wneuper/isa: src/Tools/isac/ProgLang/termC.sml@f08422eeef24

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

     2    Author: Walther Neuper 1999, Mathias Lehnfeld

     3    (c) due to copyright terms

     4 *)

     6 fun isastr_of_int i = if i >= 0 then string_of_int i else "-" ^ string_of_int (abs i)

     8 (*

     9 > (cterm_of thy) a_term;

    10 val it = "empty" : cterm        *)

    12 (*2003 fun match thy t pat =

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

    14     handle _ => [];

    15 fn : theory ->

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

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

    18 (*2003 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 = (*WN10 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 tracing (ato 0 t ^ "\n") end;

    40 (*

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

    42 > atomtyp T;

    43 *** Type (fun,[

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

    45 ***   Type (fun,[

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

    47 ***     Type (nat,[])

    48 ***     ]

    49 ***   ]

    50 *)

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

    53 local

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

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

    56    fun pp_str s   = Pretty.str s

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

    58    fun pp_int i   = pp_str (string_of_int i)

    59    fun pp_sort S = pp_list (map pp_qstr S)

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

    61 in

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

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

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

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

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

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

    68 end

    69 (* install

    70 PolyML.addPrettyPrinter

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

    72 de-install

    73 PolyML.addPrettyPrinter

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

    75 *)

    77 local

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

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

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

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

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

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

    84                                                string_of_int i ^ "), _)"

    85 	  | ato (Bound i) n =

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

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

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

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

    90 in

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

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

    93 end;

    95 fun term_detail2str t =

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

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

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

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

   100 	  | ato (Var ((a, i), T)) n =

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

   102 	    string_of_typ T ^ ")"

   103 	  | ato (Bound i) n =

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

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

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

   107 	    ^ ato body (n + 1)

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

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

   110 fun term_detail2str_thy thy t =

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

   112 	    "\n*** " ^ indent n ^ "Const (" ^ a ^ ", " ^ string_of_typ_thy thy T ^ ")"

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

   114 	    "\n*** " ^ indent n ^ "Free (" ^ a ^ ", " ^ string_of_typ_thy thy T ^ ")"

   115 	  | ato (Var ((a, i), T)) n =

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

   117 	    string_of_typ_thy thy T ^ ")"

   118 	  | ato (Bound i) n =

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

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

   121 	    "\n*** " ^ indent n ^ "Abs (" ^ a ^ ", " ^ string_of_typ_thy thy T ^ ",.."

   122 	    ^ ato body (n + 1)

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

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

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

   126 fun atomty t = (tracing o term_detail2str) t;

   127 fun atomty_thy thy t = (tracing o (term_detail2str_thy thy)) t;

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

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

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

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

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

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

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

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

   138   | contains_term (f $ f') t =

   139     contains_term f t orelse contains_term f' t

   140   | contains_term s t = t = s;

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

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

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

   144   | contains_Var (Var _) = true

   145   | contains_Var _ = false;

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

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

   148    *)

   150 (*fun int_of_str str =

   151     let val ss = Symbol.explode str

   152 	val str' = case ss of

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

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

   155 	     SOME i => SOME i

   156 	   | NONE => NONE end;*)

   157 fun int_of_str str =

   158     let val ss = Symbol.explode str

   159 	val str' = case ss of

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

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

   162 (*

   163 > int_of_str "123";

   164 val it = SOME 123 : int option

   165 > int_of_str "(-123)";

   166 val it = SOME 123 : int option

   167 > int_of_str "#123";

   168 val it = NONE : int option

   169 > int_of_str "-123";

   170 val it = SOME ~123 : int option

   171 *)

   172 fun int_of_str' str =

   173     case int_of_str str of

   174 	SOME i => i

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

   176 val str2int = int_of_str';

   178 fun is_numeral str = case int_of_str str of

   179 			 SOME _ => true

   180 		       | NONE => false;

   181 val is_no = is_numeral;

   182 (* see /home/neuper/repos/FHpoly/src/HOL/Decision_Procs/Approximation.thy:

   184   val mk_int = HOLogic.mk_number @{typ int} o @{code integer_of_int};

   185   val dest_int = @{code int_of_integer} o snd o HOLogic.dest_number;

   187   fun nat_of_term t = @{code nat_of_integer}

   188     (HOLogic.dest_nat t handle TERM _ => snd (HOLogic.dest_number t));

   189   etc...

   190 *)

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

   192   | is_num _ = false;

   193 (*>

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

   195 val it = true : bool

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

   197 val it = true : bool

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

   199 val it = false : bool

   200 *)

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

   203     (case BasisLibrary.Int.fromString intstr of

   204 	     SOME i => i

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

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

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

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

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

   211 fun vars t =

   212   let

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

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

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

   216       | scan vs (Bound i) = vs

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

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

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

   221 fun is_Free (Free _) = true

   222   | is_Free _ = false;

   223 fun is_fun_id (Const _) = true

   224   | is_fun_id (Free _) = true

   225   | is_fun_id _ = false;

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

   227   | is_f_x _ = false;

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

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

   230   *)

   231 fun vars_str t =

   232   let

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

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

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

   236       | scan vs (Bound i) = vs

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

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

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

   241 fun ids2str t =

   242   let

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

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

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

   246       | scan vs (Bound i) = vs

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

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

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

   250 fun is_bdv str =

   251     case Symbol.explode str of

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

   253       | _ => false;

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

   255   | is_bdv_ _ = false;

   257 (* is a term a substitution for a bdv as found in programs *)

   258 fun is_bdv_subst (Const ("List.list.Cons", _) $

   259       (Const ("Product_Type.Pair", _) $ Free (str, _) $ _) $ _) = is_bdv str

   260   | is_bdv_subst _ = false;

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

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

   264 fun str_of_free_opt (Free (s,_)) = SOME s

   265   | str_of_free_opt _ = NONE

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

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

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

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

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

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

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

   274   | var2free (t as Bound i) = t

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

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

   278 (*27.8.01: doesn't find some subterm ???!???*)

   279 (*2010 free2var -> Logic.varify, but take care of 'Free ("1",_)'*)

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

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

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

   283   | free2var (t as Bound i) = t

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

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

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

   289 fun list_const T =

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

   291 (*28.8.01: TODO: get type from head of list: 1 arg less!!!*)

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

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

   294 (*

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

   296 > val TT = type_of tt;

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

   298 > (cterm_of thy) ss;

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

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

   302   | isapair2pair t =

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

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

   306 fun isalist2list ls =

   307   let

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

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

   310       | get _ t =

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

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

   313 (*

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

   315 > val l = isalist2list il;

   316 > (tracing o terms2str) l;

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

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

   320 > val l = isalist2list il;

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

   322 *)

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

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

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

   327 val Trueprop = HOLogic.Trueprop;

   328 fun mk_prop t = HOLogic.mk_Trueprop t;

   329 val true_as_cterm = cterm_of (Thy_Info.get_theory "HOL") @{term True};

   330 val false_as_cterm = cterm_of (Thy_Info.get_theory "HOL") @{term False};

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

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

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

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

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

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

   340 (** substitution **)

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

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

   344                                           else (x,y)::al)

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

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

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

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

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

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

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

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

   353         | renAbs(t) = t

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

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

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

   363 val lhs_ = (fst o dest_equals');

   364 val rhs_ = (snd o dest_equals');

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

   367   | is_equality _ = false;

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

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

   370   | is_expliceq _ = false;

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

   372   | strip_trueprop t = t;

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

   374 *)

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

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

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

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

   380 	  | coll_prems As _ = SOME As

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

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

   383 (*

   384   val thm = real_mult_div_cancel1;

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

   386   atomt prop;

   387 *** -------------

   388 *** Const ( ==>)

   389 *** . Const ( Trueprop)

   390 *** . . Const ( Not)

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

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

   393 *** . . . . Const ( 0)

   394 *** . Const ( Trueprop)

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

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

   397   atomt t;

   398 *** -------------

   399 *** Const ( ==>)

   400 *** . Const ( Trueprop)

   401 *** . . Const ( Not)

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

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

   404 *** . . . . Const ( 0)

   406   val thm = real_le_anti_sym;

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

   408   atomt prop;

   409 *** -------------

   410 *** Const ( ==>)

   411 *** . Const ( Trueprop)

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

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

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

   415 *** . Const ( ==>)

   416 *** . . Const ( Trueprop)

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

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

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

   420 *** . . Const ( Trueprop)

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

   422 *** .............

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

   424   atomt t;

   425 *** -------------

   426 *** Const ( ==>)

   427 *** . Const ( Trueprop)

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

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

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

   431 *** . Const ( ==>)

   432 *** . . Const ( Trueprop)

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

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

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

   436 *)

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

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

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

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

   442 (*

   443   val thm = real_le_anti_sym;

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

   445   val concl = Logic.strip_imp_concl prop;

   446   val SOME prems = strip_imp_prems' prop;

   447   val prop' = ins_concl prems concl;

   448   prop = prop';

   449   atomt prop;

   450   atomt prop';

   451 *)

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

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

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

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

   459 (*2002 cp from Pure/term.ML --- since 2009 in Pure/old_term.ML*)

   460 fun mem_term (_, []) = false

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

   462 fun subset_term ([], ys) = true

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

   464 fun eq_set_term (xs, ys) =

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

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

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

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

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

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

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

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

   473   | atless _  =  false;

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

   475 fun insert_aterm (t,us) =

   476   let fun inserta [] = [t]

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

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

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

   480               else u :: inserta(us')

   481   in  inserta us  end;

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

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

   485     Var   _ => insert_aterm(t,vars)

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

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

   488   | _ => vars;

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

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

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

   495 (*2002 fun decomp_simp, Pure/thm.ML *)

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

   497     andalso not (is_Var lhs);

   500 fun str_of_int n =

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

   502   else string_of_int n;

   503 (*

   504 > str_of_int 1;

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

   506 val it = "-1" : string

   507 *)

   510 fun power b 0 = 1

   511   | power b n =

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

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

   514 (*

   515 > power 2 3;

   516 val it = 8 : int

   517 > power ~2 3;

   518 val it = ~8 : int

   519 > power ~3 2;

   520 val it = 9 : int

   521 > power 3 ~2;

   522 *)

   523 fun gcd 0 b = b

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

   525 	      else gcd (a mod b) b;

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

   527 	     else if n = 0 then 0 else 1;

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

   530 infix dvd;

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

   533 fun divisors n =

   534   let fun pdiv ds d n =

   535     if d=n then d::ds

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

   537 	 else pdiv ds (d+1) n

   538   in pdiv [] 2 n end;

   540 divisors 30;

   541 divisors 32;

   542 divisors 60;

   543 divisors 11;

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

   546   let fun dbls ds [] = ds

   547 	| dbls ds [i] = ds

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

   549 				else dbls ds (i'::is)

   550   in dbls [] ds end;

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

   552 val it = [] : int list

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

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

   556 fun squfact 0 = 0

   557   | squfact 1 = 1

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

   559 (*> squfact 30;

   560 val it = 1 : int

   561 > squfact 32;

   562 val it = 4 : int

   563 > squfact 60;

   564 val it = 2 : int

   565 > squfact 11;

   566 val it = 1 : int*)

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

   570   | dest_type T =

   571     (atomtyp T;

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

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

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

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

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

   579 val it = true : bool

   580 *)

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

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

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

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

   585 val it = true : bool

   586 *)

   587 fun pairt t1 t2 =

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

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

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

   591 > t = pairt t1 t2;

   592 val it = true : bool*)

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

   596     (case int_of_str s of

   597 	 SOME s' => s'

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

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

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

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

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

   604 (*

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

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

   607 (cterm_of thy) t;

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

   609 *)

   610 fun var_op_num v op_ optype ntyp n =

   611   Const (op_, optype) $ v $

   612    Free (str_of_int  n, ntyp);

   614 fun num_op_var v op_ optype ntyp n =

   615   Const (op_,optype) $

   616    Free (str_of_int n, ntyp) $ v;

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

   619   Const (op_,Top) $

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

   621 (*

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

   623 > atomty t;

   624 > string_of_cterm ((cterm_of thy) t);

   625 *)

   629 fun const_in str (Const _) = false

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

   631   | const_in str (Bound _) = false

   632   | const_in str (Var _) = false

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

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

   635 (*

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

   637 > const_in "sqrt" t;

   638 val it = true : bool

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

   640 > const_in "sqrt" t;

   641 val it = false : bool

   642 *)

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

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

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

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

   648   | calc "Fields.inverse_class.divide"(n1, n2) = n1 div n2

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

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

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

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

   653   | calc_equ op_ _ =

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

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

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

   658 fun mk_thmid thmid op_ n1 n2 =

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

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

   662   (arg1,arg2,range)

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

   664 (* -----

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

   666 > val hT = type_of (head_of t);

   667 > dest_binop_typ hT;

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

   669  ----- *)

   672 (** transform binary numeralsstrings **)

   673 (*Makarius 100308, hacked by WN*)

   674 val numbers_to_string =

   675   let

   676     fun dest_num t =

   677       (case try HOLogic.dest_number t of

   678         SOME (T, i) =>

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

   680             SOME (Free (signed_string_of_int i, T))

   681           (*else NONE  WN*)

   682       | NONE => NONE);

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

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

   686           (case dest_num t of

   687             SOME t' => t'

   688           | NONE => to_str u1 $ to_str u2)

   689       | to_str t = perhaps dest_num t;

   690   in to_str end

   692 (*.make uminus uniform:

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

   694 to be used immediately before evaluation of numerals;

   695 see Scripts/calculate.sml .*)

   696 (*2002 fun(*app_num_tr'2 (Const("0",T)) = Free("0",T)

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

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

   699     (case int_of_str s of SOME i =>

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

   701 		       | NONE => t)

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

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

   704     Free(NumeralSyntax.dest_bin_str t, T)

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

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

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

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

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

   710   | app_num_tr'2 t = t;

   711 *)

   712 val uminus_to_string =

   713     let

   714 	fun dest_num t =

   715 	    (case t of

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

   717 		 (case int_of_str s of

   718 		      SOME i =>

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

   720 		    | NONE => NONE)

   721 	       | _ => NONE);

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

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

   725             (case dest_num t of

   726 		 SOME t' => t'

   727                | NONE => to_str u1 $ to_str u2)

   728 	  | to_str t = perhaps dest_num t;

   729     in to_str end;

   732 (*2002 fun num_str thm =

   733   let

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

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

   736 	rep_thm_G thm;

   737     val prop' = app_num_tr'1 prop;

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

   739 fun num_str thm =

   740   let val (deriv,

   741 	   {thy = thy, tags = tags, maxidx = maxidx, shyps = shyps,

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

   743     val prop' = numbers_to_string prop;

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

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

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

   748     Thm (xstring,

   749 	 num_str (Proof_Context.get_thm (thy2ctxt' "Isac") xstring));

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

   752 (*11.1.00: not used, fix-typed +,*,-,^ instead *)

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

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

   757 (* assumes only 1 type for numerals

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

   759 fun get_types t =

   760   let

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

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

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

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

   765       | get ts  (Bound i) = ts

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

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

   768   in distinct (get [] t) end;

   769 (*

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

   771 get_types t;

   772 *)

   774 (*11.1.00: not used, fix-typed +,*,-,^ instead *)

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

   776     (case assoc (al,s) of

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

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

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

   780   if is_no s then

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

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

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

   784   else (case assoc (al,s) of

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

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

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

   788   | set_types al (Bound i) = Bound i

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

   790 		 (case assoc (al,s) of

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

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

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

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

   795 (*

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

   797 val al = get_types t;

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

   800 atomty t;                         (* 'a *)

   801 val t' = set_types al t;

   802 atomty t';                        (*real*)

   803 (cterm_of thy) t';

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

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

   807   "#5 * x + x ^^^ #2 = (#2 + x) ^^^ #2";

   808 atomty t;

   809 val t' = set_types al t;

   810 atomty t';

   811 (cterm_of thy) t';

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

   813 *)

   816 (** from Descript.ML **)

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

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

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

   822   | is_list _ = false;

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

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

   825 > is_list ty;

   826 val it = false : bool

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

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

   829 > is_list ty;

   830 val it = true : bool *)

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

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

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

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

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

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

   841             else  if i=lev then incr_boundvars lev arg

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

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

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

   845         | subst (t,lev) = t

   846   in  subst (t,0)  end;

   848 (*instantiate let; necessary for ass_up*)

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

   850   | inst_abs thy (Free sT) = Free sT

   851   | inst_abs thy (Bound n) = Bound n

   852   | inst_abs thy (Var iT) = Var iT

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

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

   855     (*fun variant_abs: term.ML*)

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

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

   858   | inst_abs thy t = t;

   859 (*val scr =

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

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

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

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

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

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

   866    \                          [BOOL e_1, REAL v_1])\

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

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

   869 > tracing(term2str ttt);

   870 > atomt ttt;

   871 *** -------------

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

   873 *** . Free ( f_, )

   874 *** . Free ( v_, )

   875 *** . Free ( eqs_, )

   876 *** . Const ( Let)

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

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

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

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

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

   882 *** . . Abs( h_,..

   883 *** . . . Const ( Let)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   918 *** . . . . . . . . . . . . Const ( Script.BOOL)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   936 > val ttt' = inst_abs thy ttt;

   937 > tracing(term2str ttt');

   938 Script Make_fun_by_explicit f_ v_ eqs_ =

   939   ... as above ...

   940 > atomt ttt';

   941 *** -------------

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

   943 *** . Free ( f_, )

   944 *** . Free ( v_, )

   945 *** . Free ( eqs_, )

   946 *** . Const ( Let)

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

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

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

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

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

   952 *** . . Abs( h_,..

   953 *** . . . Const ( Let)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   988 *** . . . . . . . . . . . . Const ( Script.BOOL)

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

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

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

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

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

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

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

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

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

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

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

  1000 *** . . . . . . . . . . . . . . . Const ( Tools.rhs)

  1001 *** . . . . . . . . . . . . . . . Const ( List.hd)

  1002 *** . . . . . . . . . . . . . . . Free ( s_1, )         <----- Bound 0

  1003 *** . . . . . . . . . . . . . Const ( List.list.Nil)

  1004 *** . . . . . . . . . . . . Free ( h_, )                <----- Bound 4

  1006 Note numbering of de Bruijn indexes !

  1008 Script Make_fun_by_explicit f_ v_ eqs_ =

  1009  let h_ = (hd o filterVar f_) eqs_;

  1010      e_1 = hd (dropWhile (ident h_ BOUND_0) eqs_);

  1011      vs_ = dropWhile (ident f_) (Vars h_ BOUND_1);

  1012      v_1 = hd (dropWhile (ident v_) vs_ BOUND_0);

  1013      s_1 =

  1014        SubProblem (DiffApp_, [univar, equation], [no_met])

  1015         [BOOL e_1 BOUND_2, REAL v_1 BOUND_0]

  1016  in Substitute [(v_1 BOUND_1 = (rhs o hd) s_1 BOUND_0)] h_ BOUND_4

  1017 *)

  1019 (* for parse and parse_patt: fix all types to real *)

  1020 fun T_a2real (Type (s, [])) =

  1021     if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT

  1022     else Type (s, [])

  1023   | T_a2real (Type (s, Ts)) = Type (s, map T_a2real Ts)

  1024   | T_a2real (TFree (s, srt)) =

  1025     if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT

  1026     else TFree (s, srt)

  1027   | T_a2real (TVar ((s, i), srt)) =

  1028     if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT

  1029     else TVar ((s, i), srt)

  1030   | T_a2real (TVar (("DUMMY",_), srt)) = HOLogic.realT;

  1032 (*FIXME .. fixes the type (+see Typefix.thy*)

  1033 fun typ_a2real (Const( s, T)) = (Const( s, T_a2real T))

  1034   | typ_a2real (Free( s, T)) = (Free( s, T_a2real T))

  1035   | typ_a2real (Var( n, T)) = (Var( n, T_a2real T))

  1036   | typ_a2real (Bound i) = (Bound i)

  1037   | typ_a2real (Abs(s,T,t)) = Abs(s, T, typ_a2real t)

  1038   | typ_a2real (t1 $ t2) = (typ_a2real t1) $ (typ_a2real t2);

  1041 (* before 2002 *)

  1042 fun parseold thy str =

  1043   (let val t = ((*typ_a2real o*) numbers_to_string)

  1044 		   (Syntax.read_term_global thy str)

  1045    in SOME (cterm_of thy t) end)

  1046     handle _ => NONE;

  1047 (*2002 fun parseN thy str =

  1048   (let

  1049      val sgn = sign_of thy;

  1050      val t = ((*typ_a2real o app_num_tr'1 o*) term_of)

  1051        (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));

  1052    in SOME (cterm_of sgn t) end)

  1053      handle _ => NONE;*)

  1054 fun parseN thy str =

  1055   (let val t = (*(typ_a2real o numbers_to_string)*)

  1056 	   (Syntax.read_term_global thy str)

  1057    in SOME (cterm_of thy t) end)

  1058     handle _ => NONE;

  1059 (*2002 fun parse thy str =

  1060   (let

  1061      val sgn = sign_of thy;

  1062      val t = (typ_a2real o app_num_tr'1 o term_of)

  1063        (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));

  1064    in SOME (cterm_of sgn t) end) (*FIXXXXME 10.8.02: return term !!!*)

  1065      handle _ => NONE;*)

  1066 (*2010 fun parse thy str =

  1067   (let val t = (typ_a2real o app_num_tr'1) (Syntax.read_term_global thy str)

  1068    in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*)

  1069      handle _ => NONE;*)

  1070 fun parse thy str =

  1071   (let val t = (typ_a2real o numbers_to_string)

  1072 		   (Syntax.read_term_global thy str)

  1073    in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*)

  1074      handle _ => NONE;

  1075 (*

  1076 > val (SOME ct) = parse thy "(-#5)^^^#3";

  1077 > atomty (term_of ct);

  1078 *** -------------

  1079 *** Const ( Nat.op ^, ['a, nat] => 'a)

  1080 ***   Const ( uminus, 'a => 'a)

  1081 ***     Free ( #5, 'a)

  1082 ***   Free ( #3, nat)

  1083 > val (SOME ct) = parse thy "R=R";

  1084 > atomty (term_of ct);

  1085 *** -------------

  1086 *** Const ( op =, [real, real] => bool)

  1087 ***   Free ( R, real)

  1088 ***   Free ( R, real)

  1090 THIS IS THE OUTPUT FOR VERSION (3) above at typ_a2real !!!!!

  1091 *** -------------

  1092 *** Const ( op =, [RealDef.real, RealDef.real] => bool)

  1093 ***   Free ( R, RealDef.real)

  1094 ***   Free ( R, RealDef.real)                  *)

  1096 (*WN110317 parseNEW will replace parse after introduction of ctxt completed*)

  1097 fun parseNEW ctxt str = SOME (Syntax.read_term ctxt str |> numbers_to_string)

  1098       handle _ => NONE;

  1100 (* parse term patterns; Var ("v",_), i.e. "?v", are required for instantiation

  1101   WN130613 probably compare to

  1102   http://www.mail-archive.com/isabelle-dev@mailbroy.informatik.tu-muenchen.de/msg04249.html*)

  1103 fun parse_patt thy str = (thy, str) |>> thy2ctxt

  1104                                     |-> Proof_Context.read_term_pattern

  1105                                     |> numbers_to_string (*TODO drop*)

  1106                                     |> typ_a2real;       (*TODO drop*)

  1108 (*version for testing local to theories*)

  1109 fun str2term_ thy str = (term_of o the o (parse thy)) str;

  1110 (*WN110520

  1111 fun str2term str = (term_of o the o (parse (Thy_Info.get_theory "Isac"))) str;*)

  1112 fun str2term str = parse_patt (Thy_Info.get_theory "Isac") str

  1113 fun strs2terms ss = map str2term ss;

  1114 fun str2termN str = (term_of o the o (parseN (Thy_Info.get_theory "Isac"))) str;

  1116 (*+ makes a substitution from the output of Pattern.match +*)

  1117 (*fun mk_subs ((id, _):indexname, t:term) = (Free (id,type_of t), t);*)

  1118 fun mk_subs (subs: ((string * int) * (Term.typ * Term.term)) list) =

  1119 let fun mk_sub ((id, _), (ty, tm)) = (Free (id, ty), tm) in

  1120 map mk_sub subs end;

  1122 val atomthm = atomt o #prop o rep_thm;

  1124 (*.instantiate #prop thm with bound variables (as Free).*)

  1125 fun inst_bdv [] t = t : term

  1126   | inst_bdv (instl: (term*term) list) t =

  1127       let fun subst (v as Var((s,_),T)) =

  1128 	      (case Symbol.explode s of

  1129 		   "b"::"d"::"v"::_ =>

  1130 		   if_none (assoc(instl,Free(s,T))) (Free(s,T))

  1131 		 | _ => v)

  1132             | subst (Abs(a,T,body)) = Abs(a, T, subst body)

  1133             | subst (f$t') = subst f $ subst t'

  1134             | subst t = if_none (assoc(instl,t)) t

  1135       in  subst t  end;

  1138 (*WN050829 caution: is_atom (str2term"q_0/2 * L * x") = true !!!

  1139   use length (vars term) = 1 instead*)

  1140 fun is_atom (Const ("Float.Float",_) $ _) = true

  1141   | is_atom (Const ("ComplexI.I'_'_",_)) = true

  1142   | is_atom (Const ("Groups.times_class.times",_) $ t $ Const ("ComplexI.I'_'_",_)) = is_atom t

  1143   | is_atom (Const ("Groups.plus_class.plus",_) $ t1 $ Const ("ComplexI.I'_'_",_)) = is_atom t1

  1144   | is_atom (Const ("Groups.plus_class.plus",_) $ t1 $

  1145 		   (Const ("Groups.times_class.times",_) $ t2 $ Const ("ComplexI.I'_'_",_))) =

  1146     is_atom t1 andalso is_atom t2

  1147   | is_atom (Const _) = true

  1148   | is_atom (Free _) = true

  1149   | is_atom (Var _) = true

  1150   | is_atom _ = false;

  1151 (* val t = str2term "q_0/2 * L * x";

  1154 *)

  1155 (*val t = str2term "Float ((1,2),(0,0))";

  1156 > is_atom t;

  1157 val it = true : bool

  1158 > val t = str2term "Float ((1,2),(0,0)) * I__";

  1159 > is_atom t;

  1160 val it = true : bool

  1161 > val t = str2term "Float ((1,2),(0,0)) + Float ((3,4),(0,0)) * I__";

  1162 > is_atom t;

  1163 val it = true : bool

  1164 > val t = str2term "1 + 2*I__";

  1165 > val Const ("Groups.plus_class.plus",_) $ t1 $ (Const ("Groups.times_class.times",_) $ t2 $ Const ("ComplexI.I'_'_",_)) = t;

  1166 *)

  1168 (*.adaption from Isabelle/src/Pure/term.ML; reports if ALL Free's

  1169    have found a substitution (required for evaluating the preconditions

  1170    of _incomplete_ models).*)

  1171 fun subst_atomic_all [] t = (false, (*TODO may be 'true' for some terms ?*)

  1172 			     t : term)

  1173   | subst_atomic_all (instl: (term*term) list) t =

  1174       let fun subst (Abs(a,T,body)) =

  1175 	      let val (all, body') = subst body

  1176 	      in (all, Abs(a, T, body')) end

  1177             | subst (f$tt) =

  1178 	      let val (all1, f') = subst f

  1179 		  val (all2, tt') = subst tt

  1180 	      in (all1 andalso all2, f' $ tt') end

  1181             | subst (t as Free _) =

  1182 	      if is_num t then (true, t) (*numerals cannot be subst*)

  1183 	      else (case assoc(instl,t) of

  1184 					 SOME t' => (true, t')

  1185 				       | NONE => (false, t))

  1186             | subst t = (true, if_none (assoc(instl,t)) t)

  1187       in  subst t  end;

  1189 (*.add two terms with a type given.*)

  1190 fun mk_add t1 t2 =

  1191     let val T1 = type_of t1

  1192 	val T2 = type_of t2

  1193     in if T1 <> T2 then raise TYPE ("mk_add gets ",[T1, T2],[t1,t2])

  1194        else (Const ("Groups.plus_class.plus", [T1, T2] ---> T1) $ t1 $ t2)

  1195     end;

author	Walther Neuper <neuper@ist.tugraz.at>
	Thu, 21 Nov 2013 11:17:42 +0100
changeset 55275	f08422eeef24
parent 52105	2786cc9704c8
child 59184	831fa972f73b
permissions	-rw-r--r--