1 (* extends Isabelle/src/Pure/term.ML
2 (c) Walther Neuper 1999
4 use"ProgLang/term.sml";
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)))
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)
23 fun atomtyp t = (*WN10 see raw_pp_typ*)
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)
37 ("\n*** "^indent n^"]")
38 | atol n (T::Ts) = (ato n T ^ atol n Ts)
39 (*in print (ato 0 t ^ "\n") end; TODO TUM10*)
40 in writeln (ato 0 t) end;
42 > val T = (type_of o term_of o the o (parse thy)) "a::[real,int] => nat";
45 *** Type (RealDef.real,[])
47 *** Type (IntDef.int,[])
53 (*Prog.Tutorial.p.34, Makarius 1005 does the above like this..*)
55 fun pp_pair (x, y) = Pretty.list "(" ")" [x, y]
56 fun pp_list xs = Pretty.list "[" "]" xs
57 fun pp_str s = Pretty.str s
58 fun pp_qstr s = Pretty.quote (pp_str s)
59 fun pp_int i = pp_str (string_of_int i)
60 fun pp_sort S = pp_list (map pp_qstr S)
61 fun pp_constr a args = Pretty.block [pp_str a, Pretty.brk 1, args]
63 fun raw_pp_typ (TVar ((a, i), S)) =
64 pp_constr "TVar" (pp_pair (pp_pair (pp_qstr a, pp_int i), pp_sort S))
65 | raw_pp_typ (TFree (a, S)) =
66 pp_constr "TFree" (pp_pair (pp_qstr a, pp_sort S))
67 | raw_pp_typ (Type (a, tys)) =
68 pp_constr "Type" (pp_pair (pp_qstr a, pp_list (map raw_pp_typ tys)))
71 PolyML.addPrettyPrinter
72 (fn _ => fn _ => ml_pretty o Pretty.to_ML o raw_pp_typ);
74 PolyML.addPrettyPrinter
75 (fn _ => fn _ => ml_pretty o Pretty.to_ML o Proof_Display.pp_typ Pure.thy);
79 let fun ato (Const (a, _)) n =
80 "\n*** " ^ indent n ^ "Const (" ^ a ^ ", _)"
81 | ato (Free (a, _)) n =
82 "\n*** " ^ indent n ^ "Free (" ^ a ^ ", _)"
83 | ato (Var ((a, i), _)) n =
84 "\n*** " ^ indent n ^ "Var (" ^ a ^ ", " ^
85 string_of_int i ^ "), _)"
87 "\n*** " ^ indent n ^ "Bound " ^ string_of_int i
88 | ato (Abs (a, _, body)) n =
89 "\n*** " ^ indent n ^ "Abs(" ^ a ^ ", _" ^ ato body (n+1)
90 | ato (f $ t) n = (ato f n ^ ato t (n + 1))
91 in writeln ("\n*** -------------" ^ ato t 0 ^ "\n***") end;
93 fun term_detail2str t =
94 let fun ato (Const (a, T)) n =
95 "\n*** " ^ indent n ^ "Const (" ^ a ^ ", " ^ string_of_typ T ^ ")"
96 | ato (Free (a, T)) n =
97 "\n*** " ^ indent n ^ "Free (" ^ a ^ ", " ^ string_of_typ T ^ ")"
98 | ato (Var ((a, i), T)) n =
99 "\n*** " ^ indent n ^ "Var ((" ^ a ^ ", " ^ string_of_int i ^ "), "^
100 string_of_typ T ^ ")"
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 ^ ",.."
106 | ato (f $ t) n = ato f n ^ ato t (n + 1)
107 in "\n*** " ^ ato t 0 ^ "\n***" end;
108 fun atomty t = (writeln o term_detail2str) t; (*WN100907 broken*)
110 fun term_str thy (Const(s,_)) = s
111 | term_str thy (Free(s,_)) = s
112 | term_str thy (Var((s,i),_)) = s^(string_of_int i)
113 | term_str thy (Bound i) = "B."^(string_of_int i)
114 | term_str thy (Abs(s,_,_)) = s
115 | term_str thy t = raise error("term_str not for "^term2str t);
117 (*.contains the fst argument the second argument (a leave! of term).*)
118 fun contains_term (Abs(_,_,body)) t = contains_term body t
119 | contains_term (f $ f') t =
120 contains_term f t orelse contains_term f' t
121 | contains_term s t = t = s;
122 (*.contains the term a VAR(("*",_),_) ?.*)
123 fun contains_Var (Abs(_,_,body)) = contains_Var body
124 | contains_Var (f $ f') = contains_Var f orelse contains_Var f'
125 | contains_Var (Var _) = true
126 | contains_Var _ = false;
127 (* contains_Var (str2term "?z = 3") (*true*);
128 contains_Var (str2term "z = 3") (*false*);
131 (*fun int_of_str str =
132 let val ss = explode str
133 val str' = case ss of
134 "("::s => drop_last s | _ => ss
135 in case BasisLibrary.Int.fromString (implode str') of
137 | NONE => NONE end;*)
139 let val ss = explode str
140 val str' = case ss of
141 "("::s => drop_last s | _ => ss
142 in (SOME (Thy_Output.integer (implode str'))) handle _ => NONE end;
145 val it = SOME 123 : int option
146 > int_of_str "(-123)";
147 val it = SOME 123 : int option
149 val it = NONE : int option
151 val it = SOME ~123 : int option
153 fun int_of_str' str =
154 case int_of_str str of
156 | NONE => raise TERM ("int_of_string: no int-string",[]);
157 val str2int = int_of_str';
159 fun is_numeral str = case int_of_str str of
162 val is_no = is_numeral;
163 fun is_num (Free (s,_)) = if is_numeral s then true else false
166 > is_num ((term_of o the o (parse thy)) "#1");
168 > is_num ((term_of o the o (parse thy)) "#-1");
170 > is_num ((term_of o the o (parse thy)) "a123");
171 val it = false : bool
174 (*fun int_of_Free (Free (intstr, _)) =
175 (case BasisLibrary.Int.fromString intstr of
177 | NONE => raise error ("int_of_Free ( "^ intstr ^", _)"))
178 | int_of_Free t = raise error ("int_of_Free ( "^ term2str t ^" )");*)
179 fun int_of_Free (Free (intstr, _)) = (Thy_Output.integer intstr
180 handle _ => raise error ("int_of_Free ( "^ intstr ^", _)"))
181 | int_of_Free t = raise error ("int_of_Free ( "^ term2str t ^" )");
185 fun scan vs (Const(s,T)) = vs
186 | scan vs (t as Free(s,T)) = if is_no s then vs else t::vs
187 | scan vs (t as Var((s,i),T)) = t::vs
188 | scan vs (Bound i) = vs
189 | scan vs (Abs(s,T,t)) = scan vs t
190 | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)
191 in (distinct o (scan [])) t end;
193 fun is_Free (Free _) = true
195 fun is_fun_id (Const _) = true
196 | is_fun_id (Free _) = true
197 | is_fun_id _ = false;
198 fun is_f_x (f $ x) = is_fun_id f andalso is_Free x
200 (* is_f_x (str2term "q_0/2 * L * x") (*false*);
201 is_f_x (str2term "M_b x") (*true*);
205 fun scan vs (Const(s,T)) = vs
206 | scan vs (t as Free(s,T)) = if is_no s then vs else s::vs
207 | scan vs (t as Var((s,i),T)) = (s^"_"^(string_of_int i))::vs
208 | scan vs (Bound i) = vs
209 | scan vs (Abs(s,T,t)) = scan vs t
210 | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)
211 in (distinct o (scan [])) t end;
215 fun scan vs (Const(s,T)) = if is_no s then vs else s::vs
216 | scan vs (t as Free(s,T)) = if is_no s then vs else s::vs
217 | scan vs (t as Var((s,i),T)) = (s^"_"^(string_of_int i))::vs
218 | scan vs (Bound i) = vs
219 | scan vs (Abs(s,T,t)) = scan (s::vs) t
220 | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)
221 in (distinct o (scan [])) t end;
224 "b"::"d"::"v"::_ => true
226 fun is_bdv_ (Free (s,_)) = is_bdv s
229 fun free2str (Free (s,_)) = s
230 | free2str t = raise error ("free2str not for "^ term2str t);
231 fun free2int (t as Free (s, _)) = ((str2int s)
232 handle _ => raise error ("free2int: "^term_detail2str t))
233 | free2int t = raise error ("free2int: "^term_detail2str t);
236 fun var2free (t as Const(s,T)) = t
237 | var2free (t as Free(s,T)) = t
238 | var2free (Var((s,i),T)) = Free(s,T)
239 | var2free (t as Bound i) = t
240 | var2free (Abs(s,T,t)) = Abs(s,T,var2free t)
241 | var2free (t1 $ t2) = (var2free t1) $ (var2free t2);
243 (*27.8.01: doesn't find some subterm ???!???*)
244 (*2010 Logic.varify !!!*)
245 fun free2var (t as Const(s,T)) = t
246 | free2var (t as Free(s,T)) = if is_no s then t else Var((s,0),T)
247 | free2var (t as Var((s,i),T)) = t
248 | free2var (t as Bound i) = t
249 | free2var (Abs(s,T,t)) = Abs(s,T,free2var t)
250 | free2var (t1 $ t2) = (free2var t1) $ (free2var t2);
253 fun mk_listT T = Type ("List.list", [T]);
255 Const("List.list.Cons", [T, mk_listT T] ---> mk_listT T);
256 (*28.8.01: TODO: get type from head of list: 1 arg less!!!*)
257 fun list2isalist T [] = Const("List.list.Nil",mk_listT T)
258 | list2isalist T (t::ts) = (list_const T) $ t $ (list2isalist T ts);
260 > val tt = (term_of o the o (parse thy)) "R=(R::real)";
261 > val TT = type_of tt;
262 > val ss = list2isalist TT [tt,tt,tt];
264 val it = "[R = R, R = R, R = R]" : cterm *)
266 fun isapair2pair (Const ("Pair",_) $ a $ b) = (a,b)
268 raise error ("isapair2pair called with "^term2str t);
270 val listType = Type ("List.list",[Type ("bool",[])]);
271 fun isalist2list ls =
273 fun get es (Const("List.list.Cons",_) $ t $ ls) = get (t::es) ls
274 | get es (Const("List.list.Nil",_)) = es
276 raise error ("isalist2list applied to NON-list '"^term2str t^"'")
277 in (rev o (get [])) ls end;
279 > val il = str2term "[a=b,c=d,e=f]";
280 > val l = isalist2list il;
281 > (writeln o terms2str) l;
282 ["a = b","c = d","e = f"]
284 > val il = str2term "ss___::bool list";
285 > val l = isalist2list il;
286 [Free ("ss___", "bool List.list")]
290 (*review Isabelle2009/src/HOL/Tools/hologic.ML*)
291 val prop = Type ("prop",[]); (* ~/Diss.99/Integers-Isa/tools.sml*)
292 val bool = Type ("bool",[]); (* 2002 Integ.int *)
293 val Trueprop = Const("Trueprop",bool-->prop);
294 fun mk_prop t = Trueprop $ t;
295 val true_as_term = Const("True",bool);
296 val false_as_term = Const("False",bool);
297 val true_as_cterm = cterm_of (theory "HOL") true_as_term;
298 val false_as_cterm = cterm_of (theory "HOL") false_as_term;
300 infixr 5 -->; (*2002 /Pure/term.ML *)
301 infixr --->; (*2002 /Pure/term.ML *)
302 fun S --> T = Type("fun",[S,T]); (*2002 /Pure/term.ML *)
303 val op ---> = foldr (op -->); (*2002 /Pure/term.ML *)
304 fun list_implies ([], B) = B : term (*2002 /term.ML *)
305 | list_implies (A::AS, B) = Logic.implies $ A $ list_implies(AS,B);
311 fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = (* = thm.ML *)
312 match_bvs(s, t, if x="" orelse y="" then al
314 | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
315 | match_bvs(_,_,al) = al;
316 fun ren_inst(insts,prop,pat,obj) = (* = thm.ML *)
317 let val ren = match_bvs(pat,obj,[])
318 fun renAbs(Abs(x,T,b)) =
319 Abs(case assoc_string(ren,x) of NONE => x
320 | SOME(y) => y, T, renAbs(b))
321 | renAbs(f$t) = renAbs(f) $ renAbs(t)
323 in subst_vars insts (if null(ren) then prop else renAbs(prop)) end;
330 fun dest_equals' (Const("op =",_) $ t $ u) = (t,u)(* logic.ML: Const("=="*)
331 | dest_equals' t = raise TERM("dest_equals'", [t]);
332 val lhs_ = (fst o dest_equals');
333 val rhs_ = (snd o dest_equals');
335 fun is_equality (Const("op =",_) $ t $ u) = true (* logic.ML: Const("=="*)
336 | is_equality _ = false;
337 fun mk_equality (t,u) = (Const("op =",[type_of t,type_of u]--->bool) $ t $ u);
338 fun is_expliceq (Const("op =",_) $ (Free _) $ u) = true
339 | is_expliceq _ = false;
340 fun strip_trueprop (Const("Trueprop",_) $ t) = t
341 | strip_trueprop t = t;
342 (* | strip_trueprop t = raise TERM("strip_trueprop", [t]);
345 (*.(A1==>...An==>B) goes to (A1==>...An==>).*)
346 fun strip_imp_prems' (Const("==>", T) $ A $ t) =
347 let fun coll_prems As (Const("==>", _) $ A $ t) =
348 coll_prems (As $ (Logic.implies $ A)) t
349 | coll_prems As _ = SOME As
350 in coll_prems (Logic.implies $ A) t end
351 | strip_imp_prems' _ = NONE; (* logic.ML: term -> term list*)
353 val thm = real_mult_div_cancel1;
354 val prop = (#prop o rep_thm) thm;
358 *** . Const ( Trueprop)
360 *** . . . Const ( op =)
361 *** . . . . Var ((k, 0), )
362 *** . . . . Const ( 0)
363 *** . Const ( Trueprop)
364 *** . . Const ( op =) *** .............
365 val SOME t = strip_imp_prems' ((#prop o rep_thm) thm);
369 *** . Const ( Trueprop)
371 *** . . . Const ( op =)
372 *** . . . . Var ((k, 0), )
373 *** . . . . Const ( 0)
375 val thm = real_le_anti_sym;
376 val prop = (#prop o rep_thm) thm;
380 *** . Const ( Trueprop)
381 *** . . Const ( op <=)
382 *** . . . Var ((z, 0), )
383 *** . . . Var ((w, 0), )
385 *** . . Const ( Trueprop)
386 *** . . . Const ( op <=)
387 *** . . . . Var ((w, 0), )
388 *** . . . . Var ((z, 0), )
389 *** . . Const ( Trueprop)
390 *** . . . Const ( op =)
392 val SOME t = strip_imp_prems' ((#prop o rep_thm) thm);
396 *** . Const ( Trueprop)
397 *** . . Const ( op <=)
398 *** . . . Var ((z, 0), )
399 *** . . . Var ((w, 0), )
401 *** . . Const ( Trueprop)
402 *** . . . Const ( op <=)
403 *** . . . . Var ((w, 0), )
404 *** . . . . Var ((z, 0), )
407 (*. (A1==>...An==>) (B) goes to (A1==>...An==>B), where B is lowest branch.*)
408 fun ins_concl (Const("==>", T) $ A $ t) B = Logic.implies $ A $ (ins_concl t B)
409 | ins_concl (Const("==>", T) $ A ) B = Logic.implies $ A $ B
410 | ins_concl t B = raise TERM("ins_concl", [t, B]);
412 val thm = real_le_anti_sym;
413 val prop = (#prop o rep_thm) thm;
414 val concl = Logic.strip_imp_concl prop;
415 val SOME prems = strip_imp_prems' prop;
416 val prop' = ins_concl prems concl;
423 fun vperm (Var _, Var _) = true (*2002 Pure/thm.ML *)
424 | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t)
425 | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2)
426 | vperm (t, u) = (t = u);
428 (*2002 cp from Pure/term.ML --- since 2009 in Pure/old_term.ML*)
429 fun mem_term (_, []) = false
430 | mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts);
431 fun subset_term ([], ys) = true
432 | subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys);
433 fun eq_set_term (xs, ys) =
434 xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs));
435 (*a total, irreflexive ordering on index names*)
436 fun xless ((a,i), (b,j): indexname) = i<j orelse (i=j andalso a<b);
437 (*a partial ordering (not reflexive) for atomic terms*)
438 fun atless (Const (a,_), Const (b,_)) = a<b
439 | atless (Free (a,_), Free (b,_)) = a<b
440 | atless (Var(v,_), Var(w,_)) = xless(v,w)
441 | atless (Bound i, Bound j) = i<j
443 (*insert atomic term into partially sorted list, suppressing duplicates (?)*)
444 fun insert_aterm (t,us) =
445 let fun inserta [] = [t]
446 | inserta (us as u::us') =
447 if atless(t,u) then t::us
448 else if t=u then us (*duplicate*)
449 else u :: inserta(us')
452 (*Accumulates the Vars in the term, suppressing duplicates*)
453 fun add_term_vars (t, vars: term list) = case t of
454 Var _ => insert_aterm(t,vars)
455 | Abs (_,_,body) => add_term_vars(body,vars)
456 | f$t => add_term_vars (f, add_term_vars(t, vars))
458 fun term_vars t = add_term_vars(t,[]);
461 fun var_perm (t, u) = (*2002 Pure/thm.ML *)
462 vperm (t, u) andalso eq_set_term (term_vars t, term_vars u);
464 (*2002 fun decomp_simp, Pure/thm.ML *)
465 fun perm lhs rhs = var_perm (lhs, rhs) andalso not (lhs aconv rhs)
466 andalso not (is_Var lhs);
470 if n < 0 then "-"^((string_of_int o abs) n)
471 else string_of_int n;
474 val it = "1" : string > str_of_int ~1;
475 val it = "-1" : string
481 if n>0 then b*(power b (n-1))
482 else raise error ("power "^(str_of_int b)^" "^(str_of_int n));
493 | gcd a b = if a < b then gcd (b mod a) a
494 else gcd (a mod b) b;
495 fun sign n = if n < 0 then ~1
496 else if n = 0 then 0 else 1;
497 fun sign2 n1 n2 = (sign n1) * (sign n2);
500 fun d dvd n = n mod d = 0;
503 let fun pdiv ds d n =
505 else if d dvd n then pdiv (d::ds) d (n div d)
514 fun doubles ds = (* ds is ordered *)
515 let fun dbls ds [] = ds
517 | dbls ds (i::i'::is) = if i=i' then dbls (i::ds) is
518 else dbls ds (i'::is)
521 val it = [] : int list
522 > doubles [2,3,3,5,5,7];
523 val it = [5,3] : int list*)
527 | squfact n = foldl op* (1, (doubles o divisors) n);
538 fun dest_type (Type(T,[])) = T
541 raise error ("... dest_type: not impl. for this type"));
543 fun term_of_num ntyp n = Free (str_of_int n, ntyp);
545 fun pairT T1 T2 = Type ("*", [T1, T2]);
546 (*> val t = str2term "(1,2)";
547 > type_of t = pairT HOLogic.realT HOLogic.realT;
550 fun PairT T1 T2 = ([T1, T2] ---> Type ("*", [T1, T2]));
551 (*> val t = str2term "(1,2)";
552 > val Const ("Pair",pT) $ _ $ _ = t;
553 > pT = PairT HOLogic.realT HOLogic.realT;
557 Const ("Pair", PairT (type_of t1) (type_of t2)) $ t1 $ t2;
558 (*> val t = str2term "(1,2)";
559 > val (t1, t2) = (str2term "1", str2term "2");
561 val it = true : bool*)
564 fun num_of_term (t as Free (s,_)) =
565 (case int_of_str s of
567 | NONE => raise error ("num_of_term not for "^ term2str t))
568 | num_of_term t = raise error ("num_of_term not for "^term2str t);
570 fun mk_factroot op_(*=thy.sqrt*) T fact root =
571 Const ("op *", [T, T] ---> T) $ (term_of_num T fact) $
572 (Const (op_, T --> T) $ term_of_num T root);
574 val T = (type_of o term_of o the) (parse thy "#12::real");
575 val t = mk_factroot "SqRoot.sqrt" T 2 3;
577 val it = "#2 * sqrt #3 " : cterm
579 fun var_op_num v op_ optype ntyp n =
580 Const (op_, optype) $ v $
581 Free (str_of_int n, ntyp);
583 fun num_op_var v op_ optype ntyp n =
585 Free (str_of_int n, ntyp) $ v;
587 fun num_op_num T1 T2 (op_,Top) n1 n2 =
589 Free (str_of_int n1, T1) $ Free (str_of_int n2, T2);
591 > val t = num_op_num "Int" 3 4;
593 > string_of_cterm ((cterm_of thy) t);
596 fun const_in str (Const _) = false
597 | const_in str (Free (s,_)) = if strip_thy s = str then true else false
598 | const_in str (Bound _) = false
599 | const_in str (Var _) = false
600 | const_in str (Abs (_,_,body)) = const_in str body
601 | const_in str (f$u) = const_in str f orelse const_in str u;
603 > val t = (term_of o the o (parse thy)) "6 + 5 * sqrt 4 + 3";
606 > val t = (term_of o the o (parse thy)) "6 + 5 * 4 + 3";
608 val it = false : bool
611 (*used for calculating built in binary operations in Isabelle2002->Float.ML*)
612 (*fun calc "op +" (n1, n2) = n1+n2
613 | calc "op -" (n1, n2) = n1-n2
614 | calc "op *" (n1, n2) = n1*n2
615 | calc "HOL.divide"(n1, n2) = n1 div n2
616 | calc "Atools.pow"(n1, n2) = power n1 n2
617 | calc op_ _ = raise error ("calc: operator = "^op_^" not defined");-----*)
618 fun calc_equ "op <" (n1, n2) = n1 < n2
619 | calc_equ "op <=" (n1, n2) = n1 <= n2
621 raise error ("calc_equ: operator = "^op_^" not defined");
622 fun sqrt (n:int) = if n < 0 then 0
623 (*FIXME ~~~*) else (trunc o Math.sqrt o Real.fromInt) n;
625 fun mk_thmid thmid op_ n1 n2 =
626 thmid ^ (strip_thy n1) ^ "_" ^ (strip_thy n2);
628 fun dest_binop_typ (Type("fun",[range,Type("fun",[arg2,arg1])])) =
630 | dest_binop_typ _ = raise error "dest_binop_typ: not binary";
632 > val t = (term_of o the o (parse thy)) "#3^#4";
633 > val hT = type_of (head_of t);
635 val it = ("'a","nat","'a") : typ * typ * typ
639 (** transform binary numeralsstrings **)
640 (*Makarius 100308, hacked by WN*)
641 val numbers_to_string =
644 (case try HOLogic.dest_number t of
646 (*if T = @{typ int} orelse T = @{typ real} then WN*)
647 SOME (Free (signed_string_of_int i, T))
651 fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b)
652 | to_str (t as (u1 $ u2)) =
655 | NONE => to_str u1 $ to_str u2)
656 | to_str t = perhaps dest_num t;
659 (*.make uminus uniform:
660 Const ("uminus", _) $ Free ("2", "RealDef.real") --> Free ("-2", _)
661 to be used immediately before evaluation of numerals;
662 see Scripts/calculate.sml .*)
663 (*2002 fun(*app_num_tr'2 (Const("0",T)) = Free("0",T)
664 | app_num_tr'2 (Const("1",T)) = Free("1",T)
665 |*)app_num_tr'2 (t as Const("uminus",_) $ Free(s,T)) =
666 (case int_of_str s of SOME i =>
667 if i > 0 then Free("-"^s,T) else Free(s,T)
669 (*| app_num_tr'2 (t as Const(s,T)) = t
670 | app_num_tr'2 (Const("Numeral.number_of",Type ("fun", [_, T])) $ t) =
671 Free(NumeralSyntax.dest_bin_str t, T)
672 | app_num_tr'2 (t as Free(s,T)) = t
673 | app_num_tr'2 (t as Var(n,T)) = t
674 | app_num_tr'2 (t as Bound i) = t
675 *)| app_num_tr'2 (Abs(s,T,body)) = Abs(s,T, app_num_tr'2 body)
676 | app_num_tr'2 (t1 $ t2) = (app_num_tr'2 t1) $ (app_num_tr'2 t2)
677 | app_num_tr'2 t = t;
679 val uminus_to_string =
683 (Const ("HOL.uminus_class.uminus", _) $ Free (s, T)) =>
684 (case int_of_str s of
686 SOME (Free (signed_string_of_int (~1 * i), T))
690 fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b)
691 | to_str (t as (u1 $ u2)) =
694 | NONE => to_str u1 $ to_str u2)
695 | to_str t = perhaps dest_num t;
699 (*2002 fun num_str thm =
701 val {sign_ref = sign_ref, der = der, maxidx = maxidx,
702 shyps = shyps, hyps = hyps, (*tpairs = tpairs,*) prop = prop} =
704 val prop' = app_num_tr'1 prop;
705 in assbl_thm sign_ref der maxidx shyps hyps (*tpairs*) prop' end;*)
708 {thy_ref = thy_ref, tags = tags, maxidx = maxidx, shyps = shyps,
709 hyps = hyps, tpairs = tpairs, prop = prop}) = rep_thm_G thm
710 val prop' = numbers_to_string prop;
711 in assbl_thm deriv thy_ref tags maxidx shyps hyps tpairs prop' end;
713 fun get_thm' xstring = (*?covers 2009 Thm?!, replaces 2002 fun get_thm :
714 val it = fn : theory -> xstring -> Thm.thm*)
716 num_str (ProofContext.get_thm (thy2ctxt' "Isac") xstring));
718 (** get types of Free and Abs for parse' **)
719 (*11.1.00: not used, fix-typed +,*,-,^ instead *)
721 val dummyT = Type ("dummy",[]);
722 val dummyT = TVar (("DUMMY",0),[]);
724 (* assumes only 1 type for numerals
725 and different identifiers for Const, Free and Abs *)
728 fun get ts (Const(s,T)) = (s,T)::ts
729 | get ts (Free(s,T)) = if is_no s
730 then ("#",T)::ts else (s,T)::ts
731 | get ts (Var(n,T)) = ts
732 | get ts (Bound i) = ts
733 | get ts (Abs(s,T,body)) = get ((s,T)::ts) body
734 | get ts (t1 $ t2) = (get ts t1) @ (get ts t2)
735 in distinct (get [] t) end;
737 val t = (term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)";
741 (*11.1.00: not used, fix-typed +,*,-,^ instead *)
742 fun set_types al (Const(s,T)) =
743 (case assoc (al,s) of
744 SOME T' => Const(s,T')
745 | NONE => (warning ("set_types: no type for "^s); Const(s,dummyT)))
746 | set_types al (Free(s,T)) =
748 (case assoc (al,"#") of
749 SOME T' => Free(s,T')
750 | NONE => (warning ("set_types: no type for numerals"); Free(s,T)))
751 else (case assoc (al,s) of
752 SOME T' => Free(s,T')
753 | NONE => (warning ("set_types: no type for "^s); Free(s,T)))
754 | set_types al (Var(n,T)) = Var(n,T)
755 | set_types al (Bound i) = Bound i
756 | set_types al (Abs(s,T,body)) =
757 (case assoc (al,s) of
758 SOME T' => Abs(s,T', set_types al body)
759 | NONE => (warning ("set_types: no type for "^s);
760 Abs(s,T, set_types al body)))
761 | set_types al (t1 $ t2) = (set_types al t1) $ (set_types al t2);
763 val t = (term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)";
764 val al = get_types t;
766 val t = (term_of o the o (parse thy)) "x = #0 + #-1 * #-4";
768 val t' = set_types al t;
771 val it = "x = #0 + #-1 * #-4" : cterm
773 val t = (term_of o the o (parse thy))
774 "#5 * x + x ^^^ #2 = (#2 + x) ^^^ #2";
776 val t' = set_types al t;
779 uncaught exception TYPE (*^^^ is new, NOT in al*)
783 (** from Descript.ML **)
785 (** decompose an isa-list to an ML-list
786 i.e. [] belong to the meta-language, too **)
788 fun is_list ((Const("List.list.Cons",_)) $ _ $ _) = true
790 (* val (SOME ct) = parse thy "lll::real list";
791 > val ty = (#t o rep_cterm) ct;
793 val it = false : bool
794 > val (SOME ct) = parse thy "[lll]";
795 > val ty = (#t o rep_cterm) ct;
797 val it = true : bool *)
801 fun mk_Free (s,T) = Free(s,T);
802 fun mk_free T s = Free(s,T);
804 (*Special case: one argument cp from Isabelle2002/src/Pure/term.ML*)
805 fun subst_bound (arg, t) : term = (*WN100908 neglects 'raise Same.SAME'*)
806 let fun subst (t as Bound i, lev) =
807 if i<lev then t (*var is locally bound*)
808 else if i=lev then incr_boundvars lev arg
809 else Bound(i-1) (*loose: change it*)
810 | subst (Abs(a,T,body), lev) = Abs(a, T, subst(body,lev+1))
811 | subst (f$t, lev) = subst(f,lev) $ subst(t,lev)
815 (*instantiate let; necessary for ass_up*)
816 fun inst_abs thy (Const sT) = Const sT (*TODO.WN100907 drop thy*)
817 | inst_abs thy (Free sT) = Free sT
818 | inst_abs thy (Bound n) = Bound n
819 | inst_abs thy (Var iT) = Var iT
820 | inst_abs thy (Const ("Let",T1) $ e $ (Abs (v, T2, b))) =
821 let val b' = subst_bound (Free (v, T2), b);
822 (*fun variant_abs: term.ML*)
823 in Const ("Let", T1) $ inst_abs thy e $ (Abs (v, T2, inst_abs thy b')) end
824 | inst_abs thy (t1 $ t2) = inst_abs thy t1 $ inst_abs thy t2
825 | inst_abs thy t = t;
827 "Script Make_fun_by_explicit (f_::real) (v_::real) (eqs_::bool list) = \
828 \ (let h_ = (hd o (filterVar f_)) eqs_; \
829 \ e_1 = hd (dropWhile (ident h_) eqs_); \
830 \ vs_ = dropWhile (ident f_) (Vars h_); \
831 \ v_1 = hd (dropWhile (ident v_) vs_); \
832 \ (s_1::bool list)=(SubProblem(DiffApp_,[univar,equation],[no_met])\
833 \ [BOOL e_1, REAL v_1])\
834 \ in Substitute [(v_1 = (rhs o hd) s_1)] h_)";
835 > val ttt = (term_of o the o (parse thy)) scr;
836 > writeln(term2str ttt);
839 *** Const ( DiffApp.Make'_fun'_by'_explicit)
844 *** . . Const ( Fun.op o)
845 *** . . . Const ( List.hd)
846 *** . . . Const ( DiffApp.filterVar)
847 *** . . . . Free ( f_, )
848 *** . . . Free ( eqs_, )
850 *** . . . Const ( Let)
851 *** . . . . Const ( List.hd)
852 *** . . . . . Const ( List.dropWhile)
853 *** . . . . . . Const ( Atools.ident)
854 *** . . . . . . . Bound 0 <---- Free ( h_, )
855 *** . . . . . . Free ( eqs_, )
856 *** . . . . Abs( e_1,..
857 *** . . . . . Const ( Let)
858 *** . . . . . . Const ( List.dropWhile)
859 *** . . . . . . . Const ( Atools.ident)
860 *** . . . . . . . . Free ( f_, )
861 *** . . . . . . . Const ( Tools.Vars)
862 *** . . . . . . . . Bound 1 <---- Free ( h_, )
863 *** . . . . . . Abs( vs_,..
864 *** . . . . . . . Const ( Let)
865 *** . . . . . . . . Const ( List.hd)
866 *** . . . . . . . . . Const ( List.dropWhile)
867 *** . . . . . . . . . . Const ( Atools.ident)
868 *** . . . . . . . . . . . Free ( v_, )
869 *** . . . . . . . . . . Bound 0 <---- Free ( vs_, )
870 *** . . . . . . . . Abs( v_1,..
871 *** . . . . . . . . . Const ( Let)
872 *** . . . . . . . . . . Const ( Script.SubProblem)
873 *** . . . . . . . . . . . Const ( Pair)
874 *** . . . . . . . . . . . . Free ( DiffApp_, )
875 *** . . . . . . . . . . . . Const ( Pair)
876 *** . . . . . . . . . . . . . Const ( List.list.Cons)
877 *** . . . . . . . . . . . . . . Free ( univar, )
878 *** . . . . . . . . . . . . . . Const ( List.list.Cons)
879 *** . . . . . . . . . . . . . . . Free ( equation, )
880 *** . . . . . . . . . . . . . . . Const ( List.list.Nil)
881 *** . . . . . . . . . . . . . Const ( List.list.Cons)
882 *** . . . . . . . . . . . . . . Free ( no_met, )
883 *** . . . . . . . . . . . . . . Const ( List.list.Nil)
884 *** . . . . . . . . . . . Const ( List.list.Cons)
885 *** . . . . . . . . . . . . Const ( Script.BOOL)
886 *** . . . . . . . . . . . . . Bound 2 <----- Free ( e_1, )
887 *** . . . . . . . . . . . . Const ( List.list.Cons)
888 *** . . . . . . . . . . . . . Const ( Script.real_)
889 *** . . . . . . . . . . . . . . Bound 0 <----- Free ( v_1, )
890 *** . . . . . . . . . . . . . Const ( List.list.Nil)
891 *** . . . . . . . . . . Abs( s_1,..
892 *** . . . . . . . . . . . Const ( Script.Substitute)
893 *** . . . . . . . . . . . . Const ( List.list.Cons)
894 *** . . . . . . . . . . . . . Const ( Pair)
895 *** . . . . . . . . . . . . . . Bound 1 <----- Free ( v_1, )
896 *** . . . . . . . . . . . . . . Const ( Fun.op o)
897 *** . . . . . . . . . . . . . . . Const ( Tools.rhs)
898 *** . . . . . . . . . . . . . . . Const ( List.hd)
899 *** . . . . . . . . . . . . . . . Bound 0 <----- Free ( s_1, )
900 *** . . . . . . . . . . . . . Const ( List.list.Nil)
901 *** . . . . . . . . . . . . Bound 4 <----- Free ( h_, )
903 > val ttt' = inst_abs thy ttt;
904 > writeln(term2str ttt');
905 Script Make_fun_by_explicit f_ v_ eqs_ =
909 *** Const ( DiffApp.Make'_fun'_by'_explicit)
914 *** . . Const ( Fun.op o)
915 *** . . . Const ( List.hd)
916 *** . . . Const ( DiffApp.filterVar)
917 *** . . . . Free ( f_, )
918 *** . . . Free ( eqs_, )
920 *** . . . Const ( Let)
921 *** . . . . Const ( List.hd)
922 *** . . . . . Const ( List.dropWhile)
923 *** . . . . . . Const ( Atools.ident)
924 *** . . . . . . . Free ( h_, ) <---- Bound 0
925 *** . . . . . . Free ( eqs_, )
926 *** . . . . Abs( e_1,..
927 *** . . . . . Const ( Let)
928 *** . . . . . . Const ( List.dropWhile)
929 *** . . . . . . . Const ( Atools.ident)
930 *** . . . . . . . . Free ( f_, )
931 *** . . . . . . . Const ( Tools.Vars)
932 *** . . . . . . . . Free ( h_, ) <---- Bound 1
933 *** . . . . . . Abs( vs_,..
934 *** . . . . . . . Const ( Let)
935 *** . . . . . . . . Const ( List.hd)
936 *** . . . . . . . . . Const ( List.dropWhile)
937 *** . . . . . . . . . . Const ( Atools.ident)
938 *** . . . . . . . . . . . Free ( v_, )
939 *** . . . . . . . . . . Free ( vs_, ) <---- Bound 0
940 *** . . . . . . . . Abs( v_1,..
941 *** . . . . . . . . . Const ( Let)
942 *** . . . . . . . . . . Const ( Script.SubProblem)
943 *** . . . . . . . . . . . Const ( Pair)
944 *** . . . . . . . . . . . . Free ( DiffApp_, )
945 *** . . . . . . . . . . . . Const ( Pair)
946 *** . . . . . . . . . . . . . Const ( List.list.Cons)
947 *** . . . . . . . . . . . . . . Free ( univar, )
948 *** . . . . . . . . . . . . . . Const ( List.list.Cons)
949 *** . . . . . . . . . . . . . . . Free ( equation, )
950 *** . . . . . . . . . . . . . . . Const ( List.list.Nil)
951 *** . . . . . . . . . . . . . Const ( List.list.Cons)
952 *** . . . . . . . . . . . . . . Free ( no_met, )
953 *** . . . . . . . . . . . . . . Const ( List.list.Nil)
954 *** . . . . . . . . . . . Const ( List.list.Cons)
955 *** . . . . . . . . . . . . Const ( Script.BOOL)
956 *** . . . . . . . . . . . . . Free ( e_1, ) <----- Bound 2
957 *** . . . . . . . . . . . . Const ( List.list.Cons)
958 *** . . . . . . . . . . . . . Const ( Script.real_)
959 *** . . . . . . . . . . . . . . Free ( v_1, ) <----- Bound 0
960 *** . . . . . . . . . . . . . Const ( List.list.Nil)
961 *** . . . . . . . . . . Abs( s_1,..
962 *** . . . . . . . . . . . Const ( Script.Substitute)
963 *** . . . . . . . . . . . . Const ( List.list.Cons)
964 *** . . . . . . . . . . . . . Const ( Pair)
965 *** . . . . . . . . . . . . . . Free ( v_1, ) <----- Bound 1
966 *** . . . . . . . . . . . . . . Const ( Fun.op o)
967 *** . . . . . . . . . . . . . . . Const ( Tools.rhs)
968 *** . . . . . . . . . . . . . . . Const ( List.hd)
969 *** . . . . . . . . . . . . . . . Free ( s_1, ) <----- Bound 0
970 *** . . . . . . . . . . . . . Const ( List.list.Nil)
971 *** . . . . . . . . . . . . Free ( h_, ) <----- Bound 4
973 Note numbering of de Bruijn indexes !
975 Script Make_fun_by_explicit f_ v_ eqs_ =
976 let h_ = (hd o filterVar f_) eqs_;
977 e_1 = hd (dropWhile (ident h_ BOUND_0) eqs_);
978 vs_ = dropWhile (ident f_) (Vars h_ BOUND_1);
979 v_1 = hd (dropWhile (ident v_) vs_ BOUND_0);
981 SubProblem (DiffApp_, [univar, equation], [no_met])
982 [BOOL e_1 BOUND_2, REAL v_1 BOUND_0]
983 in Substitute [(v_1 BOUND_1 = (rhs o hd) s_1 BOUND_0)] h_ BOUND_4
987 fun T_a2real (Type (s, [])) =
988 if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else Type (s, [])
989 | T_a2real (Type (s, Ts)) = Type (s, map T_a2real Ts)
990 | T_a2real (TFree (s, srt)) =
991 if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else TFree (s, srt)
992 | T_a2real (TVar (("DUMMY",_),srt)) = HOLogic.realT;
994 (*FIXME .. fixes the type (+see Typefix.thy*)
995 fun typ_a2real (Const( s, T)) = (Const( s, T_a2real T))
996 | typ_a2real (Free( s, T)) = (Free( s, T_a2real T))
997 | typ_a2real (Var( n, T)) = (Var( n, T_a2real T))
998 | typ_a2real (Bound i) = (Bound i)
999 | typ_a2real (Abs(s,T,t)) = Abs(s, T, typ_a2real t)
1000 | typ_a2real (t1 $ t2) = (typ_a2real t1) $ (typ_a2real t2);
1002 ----------------6.8.02---------------------------------------------------
1004 val t = read_cterm (sign_of thy) (str,(TVar(("DUMMY",0),[])));
1008 val t = (app_num_tr' o term_of) t;
1012 val t = typ_a2real t;
1015 *** Const ( 1, real)
1018 val t = read_cterm (sign_of thy) (str,(TVar(("DUMMY",0),[])));
1021 *** Const ( Numeral.number_of, bin => 'a)
1022 *** . Const ( Numeral.bin.Bit, [bin, bool] => bin)
1023 *** . . Const ( Numeral.bin.Bit, [bin, bool] => bin)
1024 *** . . . Const ( Numeral.bin.Pls, bin)
1025 *** . . . Const ( True, bool)
1026 *** . . Const ( False, bool)
1027 val t = (app_num_tr' o term_of) t;
1031 val t = typ_a2real t;
1035 ----------------6.8.02---------------------------------------------------
1039 > val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[]))));
1040 val t = Free ("R","?DUMMY") : term
1041 > val t' = typ_a2real t;
1042 > (cterm_of thy) t';
1043 val it = "R::RealDef.real" : cterm
1046 > val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[]))));
1047 > atomty (typ_a2real t);
1049 *** Const ( op =, [RealDef.real, RealDef.real] => bool)
1050 *** Free ( R, RealDef.real)
1051 *** Free ( R, RealDef.real)
1052 > val t' = typ_a2real t;
1053 > (cterm_of thy) t';
1054 val it = "(R::RealDef.real) = R" : cterm
1056 > val str = "fixed_values [R=R]";
1057 > val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[]))));
1058 > val t' = typ_a2real t;
1059 > (cterm_of thy) t';
1060 val it = "fixed_values [(R::RealDef.real) = R]" : cterm
1063 (*TODO.WN0609: parse should return a term or a string
1064 (or even more comprehensive datastructure for error-messages)
1065 i.e. in wrapping with SOME term or NONE the latter is not sufficient*)
1066 (*2002 fun parseold thy str =
1068 val sgn = sign_of thy;
1069 val t = ((*typ_a2real o*) app_num_tr'1 o term_of)
1070 (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));
1071 in SOME (cterm_of sgn t) end)
1076 fun parseold thy str =
1077 (let val t = ((*typ_a2real o*) numbers_to_string)
1078 (Syntax.read_term_global thy str)
1079 in SOME (cterm_of thy t) end)
1081 (*2002 fun parseN thy str =
1083 val sgn = sign_of thy;
1084 val t = ((*typ_a2real o app_num_tr'1 o*) term_of)
1085 (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));
1086 in SOME (cterm_of sgn t) end)
1088 fun parseN thy str =
1089 (let val t = (*(typ_a2real o numbers_to_string)*)
1090 (Syntax.read_term_global thy str)
1091 in SOME (cterm_of thy t) end)
1093 (*2002 fun parse thy str =
1095 val sgn = sign_of thy;
1096 val t = (typ_a2real o app_num_tr'1 o term_of)
1097 (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));
1098 in SOME (cterm_of sgn t) end) (*FIXXXXME 10.8.02: return term !!!*)
1100 (*2010 fun parse thy str =
1101 (let val t = (typ_a2real o app_num_tr'1) (Syntax.read_term_global thy str)
1102 in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*)
1105 (let val t = (typ_a2real o numbers_to_string)
1106 (Syntax.read_term_global thy str)
1107 in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*)
1110 > val (SOME ct) = parse thy "(-#5)^^^#3";
1111 > atomty (term_of ct);
1113 *** Const ( Nat.op ^, ['a, nat] => 'a)
1114 *** Const ( uminus, 'a => 'a)
1117 > val (SOME ct) = parse thy "R=R";
1118 > atomty (term_of ct);
1120 *** Const ( op =, [real, real] => bool)
1124 THIS IS THE OUTPUT FOR VERSION (3) above at typ_a2real !!!!!
1126 *** Const ( op =, [RealDef.real, RealDef.real] => bool)
1127 *** Free ( R, RealDef.real)
1128 *** Free ( R, RealDef.real) *)
1130 fun parse_patt thy str =
1131 ProofContext.read_term_pattern (thy2ctxt thy) str;
1133 (*version for testing local to theories*)
1134 fun str2term_ thy str = (term_of o the o (parse thy)) str;
1135 fun str2term str = (term_of o the o (parse (theory "Isac"))) str;
1136 fun strs2terms ss = map str2term ss;
1137 fun str2termN str = (term_of o the o (parseN (theory "Isac"))) str;
1139 (*+ makes a substitution from the output of Pattern.match +*)
1140 (*fun mk_subs ((id, _):indexname, t:term) = (Free (id,type_of t), t);*)
1141 fun mk_subs (subs: ((string * int) * (Term.typ * Term.term)) list) =
1142 let fun mk_sub ((id, _), (ty, tm)) = (Free (id, ty), tm) in
1143 map mk_sub subs end;
1145 val atomthm = atomt o #prop o rep_thm;
1147 (*.instantiate #prop thm with bound variables (as Free).*)
1148 fun inst_bdv [] t = t : term
1149 | inst_bdv (instl: (term*term) list) t =
1150 let fun subst (v as Var((s,_),T)) =
1153 if_none (assoc(instl,Free(s,T))) (Free(s,T))
1155 | subst (Abs(a,T,body)) = Abs(a, T, subst body)
1156 | subst (f$t') = subst f $ subst t'
1157 | subst t = if_none (assoc(instl,t)) t
1161 (*WN050829 caution: is_atom (str2term"q_0/2 * L * x") = true !!!
1162 use length (vars term) = 1 instead*)
1163 fun is_atom (Const ("Float.Float",_) $ _) = true
1164 | is_atom (Const ("ComplexI.I'_'_",_)) = true
1165 | is_atom (Const ("op *",_) $ t $ Const ("ComplexI.I'_'_",_)) = is_atom t
1166 | is_atom (Const ("op +",_) $ t1 $ Const ("ComplexI.I'_'_",_)) = is_atom t1
1167 | is_atom (Const ("op +",_) $ t1 $
1168 (Const ("op *",_) $ t2 $ Const ("ComplexI.I'_'_",_))) =
1169 is_atom t1 andalso is_atom t2
1170 | is_atom (Const _) = true
1171 | is_atom (Free _) = true
1172 | is_atom (Var _) = true
1173 | is_atom _ = false;
1174 (* val t = str2term "q_0/2 * L * x";
1178 (*val t = str2term "Float ((1,2),(0,0))";
1180 val it = true : bool
1181 > val t = str2term "Float ((1,2),(0,0)) * I__";
1183 val it = true : bool
1184 > val t = str2term "Float ((1,2),(0,0)) + Float ((3,4),(0,0)) * I__";
1186 val it = true : bool
1187 > val t = str2term "1 + 2*I__";
1188 > val Const ("op +",_) $ t1 $ (Const ("op *",_) $ t2 $ Const ("ComplexI.I'_'_",_)) = t;
1191 (*.adaption from Isabelle/src/Pure/term.ML; reports if ALL Free's
1192 have found a substitution (required for evaluating the preconditions
1193 of _incomplete_ models).*)
1194 fun subst_atomic_all [] t = (false, (*TODO may be 'true' for some terms ?*)
1196 | subst_atomic_all (instl: (term*term) list) t =
1197 let fun subst (Abs(a,T,body)) =
1198 let val (all, body') = subst body
1199 in (all, Abs(a, T, body')) end
1201 let val (all1, f') = subst f
1202 val (all2, tt') = subst tt
1203 in (all1 andalso all2, f' $ tt') end
1204 | subst (t as Free _) =
1205 if is_num t then (true, t) (*numerals cannot be subst*)
1206 else (case assoc(instl,t) of
1207 SOME t' => (true, t')
1208 | NONE => (false, t))
1209 | subst t = (true, if_none (assoc(instl,t)) t)
1212 (*.add two terms with a type given.*)
1214 let val T1 = type_of t1
1216 in if T1 <> T2 then raise TYPE ("mk_add gets ",[T1, T2],[t1,t2])
1217 else (Const ("op +", [T1, T2] ---> T1) $ t1 $ t2)