1 (* Title: extends Isabelle/src/Pure/term.ML
2 Author: Walther Neuper 1999, Mathias Lehnfeld
3 (c) due to copyright terms
6 fun isastr_of_int i = if i >= 0 then string_of_int i else "-" ^ string_of_int (abs i)
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 tracing (ato 0 t ^ "\n") end;
41 > val T = (type_of o term_of o the o (parse thy)) "a::[real,int] => nat";
44 *** Type (RealDef.real,[])
46 *** Type (IntDef.int,[])
52 (*Prog.Tutorial.p.34, Makarius 1005 does the above like this..*)
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]
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)))
70 PolyML.addPrettyPrinter
71 (fn _ => fn _ => ml_pretty o Pretty.to_ML o raw_pp_typ);
73 PolyML.addPrettyPrinter
74 (fn _ => fn _ => ml_pretty o Pretty.to_ML o Proof_Display.pp_typ Pure.thy);
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 ^ "), _)"
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))
91 fun atomw t = writeln ("\n*** -------------" ^ ato t 0 ^ "\n***");
92 fun atomt t = tracing ("\n*** -------------" ^ ato t 0 ^ "\n***");
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 ^ ")"
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 ^ ",.."
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 ^ ")"
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 ^ ",.."
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*);
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
156 | NONE => NONE end;*)
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;
164 val it = SOME 123 : int option
165 > int_of_str "(-123)";
166 val it = SOME 123 : int option
168 val it = NONE : int option
170 val it = SOME ~123 : int option
172 fun int_of_str' str =
173 case int_of_str str of
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
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));
191 fun is_num (Free (s,_)) = if is_numeral s then true else false
194 > is_num ((term_of o the o (parse thy)) "#1");
196 > is_num ((term_of o the o (parse thy)) "#-1");
198 > is_num ((term_of o the o (parse thy)) "a123");
199 val it = false : bool
202 (*fun int_of_Free (Free (intstr, _)) =
203 (case BasisLibrary.Int.fromString intstr of
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 ^" )");
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
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
228 (* is_f_x (str2term "q_0/2 * L * x") (*false*);
229 is_f_x (str2term "M_b x") (*true*);
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;
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;
251 case Symbol.explode str of
252 "b"::"d"::"v"::_ => true
254 fun is_bdv_ (Free (s,_)) = is_bdv s
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]);
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);
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];
299 val it = "[R = R, R = R, R = R]" : cterm *)
301 fun isapair2pair (Const ("Product_Type.Pair",_) $ a $ b) = (a,b)
303 error ("isapair2pair called with "^term2str t);
305 val listType = Type ("List.list",[Type ("bool",[])]);
306 fun isalist2list ls =
308 fun get es (Const("List.list.Cons",_) $ t $ ls) = get (t::es) ls
309 | get es (Const("List.list.Nil",_)) = es
311 error ("isalist2list applied to NON-list '"^term2str t^"'")
312 in (rev o (get [])) ls end;
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")]
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);
342 fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = (* = thm.ML *)
343 match_bvs(s, t, if x="" orelse y="" then 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)
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]);
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*)
384 val thm = real_mult_div_cancel1;
385 val prop = (#prop o rep_thm) thm;
389 *** . Const ( Trueprop)
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);
400 *** . Const ( Trueprop)
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;
411 *** . Const ( Trueprop)
412 *** . . Const ( op <=)
413 *** . . . Var ((z, 0), )
414 *** . . . Var ((w, 0), )
416 *** . . Const ( Trueprop)
417 *** . . . Const ( op <=)
418 *** . . . . Var ((w, 0), )
419 *** . . . . Var ((z, 0), )
420 *** . . Const ( Trueprop)
421 *** . . . Const ( op =)
423 val SOME t = strip_imp_prems' ((#prop o rep_thm) thm);
427 *** . Const ( Trueprop)
428 *** . . Const ( op <=)
429 *** . . . Var ((z, 0), )
430 *** . . . Var ((w, 0), )
432 *** . . Const ( Trueprop)
433 *** . . . Const ( op <=)
434 *** . . . . Var ((w, 0), )
435 *** . . . . Var ((z, 0), )
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]);
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;
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
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')
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))
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);
501 if n < 0 then "-"^((string_of_int o abs) n)
502 else string_of_int n;
505 val it = "1" : string > str_of_int ~1;
506 val it = "-1" : string
512 if n>0 then b*(power b (n-1))
513 else error ("power "^(str_of_int b)^" "^(str_of_int n));
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);
531 fun d dvd n = n mod d = 0;
534 let fun pdiv ds d n =
536 else if d dvd n then pdiv (d::ds) d (n div d)
545 fun doubles ds = (* ds is ordered *)
546 let fun dbls ds [] = ds
548 | dbls ds (i::i'::is) = if i=i' then dbls (i::ds) is
549 else dbls ds (i'::is)
552 val it = [] : int list
553 > doubles [2,3,3,5,5,7];
554 val it = [5,3] : int list*)
558 | squfact n = foldl op* (1, (doubles o divisors) n);
569 fun dest_type (Type(T,[])) = 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;
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;
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");
592 val it = true : bool*)
595 fun num_of_term (t as Free (s,_)) =
596 (case int_of_str s of
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);
605 val T = (type_of o term_of o the) (parse thy "#12::real");
606 val t = mk_factroot "SqRoot.sqrt" T 2 3;
608 val it = "#2 * sqrt #3 " : cterm
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 =
616 Free (str_of_int n, ntyp) $ v;
618 fun num_op_num T1 T2 (op_,Top) n1 n2 =
620 Free (str_of_int n1, T1) $ Free (str_of_int n2, T2);
622 > val t = num_op_num "Int" 3 4;
624 > string_of_cterm ((cterm_of thy) t);
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;
636 > val t = (term_of o the o (parse thy)) "6 + 5 * sqrt 4 + 3";
639 > val t = (term_of o the o (parse thy)) "6 + 5 * 4 + 3";
641 val it = false : bool
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
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])])) =
663 | dest_binop_typ _ = error "dest_binop_typ: not binary";
665 > val t = (term_of o the o (parse thy)) "#3^#4";
666 > val hT = type_of (head_of t);
668 val it = ("'a","nat","'a") : typ * typ * typ
672 (** transform binary numeralsstrings **)
673 (*Makarius 100308, hacked by WN*)
674 val numbers_to_string =
677 (case try HOLogic.dest_number t of
679 (*if T = @{typ int} orelse T = @{typ real} then WN*)
680 SOME (Free (signed_string_of_int i, T))
684 fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b)
685 | to_str (t as (u1 $ u2)) =
688 | NONE => to_str u1 $ to_str u2)
689 | to_str t = perhaps dest_num t;
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)
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;
712 val uminus_to_string =
716 (Const ("Groups.uminus_class.uminus", _) $ Free (s, T)) =>
717 (case int_of_str s of
719 SOME (Free (signed_string_of_int (~1 * i), T))
723 fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b)
724 | to_str (t as (u1 $ u2)) =
727 | NONE => to_str u1 $ to_str u2)
728 | to_str t = perhaps dest_num t;
732 (*2002 fun num_str thm =
734 val {sign_ref = sign_ref, der = der, maxidx = maxidx,
735 shyps = shyps, hyps = hyps, (*tpairs = tpairs,*) prop = prop} =
737 val prop' = app_num_tr'1 prop;
738 in assbl_thm sign_ref der maxidx shyps hyps (*tpairs*) prop' end;*)
741 {thy_ref = thy_ref, 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_ref 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*)
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 *)
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;
770 val t = (term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)";
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)) =
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);
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";
801 val t' = set_types al 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";
809 val t' = set_types al t;
812 uncaught exception TYPE (*^^^ is new, NOT in al*)
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
823 (* val (SOME ct) = parse thy "lll::real list";
824 > val ty = (#t o rep_cterm) ct;
826 val it = false : bool
827 > val (SOME ct) = parse thy "[lll]";
828 > val ty = (#t o rep_cterm) ct;
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)
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;
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);
872 *** Const ( DiffApp.Make'_fun'_by'_explicit)
877 *** . . Const ( Fun.op o)
878 *** . . . Const ( List.hd)
879 *** . . . Const ( DiffApp.filterVar)
880 *** . . . . Free ( f_, )
881 *** . . . Free ( eqs_, )
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_ =
942 *** Const ( DiffApp.Make'_fun'_by'_explicit)
947 *** . . Const ( Fun.op o)
948 *** . . . Const ( List.hd)
949 *** . . . Const ( DiffApp.filterVar)
950 *** . . . . Free ( f_, )
951 *** . . . Free ( eqs_, )
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);
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
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
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
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);
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)
1047 (*2002 fun parseN thy str =
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)
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)
1059 (*2002 fun parse thy str =
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 !!!*)
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 !!!*)
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 !!!*)
1076 > val (SOME ct) = parse thy "(-#5)^^^#3";
1077 > atomty (term_of ct);
1079 *** Const ( Nat.op ^, ['a, nat] => 'a)
1080 *** Const ( uminus, 'a => 'a)
1083 > val (SOME ct) = parse thy "R=R";
1084 > atomty (term_of ct);
1086 *** Const ( op =, [real, real] => bool)
1090 THIS IS THE OUTPUT FOR VERSION (3) above at typ_a2real !!!!!
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)
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;
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
1130 if_none (assoc(instl,Free(s,T))) (Free(s,T))
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
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";
1155 (*val t = str2term "Float ((1,2),(0,0))";
1157 val it = true : bool
1158 > val t = str2term "Float ((1,2),(0,0)) * I__";
1160 val it = true : bool
1161 > val t = str2term "Float ((1,2),(0,0)) + Float ((3,4),(0,0)) * I__";
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;
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 ?*)
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
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)
1189 (*.add two terms with a type given.*)
1191 let val T1 = type_of t1
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)