wneuper/isa: src/Tools/isac/ProgLang/termC.sml@9e59542132b3

     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 term_detail2str_thy thy t =

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

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

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

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

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

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

   115 	    string_of_typ_thy thy T ^ ")"

   116 	  | ato (Bound i) n =

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

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

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

   120 	    ^ ato body (n + 1)

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

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

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

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

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

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

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

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

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

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

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

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

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

   136   | contains_term (f $ f') t =

   137     contains_term f t orelse contains_term f' t

   138   | contains_term s t = t = s;

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

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

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

   142   | contains_Var (Var _) = true

   143   | contains_Var _ = false;

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

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

   146    *)

   148 (*fun int_of_str str =

   149     let val ss = Symbol.explode str

   150 	val str' = case ss of

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

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

   153 	     SOME i => SOME i

   154 	   | NONE => NONE end;*)

   155 fun int_of_str str =

   156     let val ss = Symbol.explode str

   157 	val str' = case ss of

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

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

   160 (*

   161 > int_of_str "123";

   162 val it = SOME 123 : int option

   163 > int_of_str "(-123)";

   164 val it = SOME 123 : int option

   165 > int_of_str "#123";

   166 val it = NONE : int option

   167 > int_of_str "-123";

   168 val it = SOME ~123 : int option

   169 *)

   170 fun int_of_str' str =

   171     case int_of_str str of

   172 	SOME i => i

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

   174 val str2int = int_of_str';

   176 fun is_numeral str = case int_of_str str of

   177 			 SOME _ => true

   178 		       | NONE => false;

   179 val is_no = is_numeral;

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

   181   | is_num _ = false;

   182 (*>

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

   184 val it = true : bool

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

   186 val it = true : bool

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

   188 val it = false : bool

   189 *)

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

   192     (case BasisLibrary.Int.fromString intstr of

   193 	     SOME i => i

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

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

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

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

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

   200 fun vars t =

   201   let

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

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

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

   205       | scan vs (Bound i) = vs

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

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

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

   210 fun is_Free (Free _) = true

   211   | is_Free _ = false;

   212 fun is_fun_id (Const _) = true

   213   | is_fun_id (Free _) = true

   214   | is_fun_id _ = false;

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

   216   | is_f_x _ = false;

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

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

   219   *)

   220 fun vars_str t =

   221   let

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

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

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

   225       | scan vs (Bound i) = vs

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

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

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

   230 fun ids2str t =

   231   let

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

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

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

   235       | scan vs (Bound i) = vs

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

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

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

   239 fun is_bdv str =

   240     case Symbol.explode str of

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

   242       | _ => false;

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

   244   | is_bdv_ _ = false;

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

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

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

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

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

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

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

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

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

   256   | var2free (t as Bound i) = t

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

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

   260 (*27.8.01: doesn't find some subterm ???!???*)

   261 (*2010 free2var -> Logic.varify, but take care of 'Free ("1",_)'*)

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

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

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

   265   | free2var (t as Bound i) = t

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

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

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

   271 fun list_const T =

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

   273 (*28.8.01: TODO: get type from head of list: 1 arg less!!!*)

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

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

   276 (*

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

   278 > val TT = type_of tt;

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

   280 > (cterm_of thy) ss;

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

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

   284   | isapair2pair t =

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

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

   288 fun isalist2list ls =

   289   let

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

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

   292       | get _ t =

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

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

   295 (*

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

   297 > val l = isalist2list il;

   298 > (tracing o terms2str) l;

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

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

   302 > val l = isalist2list il;

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

   304 *)

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

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

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

   309 val Trueprop = HOLogic.Trueprop;

   310 fun mk_prop t = HOLogic.mk_Trueprop t;

   311 val true_as_term = HOLogic.true_const;

   312 val false_as_term = HOLogic.false_const;

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

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

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

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

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

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

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

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

   324 (** substitution **)

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

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

   328                                           else (x,y)::al)

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

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

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

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

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

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

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

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

   337         | renAbs(t) = t

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

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

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

   347 val lhs_ = (fst o dest_equals');

   348 val rhs_ = (snd o dest_equals');

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

   351   | is_equality _ = false;

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

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

   354   | is_expliceq _ = false;

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

   356   | strip_trueprop t = t;

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

   358 *)

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

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

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

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

   364 	  | coll_prems As _ = SOME As

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

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

   367 (*

   368   val thm = real_mult_div_cancel1;

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

   370   atomt prop;

   371 *** -------------

   372 *** Const ( ==>)

   373 *** . Const ( Trueprop)

   374 *** . . Const ( Not)

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

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

   377 *** . . . . Const ( 0)

   378 *** . Const ( Trueprop)

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

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

   381   atomt t;

   382 *** -------------

   383 *** Const ( ==>)

   384 *** . Const ( Trueprop)

   385 *** . . Const ( Not)

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

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

   388 *** . . . . Const ( 0)

   390   val thm = real_le_anti_sym;

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

   392   atomt prop;

   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 *** . . Const ( Trueprop)

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

   406 *** .............

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

   408   atomt t;

   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 *)

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

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

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

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

   426 (*

   427   val thm = real_le_anti_sym;

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

   429   val concl = Logic.strip_imp_concl prop;

   430   val SOME prems = strip_imp_prems' prop;

   431   val prop' = ins_concl prems concl;

   432   prop = prop';

   433   atomt prop;

   434   atomt prop';

   435 *)

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

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

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

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

   443 (*2002 cp from Pure/term.ML --- since 2009 in Pure/old_term.ML*)

   444 fun mem_term (_, []) = false

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

   446 fun subset_term ([], ys) = true

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

   448 fun eq_set_term (xs, ys) =

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

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

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

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

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

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

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

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

   457   | atless _  =  false;

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

   459 fun insert_aterm (t,us) =

   460   let fun inserta [] = [t]

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

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

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

   464               else u :: inserta(us')

   465   in  inserta us  end;

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

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

   469     Var   _ => insert_aterm(t,vars)

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

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

   472   | _ => vars;

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

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

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

   479 (*2002 fun decomp_simp, Pure/thm.ML *)

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

   481     andalso not (is_Var lhs);

   484 fun str_of_int n =

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

   486   else string_of_int n;

   487 (*

   488 > str_of_int 1;

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

   490 val it = "-1" : string

   491 *)

   494 fun power b 0 = 1

   495   | power b n =

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

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

   498 (*

   499 > power 2 3;

   500 val it = 8 : int

   501 > power ~2 3;

   502 val it = ~8 : int

   503 > power ~3 2;

   504 val it = 9 : int

   505 > power 3 ~2;

   506 *)

   507 fun gcd 0 b = b

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

   509 	      else gcd (a mod b) b;

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

   511 	     else if n = 0 then 0 else 1;

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

   514 infix dvd;

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

   517 fun divisors n =

   518   let fun pdiv ds d n =

   519     if d=n then d::ds

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

   521 	 else pdiv ds (d+1) n

   522   in pdiv [] 2 n end;

   524 divisors 30;

   525 divisors 32;

   526 divisors 60;

   527 divisors 11;

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

   530   let fun dbls ds [] = ds

   531 	| dbls ds [i] = ds

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

   533 				else dbls ds (i'::is)

   534   in dbls [] ds end;

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

   536 val it = [] : int list

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

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

   540 fun squfact 0 = 0

   541   | squfact 1 = 1

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

   543 (*> squfact 30;

   544 val it = 1 : int

   545 > squfact 32;

   546 val it = 4 : int

   547 > squfact 60;

   548 val it = 2 : int

   549 > squfact 11;

   550 val it = 1 : int*)

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

   554   | dest_type T =

   555     (atomtyp T;

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

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

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

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

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

   563 val it = true : bool

   564 *)

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

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

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

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

   569 val it = true : bool

   570 *)

   571 fun pairt t1 t2 =

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

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

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

   575 > t = pairt t1 t2;

   576 val it = true : bool*)

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

   580     (case int_of_str s of

   581 	 SOME s' => s'

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

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

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

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

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

   588 (*

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

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

   591 (cterm_of thy) t;

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

   593 *)

   594 fun var_op_num v op_ optype ntyp n =

   595   Const (op_, optype) $ v $

   596    Free (str_of_int  n, ntyp);

   598 fun num_op_var v op_ optype ntyp n =

   599   Const (op_,optype) $

   600    Free (str_of_int n, ntyp) $ v;

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

   603   Const (op_,Top) $

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

   605 (*

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

   607 > atomty t;

   608 > string_of_cterm ((cterm_of thy) t);

   609 *)

   613 fun const_in str (Const _) = false

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

   615   | const_in str (Bound _) = false

   616   | const_in str (Var _) = false

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

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

   619 (*

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

   621 > const_in "sqrt" t;

   622 val it = true : bool

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

   624 > const_in "sqrt" t;

   625 val it = false : bool

   626 *)

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

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

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

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

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

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

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

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

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

   637   | calc_equ op_ _ =

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

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

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

   642 fun mk_thmid thmid op_ n1 n2 =

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

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

   646   (arg1,arg2,range)

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

   648 (* -----

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

   650 > val hT = type_of (head_of t);

   651 > dest_binop_typ hT;

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

   653  ----- *)

   656 (** transform binary numeralsstrings **)

   657 (*Makarius 100308, hacked by WN*)

   658 val numbers_to_string =

   659   let

   660     fun dest_num t =

   661       (case try HOLogic.dest_number t of

   662         SOME (T, i) =>

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

   664             SOME (Free (signed_string_of_int i, T))

   665           (*else NONE  WN*)

   666       | NONE => NONE);

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

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

   670           (case dest_num t of

   671             SOME t' => t'

   672           | NONE => to_str u1 $ to_str u2)

   673       | to_str t = perhaps dest_num t;

   674   in to_str end

   676 (*.make uminus uniform:

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

   678 to be used immediately before evaluation of numerals;

   679 see Scripts/calculate.sml .*)

   680 (*2002 fun(*app_num_tr'2 (Const("0",T)) = Free("0",T)

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

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

   683     (case int_of_str s of SOME i =>

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

   685 		       | NONE => t)

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

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

   688     Free(NumeralSyntax.dest_bin_str t, T)

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

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

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

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

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

   694   | app_num_tr'2 t = t;

   695 *)

   696 val uminus_to_string =

   697     let

   698 	fun dest_num t =

   699 	    (case t of

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

   701 		 (case int_of_str s of

   702 		      SOME i =>

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

   704 		    | NONE => NONE)

   705 	       | _ => NONE);

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

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

   709             (case dest_num t of

   710 		 SOME t' => t'

   711                | NONE => to_str u1 $ to_str u2)

   712 	  | to_str t = perhaps dest_num t;

   713     in to_str end;

   716 (*2002 fun num_str thm =

   717   let

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

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

   720 	rep_thm_G thm;

   721     val prop' = app_num_tr'1 prop;

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

   723 fun num_str thm =

   724   let val (deriv,

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

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

   727     val prop' = numbers_to_string prop;

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

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

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

   732     Thm (xstring,

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

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

   736 (*11.1.00: not used, fix-typed +,*,-,^ instead *)

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

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

   741 (* assumes only 1 type for numerals

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

   743 fun get_types t =

   744   let

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

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

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

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

   749       | get ts  (Bound i) = ts

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

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

   752   in distinct (get [] t) end;

   753 (*

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

   755 get_types t;

   756 *)

   758 (*11.1.00: not used, fix-typed +,*,-,^ instead *)

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

   760     (case assoc (al,s) of

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

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

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

   764   if is_no s then

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

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

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

   768   else (case assoc (al,s) of

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

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

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

   772   | set_types al (Bound i) = Bound i

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

   774 		 (case assoc (al,s) of

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

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

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

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

   779 (*

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

   781 val al = get_types t;

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

   784 atomty t;                         (* 'a *)

   785 val t' = set_types al t;

   786 atomty t';                        (*real*)

   787 (cterm_of thy) t';

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

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

   791   "#5 * x + x ^^^ #2 = (#2 + x) ^^^ #2";

   792 atomty t;

   793 val t' = set_types al t;

   794 atomty t';

   795 (cterm_of thy) t';

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

   797 *)

   800 (** from Descript.ML **)

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

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

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

   806   | is_list _ = false;

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

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

   809 > is_list ty;

   810 val it = false : bool

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

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

   813 > is_list ty;

   814 val it = true : bool *)

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

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

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

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

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

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

   825             else  if i=lev then incr_boundvars lev arg

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

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

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

   829         | subst (t,lev) = t

   830   in  subst (t,0)  end;

   832 (*instantiate let; necessary for ass_up*)

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

   834   | inst_abs thy (Free sT) = Free sT

   835   | inst_abs thy (Bound n) = Bound n

   836   | inst_abs thy (Var iT) = Var iT

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

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

   839     (*fun variant_abs: term.ML*)

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

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

   842   | inst_abs thy t = t;

   843 (*val scr =

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

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

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

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

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

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

   850    \                          [BOOL e_1, REAL v_1])\

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

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

   853 > tracing(term2str ttt);

   854 > atomt ttt;

   855 *** -------------

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

   857 *** . Free ( f_, )

   858 *** . Free ( v_, )

   859 *** . Free ( eqs_, )

   860 *** . Const ( Let)

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

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

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

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

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

   866 *** . . Abs( h_,..

   867 *** . . . Const ( Let)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   902 *** . . . . . . . . . . . . Const ( Script.BOOL)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   920 > val ttt' = inst_abs thy ttt;

   921 > tracing(term2str ttt');

   922 Script Make_fun_by_explicit f_ v_ eqs_ =

   923   ... as above ...

   924 > atomt ttt';

   925 *** -------------

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

   927 *** . Free ( f_, )

   928 *** . Free ( v_, )

   929 *** . Free ( eqs_, )

   930 *** . Const ( Let)

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

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

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

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

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

   936 *** . . Abs( h_,..

   937 *** . . . Const ( Let)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   972 *** . . . . . . . . . . . . Const ( Script.BOOL)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   990 Note numbering of de Bruijn indexes !

   992 Script Make_fun_by_explicit f_ v_ eqs_ =

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

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

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

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

   997      s_1 =

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

   999         [BOOL e_1 BOUND_2, REAL v_1 BOUND_0]

  1000  in Substitute [(v_1 BOUND_1 = (rhs o hd) s_1 BOUND_0)] h_ BOUND_4

  1001 *)

  1003 (* for parse and parse_patt: fix all types to real *)

  1004 fun T_a2real (Type (s, [])) =

  1005     if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT

  1006     else Type (s, [])

  1007   | T_a2real (Type (s, Ts)) = Type (s, map T_a2real Ts)

  1008   | T_a2real (TFree (s, srt)) =

  1009     if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT

  1010     else TFree (s, srt)

  1011   | T_a2real (TVar ((s, i), srt)) =

  1012     if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT

  1013     else TVar ((s, i), srt)

  1014   | T_a2real (TVar (("DUMMY",_), srt)) = HOLogic.realT;

  1016 (*FIXME .. fixes the type (+see Typefix.thy*)

  1017 fun typ_a2real (Const( s, T)) = (Const( s, T_a2real T))

  1018   | typ_a2real (Free( s, T)) = (Free( s, T_a2real T))

  1019   | typ_a2real (Var( n, T)) = (Var( n, T_a2real T))

  1020   | typ_a2real (Bound i) = (Bound i)

  1021   | typ_a2real (Abs(s,T,t)) = Abs(s, T, typ_a2real t)

  1022   | typ_a2real (t1 $ t2) = (typ_a2real t1) $ (typ_a2real t2);

  1025 (* before 2002 *)

  1026 fun parseold thy str =

  1027   (let val t = ((*typ_a2real o*) numbers_to_string)

  1028 		   (Syntax.read_term_global thy str)

  1029    in SOME (cterm_of thy t) end)

  1030     handle _ => NONE;

  1031 (*2002 fun parseN thy str =

  1032   (let

  1033      val sgn = sign_of thy;

  1034      val t = ((*typ_a2real o app_num_tr'1 o*) term_of)

  1035        (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));

  1036    in SOME (cterm_of sgn t) end)

  1037      handle _ => NONE;*)

  1038 fun parseN 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)

  1042     handle _ => NONE;

  1043 (*2002 fun parse thy str =

  1044   (let

  1045      val sgn = sign_of thy;

  1046      val t = (typ_a2real o app_num_tr'1 o term_of)

  1047        (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));

  1048    in SOME (cterm_of sgn t) end) (*FIXXXXME 10.8.02: return term !!!*)

  1049      handle _ => NONE;*)

  1050 (*2010 fun parse thy str =

  1051   (let val t = (typ_a2real o app_num_tr'1) (Syntax.read_term_global thy str)

  1052    in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*)

  1053      handle _ => NONE;*)

  1054 fun parse 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) (*FIXXXXME 10.8.02: return term !!!*)

  1058      handle _ => NONE;

  1059 (*

  1060 > val (SOME ct) = parse thy "(-#5)^^^#3";

  1061 > atomty (term_of ct);

  1062 *** -------------

  1063 *** Const ( Nat.op ^, ['a, nat] => 'a)

  1064 ***   Const ( uminus, 'a => 'a)

  1065 ***     Free ( #5, 'a)

  1066 ***   Free ( #3, nat)

  1067 > val (SOME ct) = parse thy "R=R";

  1068 > atomty (term_of ct);

  1069 *** -------------

  1070 *** Const ( op =, [real, real] => bool)

  1071 ***   Free ( R, real)

  1072 ***   Free ( R, real)

  1074 THIS IS THE OUTPUT FOR VERSION (3) above at typ_a2real !!!!!

  1075 *** -------------

  1076 *** Const ( op =, [RealDef.real, RealDef.real] => bool)

  1077 ***   Free ( R, RealDef.real)

  1078 ***   Free ( R, RealDef.real)                  *)

  1080 (*WN110317 parseNEW will replace parse after introduction of ctxt completed*)

  1081 fun parseNEW ctxt str = SOME (Syntax.read_term ctxt str |> numbers_to_string)

  1082       handle _ => NONE;

  1084 (* parse term patterns; Var ("v",_), i.e. "?v", are required for instantiation*)

  1085 fun parse_patt thy str = (thy, str) |>> thy2ctxt

  1086                                     |-> ProofContext.read_term_pattern

  1087                                     |> numbers_to_string (*TODO drop*)

  1088                                     |> typ_a2real;       (*TODO drop*)

  1090 (*version for testing local to theories*)

  1091 fun str2term_ thy str = (term_of o the o (parse thy)) str;

  1092 (*WN110520

  1093 fun str2term str = (term_of o the o (parse (Thy_Info.get_theory "Isac"))) str;*)

  1094 fun str2term str = parse_patt (Thy_Info.get_theory "Isac") str

  1095 fun strs2terms ss = map str2term ss;

  1096 fun str2termN str = (term_of o the o (parseN (Thy_Info.get_theory "Isac"))) str;

  1098 (*+ makes a substitution from the output of Pattern.match +*)

  1099 (*fun mk_subs ((id, _):indexname, t:term) = (Free (id,type_of t), t);*)

  1100 fun mk_subs (subs: ((string * int) * (Term.typ * Term.term)) list) =

  1101 let fun mk_sub ((id, _), (ty, tm)) = (Free (id, ty), tm) in

  1102 map mk_sub subs end;

  1104 val atomthm = atomt o #prop o rep_thm;

  1106 (*.instantiate #prop thm with bound variables (as Free).*)

  1107 fun inst_bdv [] t = t : term

  1108   | inst_bdv (instl: (term*term) list) t =

  1109       let fun subst (v as Var((s,_),T)) =

  1110 	      (case Symbol.explode s of

  1111 		   "b"::"d"::"v"::_ =>

  1112 		   if_none (assoc(instl,Free(s,T))) (Free(s,T))

  1113 		 | _ => v)

  1114             | subst (Abs(a,T,body)) = Abs(a, T, subst body)

  1115             | subst (f$t') = subst f $ subst t'

  1116             | subst t = if_none (assoc(instl,t)) t

  1117       in  subst t  end;

  1120 (*WN050829 caution: is_atom (str2term"q_0/2 * L * x") = true !!!

  1121   use length (vars term) = 1 instead*)

  1122 fun is_atom (Const ("Float.Float",_) $ _) = true

  1123   | is_atom (Const ("ComplexI.I'_'_",_)) = true

  1124   | is_atom (Const ("Groups.times_class.times",_) $ t $ Const ("ComplexI.I'_'_",_)) = is_atom t

  1125   | is_atom (Const ("Groups.plus_class.plus",_) $ t1 $ Const ("ComplexI.I'_'_",_)) = is_atom t1

  1126   | is_atom (Const ("Groups.plus_class.plus",_) $ t1 $

  1127 		   (Const ("Groups.times_class.times",_) $ t2 $ Const ("ComplexI.I'_'_",_))) =

  1128     is_atom t1 andalso is_atom t2

  1129   | is_atom (Const _) = true

  1130   | is_atom (Free _) = true

  1131   | is_atom (Var _) = true

  1132   | is_atom _ = false;

  1133 (* val t = str2term "q_0/2 * L * x";

  1136 *)

  1137 (*val t = str2term "Float ((1,2),(0,0))";

  1138 > is_atom t;

  1139 val it = true : bool

  1140 > val t = str2term "Float ((1,2),(0,0)) * I__";

  1141 > is_atom t;

  1142 val it = true : bool

  1143 > val t = str2term "Float ((1,2),(0,0)) + Float ((3,4),(0,0)) * I__";

  1144 > is_atom t;

  1145 val it = true : bool

  1146 > val t = str2term "1 + 2*I__";

  1147 > val Const ("Groups.plus_class.plus",_) $ t1 $ (Const ("Groups.times_class.times",_) $ t2 $ Const ("ComplexI.I'_'_",_)) = t;

  1148 *)

  1150 (*.adaption from Isabelle/src/Pure/term.ML; reports if ALL Free's

  1151    have found a substitution (required for evaluating the preconditions

  1152    of _incomplete_ models).*)

  1153 fun subst_atomic_all [] t = (false, (*TODO may be 'true' for some terms ?*)

  1154 			     t : term)

  1155   | subst_atomic_all (instl: (term*term) list) t =

  1156       let fun subst (Abs(a,T,body)) =

  1157 	      let val (all, body') = subst body

  1158 	      in (all, Abs(a, T, body')) end

  1159             | subst (f$tt) =

  1160 	      let val (all1, f') = subst f

  1161 		  val (all2, tt') = subst tt

  1162 	      in (all1 andalso all2, f' $ tt') end

  1163             | subst (t as Free _) =

  1164 	      if is_num t then (true, t) (*numerals cannot be subst*)

  1165 	      else (case assoc(instl,t) of

  1166 					 SOME t' => (true, t')

  1167 				       | NONE => (false, t))

  1168             | subst t = (true, if_none (assoc(instl,t)) t)

  1169       in  subst t  end;

  1171 (*.add two terms with a type given.*)

  1172 fun mk_add t1 t2 =

  1173     let val T1 = type_of t1

  1174 	val T2 = type_of t2

  1175     in if T1 <> T2 then raise TYPE ("mk_add gets ",[T1, T2],[t1,t2])

  1176        else (Const ("Groups.plus_class.plus", [T1, T2] ---> T1) $ t1 $ t2)

  1177     end;

author	Walther Neuper <neuper@ist.tugraz.at>
	Mon, 20 Feb 2012 18:18:03 +0100
changeset 42376	9e59542132b3
parent 42360	2c8de368c64c
child 42426	fc042a668d7a
permissions	-rw-r--r--