1 (* Title: extends Isabelle/src/Pure/term.ML
2 Author: Walther Neuper 1999, Mathias Lehnfeld
3 (c) due to copyright terms
7 (* TERM_C extends Isabelle's naming conventions: "C" indicates Isac add-ons to an Isabelle module *)
14 datatype lrd = D | L | R
16 val string_of_path: path -> string
17 val sub_at: path -> term -> term
18 val go_up: Proof.context -> path -> term -> term
20 val perm: term -> term -> bool (*old original Isabelle code*)
21 val contains_Var: term -> bool
22 val dest_binop_typ: typ -> typ * typ * typ
23 val dest_equals: term -> term * term
26 val cut_longid: string -> id
27 val free2str: term -> string
28 val str_of_free_opt: term -> string option
29 val str_of_int: int -> string
30 val id_of: term -> string
31 val ids_of: term -> string list
32 val ids2str: term -> string list (*double?*)
34 val ins_concl: term -> term -> term
35 val inst_abs: term -> term
36 val inst_bdv: LibraryC.subst -> term -> term
40 val the_single: term -> term
42 val mk_frac: typ -> int * (int * int) -> term
43 val numerals_to_Free: term -> term
44 val term_of_num: typ -> int -> term
45 val num_of_term: term -> int
46 val to_string: term -> string
47 val int_of_str: string -> int
48 val isastr_of_int: int -> string
49 val int_opt_of_string: string -> int option
51 val isalist2list: term -> term list
52 val list2isalist: typ -> term list -> term
53 val list2isalist': term list -> term
54 val wrap_HOL_list: term -> term
55 val single_to_list: term -> term
56 val isapair2pair: term -> term * term (* rename to dest_pair, compare HOLogic.dest_string *)
58 val is_atom: term -> bool
59 val string_of_atom: term -> string
60 val is_variable: term -> bool
61 val is_bdv: string -> bool
62 val is_bdv_subst: term -> bool
63 val guess_bdv_typ: term -> typ
64 val is_equality: term -> bool
65 val is_expliceq: term -> bool
66 val is_f_x: term -> bool
67 val is_list: term -> bool
68 val is_bool_list: term -> bool
69 val dest_listT: typ -> typ
70 val is_num: term -> bool
71 val is_num': string -> bool
72 val string_of_num: term -> string
73 val variable_constant_pair: term * term -> bool
75 val mk_add: term -> term -> term
76 val mk_free: typ -> string -> term
77 val mk_equality: term * term -> term
78 val mk_factroot: string -> typ -> int -> int -> term
79 val mk_Free: string * typ -> term
80 val mk_thmid: string -> string -> string -> string
81 val mk_num_op_num: typ -> typ -> string * typ -> int -> int -> term
82 val mk_num_op_var: term -> string -> typ -> typ -> int -> term
83 val mk_var_op_num: term -> string -> typ -> typ -> int -> term
85 val matches: theory -> term -> term -> bool
87 val strip_imp_prems': term -> term option
88 val subst_atomic_all: LibraryC.subst -> term -> bool * term
90 val pairt: term -> term -> term
91 val pairT: typ -> typ -> typ
92 val raise_type_conflicts: term list -> unit
93 val strip_trueprop: term -> term
95 val var2free: term -> term
96 val vars: term -> term list (* recognises numerals, should replace "fun vars_of" TODOO*)
97 val vars': term list -> term list
98 val vars_of: term -> term list (* deprecated TODOO: see differences in test/../termC.sml*)
99 val dest_list': term -> term list
100 val negates: term -> term -> bool
102 val contains_one_of: thm * (string * typ) list -> bool
103 val contains_Const_typeless: term list -> term -> bool
104 val sym_trm : term -> term (* unused code, kept as hints to design ideas *)
106 val string_of_detail: Proof.context -> term -> string
107 (*from isac_test for Minisubpbl*)
108 val atom_typ: Proof.context -> typ -> unit
109 val atom_trace_detail: Proof.context -> term -> unit
112 val mk_negative: typ -> term -> term
113 val mk_Var: term -> term
114 val scala_of_term: term -> string
116 val atom_write: Proof.context -> term -> unit
117 val atom_trace: Proof.context -> term -> unit
119 val atom_write_detail: Proof.context -> term -> unit
120 (*val atom_trace_detail: Proof.context -> term -> unit*)
125 structure TermC(**): TERM_ISAC(**) =
129 type as_string = UnparseC.term_as_string
130 val empty = UnparseC.term_empty
131 val typ_empty = UnparseC.typ_empty
133 datatype lrd = L (*t1 in "t1$t2"*)
134 | R (*t2 in "t1$t2"*) | D; (*b in Abs(_,_,b*)
135 type path = lrd list;
139 fun string_of_path k = (strs2str' o (map ldr2str)) k;
140 (*go to a location in a term and fetch the resective sub-term*)
142 | sub_at (D :: p) (Abs(_, _, body)) = sub_at p body
143 | sub_at (L :: p) (t1 $ _) = sub_at p t1
144 | sub_at (R :: p) (_ $ t2) = sub_at p t2
145 | sub_at l t = raise TERM ("sub_at: no " ^ string_of_path l ^ " for ", [t]);
147 if length l > 1 then sub_at (drop_last l) t else raise ERROR ("go_up [] " ^ UnparseC.term ctxt t)
149 fun isastr_of_int i = if i >= 0 then string_of_int i else "-" ^ string_of_int (abs i)
151 fun matches thy tm pa =
152 (Pattern.match thy (pa, tm) (Vartab.empty, Vartab.empty); true)
153 handle Pattern.MATCH => false
155 (** transform typ / term to a String to be parsed by Scala after transport via libisabelle **)
156 fun string_of_detail ctxt t =
158 fun ato (Const (a, T)) n = "\n*** " ^ indent n ^ "Const (" ^ a ^ ", " ^ UnparseC.typ ctxt T ^ ")"
159 | ato (Free (a, T)) n = "\n*** " ^ indent n ^ "Free (" ^ a ^ ", " ^ UnparseC.typ ctxt T ^ ")"
160 | ato (Var ((a, i), T)) n =
161 "\n*** " ^ indent n ^ "Var ((" ^ a ^ ", " ^ string_of_int i ^ "), " ^ UnparseC.typ ctxt T ^ ")"
162 | ato (Bound i) n = "\n*** " ^ indent n ^ "Bound " ^ string_of_int i
163 | ato (Abs(a, T, body)) n =
164 "\n*** " ^ indent n ^ "Abs (" ^ a ^ ", " ^ UnparseC.typ ctxt T ^ ",.." ^ ato body (n + 1)
165 | ato (f $ t) n = ato f n ^ ato t (n + 1)
166 in "\n*** " ^ ato t 0 ^ "\n***" end;
170 fun scala_of_typ (Type (s, typs)) =
171 enclose "Type(" ")" (quote s ^ ", " ^
172 (typs |> map scala_of_typ |> commas |> enclose "List(" ")"))
173 | scala_of_typ (TFree (s, sort)) =
174 enclose "TFree(" ")" (quote s ^ ", " ^ (sort |> map quote |> commas |> enclose "List(" ")"))
175 | scala_of_typ (TVar ((s, i), sort)) =
176 enclose "TVar(" ")" (
177 enclose "(" ")," (quote s ^ ", " ^ quote (string_of_int i)) ^
178 (sort |> map quote |> commas |> enclose "List(" ")"))
180 fun scala_of_term (Const (s, T)) =
181 enclose "Const (" ")" (quote s ^ ", " ^ scala_of_typ T)
182 | scala_of_term (Free (s, T)) =
183 enclose "Free(" ")" (quote s ^ ", " ^ scala_of_typ T)
184 | scala_of_term (Var ((s, i), T)) =
185 enclose "TVar(" ")" (
186 enclose "(" ")," (quote s ^ ", " ^ quote (string_of_int i)) ^
188 | scala_of_term (Bound i) = enclose "Bound(" ")" (string_of_int i)
189 | scala_of_term (Abs (s, T, t)) =
192 scala_of_typ T ^ ", " ^
194 | scala_of_term (t1 $ t2) =
195 enclose "App(" ")" (scala_of_term t1 ^ ", " ^ scala_of_term t2)
198 (* see structure's bare bones.
199 for Isabelle standard output compare 2017 "structure ML_PP" *)
202 fun ato n (Type (s, [])) = "\n*** " ^ indent n ^ "Type (" ^ s ^",[])"
203 | ato n (Type (s, Ts)) = "\n*** " ^ indent n ^ "Type (" ^ s ^ ",[" ^ atol (n + 1) Ts
204 | ato n (TFree (s, sort)) = "\n*** " ^ indent n ^ "TFree (" ^ s ^ ", " ^ strs2str' sort
205 | ato n (TVar ((s, i), sort)) =
206 "\n*** " ^ indent n ^ "TVar ((" ^ s ^ ", " ^ string_of_int i ^ strs2str' sort
207 and atol n [] = "\n*** " ^ indent n ^ "]"
208 | atol n (T :: Ts) = (ato n T ^ atol n Ts)
209 in tracing (ato 0 t ^ "\n") end;
214 fun ato (Const (a, _)) n = "\n*** " ^ indent n ^ "Const (" ^ a ^ ", _)"
215 | ato (Free (a, _)) n = "\n*** " ^ indent n ^ "Free (" ^ a ^ ", _)"
216 | ato (Var ((a, i), _)) n =
217 "\n*** " ^ indent n ^ "Var (" ^ a ^ ", " ^ string_of_int i ^ "), _)"
218 | ato (Bound i) n = "\n*** " ^ indent n ^ "Bound " ^ string_of_int i
219 | ato (Abs (a, _, body)) n = "\n*** " ^ indent n ^ "Abs(" ^ a ^ ", _" ^ ato body (n+1)
220 | ato (f $ t) n = (ato f n ^ ato t (n + 1))
222 fun atom_write _ t = writeln ("\n*** -------------" ^ ato t 0 ^ "\n***");
223 fun atom_trace _ t = tracing ("\n*** -------------" ^ ato t 0 ^ "\n***");
226 fun atom_write_detail ctxt t = (writeln o (string_of_detail ctxt)) t;
228 fun atom_trace_detail ctxt t = (tracing o (string_of_detail ctxt)) t;
230 (* contains the term a VAR(("*",_),_) ? *)
231 fun contains_Var (Abs(_,_,body)) = contains_Var body
232 | contains_Var (f $ f') = contains_Var f orelse contains_Var f'
233 | contains_Var (Var _) = true
234 | contains_Var _ = false;
237 if n < 0 then "-" ^ ((string_of_int o abs) n)
238 else string_of_int n;
239 val int_of_str = Value.parse_int;
241 val int_opt_of_string = ThmC_Def.int_opt_of_string
242 fun is_num' str = case int_opt_of_string str of SOME _ => true | NONE => false;
244 fun is_num (Const (\<^const_name>\<open>numeral\<close>, _) $ _) = true
245 | is_num (Const (\<^const_name>\<open>uminus\<close>, _) $
246 (Const (\<^const_name>\<open>numeral\<close>, _) $ _)) = true
247 | is_num (Const (\<^const_name>\<open>one_class.one\<close>, _)) = true
248 | is_num (Const (\<^const_name>\<open>uminus\<close>, _) $ Const (\<^const_name>\<open>one_class.one\<close>, _)) = true
249 | is_num (Const (\<^const_name>\<open>zero_class.zero\<close>, _)) = true
250 | is_num (Const (\<^const_name>\<open>uminus\<close>, _) $ Const (\<^const_name>\<open>zero_class.zero\<close>, _)) = true
253 fun string_of_num n = (n |> HOLogic.dest_number |> snd |> string_of_int)
255 fun lhs (Const (\<^const_name>\<open>HOL.eq\<close>,_) $ l $ _) = l
256 | lhs t = raise TERM ("lhs called with ", [t]);
257 fun rhs (Const (\<^const_name>\<open>HOL.eq\<close>,_) $ _ $ r) = r
258 | rhs t = raise TERM ("rhs called with ", [t]);
259 fun the_single (Const ("List.list.Cons", _) $ t $ Const ("List.list.Nil", _)) = t
260 | the_single t = raise TERM ("the_single", [t])
263 fun mk_negative T t = Const (\<^const_name>\<open>uminus\<close>, T --> T) $ t
264 fun mk_frac T (sg, (i1, i2)) =
266 if i2 = 1 then HOLogic.mk_number T i1
267 else Const (\<^const_name>\<open>divide_class.divide\<close>, T --> T --> T) $
268 HOLogic.mk_number T i1 $ HOLogic.mk_number T i2
269 else (*take negative*)
270 if i2 = 1 then mk_negative T (HOLogic.mk_number T i1)
271 else Const (\<^const_name>\<open>divide_class.divide\<close>, T --> T --> T) $
272 mk_negative T (HOLogic.mk_number T i1) $ HOLogic.mk_number T i2
274 val numerals_to_Free = (* Makarius 100308 *)
277 (case try HOLogic.dest_number t of
278 SOME (T, i) => SOME (Free (signed_string_of_int i, T))
280 fun to_str (Abs (x, T, b)) = Abs (x, T, to_str b)
281 | to_str (t as (u1 $ u2)) =
282 (case dest_num t of SOME t' => t' | NONE => to_str u1 $ to_str u2)
283 | to_str t = perhaps dest_num t;
286 val term_of_num = HOLogic.mk_number;
287 fun num_of_term t = t |> HOLogic.dest_number |> snd;
288 (* accomodate string-representation for int to term-orders *)
289 fun to_string t = t |> num_of_term |> signed_string_of_int
291 fun is_variable (t as Free _) = not (is_num t)
292 | is_variable _ = false;
293 fun is_Free (Free _) = true | is_Free _ = false;
294 fun is_fun_id (Const _) = true
295 | is_fun_id (Free _) = true
296 | is_fun_id _ = false;
297 fun is_f_x (f $ x) = is_fun_id f andalso is_Free x
299 (* precondition: TermC.is_atom v andalso TermC.is_atom c *)
300 fun is_const (Const _) = true | is_const _ = false;
301 fun variable_constant_pair (v, c) =
302 if (is_variable v andalso (is_const c orelse is_num c)) orelse
303 (is_variable c andalso (is_const v orelse is_num v))
309 fun scan vs (Const _) = vs
310 | scan vs (t as Free _) = (*if is_num' s then vs else*) t :: vs
311 | scan vs (t as Var _) = t :: vs
312 | scan vs (Bound _) = vs
313 | scan vs (Abs (_, _, t)) = scan vs t
314 | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)
315 in ((distinct op =) o (scan [])) t end;
316 fun vars' ts = ts |> map vars |> flat |> distinct op =
318 (* bypass Isabelle's Pretty, which requires ctxt *)
321 fun scan vs (t as Const (s, _) $ arg) =
322 if is_num t then vs else scan (s :: vs) arg
323 | scan vs (Const (s as "Partial_Fractions.AA", _)) = s :: vs (*how get rid of spec.case?*)
324 | scan vs (Const (s as "Partial_Fractions.BB", _)) = s :: vs (*how get rid of spec.case?*)
325 | scan vs (Const _) = vs
326 | scan vs (Free (s, _)) = if is_num' s then vs else s :: vs
327 | scan vs (Var ((s, i), _)) = (s ^ "_" ^ string_of_int i) :: vs
328 | scan vs (Bound _) = vs
329 | scan vs (Abs (s, _, t)) = scan (s :: vs) t
330 | scan vs (t1 $ t2) = (scan vs t1) @ (scan vs t2)
331 in ((distinct op =) o (scan [])) t
333 fun is_bdv str = case Symbol.explode str of "b"::"d"::"v"::_ => true | _ => false;
334 (* instantiate #prop thm with bound vars_of (as Free) *)
335 fun inst_bdv [] t = t
336 | inst_bdv (instl: (term*term) list) t =
338 fun subst (v as Var((s, _), T)) =
339 (case Symbol.explode s of
340 "b"::"d"::"v"::_ => if_none (assoc(instl,Free(s,T))) (Free(s,T))
342 | subst (Abs(a, T, body)) = Abs(a, T, subst body)
343 | subst (f $ t') = subst f $ subst t'
344 | subst t = if_none (assoc (instl, t)) t
347 (* is a term a substitution for a bdv as found in programs and tactics *)
348 fun is_bdv_subst (Const (\<^const_name>\<open>Cons\<close>, _) $
349 (Const (\<^const_name>\<open>Pair\<close>, _) $ str $ _) $ _) = is_bdv (HOLogic.dest_string str)
350 | is_bdv_subst _ = false;
352 (* this shall be improved due to future requirements *)
353 fun guess_bdv_typ t = t |> vars |> hd |> type_of
355 type id = string (*the shortest significant*)
356 val cut_longid = ThmC.cut_longid
357 fun free2str (Free (s, _)) = s
358 | free2str t = raise TERM ("free2str not for ", [t]);
359 fun str_of_free_opt (Free (s, _)) = SOME s
360 | str_of_free_opt _ = NONE
361 fun id_of (Var ((id,ix),_)) = if ix= 0 then id else id ^ string_of_int ix
362 | id_of (Free (id ,_)) = id
363 | id_of (Const(id ,_)) = id
364 | id_of _ = ""; (* never such an identifier *)
367 let fun con ss (Const (s,_)) = s::ss
368 | con ss (Free (s,_)) = s::ss
369 | con ss (Abs (s,_,b)) = s::(con ss b)
370 | con ss (t1 $ t2) = (con ss t1) @ (con ss t2)
372 in map cut_longid (((distinct op =) o (con [])) t) end;
374 (* compare Logic.unvarify_global, which rejects Free *)
375 fun var2free (t as Const _) = t
376 | var2free (t as Free _) = t
377 | var2free (Var((s, _), T)) = Free (s,T)
378 | var2free (t as Bound _) = t
379 | var2free (Abs(s, T, t)) = Abs(s, T, var2free t)
380 | var2free (t1 $ t2) = (var2free t1) $ (var2free t2);
383 \<^isac_test>\<open> (*TODO: check with new numerals --vv*)
384 (* Logic.varify does NOT take care of 'Free ("1", _)'*)
385 fun mk_Var (t as Const _) = t
386 | mk_Var (t as Free (s, T)) = if is_num' s then t else Var ((s, 0), T)
387 | mk_Var (t as Var _) = t
388 | mk_Var (t as Bound _) = t
389 | mk_Var (Abs (s, T, t)) = Abs (s, T, mk_Var t)
390 | mk_Var (t1 $ t2) = (mk_Var t1) $ (mk_Var t2);
393 fun mk_listT T = Type (\<^type_name>\<open>list\<close>, [T]);
394 fun list_const T = Const (\<^const_name>\<open>Cons\<close>, [T, mk_listT T] ---> mk_listT T);
395 fun list2isalist T [] = Const (\<^const_name>\<open>Nil\<close>, mk_listT T)
396 | list2isalist T (t :: ts) = (list_const T) $ t $ (list2isalist T ts);
397 fun list2isalist' ts = list2isalist (type_of (hd ts)) ts
398 fun wrap_HOL_list t = [t] |> list2isalist'
400 (*maps [<a>, <b>, <c>] to [<[a]>, <[b]>, <[c]>]*)
401 fun single_to_list t = t |> single |> list2isalist (type_of t)
404 fun isapair2pair (Const (\<^const_name>\<open>Pair\<close>,_) $ a $ b) = (a, b)
406 raise TERM ("isapair2pair called with ", [t]);
407 fun isalist2list ls =
409 fun get es (Const(\<^const_name>\<open>Cons\<close>, _) $ t $ ls) = get (t :: es) ls
410 | get es (Const(\<^const_name>\<open>Nil\<close>, _)) = es
411 | get _ t = raise TERM ("isalist2list applied to NON-list: ", [t])
412 in (rev o (get [])) ls end;
414 fun is_list ((Const (\<^const_name>\<open>Cons\<close>, _)) $ _ $ _) = true
416 fun dest_listT (Type (\<^type_name>\<open>list\<close>, [T])) = T
417 | dest_listT T = raise TYPE ("dest_listT: list type expected", [T], []);
419 (if dest_listT (Term.type_of t) = HOLogic.boolT then true else false)
420 handle TYPE _ => false
423 fun dest_binop_typ (Type (\<^type_name>\<open>fun\<close>, [range, Type (\<^type_name>\<open>fun\<close>, [arg2, arg1])])) = (arg1, arg2, range)
424 | dest_binop_typ _ = raise ERROR "dest_binop_typ: not binary";
425 fun dest_equals (Const(\<^const_name>\<open>HOL.eq\<close>, _) $ t $ u) = (t, u) (* Pure/logic.ML: Const ("==", ..*)
426 | dest_equals t = raise TERM ("dest_equals'", [t]);
427 fun is_equality (Const(\<^const_name>\<open>HOL.eq\<close>,_) $ _ $ _) = true (* logic.ML: Const ("=="*)
428 | is_equality _ = false;
429 fun mk_equality (t, u) = (Const(\<^const_name>\<open>HOL.eq\<close>, [type_of t, type_of u] ---> HOLogic.boolT) $ t $ u);
430 fun is_expliceq (Const(\<^const_name>\<open>HOL.eq\<close>,_) $ (Free _) $ _) = true
431 | is_expliceq _ = false;
432 fun strip_trueprop (Const (\<^const_name>\<open>Trueprop\<close>, _) $ t) = t
433 | strip_trueprop t = t;
435 (* (A1==>...An==>B) goes to (A1==>...An==>) Pure/logic.ML: term -> term list*)
436 fun strip_imp_prems' (Const (\<^const_name>\<open>Pure.imp\<close>, _) $ A $ t) =
438 fun coll_prems As (Const(\<^const_name>\<open>Pure.imp\<close>, _) $ A $ t) =
439 coll_prems (As $ (Logic.implies $ A)) t
440 | coll_prems As _ = SOME As
441 in coll_prems (Logic.implies $ A) t end
442 | strip_imp_prems' _ = NONE; (* *)
444 (* (A1==>...An==>) (B) goes to (A1==>...An==>B), where B is lowest branch, 2002 Pure/thm.ML *)
445 fun ins_concl (Const (\<^const_name>\<open>Pure.imp\<close>, _) $ A $ t) B = Logic.implies $ A $ (ins_concl t B)
446 | ins_concl (Const (\<^const_name>\<open>Pure.imp\<close>, _) $ A ) B = Logic.implies $ A $ B
447 | ins_concl t B = raise TERM ("ins_concl", [t, B]);
449 fun vperm (Var _, Var _) = true (* 2002 Pure/thm.ML *)
450 | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t)
451 | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2)
452 | vperm (t, u) = (t = u);
454 (*2002 cp from Pure/term.ML --- since 2009 in Pure/old_term.ML*)
455 fun mem_term (_, []) = false
456 | mem_term (t, t' :: ts) = t aconv t' orelse mem_term (t, ts);
457 fun subset_term ([], _) = true
458 | subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term (xs, ys);
459 fun eq_set_term (xs, ys) =
460 xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs));
461 (*a total, irreflexive ordering on index names*)
462 fun xless ((a, i), (b, j): indexname) = i<j orelse (i = j andalso a < b);
463 (*a partial ordering (not reflexive) for atomic terms*)
464 fun atless (Const (a, _), Const (b, _)) = a < b
465 | atless (Free (a, _), Free (b, _)) = a < b
466 | atless (Var (v, _), Var (w, _)) = xless (v, w)
467 | atless (Bound i, Bound j) = i < j
469 (*insert atomic term into partially sorted list, suppressing duplicates (?)*)
470 fun insert_aterm (t,us) =
471 let fun inserta [] = [t]
472 | inserta (us as u::us') =
473 if atless(t,u) then t::us
474 else if t=u then us (*duplicate*)
475 else u :: inserta us'
478 (* Accumulates the Vars in the term, suppressing duplicates *)
479 fun add_term_vars (t, vars: term list) = case t of
480 Var _ => insert_aterm (t, vars)
481 | Abs (_, _, body) => add_term_vars (body, vars)
482 | f$t => add_term_vars (f, add_term_vars (t, vars))
484 fun term_vars t = add_term_vars (t, []);
486 (*2002 Pure/thm.ML *)
487 fun var_perm (t, u) = vperm (t, u) andalso eq_set_term (term_vars t, term_vars u);
488 (*2002 fun decomp_simp, Pure/thm.ML *)
489 fun perm lhs rhs = var_perm (lhs, rhs) andalso not (lhs aconv rhs) andalso not (is_Var lhs);
492 fun pairT T1 T2 = Type (\<^type_name>\<open>prod\<close>, [T1, T2]);
493 fun PairT T1 T2 = ([T1, T2] ---> Type (\<^type_name>\<open>prod\<close>, [T1, T2]));
494 fun pairt t1 t2 = Const (\<^const_name>\<open>Pair\<close>, PairT (type_of t1) (type_of t2)) $ t1 $ t2;
496 fun mk_factroot op_(*=thy.sqrt*) T fact root =
497 Const (\<^const_name>\<open>times\<close>, [T, T] ---> T) $ (term_of_num T fact) $
498 (Const (op_, T --> T) $ term_of_num T root);
499 fun mk_var_op_num v op_ optype ntyp n = Const (op_, optype) $ v $ HOLogic.mk_number ntyp n;
500 fun mk_num_op_var v op_ optype ntyp n = Const (op_, optype) $ HOLogic.mk_number ntyp n $ v;
501 fun mk_num_op_num T1 T2 (op_, Top) n1 n2 =
502 Const (op_, Top) $ HOLogic.mk_number T1 n1 $ HOLogic.mk_number T2 n2;
503 fun mk_thmid thmid n1 n2 =
504 thmid ^ (cut_longid n1) ^ "_" ^ (cut_longid n2);
507 val (T1, T2) = (type_of t1, type_of t2)
509 if T1 <> T2 then raise TYPE ("mk_add gets ", [T1, T2], [t1,t2])
510 else (Const (\<^const_name>\<open>plus\<close>, [T1, T2] ---> T1) $ t1 $ t2)
513 (** transform binary numeralsstrings **)
514 fun mk_Free (s,T) = Free (s, T);
515 fun mk_free T s = Free (s, T);
517 (*Special case: one argument cp from Isabelle2002/src/Pure/term.ML*)
518 fun subst_bound (arg, t) =
520 fun subst (t as Bound i, lev) =
521 if i < lev then t (*var is locally bound*)
522 else if i = lev then incr_boundvars lev arg
523 else Bound (i - 1) (*loose: change it*)
524 | subst (Abs(a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
525 | subst (f$t, lev) = subst(f, lev) $ subst(t, lev)
529 (* instantiate let; necessary for scan_up1 *)
530 fun inst_abs (Const sT) = Const sT
531 | inst_abs (Free sT) = Free sT
532 | inst_abs (Bound n) = Bound n
533 | inst_abs (Var iT) = Var iT
534 | inst_abs (Const (\<^const_name>\<open>Let\<close>,T1) $ e $ (Abs (v, T2, b))) =
535 let val b' = subst_bound (Free (v, T2), b); (*fun variant_abs: term.ML*)
536 in Const (\<^const_name>\<open>Let\<close>, T1) $ inst_abs e $ (Abs (v, T2, inst_abs b')) end
537 | inst_abs (t1 $ t2) = inst_abs t1 $ inst_abs t2
540 fun is_atom (Const _) = true
541 | is_atom (Free _) = true
542 | is_atom (Var _) = true
543 | is_atom t = is_num t;
544 fun string_of_atom (t as Const (\<^const_name>\<open>numeral\<close>, _) $ _) = to_string t
545 | string_of_atom (t as Const (\<^const_name>\<open>one_class.one\<close>, _)) = to_string t
546 | string_of_atom (t as Const (\<^const_name>\<open>zero_class.zero\<close>, _)) = to_string t
547 | string_of_atom (Const (str, _)) = str
548 | string_of_atom (Free (str, _)) = str
549 | string_of_atom (Var ((str, int), _)) = str ^ "_" ^ string_of_int int
550 | string_of_atom _ = "DUMMY-string_of_atom";
552 (* from Pure/term.ML; reports if ALL Free's have found a substitution
553 (required for evaluating the preconditions of _incomplete_ models) *)
554 fun subst_atomic_all [] t = (false (*TODO may be 'true' for some terms ?*), t)
555 | subst_atomic_all instl t =
557 fun subst (Abs (a, T, body)) =
559 val (all, body') = subst body
560 in (all, Abs(a, T, body')) end
563 val (all1, f') = subst f
564 val (all2, tt') = subst tt
565 in (all1 andalso all2, f' $ tt') end
566 | subst (t as Free _) =
567 if is_num t then (true, t) (*numerals cannot be subst*)
568 else (case assoc (instl, t) of
569 SOME t' => (true, t')
570 | NONE => (false, t))
571 | subst t = (true, if_none (assoc (instl, t)) t)
574 fun op contains_one_of (thm, ids) =
575 Term.exists_Const (fn id => member op= ids id) (Thm.prop_of thm)
577 fun var_for vs (t as Const (str, _)) id =
579 else if id = cut_longid str then t :: vs else vs
580 | var_for vs (t as Free (str, _)) id = if id = str then t :: vs else vs
581 | var_for vs (t as Var (idn, _)) id = if id = Term.string_of_vname idn then t :: vs else vs
582 | var_for vs (Bound _) _ = vs
583 | var_for vs (Abs (_, _, t)) id = var_for vs t id
584 | var_for vs (t1 $ t2) id = (var_for vs t1 id) @ (var_for vs t2 id)
587 [\<^const_name>\<open>plus\<close>, \<^const_name>\<open>minus\<close>,
588 \<^const_name>\<open>divide\<close>, \<^const_name>\<open>times\<close>,
589 \<^const_name>\<open>realpow\<close>];
590 (* treat Free, Const, Var as vars_of in polynomials *)
593 val var_ids = t |> ids2str |> subtract op = poly_consts |> map cut_longid |> sort string_ord
594 in (map (var_for [] t) var_ids) |> flat |> distinct op = end
596 (* this may decompose an object-language isa-list;
597 use only, if description is not available, eg. not input ?WN:14.5.03 ??!?*)
598 fun dest_list' t = if is_list t then isalist2list t else [t];
600 fun negat (Const (\<^const_name>\<open>Not\<close>, _) $ P, P') = P = P'
602 fun negates p1 p2 = negat (p1, p2) orelse negat (swap (p1, p2));
604 fun raise_type_conflicts ts =
606 val dups = duplicates (op =) (map (fst o dest_Free) ts)
607 val confl = filter (fn Free (str, _) => member op = dups str
612 else raise TYPE ("formalisation inconsistent w.r.t. type inference: ",
613 map (snd o dest_Free)confl, confl)
616 (* expects t as Const *)
617 fun contains_Const_typeless ts t = (t
619 |> member (fn (t1, t2) => fst (dest_Const t1) = fst (dest_Const t2)) ts
620 ) handle TERM("dest_Const", _) => raise TERM ("contains_Const_typeless", [t])
622 (* WN100910 weaker than fun sym_thm for Theory.axioms_of in isa02 *)
625 val (lhs, rhs) = (dest_equals o strip_trueprop o Logic.strip_imp_concl) trm
626 val trm' = case strip_imp_prems' trm of
627 NONE => mk_equality (rhs, lhs)
628 | SOME cs => ins_concl cs (mk_equality (rhs, lhs))