1 (* extends Isabelle/src/Pure/term.ML
2 (c) Walther Neuper 1999
4 use"Scripts/term_G.sml";
9 > cterm_of (sign_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 = (*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 (*Prog.Tutorial.p.34*)
44 fun pp_pair (x, y) = Pretty.list "(" ")" [x, y]
45 fun pp_list xs = Pretty.list "[" "]" xs
46 fun pp_str s = Pretty.str s
47 fun pp_qstr s = Pretty.quote (pp_str s)
48 fun pp_int i = pp_str (string_of_int i)
49 fun pp_sort S = pp_list (map pp_qstr S)
50 fun pp_constr a args = Pretty.block [pp_str a, Pretty.brk 1, args]
52 fun raw_pp_typ (TVar ((a, i), S)) =
53 pp_constr "TVar" (pp_pair (pp_pair (pp_qstr a, pp_int i), pp_sort S))
54 | raw_pp_typ (TFree (a, S)) =
55 pp_constr "TFree" (pp_pair (pp_qstr a, pp_sort S))
56 | raw_pp_typ (Type (a, tys)) =
57 pp_constr "Type" (pp_pair (pp_qstr a, pp_list (map raw_pp_typ tys)))
60 PolyML.addPrettyPrinter
61 (fn _ => fn _ => ml_pretty o Pretty.to_ML o raw_pp_typ);
63 PolyML.addPrettyPrinter
64 (fn _ => fn _ => ml_pretty o Pretty.to_ML o Proof_Display.pp_typ Pure.thy);
68 > val T = (type_of o term_of o the o (parse thy)) "a::[real,int] => nat";
71 *** Type (RealDef.real,[])
73 *** Type (IntDef.int,[])
80 let fun ato (Const(a,T)) n =
81 ("\n*** "^indent n^"Const ("^a^")")
82 | ato (Free (a,T)) n =
83 ("\n*** "^indent n^"Free ("^a^", "^")")
84 | ato (Var ((a,ix),T)) n =
85 ("\n*** "^indent n^"Var (("^a^", "^(string_of_int ix)^"), "^")")
87 ("\n*** "^indent n^"Bound "^(string_of_int ix))
88 | ato (Abs(a,T,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, ix), T)) n =
99 "\n*** "^indent n^"Var (("^a^", "^string_of_int ix^"), "^
102 "\n*** "^indent n^"Bound "^string_of_int ix
103 | ato (Abs(a, T, body)) n =
104 "\n*** "^indent n^"Abs ("^a^", "^
105 (string_of_typ T)^",.."
107 | ato (f $ t') n = ato f n^ato t' (n+1)
108 in "\n*** "^ato t 0^"\n***" end;
109 fun atomty t = (writeln o term_detail2str) t;
111 fun term_str thy (Const(s,_)) = s
112 | term_str thy (Free(s,_)) = s
113 | term_str thy (Var((s,i),_)) = s^(string_of_int i)
114 | term_str thy (Bound i) = "B."^(string_of_int i)
115 | term_str thy (Abs(s,_,_)) = s
116 | term_str thy t = raise error("term_str not for "^term2str t);
118 (*.contains the fst argument the second argument (a leave! of term).*)
119 fun contains_term (Abs(_,_,body)) t = contains_term body t
120 | contains_term (f $ f') t =
121 contains_term f t orelse contains_term f' t
122 | contains_term s t = t = s;
123 (*.contains the term a VAR(("*",_),_) ?.*)
124 fun contains_Var (Abs(_,_,body)) = contains_Var body
125 | contains_Var (f $ f') = contains_Var f orelse contains_Var f'
126 | contains_Var (Var _) = true
127 | contains_Var _ = false;
128 (* contains_Var (str2term "?z = 3") (*true*);
129 contains_Var (str2term "z = 3") (*false*);
132 (*fun int_of_str str =
133 let val ss = explode str
134 val str' = case ss of
135 "("::s => drop_last s | _ => ss
136 in case BasisLibrary.Int.fromString (implode str') of
138 | NONE => NONE end;*)
140 let val ss = explode str
141 val str' = case ss of
142 "("::s => drop_last s | _ => ss
143 in (SOME (Thy_Output.integer (implode str'))) handle _ => NONE end;
146 val it = SOME 123 : int option
147 > int_of_str "(-123)";
148 val it = SOME 123 : int option
150 val it = NONE : int option
152 val it = SOME ~123 : int option
154 fun int_of_str' str =
155 case int_of_str str of
157 | NONE => raise TERM ("int_of_string: no int-string",[]);
158 val str2int = int_of_str';
160 fun is_numeral str = case int_of_str str of
163 val is_no = is_numeral;
164 fun is_num (Free (s,_)) = if is_numeral s then true else false
167 > is_num ((term_of o the o (parse thy)) "#1");
169 > is_num ((term_of o the o (parse thy)) "#-1");
171 > is_num ((term_of o the o (parse thy)) "a123");
172 val it = false : bool
175 (*fun int_of_Free (Free (intstr, _)) =
176 (case BasisLibrary.Int.fromString intstr of
178 | NONE => raise error ("int_of_Free ( "^ intstr ^", _)"))
179 | int_of_Free t = raise error ("int_of_Free ( "^ term2str t ^" )");*)
180 fun int_of_Free (Free (intstr, _)) = (Thy_Output.integer intstr
181 handle _ => raise error ("int_of_Free ( "^ intstr ^", _)"))
182 | int_of_Free t = raise error ("int_of_Free ( "^ term2str t ^" )");
186 fun scan vs (Const(s,T)) = vs
187 | scan vs (t as Free(s,T)) = if is_no s then vs else t::vs
188 | scan vs (t as Var((s,i),T)) = t::vs
189 | scan vs (Bound i) = vs
190 | scan vs (Abs(s,T,t)) = scan vs t
191 | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)
192 in (distinct o (scan [])) t end;
194 fun is_Free (Free _) = true
196 fun is_fun_id (Const _) = true
197 | is_fun_id (Free _) = true
198 | is_fun_id _ = false;
199 fun is_f_x (f $ x) = is_fun_id f andalso is_Free x
201 (* is_f_x (str2term "q_0/2 * L * x") (*false*);
202 is_f_x (str2term "M_b x") (*true*);
206 fun scan vs (Const(s,T)) = vs
207 | scan vs (t as Free(s,T)) = if is_no s then vs else s::vs
208 | scan vs (t as Var((s,i),T)) = (s^"_"^(string_of_int i))::vs
209 | scan vs (Bound i) = vs
210 | scan vs (Abs(s,T,t)) = scan vs t
211 | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)
212 in (distinct o (scan [])) t end;
216 fun scan vs (Const(s,T)) = if is_no s then vs else s::vs
217 | scan vs (t as Free(s,T)) = if is_no s then vs else s::vs
218 | scan vs (t as Var((s,i),T)) = (s^"_"^(string_of_int i))::vs
219 | scan vs (Bound i) = vs
220 | scan vs (Abs(s,T,t)) = scan (s::vs) t
221 | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)
222 in (distinct o (scan [])) t end;
225 "b"::"d"::"v"::_ => true
227 fun is_bdv_ (Free (s,_)) = is_bdv s
230 fun free2str (Free (s,_)) = s
231 | free2str t = raise error ("free2str not for "^ term2str t);
232 fun free2int (t as Free (s, _)) = ((str2int s)
233 handle _ => raise error ("free2int: "^term_detail2str t))
234 | free2int t = raise error ("free2int: "^term_detail2str t);
237 fun var2free (t as Const(s,T)) = t
238 | var2free (t as Free(s,T)) = t
239 | var2free (Var((s,i),T)) = Free(s,T)
240 | var2free (t as Bound i) = t
241 | var2free (Abs(s,T,t)) = Abs(s,T,var2free t)
242 | var2free (t1 $ t2) = (var2free t1) $ (var2free t2);
244 (*27.8.01: doesn't find some subterm ???!???*)
245 (*2010 Logic.varify !!!*)
246 fun free2var (t as Const(s,T)) = t
247 | free2var (t as Free(s,T)) = if is_no s then t else Var((s,0),T)
248 | free2var (t as Var((s,i),T)) = t
249 | free2var (t as Bound i) = t
250 | free2var (Abs(s,T,t)) = Abs(s,T,free2var t)
251 | free2var (t1 $ t2) = (free2var t1) $ (free2var t2);
254 fun mk_listT T = Type ("List.list", [T]);
256 Const("List.list.Cons", [T, mk_listT T] ---> mk_listT T);
257 (*28.8.01: TODO: get type from head of list: 1 arg less!!!*)
258 fun list2isalist T [] = Const("List.list.Nil",mk_listT T)
259 | list2isalist T (t::ts) = (list_const T) $ t $ (list2isalist T ts);
261 > val tt = (term_of o the o (parse thy)) "R=(R::real)";
262 > val TT = type_of tt;
263 > val ss = list2isalist TT [tt,tt,tt];
264 > cterm_of (sign_of thy) ss;
265 val it = "[R = R, R = R, R = R]" : cterm *)
267 fun isapair2pair (Const ("Pair",_) $ a $ b) = (a,b)
269 raise error ("isapair2pair called with "^term2str t);
271 val listType = Type ("List.list",[Type ("bool",[])]);
272 fun isalist2list ls =
274 fun get es (Const("List.list.Cons",_) $ t $ ls) = get (t::es) ls
275 | get es (Const("List.list.Nil",_)) = es
277 raise error ("isalist2list applied to NON-list '"^term2str t^"'")
278 in (rev o (get [])) ls end;
280 > val il = str2term "[a=b,c=d,e=f]";
281 > val l = isalist2list il;
282 > (writeln o terms2str) l;
283 ["a = b","c = d","e = f"]
285 > val il = str2term "ss___::bool list";
286 > val l = isalist2list il;
287 [Free ("ss___", "bool List.list")]
291 (*review Isabelle2009/src/HOL/Tools/hologic.ML*)
292 val prop = Type ("prop",[]); (* ~/Diss.99/Integers-Isa/tools.sml*)
293 val bool = Type ("bool",[]); (* 2002 Integ.int *)
294 val Trueprop = Const("Trueprop",bool-->prop);
295 fun mk_prop t = Trueprop $ t;
296 val true_as_term = Const("True",bool);
297 val false_as_term = Const("False",bool);
298 val true_as_cterm = cterm_of (theory "HOL") true_as_term;
299 val false_as_cterm = cterm_of (theory "HOL") false_as_term;
301 infixr 5 -->; (*2002 /Pure/term.ML *)
302 infixr --->; (*2002 /Pure/term.ML *)
303 fun S --> T = Type("fun",[S,T]); (*2002 /Pure/term.ML *)
304 val op ---> = foldr (op -->); (*2002 /Pure/term.ML *)
305 fun list_implies ([], B) = B : term (*2002 /term.ML *)
306 | list_implies (A::AS, B) = Logic.implies $ A $ list_implies(AS,B);
312 fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = (* = thm.ML *)
313 match_bvs(s, t, if x="" orelse y="" then al
315 | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
316 | match_bvs(_,_,al) = al;
317 fun ren_inst(insts,prop,pat,obj) = (* = thm.ML *)
318 let val ren = match_bvs(pat,obj,[])
319 fun renAbs(Abs(x,T,b)) =
320 Abs(case assoc_string(ren,x) of NONE => x
321 | SOME(y) => y, T, renAbs(b))
322 | renAbs(f$t) = renAbs(f) $ renAbs(t)
324 in subst_vars insts (if null(ren) then prop else renAbs(prop)) end;
331 fun dest_equals' (Const("op =",_) $ t $ u) = (t,u)(* logic.ML: Const("=="*)
332 | dest_equals' t = raise TERM("dest_equals'", [t]);
333 val lhs_ = (fst o dest_equals');
334 val rhs_ = (snd o dest_equals');
336 fun is_equality (Const("op =",_) $ t $ u) = true (* logic.ML: Const("=="*)
337 | is_equality _ = false;
338 fun mk_equality (t,u) = (Const("op =",[type_of t,type_of u]--->bool) $ t $ u);
339 fun is_expliceq (Const("op =",_) $ (Free _) $ u) = true
340 | is_expliceq _ = false;
341 fun strip_trueprop (Const("Trueprop",_) $ t) = t
342 | strip_trueprop t = t;
343 (* | strip_trueprop t = raise TERM("strip_trueprop", [t]);
346 (*.(A1==>...An==>B) goes to (A1==>...An==>).*)
347 fun strip_imp_prems' (Const("==>", T) $ A $ t) =
348 let fun coll_prems As (Const("==>", _) $ A $ t) =
349 coll_prems (As $ (Logic.implies $ A)) t
350 | coll_prems As _ = SOME As
351 in coll_prems (Logic.implies $ A) t end
352 | strip_imp_prems' _ = NONE; (* logic.ML: term -> term list*)
354 val thm = real_mult_div_cancel1;
355 val prop = (#prop o rep_thm) thm;
359 *** . Const ( Trueprop)
361 *** . . . Const ( op =)
362 *** . . . . Var ((k, 0), )
363 *** . . . . Const ( 0)
364 *** . Const ( Trueprop)
365 *** . . Const ( op =) *** .............
366 val SOME t = strip_imp_prems' ((#prop o rep_thm) thm);
370 *** . Const ( Trueprop)
372 *** . . . Const ( op =)
373 *** . . . . Var ((k, 0), )
374 *** . . . . Const ( 0)
376 val thm = real_le_anti_sym;
377 val prop = (#prop o rep_thm) thm;
381 *** . Const ( Trueprop)
382 *** . . Const ( op <=)
383 *** . . . Var ((z, 0), )
384 *** . . . Var ((w, 0), )
386 *** . . Const ( Trueprop)
387 *** . . . Const ( op <=)
388 *** . . . . Var ((w, 0), )
389 *** . . . . Var ((z, 0), )
390 *** . . Const ( Trueprop)
391 *** . . . Const ( op =)
393 val SOME t = strip_imp_prems' ((#prop o rep_thm) thm);
397 *** . Const ( Trueprop)
398 *** . . Const ( op <=)
399 *** . . . Var ((z, 0), )
400 *** . . . Var ((w, 0), )
402 *** . . Const ( Trueprop)
403 *** . . . Const ( op <=)
404 *** . . . . Var ((w, 0), )
405 *** . . . . Var ((z, 0), )
408 (*. (A1==>...An==>) (B) goes to (A1==>...An==>B), where B is lowest branch.*)
409 fun ins_concl (Const("==>", T) $ A $ t) B = Logic.implies $ A $ (ins_concl t B)
410 | ins_concl (Const("==>", T) $ A ) B = Logic.implies $ A $ B
411 | ins_concl t B = raise TERM("ins_concl", [t, B]);
413 val thm = real_le_anti_sym;
414 val prop = (#prop o rep_thm) thm;
415 val concl = Logic.strip_imp_concl prop;
416 val SOME prems = strip_imp_prems' prop;
417 val prop' = ins_concl prems concl;
424 fun vperm (Var _, Var _) = true (*2002 Pure/thm.ML *)
425 | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t)
426 | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2)
427 | vperm (t, u) = (t = u);
429 (*2002 cp from Pure/term.ML --- since 2009 in Pure/old_term.ML*)
430 fun mem_term (_, []) = false
431 | mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts);
432 fun subset_term ([], ys) = true
433 | subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys);
434 fun eq_set_term (xs, ys) =
435 xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs));
436 (*a total, irreflexive ordering on index names*)
437 fun xless ((a,i), (b,j): indexname) = i<j orelse (i=j andalso a<b);
438 (*a partial ordering (not reflexive) for atomic terms*)
439 fun atless (Const (a,_), Const (b,_)) = a<b
440 | atless (Free (a,_), Free (b,_)) = a<b
441 | atless (Var(v,_), Var(w,_)) = xless(v,w)
442 | atless (Bound i, Bound j) = i<j
444 (*insert atomic term into partially sorted list, suppressing duplicates (?)*)
445 fun insert_aterm (t,us) =
446 let fun inserta [] = [t]
447 | inserta (us as u::us') =
448 if atless(t,u) then t::us
449 else if t=u then us (*duplicate*)
450 else u :: inserta(us')
453 (*Accumulates the Vars in the term, suppressing duplicates*)
454 fun add_term_vars (t, vars: term list) = case t of
455 Var _ => insert_aterm(t,vars)
456 | Abs (_,_,body) => add_term_vars(body,vars)
457 | f$t => add_term_vars (f, add_term_vars(t, vars))
459 fun term_vars t = add_term_vars(t,[]);
462 fun var_perm (t, u) = (*2002 Pure/thm.ML *)
463 vperm (t, u) andalso eq_set_term (term_vars t, term_vars u);
465 (*2002 fun decomp_simp, Pure/thm.ML *)
466 fun perm lhs rhs = var_perm (lhs, rhs) andalso not (lhs aconv rhs)
467 andalso not (is_Var lhs);
471 if n < 0 then "-"^((string_of_int o abs) n)
472 else string_of_int n;
475 val it = "1" : string > str_of_int ~1;
476 val it = "-1" : string
482 if n>0 then b*(power b (n-1))
483 else raise error ("power "^(str_of_int b)^" "^(str_of_int n));
494 | gcd a b = if a < b then gcd (b mod a) a
495 else gcd (a mod b) b;
496 fun sign n = if n < 0 then ~1
497 else if n = 0 then 0 else 1;
498 fun sign2 n1 n2 = (sign n1) * (sign n2);
501 fun d dvd n = n mod d = 0;
504 let fun pdiv ds d n =
506 else if d dvd n then pdiv (d::ds) d (n div d)
515 fun doubles ds = (* ds is ordered *)
516 let fun dbls ds [] = ds
518 | dbls ds (i::i'::is) = if i=i' then dbls (i::ds) is
519 else dbls ds (i'::is)
522 val it = [] : int list
523 > doubles [2,3,3,5,5,7];
524 val it = [5,3] : int list*)
528 | squfact n = foldl op* (1, (doubles o divisors) n);
539 fun dest_type (Type(T,[])) = T
542 raise error ("... dest_type: not impl. for this type"));
544 fun term_of_num ntyp n = Free (str_of_int n, ntyp);
546 fun pairT T1 T2 = Type ("*", [T1, T2]);
547 (*> val t = str2term "(1,2)";
548 > type_of t = pairT HOLogic.realT HOLogic.realT;
551 fun PairT T1 T2 = ([T1, T2] ---> Type ("*", [T1, T2]));
552 (*> val t = str2term "(1,2)";
553 > val Const ("Pair",pT) $ _ $ _ = t;
554 > pT = PairT HOLogic.realT HOLogic.realT;
558 Const ("Pair", PairT (type_of t1) (type_of t2)) $ t1 $ t2;
559 (*> val t = str2term "(1,2)";
560 > val (t1, t2) = (str2term "1", str2term "2");
562 val it = true : bool*)
565 fun num_of_term (t as Free (s,_)) =
566 (case int_of_str s of
568 | NONE => raise error ("num_of_term not for "^ term2str t))
569 | num_of_term t = raise error ("num_of_term not for "^term2str t);
571 fun mk_factroot op_(*=thy.sqrt*) T fact root =
572 Const ("op *", [T, T] ---> T) $ (term_of_num T fact) $
573 (Const (op_, T --> T) $ term_of_num T root);
575 val T = (type_of o term_of o the) (parse thy "#12::real");
576 val t = mk_factroot "SqRoot.sqrt" T 2 3;
577 cterm_of (sign_of thy) t;
578 val it = "#2 * sqrt #3 " : cterm
580 fun var_op_num v op_ optype ntyp n =
581 Const (op_, optype) $ v $
582 Free (str_of_int n, ntyp);
584 fun num_op_var v op_ optype ntyp n =
586 Free (str_of_int n, ntyp) $ v;
588 fun num_op_num T1 T2 (op_,Top) n1 n2 =
590 Free (str_of_int n1, T1) $ Free (str_of_int n2, T2);
592 > val t = num_op_num "Int" 3 4;
594 > string_of_cterm (cterm_of (sign_of thy) t);
597 fun const_in str (Const _) = false
598 | const_in str (Free (s,_)) = if strip_thy s = str then true else false
599 | const_in str (Bound _) = false
600 | const_in str (Var _) = false
601 | const_in str (Abs (_,_,body)) = const_in str body
602 | const_in str (f$u) = const_in str f orelse const_in str u;
604 > val t = (term_of o the o (parse thy)) "6 + 5 * sqrt 4 + 3";
607 > val t = (term_of o the o (parse thy)) "6 + 5 * 4 + 3";
609 val it = false : bool
612 (*used for calculating built in binary operations in Isabelle2002->Float.ML*)
613 (*fun calc "op +" (n1, n2) = n1+n2
614 | calc "op -" (n1, n2) = n1-n2
615 | calc "op *" (n1, n2) = n1*n2
616 | calc "HOL.divide"(n1, n2) = n1 div n2
617 | calc "Atools.pow"(n1, n2) = power n1 n2
618 | calc op_ _ = raise error ("calc: operator = "^op_^" not defined");-----*)
619 fun calc_equ "op <" (n1, n2) = n1 < n2
620 | calc_equ "op <=" (n1, n2) = n1 <= n2
622 raise error ("calc_equ: operator = "^op_^" not defined");
623 fun sqrt (n:int) = if n < 0 then 0
624 (*FIXME ~~~*) else (trunc o Math.sqrt o Real.fromInt) n;
626 fun mk_thmid thmid op_ n1 n2 =
627 thmid ^ (strip_thy n1) ^ "_" ^ (strip_thy n2);
629 fun dest_binop_typ (Type("fun",[range,Type("fun",[arg2,arg1])])) =
631 | dest_binop_typ _ = raise error "dest_binop_typ: not binary";
633 > val t = (term_of o the o (parse thy)) "#3^#4";
634 > val hT = type_of (head_of t);
636 val it = ("'a","nat","'a") : typ * typ * typ
640 (** transform binary numeralsstrings **)
641 (*Makarius 100308, hacked by WN*)
642 val numbers_to_string =
645 (case try HOLogic.dest_number t of
647 (*if T = @{typ int} orelse T = @{typ real} then WN*)
648 SOME (Free (signed_string_of_int i, T))
652 fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b)
653 | to_str (t as (u1 $ u2)) =
656 | NONE => to_str u1 $ to_str u2)
657 | to_str t = perhaps dest_num t;
660 (*.make uminus uniform:
661 Const ("uminus", _) $ Free ("2", "RealDef.real") --> Free ("-2", _)
662 to be used immediately before evaluation of numerals;
663 see Scripts/calculate.sml .*)
664 (*2002 fun(*app_num_tr'2 (Const("0",T)) = Free("0",T)
665 | app_num_tr'2 (Const("1",T)) = Free("1",T)
666 |*)app_num_tr'2 (t as Const("uminus",_) $ Free(s,T)) =
667 (case int_of_str s of SOME i =>
668 if i > 0 then Free("-"^s,T) else Free(s,T)
670 (*| app_num_tr'2 (t as Const(s,T)) = t
671 | app_num_tr'2 (Const("Numeral.number_of",Type ("fun", [_, T])) $ t) =
672 Free(NumeralSyntax.dest_bin_str t, T)
673 | app_num_tr'2 (t as Free(s,T)) = t
674 | app_num_tr'2 (t as Var(n,T)) = t
675 | app_num_tr'2 (t as Bound i) = t
676 *)| app_num_tr'2 (Abs(s,T,body)) = Abs(s,T, app_num_tr'2 body)
677 | app_num_tr'2 (t1 $ t2) = (app_num_tr'2 t1) $ (app_num_tr'2 t2)
678 | app_num_tr'2 t = t;
680 val uminus_to_string =
684 (Const ("HOL.uminus_class.uminus", _) $ Free (s, T)) =>
685 (case int_of_str s of
687 SOME (Free (signed_string_of_int (~1 * i), T))
691 fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b)
692 | to_str (t as (u1 $ u2)) =
695 | NONE => to_str u1 $ to_str u2)
696 | to_str t = perhaps dest_num t;
700 (*2002 fun num_str thm =
702 val {sign_ref = sign_ref, der = der, maxidx = maxidx,
703 shyps = shyps, hyps = hyps, (*tpairs = tpairs,*) prop = prop} =
705 val prop' = app_num_tr'1 prop;
706 in assbl_thm sign_ref der maxidx shyps hyps (*tpairs*) prop' end;*)
709 {thy_ref = thy_ref, tags = tags, maxidx = maxidx, shyps = shyps,
710 hyps = hyps, tpairs = tpairs, prop = prop}) = rep_thm_G thm
711 val prop' = numbers_to_string prop;
712 in assbl_thm deriv thy_ref tags maxidx shyps hyps tpairs prop' end;
714 fun get_thm' xstring = (*?covers 2009 Thm?!, replaces 2002 fun get_thm :
715 val it = fn : theory -> xstring -> Thm.thm*)
717 num_str (ProofContext.get_thm (thy2ctxt' "Isac") xstring));
719 (** get types of Free and Abs for parse' **)
720 (*11.1.00: not used, fix-typed +,*,-,^ instead *)
722 val dummyT = Type ("dummy",[]);
723 val dummyT = TVar (("DUMMY",0),[]);
725 (* assumes only 1 type for numerals
726 and different identifiers for Const, Free and Abs *)
729 fun get ts (Const(s,T)) = (s,T)::ts
730 | get ts (Free(s,T)) = if is_no s
731 then ("#",T)::ts else (s,T)::ts
732 | get ts (Var(n,T)) = ts
733 | get ts (Bound i) = ts
734 | get ts (Abs(s,T,body)) = get ((s,T)::ts) body
735 | get ts (t1 $ t2) = (get ts t1) @ (get ts t2)
736 in distinct (get [] t) end;
738 val t = (term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)";
742 (*11.1.00: not used, fix-typed +,*,-,^ instead *)
743 fun set_types al (Const(s,T)) =
744 (case assoc (al,s) of
745 SOME T' => Const(s,T')
746 | NONE => (warning ("set_types: no type for "^s); Const(s,dummyT)))
747 | set_types al (Free(s,T)) =
749 (case assoc (al,"#") of
750 SOME T' => Free(s,T')
751 | NONE => (warning ("set_types: no type for numerals"); Free(s,T)))
752 else (case assoc (al,s) of
753 SOME T' => Free(s,T')
754 | NONE => (warning ("set_types: no type for "^s); Free(s,T)))
755 | set_types al (Var(n,T)) = Var(n,T)
756 | set_types al (Bound i) = Bound i
757 | set_types al (Abs(s,T,body)) =
758 (case assoc (al,s) of
759 SOME T' => Abs(s,T', set_types al body)
760 | NONE => (warning ("set_types: no type for "^s);
761 Abs(s,T, set_types al body)))
762 | set_types al (t1 $ t2) = (set_types al t1) $ (set_types al t2);
764 val t = (term_of o the o (parse thy)) "sqrt(#9+#4*x)=sqrt x + sqrt(#-3+x)";
765 val al = get_types t;
767 val t = (term_of o the o (parse thy)) "x = #0 + #-1 * #-4";
769 val t' = set_types al t;
771 cterm_of (sign_of thy) t';
772 val it = "x = #0 + #-1 * #-4" : cterm
774 val t = (term_of o the o (parse thy))
775 "#5 * x + x ^^^ #2 = (#2 + x) ^^^ #2";
777 val t' = set_types al t;
779 cterm_of (sign_of thy) t';
780 uncaught exception TYPE (*^^^ is new, NOT in al*)
784 (** from Descript.ML **)
786 (** decompose an isa-list to an ML-list
787 i.e. [] belong to the meta-language, too **)
789 fun is_list ((Const("List.list.Cons",_)) $ _ $ _) = true
791 (* val (SOME ct) = parse thy "lll::real list";
792 > val ty = (#t o rep_cterm) ct;
794 val it = false : bool
795 > val (SOME ct) = parse thy "[lll]";
796 > val ty = (#t o rep_cterm) ct;
798 val it = true : bool *)
802 fun mk_Free (s,T) = Free(s,T);
803 fun mk_free T s = Free(s,T);
805 (*instantiate let; necessary for ass_up*)
806 fun inst_abs thy (Const sT) = Const sT
807 | inst_abs thy (Free sT) = Free sT
808 | inst_abs thy (Bound n) = Bound n
809 | inst_abs thy (Var iT) = Var iT
810 | inst_abs thy (Const ("Let",T1) $ e $ (Abs (v,T2,b))) =
811 let val (v',b') = variant_abs (v,T2,b); (*fun variant_abs: term.ML*)
812 in Const ("Let",T1) $ inst_abs thy e $ (Abs (v',T2,inst_abs thy b')) end
813 | inst_abs thy (t1 $ t2) = inst_abs thy t1 $ inst_abs thy t2
815 (writeln("inst_abs: unchanged t= "^ term2str t);
817 (*val scr as (Script sc) = Script ((term_of o the o (parse thy))
818 "Script Testeq (e_::bool) = \
819 \While (contains_root e_) Do \
820 \ (let e_ = Try (Repeat (Rewrite rroot_square_inv False e_)); \
821 \ e_ = Try (Repeat (Rewrite square_equation_left True e_)) \
822 \ in Try (Repeat (Rewrite radd_0 False e_))) ");
824 *** Const ( Script.Testeq)
826 *** . Const ( Script.While)
827 *** . . Const ( RatArith.contains'_root)
828 *** . . . Free ( e_, )
830 *** . . . Const ( Script.Try)
831 *** . . . . Const ( Script.Repeat)
832 *** . . . . . Const ( Script.Rewrite)
833 *** . . . . . . Free ( rroot_square_inv, )
834 *** . . . . . . Const ( False)
835 *** . . . . . . Free ( e_, )
837 *** . . . . Const ( Let)
838 *** . . . . . Const ( Script.Try)
839 *** . . . . . . Const ( Script.Repeat)
840 *** . . . . . . . Const ( Script.Rewrite)
841 *** . . . . . . . . Free ( square_equation_left, )
842 *** . . . . . . . . Const ( True)
843 *** . . . . . . . . Bound 0 <-- !!!
844 *** . . . . . Abs( e_,..
845 *** . . . . . . Const ( Script.Try)
846 *** . . . . . . . Const ( Script.Repeat)
847 *** . . . . . . . . Const ( Script.Rewrite)
848 *** . . . . . . . . . Free ( radd_0, )
849 *** . . . . . . . . . Const ( False)
850 *** . . . . . . . . . Bound 0 <-- !!!
852 ML> atomt (inst_abs thy sc);
853 *** Const ( Script.Testeq)
855 *** . Const ( Script.While)
856 *** . . Const ( RatArith.contains'_root)
857 *** . . . Free ( e_, )
859 *** . . . Const ( Script.Try)
860 *** . . . . Const ( Script.Repeat)
861 *** . . . . . Const ( Script.Rewrite)
862 *** . . . . . . Free ( rroot_square_inv, )
863 *** . . . . . . Const ( False)
864 *** . . . . . . Free ( e_, )
866 *** . . . . Const ( Let)
867 *** . . . . . Const ( Script.Try)
868 *** . . . . . . Const ( Script.Repeat)
869 *** . . . . . . . Const ( Script.Rewrite)
870 *** . . . . . . . . Free ( square_equation_left, )
871 *** . . . . . . . . Const ( True)
872 *** . . . . . . . . Free ( e_, ) <-- !!!
873 *** . . . . . Abs( e_,..
874 *** . . . . . . Const ( Script.Try)
875 *** . . . . . . . Const ( Script.Repeat)
876 *** . . . . . . . . Const ( Script.Rewrite)
877 *** . . . . . . . . . Free ( radd_0, )
878 *** . . . . . . . . . Const ( False)
879 *** . . . . . . . . . Free ( e_, ) <-- ZUFALL vor 5.03!!!
885 fun inst_abs thy (Const sT) = Const sT
886 | inst_abs thy (Free sT) = Free sT
887 | inst_abs thy (Bound n) = Bound n
888 | inst_abs thy (Var iT) = Var iT
889 | inst_abs thy (Const ("Let",T1) $ e $ (Abs (v,T2,b))) =
890 let val b' = subst_bound (Free(v,T2),b);
891 (*fun variant_abs: term.ML*)
892 in Const ("Let",T1) $ inst_abs thy e $ (Abs (v,T2,inst_abs thy b')) end
893 | inst_abs thy (t1 $ t2) = inst_abs thy t1 $ inst_abs thy t2
895 (writeln("inst_abs: unchanged t= "^ term2str t);
898 "Script Make_fun_by_explicit (f_::real) (v_::real) (eqs_::bool list) = \
899 \ (let h_ = (hd o (filterVar f_)) eqs_; \
900 \ e_1 = hd (dropWhile (ident h_) eqs_); \
901 \ vs_ = dropWhile (ident f_) (Vars h_); \
902 \ v_1 = hd (dropWhile (ident v_) vs_); \
903 \ (s_1::bool list)=(SubProblem(DiffApp_,[univar,equation],[no_met])\
904 \ [bool_ e_1, real_ v_1])\
905 \ in Substitute [(v_1 = (rhs o hd) s_1)] h_)";
906 > val ttt = (term_of o the o (parse thy)) scr;
907 > writeln(term2str ttt);
910 *** Const ( DiffApp.Make'_fun'_by'_explicit)
915 *** . . Const ( Fun.op o)
916 *** . . . Const ( List.hd)
917 *** . . . Const ( DiffApp.filterVar)
918 *** . . . . Free ( f_, )
919 *** . . . Free ( eqs_, )
921 *** . . . Const ( Let)
922 *** . . . . Const ( List.hd)
923 *** . . . . . Const ( List.dropWhile)
924 *** . . . . . . Const ( Atools.ident)
925 *** . . . . . . . Bound 0 <---- Free ( h_, )
926 *** . . . . . . Free ( eqs_, )
927 *** . . . . Abs( e_1,..
928 *** . . . . . Const ( Let)
929 *** . . . . . . Const ( List.dropWhile)
930 *** . . . . . . . Const ( Atools.ident)
931 *** . . . . . . . . Free ( f_, )
932 *** . . . . . . . Const ( Tools.Vars)
933 *** . . . . . . . . Bound 1 <---- Free ( h_, )
934 *** . . . . . . Abs( vs_,..
935 *** . . . . . . . Const ( Let)
936 *** . . . . . . . . Const ( List.hd)
937 *** . . . . . . . . . Const ( List.dropWhile)
938 *** . . . . . . . . . . Const ( Atools.ident)
939 *** . . . . . . . . . . . Free ( v_, )
940 *** . . . . . . . . . . Bound 0 <---- Free ( vs_, )
941 *** . . . . . . . . Abs( v_1,..
942 *** . . . . . . . . . Const ( Let)
943 *** . . . . . . . . . . Const ( Script.SubProblem)
944 *** . . . . . . . . . . . Const ( Pair)
945 *** . . . . . . . . . . . . Free ( DiffApp_, )
946 *** . . . . . . . . . . . . Const ( Pair)
947 *** . . . . . . . . . . . . . Const ( List.list.Cons)
948 *** . . . . . . . . . . . . . . Free ( univar, )
949 *** . . . . . . . . . . . . . . Const ( List.list.Cons)
950 *** . . . . . . . . . . . . . . . Free ( equation, )
951 *** . . . . . . . . . . . . . . . Const ( List.list.Nil)
952 *** . . . . . . . . . . . . . Const ( List.list.Cons)
953 *** . . . . . . . . . . . . . . Free ( no_met, )
954 *** . . . . . . . . . . . . . . Const ( List.list.Nil)
955 *** . . . . . . . . . . . Const ( List.list.Cons)
956 *** . . . . . . . . . . . . Const ( Script.bool_)
957 *** . . . . . . . . . . . . . Bound 2 <----- Free ( e_1, )
958 *** . . . . . . . . . . . . Const ( List.list.Cons)
959 *** . . . . . . . . . . . . . Const ( Script.real_)
960 *** . . . . . . . . . . . . . . Bound 0 <----- Free ( v_1, )
961 *** . . . . . . . . . . . . . Const ( List.list.Nil)
962 *** . . . . . . . . . . Abs( s_1,..
963 *** . . . . . . . . . . . Const ( Script.Substitute)
964 *** . . . . . . . . . . . . Const ( List.list.Cons)
965 *** . . . . . . . . . . . . . Const ( Pair)
966 *** . . . . . . . . . . . . . . Bound 1 <----- Free ( v_1, )
967 *** . . . . . . . . . . . . . . Const ( Fun.op o)
968 *** . . . . . . . . . . . . . . . Const ( Tools.rhs)
969 *** . . . . . . . . . . . . . . . Const ( List.hd)
970 *** . . . . . . . . . . . . . . . Bound 0 <----- Free ( s_1, )
971 *** . . . . . . . . . . . . . Const ( List.list.Nil)
972 *** . . . . . . . . . . . . Bound 4 <----- Free ( h_, )
974 > val ttt' = inst_abs thy ttt;
975 > writeln(term2str ttt');
976 Script Make_fun_by_explicit f_ v_ eqs_ =
980 *** Const ( DiffApp.Make'_fun'_by'_explicit)
985 *** . . Const ( Fun.op o)
986 *** . . . Const ( List.hd)
987 *** . . . Const ( DiffApp.filterVar)
988 *** . . . . Free ( f_, )
989 *** . . . Free ( eqs_, )
991 *** . . . Const ( Let)
992 *** . . . . Const ( List.hd)
993 *** . . . . . Const ( List.dropWhile)
994 *** . . . . . . Const ( Atools.ident)
995 *** . . . . . . . Free ( h_, ) <---- Bound 0
996 *** . . . . . . Free ( eqs_, )
997 *** . . . . Abs( e_1,..
998 *** . . . . . Const ( Let)
999 *** . . . . . . Const ( List.dropWhile)
1000 *** . . . . . . . Const ( Atools.ident)
1001 *** . . . . . . . . Free ( f_, )
1002 *** . . . . . . . Const ( Tools.Vars)
1003 *** . . . . . . . . Free ( h_, ) <---- Bound 1
1004 *** . . . . . . Abs( vs_,..
1005 *** . . . . . . . Const ( Let)
1006 *** . . . . . . . . Const ( List.hd)
1007 *** . . . . . . . . . Const ( List.dropWhile)
1008 *** . . . . . . . . . . Const ( Atools.ident)
1009 *** . . . . . . . . . . . Free ( v_, )
1010 *** . . . . . . . . . . Free ( vs_, ) <---- Bound 0
1011 *** . . . . . . . . Abs( v_1,..
1012 *** . . . . . . . . . Const ( Let)
1013 *** . . . . . . . . . . Const ( Script.SubProblem)
1014 *** . . . . . . . . . . . Const ( Pair)
1015 *** . . . . . . . . . . . . Free ( DiffApp_, )
1016 *** . . . . . . . . . . . . Const ( Pair)
1017 *** . . . . . . . . . . . . . Const ( List.list.Cons)
1018 *** . . . . . . . . . . . . . . Free ( univar, )
1019 *** . . . . . . . . . . . . . . Const ( List.list.Cons)
1020 *** . . . . . . . . . . . . . . . Free ( equation, )
1021 *** . . . . . . . . . . . . . . . Const ( List.list.Nil)
1022 *** . . . . . . . . . . . . . Const ( List.list.Cons)
1023 *** . . . . . . . . . . . . . . Free ( no_met, )
1024 *** . . . . . . . . . . . . . . Const ( List.list.Nil)
1025 *** . . . . . . . . . . . Const ( List.list.Cons)
1026 *** . . . . . . . . . . . . Const ( Script.bool_)
1027 *** . . . . . . . . . . . . . Free ( e_1, ) <----- Bound 2
1028 *** . . . . . . . . . . . . Const ( List.list.Cons)
1029 *** . . . . . . . . . . . . . Const ( Script.real_)
1030 *** . . . . . . . . . . . . . . Free ( v_1, ) <----- Bound 0
1031 *** . . . . . . . . . . . . . Const ( List.list.Nil)
1032 *** . . . . . . . . . . Abs( s_1,..
1033 *** . . . . . . . . . . . Const ( Script.Substitute)
1034 *** . . . . . . . . . . . . Const ( List.list.Cons)
1035 *** . . . . . . . . . . . . . Const ( Pair)
1036 *** . . . . . . . . . . . . . . Free ( v_1, ) <----- Bound 1
1037 *** . . . . . . . . . . . . . . Const ( Fun.op o)
1038 *** . . . . . . . . . . . . . . . Const ( Tools.rhs)
1039 *** . . . . . . . . . . . . . . . Const ( List.hd)
1040 *** . . . . . . . . . . . . . . . Free ( s_1, ) <----- Bound 0
1041 *** . . . . . . . . . . . . . Const ( List.list.Nil)
1042 *** . . . . . . . . . . . . Free ( h_, ) <----- Bound 4
1044 Note numbering of de Bruijn indexes !
1046 Script Make_fun_by_explicit f_ v_ eqs_ =
1047 let h_ = (hd o filterVar f_) eqs_;
1048 e_1 = hd (dropWhile (ident h_ BOUND_0) eqs_);
1049 vs_ = dropWhile (ident f_) (Vars h_ BOUND_1);
1050 v_1 = hd (dropWhile (ident v_) vs_ BOUND_0);
1052 SubProblem (DiffApp_, [univar, equation], [no_met])
1053 [bool_ e_1 BOUND_2, real_ v_1 BOUND_0]
1054 in Substitute [(v_1 BOUND_1 = (rhs o hd) s_1 BOUND_0)] h_ BOUND_4
1058 fun T_a2real (Type (s, [])) =
1059 if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else Type (s, [])
1060 | T_a2real (Type (s, Ts)) = Type (s, map T_a2real Ts)
1061 | T_a2real (TFree (s, srt)) =
1062 if s = "'a" orelse s = "'b" orelse s = "'c" then HOLogic.realT else TFree (s, srt)
1063 | T_a2real (TVar (("DUMMY",_),srt)) = HOLogic.realT;
1065 (*FIXME .. fixes the type (+see Typefix.thy*)
1066 fun typ_a2real (Const( s, T)) = (Const( s, T_a2real T))
1067 | typ_a2real (Free( s, T)) = (Free( s, T_a2real T))
1068 | typ_a2real (Var( n, T)) = (Var( n, T_a2real T))
1069 | typ_a2real (Bound i) = (Bound i)
1070 | typ_a2real (Abs(s,T,t)) = Abs(s, T, typ_a2real t)
1071 | typ_a2real (t1 $ t2) = (typ_a2real t1) $ (typ_a2real t2);
1073 ----------------6.8.02---------------------------------------------------
1075 val t = read_cterm (sign_of thy) (str,(TVar(("DUMMY",0),[])));
1079 val t = (app_num_tr' o term_of) t;
1083 val t = typ_a2real t;
1086 *** Const ( 1, real)
1089 val t = read_cterm (sign_of thy) (str,(TVar(("DUMMY",0),[])));
1092 *** Const ( Numeral.number_of, bin => 'a)
1093 *** . Const ( Numeral.bin.Bit, [bin, bool] => bin)
1094 *** . . Const ( Numeral.bin.Bit, [bin, bool] => bin)
1095 *** . . . Const ( Numeral.bin.Pls, bin)
1096 *** . . . Const ( True, bool)
1097 *** . . Const ( False, bool)
1098 val t = (app_num_tr' o term_of) t;
1102 val t = typ_a2real t;
1106 ----------------6.8.02---------------------------------------------------
1110 > val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[]))));
1111 val t = Free ("R","?DUMMY") : term
1112 > val t' = typ_a2real t;
1113 > cterm_of (sign_of thy) t';
1114 val it = "R::RealDef.real" : cterm
1117 > val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[]))));
1118 > atomty (typ_a2real t);
1120 *** Const ( op =, [RealDef.real, RealDef.real] => bool)
1121 *** Free ( R, RealDef.real)
1122 *** Free ( R, RealDef.real)
1123 > val t' = typ_a2real t;
1124 > cterm_of (sign_of thy) t';
1125 val it = "(R::RealDef.real) = R" : cterm
1127 > val str = "fixed_values [R=R]";
1128 > val t = term_of (read_cterm(sign_of thy)(str,(TVar(("DUMMY",0),[]))));
1129 > val t' = typ_a2real t;
1130 > cterm_of (sign_of thy) t';
1131 val it = "fixed_values [(R::RealDef.real) = R]" : cterm
1134 (*TODO.WN0609: parse should return a term or a string
1135 (or even more comprehensive datastructure for error-messages)
1136 i.e. in wrapping with SOME term or NONE the latter is not sufficient*)
1137 (*2002 fun parseold thy str =
1139 val sgn = sign_of thy;
1140 val t = ((*typ_a2real o*) app_num_tr'1 o term_of)
1141 (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));
1142 in SOME (cterm_of sgn t) end)
1147 fun parseold thy str =
1148 (let val t = ((*typ_a2real o*) numbers_to_string)
1149 (Syntax.read_term_global thy str)
1150 in SOME (cterm_of thy t) end)
1152 (*2002 fun parseN thy str =
1154 val sgn = sign_of thy;
1155 val t = ((*typ_a2real o app_num_tr'1 o*) term_of)
1156 (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));
1157 in SOME (cterm_of sgn t) end)
1159 fun parseN thy str =
1160 (let val t = (*(typ_a2real o numbers_to_string)*)
1161 (Syntax.read_term_global thy str)
1162 in SOME (cterm_of thy t) end)
1164 (*2002 fun parse thy str =
1166 val sgn = sign_of thy;
1167 val t = (typ_a2real o app_num_tr'1 o term_of)
1168 (read_cterm sgn (str,(TVar(("DUMMY",0),[]))));
1169 in SOME (cterm_of sgn t) end) (*FIXXXXME 10.8.02: return term !!!*)
1171 (*2010 fun parse thy str =
1172 (let val t = (typ_a2real o app_num_tr'1) (Syntax.read_term_global thy str)
1173 in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*)
1176 (let val t = (typ_a2real o numbers_to_string)
1177 (Syntax.read_term_global thy str)
1178 in SOME (cterm_of thy t) end) (*FIXXXXME 10.8.02: return term !!!*)
1181 (* 10.8.02: for this reason we still have ^^^--------------------
1182 val thy = SqRoot.thy;
1183 val str = "(1::real) ^ (2::nat)";
1184 val sgn = sign_of thy;
1185 val ct = (read_cterm sgn (str,(TVar(("DUMMY",0),[])))) handle e =>print_exn e;
1186 (*1*)"(1::real) ^ 2";
1187 atomty (term_of ct);
1189 *** Const ( Nat.power, [real, nat] => real)
1190 *** . Const ( 1, real)
1191 *** . Const ( Numeral.number_of, bin => nat)
1192 *** . . Const ( Numeral.bin.Bit, [bin, bool] => bin)
1193 *** . . . Const ( Numeral.bin.Bit, [bin, bool] => bin)
1194 *** . . . . Const ( Numeral.bin.Pls, bin)
1195 *** . . . . Const ( True, bool)
1196 *** . . . Const ( False, bool)
1197 val t = ((app_num_tr' o term_of)
1198 (read_cterm sgn (str,(TVar(("DUMMY",0),[])))))handle e => print_exn e;
1199 val ct = (cterm_of sgn t) handle e => print_exn e;
1200 (*2*)"(1::real) ^ (2::nat)";
1201 atomty (term_of ct);
1203 *** Const ( Nat.power, [real, nat] => real)
1204 *** . Free ( 1, real)
1205 *** . Free ( 2, nat) (*1*) Const("2",_) (*2*) Free("2",_)
1208 val str = "(2::real) ^ (2::nat)";
1209 val t = (read_cterm sgn (str,(TVar(("DUMMY",0),[])))) handle e => print_exn e;
1210 val t = "(2::real) ^ 2" : cterm
1211 val t = ((app_num_tr' o term_of)
1212 (read_cterm sgn (str,(TVar(("DUMMY",0),[])))))handle e => print_exn e;
1213 val ct = (cterm_of sgn t) handle e => print_exn e;
1214 Variable "2" has two distinct types
1217 uncaught exception TYPE
1218 raised at: sign.ML:672.26-673.56
1222 val str = "(3::real) ^ (2::nat)";
1223 val t = (read_cterm sgn (str,(TVar(("DUMMY",0),[])))) handle e => print_exn e;
1224 val t = "(3::real) ^ 2" : cterm
1225 val t = ((app_num_tr' o term_of)
1226 (read_cterm sgn (str,(TVar(("DUMMY",0),[])))))handle e => print_exn e;
1227 val ct = (cterm_of sgn t) handle e => print_exn e;
1228 val ct = "(3::real) ^ (2::nat)" : cterm
1231 Conclusion: The type inference allows different types
1232 for one and the same Numeral.number_of
1233 BUT the type inference doesn't allow
1234 Free ( 2, real) and Free ( 2, nat) within one term
1235 --------------- ~~~~ ~~~ *)
1237 > val (SOME ct) = parse thy "(-#5)^^^#3";
1238 > atomty (term_of ct);
1240 *** Const ( Nat.op ^, ['a, nat] => 'a)
1241 *** Const ( uminus, 'a => 'a)
1244 > val (SOME ct) = parse thy "R=R";
1245 > atomty (term_of ct);
1247 *** Const ( op =, [real, real] => bool)
1251 THIS IS THE OUTPUT FOR VERSION (3) above at typ_a2real !!!!!
1253 *** Const ( op =, [RealDef.real, RealDef.real] => bool)
1254 *** Free ( R, RealDef.real)
1255 *** Free ( R, RealDef.real) *)
1257 (*version for testing local to theories*)
1258 fun str2term_ thy str = (term_of o the o (parse thy)) str;
1259 fun str2term str = (term_of o the o (parse (theory "Isac"))) str;
1260 fun strs2terms ss = map str2term ss;
1261 fun str2termN str = (term_of o the o (parseN (theory "Isac"))) str;
1263 (*+ makes a substitution from the output of Pattern.match +*)
1264 (*fun mk_subs ((id, _):indexname, t:term) = (Free (id,type_of t), t);*)
1265 fun mk_subs (subs: ((string * int) * (Term.typ * Term.term)) list) =
1266 let fun mk_sub ((id, _), (ty, tm)) = (Free (id, ty), tm) in
1267 map mk_sub subs end;
1269 val atomthm = atomt o #prop o rep_thm;
1271 (*.instantiate #prop thm with bound variables (as Free).*)
1272 fun inst_bdv [] t = t : term
1273 | inst_bdv (instl: (term*term) list) t =
1274 let fun subst (v as Var((s,_),T)) =
1277 if_none (assoc(instl,Free(s,T))) (Free(s,T))
1279 | subst (Abs(a,T,body)) = Abs(a, T, subst body)
1280 | subst (f$t') = subst f $ subst t'
1281 | subst t = if_none (assoc(instl,t)) t
1285 (*WN050829 caution: is_atom (str2term"q_0/2 * L * x") = true !!!
1286 use length (vars term) = 1 instead*)
1287 fun is_atom (Const ("Float.Float",_) $ _) = true
1288 | is_atom (Const ("ComplexI.I'_'_",_)) = true
1289 | is_atom (Const ("op *",_) $ t $ Const ("ComplexI.I'_'_",_)) = is_atom t
1290 | is_atom (Const ("op +",_) $ t1 $ Const ("ComplexI.I'_'_",_)) = is_atom t1
1291 | is_atom (Const ("op +",_) $ t1 $
1292 (Const ("op *",_) $ t2 $ Const ("ComplexI.I'_'_",_))) =
1293 is_atom t1 andalso is_atom t2
1294 | is_atom (Const _) = true
1295 | is_atom (Free _) = true
1296 | is_atom (Var _) = true
1297 | is_atom _ = false;
1298 (* val t = str2term "q_0/2 * L * x";
1302 (*val t = str2term "Float ((1,2),(0,0))";
1304 val it = true : bool
1305 > val t = str2term "Float ((1,2),(0,0)) * I__";
1307 val it = true : bool
1308 > val t = str2term "Float ((1,2),(0,0)) + Float ((3,4),(0,0)) * I__";
1310 val it = true : bool
1311 > val t = str2term "1 + 2*I__";
1312 > val Const ("op +",_) $ t1 $ (Const ("op *",_) $ t2 $ Const ("ComplexI.I'_'_",_)) = t;
1315 (*.adaption from Isabelle/src/Pure/term.ML; reports if ALL Free's
1316 have found a substitution (required for evaluating the preconditions
1317 of _incomplete_ models).*)
1318 fun subst_atomic_all [] t = (false, (*TODO may be 'true' for some terms ?*)
1320 | subst_atomic_all (instl: (term*term) list) t =
1321 let fun subst (Abs(a,T,body)) =
1322 let val (all, body') = subst body
1323 in (all, Abs(a, T, body')) end
1325 let val (all1, f') = subst f
1326 val (all2, tt') = subst tt
1327 in (all1 andalso all2, f' $ tt') end
1328 | subst (t as Free _) =
1329 if is_num t then (true, t) (*numerals cannot be subst*)
1330 else (case assoc(instl,t) of
1331 SOME t' => (true, t')
1332 | NONE => (false, t))
1333 | subst t = (true, if_none (assoc(instl,t)) t)
1336 (*.add two terms with a type given.*)
1338 let val T1 = type_of t1
1340 in if T1 <> T2 then raise TYPE ("mk_add gets ",[T1, T2],[t1,t2])
1341 else (Const ("op +", [T1, T2] ---> T1) $ t1 $ t2)