** Const ( op =, [real, real] => bool)

  1055 ***   Free ( R, real)

  1056 ***   Free ( R, real)

  1058 THIS IS THE OUTPUT FOR VERSION (3) above at typ_a2real !!!!!

  1059 *** -------------

  1060 *** Const ( op =, [RealDef.real, RealDef.real] => bool)

  1061 ***   Free ( R, RealDef.real)

  1062 ***   Free ( R, RealDef.real)                  *)

  1064 (*WN110317 parseNEW will replace parse after introduction of ctxt completed*)

  1065 fun parseNEW ctxt str = SOME (Syntax.read_term ctxt str |> numbers_to_string)

  1066       handle _ => NONE;

  1068 (* parse term patterns; Var ("v",_), i.e. "?v", are required for instantiation*)

  1069 fun parse_patt thy str = (thy, str) |>> thy2ctxt

  1070                                     |-> ProofContext.read_term_pattern

  1071                                     |> numbers_to_string (*TODO drop*)

  1072                                     |> typ_a2real;       (*TODO drop*)

  1074 (*version for testing local to theories*)

  1075 fun str2term_ thy str = (term_of o the o (parse thy)) str;

  1076 (*WN110520

  1077 fun str2term str = (term_of o the o (parse (Thy_Info.get_theory "Isac"))) str;*)

  1078 fun str2term str = parse_patt (Thy_Info.get_theory "Isac") str

  1079 fun strs2terms ss = map str2term ss;

  1080 fun str2termN str = (term_of o the o (parseN (Thy_Info.get_theory "Isac"))) str;

  1082 (*+ makes a substitution from the output of Pattern.match +*)

  1083 (*fun mk_subs ((id, _):indexname, t:term) = (Free (id,type_of t), t);*)

  1084 fun mk_subs (subs: ((string * int) * (Term.typ * Term.term)) list) =

  1085 let fun mk_sub ((id, _), (ty, tm)) = (Free (id, ty), tm) in

  1086 map mk_sub subs end;

  1088 val atomthm = atomt o #prop o rep_thm;

  1090 (*.instantiate #prop thm with bound variables (as Free).*)

  1091 fun inst_bdv [] t = t : term

  1092   | inst_bdv (instl: (term*term) list) t =

  1093       let fun subst (v as Var((s,_),T)) =

  1094 	      (case Symbol.explode s of

  1095 		   "b"::"d"::"v"::_ =>

  1096 		   if_none (assoc(instl,Free(s,T))) (Free(s,T))

  1097 		 | _ => v)

  1098             | subst (Abs(a,T,body)) = Abs(a, T, subst body)

  1099             | subst (f$t') = subst f $ subst t'

  1100             | subst t = if_none (assoc(instl,t)) t

  1101       in  subst t  end;

  1104 (*WN050829 caution: is_atom (str2term"q_0/2 * L * x") = true !!!

  1105   use length (vars term) = 1 instead*)

  1106 fun is_atom (Const ("Float.Float",_) $ _) = true

  1107   | is_atom (Const ("ComplexI.I'_'_",_)) = true

  1108   | is_atom (Const ("Groups.times_class.times",_) $ t $ Const ("ComplexI.I'_'_",_)) = is_atom t

  1109   | is_atom (Const ("Groups.plus_class.plus",_) $ t1 $ Const ("ComplexI.I'_'_",_)) = is_atom t1

  1110   | is_atom (Const ("Groups.plus_class.plus",_) $ t1 $

  1111 		   (Const ("Groups.times_class.times",_) $ t2 $ Const ("ComplexI.I'_'_",_))) =

  1112     is_atom t1 andalso is_atom t2

  1113   | is_atom (Const _) = true

  1114   | is_atom (Free _) = true

  1115   | is_atom (Var _) = true

  1116   | is_atom _ = false;

  1117 (* val t = str2term "q_0/2 * L * x";

  1120 *)

  1121 (*val t = str2term "Float ((1,2),(0,0))";

  1122 > is_atom t;

  1123 val it = true : bool

  1124 > val t = str2term "Float ((1,2),(0,0)) * I__";

  1125 > is_atom t;

  1126 val it = true : bool

  1127 > val t = str2term "Float ((1,2),(0,0)) + Float ((3,4),(0,0)) * I__";

  1128 > is_atom t;

  1129 val it = true : bool

  1130 > val t = str2term "1 + 2*I__";

  1131 > val Const ("Groups.plus_class.plus",_) $ t1 $ (Const ("Groups.times_class.times",_) $ t2 $ Const ("ComplexI.I'_'_",_)) = t;

  1132 *)

  1134 (*.adaption from Isabelle/src/Pure/term.ML; reports if ALL Free's

  1135    have found a substitution (required for evaluating the preconditions

  1136    of _incomplete_ models).*)

  1137 fun subst_atomic_all [] t = (false, (*TODO may be 'true' for some terms ?*)

  1138 			     t : term)

  1139   | subst_atomic_all (instl: (term*term) list) t =

  1140       let fun subst (Abs(a,T,body)) =

  1141 	      let val (all, body') = subst body

  1142 	      in (all, Abs(a, T, body')) end

  1143             | subst (f$tt) =

  1144 	      let val (all1, f') = subst f

  1145 		  val (all2, tt') = subst tt

  1146 	      in (all1 andalso all2, f' $ tt') end

  1147             | subst (t as Free _) =

  1148 	      if is_num t then (true, t) (*numerals cannot be subst*)

  1149 	      else (case assoc(instl,t) of

  1150 					 SOME t' => (true, t')

  1151 				       | NONE => (false, t))

  1152             | subst t = (true, if_none (assoc(instl,t)) t)

  1153       in  subst t  end;

  1155 (*.add two terms with a type given.*)

  1156 fun mk_add t1 t2 =

  1157     let val T1 = type_of t1

  1158 	val T2 = type_of t2

  1159     in if T1 <> T2 then raise TYPE ("mk_add gets ",[T1, T2],[t1,t2])

  1160        else (Const ("Groups.plus_class.plus", [T1, T2] ---> T1) $ t1 $ t2)

  1161     end;

author	Walther Neuper <neuper@ist.tugraz.at>
	Sat, 07 Jan 2012 10:06:06 +0100
changeset 42360	2c8de368c64c
parent 42359	b9d382f20232
child 42376	9e59542132b3
permissions	-rw-r--r--