1 (* Title: Pure/variable.ML
4 Fixed type/term variables and polymorphic term abbreviations.
9 val is_body: Proof.context -> bool
10 val set_body: bool -> Proof.context -> Proof.context
11 val restore_body: Proof.context -> Proof.context -> Proof.context
12 val names_of: Proof.context -> Name.context
13 val binds_of: Proof.context -> (typ * term) Vartab.table
14 val maxidx_of: Proof.context -> int
15 val sorts_of: Proof.context -> sort list
16 val constraints_of: Proof.context -> typ Vartab.table * sort Vartab.table
17 val is_declared: Proof.context -> string -> bool
18 val check_name: binding -> string
19 val default_type: Proof.context -> string -> typ option
20 val def_type: Proof.context -> bool -> indexname -> typ option
21 val def_sort: Proof.context -> indexname -> sort option
22 val declare_names: term -> Proof.context -> Proof.context
23 val declare_constraints: term -> Proof.context -> Proof.context
24 val declare_term: term -> Proof.context -> Proof.context
25 val declare_typ: typ -> Proof.context -> Proof.context
26 val declare_prf: Proofterm.proof -> Proof.context -> Proof.context
27 val declare_thm: thm -> Proof.context -> Proof.context
28 val global_thm_context: thm -> Proof.context
29 val variant_frees: Proof.context -> term list -> (string * 'a) list -> (string * 'a) list
30 val bind_term: indexname * term option -> Proof.context -> Proof.context
31 val expand_binds: Proof.context -> term -> term
32 val lookup_const: Proof.context -> string -> string option
33 val is_const: Proof.context -> string -> bool
34 val declare_const: string * string -> Proof.context -> Proof.context
35 val is_fixed: Proof.context -> string -> bool
36 val newly_fixed: Proof.context -> Proof.context -> string -> bool
37 val fixed_ord: Proof.context -> string * string -> order
38 val intern_fixed: Proof.context -> string -> string
39 val markup_fixed: Proof.context -> string -> Markup.T
40 val lookup_fixed: Proof.context -> string -> string option
41 val revert_fixed: Proof.context -> string -> string
42 val add_fixed_names: Proof.context -> term -> string list -> string list
43 val add_fixed: Proof.context -> term -> (string * typ) list -> (string * typ) list
44 val add_free_names: Proof.context -> term -> string list -> string list
45 val add_frees: Proof.context -> term -> (string * typ) list -> (string * typ) list
46 val add_fixes_binding: binding list -> Proof.context -> string list * Proof.context
47 val add_fixes: string list -> Proof.context -> string list * Proof.context
48 val add_fixes_direct: string list -> Proof.context -> Proof.context
49 val auto_fixes: term -> Proof.context -> Proof.context
50 val variant_fixes: string list -> Proof.context -> string list * Proof.context
51 val dest_fixes: Proof.context -> (string * string) list
52 val invent_types: sort list -> Proof.context -> (string * sort) list * Proof.context
53 val export_terms: Proof.context -> Proof.context -> term list -> term list
54 val exportT_terms: Proof.context -> Proof.context -> term list -> term list
55 val exportT: Proof.context -> Proof.context -> thm list -> thm list
56 val export_prf: Proof.context -> Proof.context -> Proofterm.proof -> Proofterm.proof
57 val export: Proof.context -> Proof.context -> thm list -> thm list
58 val export_morphism: Proof.context -> Proof.context -> morphism
59 val importT_inst: term list -> Proof.context -> ((indexname * sort) * typ) list * Proof.context
60 val import_inst: bool -> term list -> Proof.context ->
61 (((indexname * sort) * typ) list * ((indexname * typ) * term) list) * Proof.context
62 val importT_terms: term list -> Proof.context -> term list * Proof.context
63 val import_terms: bool -> term list -> Proof.context -> term list * Proof.context
64 val importT: thm list -> Proof.context -> ((ctyp * ctyp) list * thm list) * Proof.context
65 val import_prf: bool -> Proofterm.proof -> Proof.context -> Proofterm.proof * Proof.context
66 val import: bool -> thm list -> Proof.context ->
67 (((ctyp * ctyp) list * (cterm * cterm) list) * thm list) * Proof.context
68 val tradeT: (Proof.context -> thm list -> thm list) -> Proof.context -> thm list -> thm list
69 val trade: (Proof.context -> thm list -> thm list) -> Proof.context -> thm list -> thm list
70 val focus: term -> Proof.context -> ((string * (string * typ)) list * term) * Proof.context
71 val focus_cterm: cterm -> Proof.context -> ((string * cterm) list * cterm) * Proof.context
72 val focus_subgoal: int -> thm -> Proof.context -> ((string * cterm) list * cterm) * Proof.context
73 val warn_extra_tfrees: Proof.context -> Proof.context -> unit
74 val polymorphic_types: Proof.context -> term list -> (indexname * sort) list * term list
75 val polymorphic: Proof.context -> term list -> term list
78 structure Variable: VARIABLE =
81 (** local context data **)
83 type fixes = string Name_Space.table;
84 val empty_fixes: fixes = Name_Space.empty_table "fixed variable";
86 datatype data = Data of
87 {is_body: bool, (*inner body mode*)
88 names: Name.context, (*type/term variable names*)
89 consts: string Symtab.table, (*consts within the local scope*)
90 fixes: fixes, (*term fixes -- global name space, intern ~> extern*)
91 binds: (typ * term) Vartab.table, (*term bindings*)
92 type_occs: string list Symtab.table, (*type variables -- possibly within term variables*)
93 maxidx: int, (*maximum var index*)
94 sorts: sort Ord_List.T, (*declared sort occurrences*)
96 typ Vartab.table * (*type constraints*)
97 sort Vartab.table}; (*default sorts*)
99 fun make_data (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =
100 Data {is_body = is_body, names = names, consts = consts, fixes = fixes, binds = binds,
101 type_occs = type_occs, maxidx = maxidx, sorts = sorts, constraints = constraints};
103 structure Data = Proof_Data
107 make_data (false, Name.context, Symtab.empty, empty_fixes, Vartab.empty,
108 Symtab.empty, ~1, [], (Vartab.empty, Vartab.empty));
112 Data.map (fn Data {is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints} =>
113 make_data (f (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints)));
116 map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
117 (is_body, f names, consts, fixes, binds, type_occs, maxidx, sorts, constraints));
120 map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
121 (is_body, names, f consts, fixes, binds, type_occs, maxidx, sorts, constraints));
124 map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
125 (is_body, names, consts, f fixes, binds, type_occs, maxidx, sorts, constraints));
128 map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
129 (is_body, names, consts, fixes, f binds, type_occs, maxidx, sorts, constraints));
131 fun map_type_occs f =
132 map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
133 (is_body, names, consts, fixes, binds, f type_occs, maxidx, sorts, constraints));
136 map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
137 (is_body, names, consts, fixes, binds, type_occs, f maxidx, sorts, constraints));
140 map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
141 (is_body, names, consts, fixes, binds, type_occs, maxidx, f sorts, constraints));
143 fun map_constraints f =
144 map_data (fn (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
145 (is_body, names, consts, fixes, binds, type_occs, maxidx, sorts, f constraints));
147 fun rep_data ctxt = Data.get ctxt |> (fn Data args => args);
149 val is_body = #is_body o rep_data;
152 map_data (fn (_, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints) =>
153 (b, names, consts, fixes, binds, type_occs, maxidx, sorts, constraints));
155 fun restore_body ctxt = set_body (is_body ctxt);
157 val names_of = #names o rep_data;
158 val fixes_of = #fixes o rep_data;
159 val fixes_space = #1 o fixes_of;
160 val binds_of = #binds o rep_data;
161 val type_occs_of = #type_occs o rep_data;
162 val maxidx_of = #maxidx o rep_data;
163 val sorts_of = #sorts o rep_data;
164 val constraints_of = #constraints o rep_data;
166 val is_declared = Name.is_declared o names_of;
168 val check_name = Long_Name.base_name o Name_Space.full_name Name_Space.default_naming;
174 (* default sorts and types *)
176 fun default_type ctxt x = Vartab.lookup (#1 (constraints_of ctxt)) (x, ~1);
178 fun def_type ctxt pattern xi =
179 let val {binds, constraints = (types, _), ...} = rep_data ctxt in
180 (case Vartab.lookup types xi of
183 else Vartab.lookup binds xi |> Option.map (Type.mark_polymorphic o #1)
187 val def_sort = Vartab.lookup o #2 o constraints_of;
192 fun declare_type_names t =
193 map_names (fold_types (fold_atyps Term.declare_typ_names) t) #>
194 map_maxidx (fold_types Term.maxidx_typ t);
196 fun declare_names t =
197 declare_type_names t #>
198 map_names (fold_aterms Term.declare_term_frees t) #>
199 map_maxidx (Term.maxidx_term t);
202 (* type occurrences *)
204 fun decl_type_occsT T = fold_atyps (fn TFree (a, _) => Symtab.default (a, []) | _ => I) T;
206 val decl_type_occs = fold_term_types
207 (fn Free (x, _) => fold_atyps (fn TFree (a, _) => Symtab.insert_list (op =) (a, x) | _ => I)
208 | _ => decl_type_occsT);
210 val declare_type_occsT = map_type_occs o fold_types decl_type_occsT;
211 val declare_type_occs = map_type_occs o decl_type_occs;
216 fun constrain_tvar (xi, S) =
217 if S = dummyS then Vartab.delete_safe xi else Vartab.update (xi, S);
219 fun declare_constraints t = map_constraints (fn (types, sorts) =>
221 val types' = fold_aterms
222 (fn Free (x, T) => Vartab.update ((x, ~1), T)
223 | Var v => Vartab.update v
225 val sorts' = fold_types (fold_atyps
226 (fn TFree (x, S) => constrain_tvar ((x, ~1), S)
227 | TVar v => constrain_tvar v
229 in (types', sorts') end)
230 #> declare_type_occsT t
231 #> declare_type_names t;
234 (* common declarations *)
236 fun declare_internal t =
238 declare_type_occs t #>
239 map_sorts (Sorts.insert_term t);
242 declare_internal t #>
243 declare_constraints t;
245 val declare_typ = declare_term o Logic.mk_type;
247 val declare_prf = Proofterm.fold_proof_terms declare_internal (declare_internal o Logic.mk_type);
249 val declare_thm = Thm.fold_terms declare_internal;
250 fun global_thm_context th = declare_thm th (Proof_Context.init_global (Thm.theory_of_thm th));
253 (* renaming term/type frees *)
255 fun variant_frees ctxt ts frees =
257 val names = names_of (fold declare_names ts ctxt);
258 val xs = fst (fold_map Name.variant (map #1 frees) names);
259 in xs ~~ map snd frees end;
263 (** term bindings **)
265 fun bind_term (xi, NONE) = map_binds (Vartab.delete_safe xi)
266 | bind_term ((x, i), SOME t) =
268 val u = Term.close_schematic_term t;
269 val U = Term.fastype_of u;
270 in declare_term u #> map_binds (Vartab.update ((x, i), (U, u))) end;
272 fun expand_binds ctxt =
274 val binds = binds_of ctxt;
275 val get = fn Var (xi, _) => Vartab.lookup binds xi | _ => NONE;
276 in Envir.beta_norm o Envir.expand_term get end;
282 val lookup_const = Symtab.lookup o #consts o rep_data;
283 val is_const = is_some oo lookup_const;
285 val declare_fixed = map_consts o Symtab.delete_safe;
286 val declare_const = map_consts o Symtab.update;
292 (* specialized name space *)
294 fun is_fixed ctxt x = can (Name_Space.the_entry (fixes_space ctxt)) x;
295 fun newly_fixed inner outer x = is_fixed inner x andalso not (is_fixed outer x);
297 val fixed_ord = Name_Space.entry_ord o fixes_space;
298 val intern_fixed = Name_Space.intern o fixes_space;
299 val markup_fixed = Name_Space.markup o fixes_space;
301 fun lookup_fixed ctxt x =
302 let val x' = intern_fixed ctxt x
303 in if is_fixed ctxt x' then SOME x' else NONE end;
305 fun revert_fixed ctxt x =
306 (case Symtab.lookup (#2 (fixes_of ctxt)) x of
307 SOME x' => if intern_fixed ctxt x' = x then x' else x
310 fun dest_fixes ctxt =
311 let val (space, tab) = fixes_of ctxt
312 in sort (Name_Space.entry_ord space o pairself #2) (map swap (Symtab.dest tab)) end;
315 (* collect variables *)
317 fun add_free_names ctxt =
318 fold_aterms (fn Free (x, _) => not (is_fixed ctxt x) ? insert (op =) x | _ => I);
321 fold_aterms (fn Free (x, T) => not (is_fixed ctxt x) ? insert (op =) (x, T) | _ => I);
323 fun add_fixed_names ctxt =
324 fold_aterms (fn Free (x, _) => is_fixed ctxt x ? insert (op =) x | _ => I);
327 fold_aterms (fn Free (x, T) => is_fixed ctxt x ? insert (op =) (x, T) | _ => I);
335 error ("Duplicate fixed variable(s): " ^ commas (map Binding.print dups));
337 fun new_fixed ((x, x'), pos) ctxt =
338 if is_some (lookup_fixed ctxt x') then err_dups [Binding.make (x, pos)]
342 (Name_Space.define ctxt true Name_Space.default_naming (Binding.make (x', pos), x) #> snd #>>
343 Name_Space.alias Name_Space.default_naming (Binding.make (x, pos)) x')
345 |> declare_constraints (Syntax.free x');
347 fun new_fixes names' xs xs' ps =
348 map_names (K names') #>
349 fold new_fixed ((xs ~~ xs') ~~ ps) #>
354 fun add_fixes_binding bs ctxt =
357 (case filter (can Name.dest_skolem o Binding.name_of) bs of
359 | bads => error ("Illegal internal Skolem constant(s): " ^ commas (map Binding.print bads)));
361 (case duplicates (op = o pairself Binding.name_of) bs of
363 | dups => err_dups dups);
365 val xs = map check_name bs;
366 val names = names_of ctxt;
368 if is_body ctxt then fold_map Name.variant xs names |>> map Name.skolem
369 else (xs, fold Name.declare xs names);
370 in ctxt |> new_fixes names' xs xs' (map Binding.pos_of bs) end;
372 fun variant_fixes raw_xs ctxt =
374 val names = names_of ctxt;
375 val xs = map (fn x => Name.clean x |> can Name.dest_internal x ? Name.internal) raw_xs;
376 val (xs', names') = fold_map Name.variant xs names |>> (is_body ctxt ? map Name.skolem);
377 in ctxt |> new_fixes names' xs xs' (replicate (length xs) Position.none) end;
381 val add_fixes = add_fixes_binding o map Binding.name;
383 fun add_fixes_direct xs ctxt = ctxt
385 |> (snd o add_fixes xs)
386 |> restore_body ctxt;
388 fun auto_fixes t ctxt = ctxt
389 |> not (is_body ctxt) ? add_fixes_direct (rev (add_free_names ctxt t []))
392 fun invent_types Ss ctxt =
394 val tfrees = Name.invents (names_of ctxt) Name.aT (length Ss) ~~ Ss;
395 val ctxt' = fold (declare_constraints o Logic.mk_type o TFree) tfrees ctxt;
396 in (tfrees, ctxt') end;
400 (** export -- generalize type/term variables (beware of closure sizes) **)
402 fun export_inst inner outer =
404 val declared_outer = is_declared outer;
407 Symtab.fold (fn (y, _) => not (is_fixed outer y) ? cons y)
408 (#2 (fixes_of inner)) [];
409 val still_fixed = not o member (op =) gen_fixes;
411 val type_occs_inner = type_occs_of inner;
413 Symtab.fold (fn (a, xs) =>
414 if declared_outer a orelse exists still_fixed xs
415 then I else cons a) (fold decl_type_occs ts type_occs_inner) [];
416 in (gen_fixesT, gen_fixes) end;
418 fun exportT_inst inner outer = #1 (export_inst inner outer);
420 fun exportT_terms inner outer =
421 let val mk_tfrees = exportT_inst inner outer in
423 (Term_Subst.generalize (mk_tfrees ts, [])
424 (fold (Term.fold_types Term.maxidx_typ) ts ~1 + 1))
427 fun export_terms inner outer =
428 let val (mk_tfrees, tfrees) = export_inst inner outer in
430 (Term_Subst.generalize (mk_tfrees ts, tfrees)
431 (fold Term.maxidx_term ts ~1 + 1))
434 fun export_prf inner outer prf =
436 val (mk_tfrees, frees) = export_inst (declare_prf prf inner) outer;
437 val tfrees = mk_tfrees [];
438 val idx = Proofterm.maxidx_proof prf ~1 + 1;
439 val gen_term = Term_Subst.generalize_same (tfrees, frees) idx;
440 val gen_typ = Term_Subst.generalizeT_same tfrees idx;
441 in Same.commit (Proofterm.map_proof_terms_same gen_term gen_typ) prf end;
444 fun gen_export (mk_tfrees, frees) ths =
446 val tfrees = mk_tfrees (map Thm.full_prop_of ths);
447 val maxidx = fold Thm.maxidx_thm ths ~1;
448 in map (Thm.generalize (tfrees, frees) (maxidx + 1)) ths end;
450 fun exportT inner outer = gen_export (exportT_inst inner outer, []);
451 fun export inner outer = gen_export (export_inst inner outer);
453 fun export_morphism inner outer =
455 val fact = export inner outer;
456 val term = singleton (export_terms inner outer);
457 val typ = Logic.type_map term;
458 in Morphism.morphism {binding = I, typ = typ, term = term, fact = fact} end;
462 (** import -- fix schematic type/term variables **)
464 fun importT_inst ts ctxt =
466 val tvars = rev (fold Term.add_tvars ts []);
467 val (tfrees, ctxt') = invent_types (map #2 tvars) ctxt;
468 in (tvars ~~ map TFree tfrees, ctxt') end;
470 fun import_inst is_open ts ctxt =
472 val ren = Name.clean #> (if is_open then I else Name.internal);
473 val (instT, ctxt') = importT_inst ts ctxt;
474 val vars = map (apsnd (Term_Subst.instantiateT instT)) (rev (fold Term.add_vars ts []));
475 val (xs, ctxt'') = variant_fixes (map (ren o #1 o #1) vars) ctxt';
476 val inst = vars ~~ map Free (xs ~~ map #2 vars);
477 in ((instT, inst), ctxt'') end;
479 fun importT_terms ts ctxt =
480 let val (instT, ctxt') = importT_inst ts ctxt
481 in (map (Term_Subst.instantiate (instT, [])) ts, ctxt') end;
483 fun import_terms is_open ts ctxt =
484 let val (inst, ctxt') = import_inst is_open ts ctxt
485 in (map (Term_Subst.instantiate inst) ts, ctxt') end;
487 fun importT ths ctxt =
489 val thy = Proof_Context.theory_of ctxt;
490 val (instT, ctxt') = importT_inst (map Thm.full_prop_of ths) ctxt;
491 val insts' as (instT', _) = Thm.certify_inst thy (instT, []);
492 val ths' = map (Thm.instantiate insts') ths;
493 in ((instT', ths'), ctxt') end;
495 fun import_prf is_open prf ctxt =
497 val ts = rev (Proofterm.fold_proof_terms cons (cons o Logic.mk_type) prf []);
498 val (insts, ctxt') = import_inst is_open ts ctxt;
499 in (Proofterm.instantiate insts prf, ctxt') end;
501 fun import is_open ths ctxt =
503 val thy = Proof_Context.theory_of ctxt;
504 val (insts, ctxt') = import_inst is_open (map Thm.full_prop_of ths) ctxt;
505 val insts' = Thm.certify_inst thy insts;
506 val ths' = map (Thm.instantiate insts') ths;
507 in ((insts', ths'), ctxt') end;
512 fun gen_trade imp exp f ctxt ths =
513 let val ((_, ths'), ctxt') = imp ths ctxt
514 in exp ctxt' ctxt (f ctxt' ths') end;
516 val tradeT = gen_trade importT exportT;
517 val trade = gen_trade (import true) export;
520 (* focus on outermost parameters: !!x y z. B *)
522 fun focus_params t ctxt =
525 split_list (Term.variant_frees t (Term.strip_all_vars t)); (*as they are printed :-*)
526 val (xs', ctxt') = variant_fixes xs ctxt;
528 val ctxt'' = ctxt' |> fold (declare_constraints o Free) ps;
529 in ((xs, ps), ctxt'') end;
533 val ((xs, ps), ctxt') = focus_params t ctxt;
534 val t' = Term.subst_bounds (rev (map Free ps), Term.strip_all_body t);
535 in (((xs ~~ ps), t'), ctxt') end;
537 fun forall_elim_prop t prop =
538 Thm.beta_conversion false (Thm.capply (Thm.dest_arg prop) t)
539 |> Thm.cprop_of |> Thm.dest_arg;
541 fun focus_cterm goal ctxt =
543 val cert = Thm.cterm_of (Thm.theory_of_cterm goal);
544 val ((xs, ps), ctxt') = focus_params (Thm.term_of goal) ctxt;
545 val ps' = map (cert o Free) ps;
546 val goal' = fold forall_elim_prop ps' goal;
547 in ((xs ~~ ps', goal'), ctxt') end;
549 fun focus_subgoal i st =
551 val all_vars = Thm.fold_terms Term.add_vars st [];
552 val no_binds = map (fn (xi, _) => (xi, NONE)) all_vars;
554 fold bind_term no_binds #>
555 fold (declare_constraints o Var) all_vars #>
556 focus_cterm (Thm.cprem_of st i)
561 (** implicit polymorphism **)
563 (* warn_extra_tfrees *)
565 fun warn_extra_tfrees ctxt1 ctxt2 =
567 fun occs_typ a = Term.exists_subtype (fn TFree (b, _) => a = b | _ => false);
569 (case def_type ctxt1 false (x, ~1) of
570 SOME T => if occs_typ a T then I else cons (a, x)
571 | NONE => cons (a, x));
573 val occs1 = type_occs_of ctxt1;
574 val occs2 = type_occs_of ctxt2;
575 val extras = Symtab.fold (fn (a, xs) =>
576 if Symtab.defined occs1 a then I else fold (occs_free a) xs) occs2 [];
577 val tfrees = map #1 extras |> sort_distinct string_ord;
578 val frees = map #2 extras |> sort_distinct string_ord;
580 if null extras orelse not (Context_Position.is_visible ctxt2) then ()
581 else warning ("Introduced fixed type variable(s): " ^ commas tfrees ^ " in " ^
582 space_implode " or " (map quote frees))
586 (* polymorphic terms *)
588 fun polymorphic_types ctxt ts =
590 val ctxt' = fold declare_term ts ctxt;
591 val occs = type_occs_of ctxt;
592 val occs' = type_occs_of ctxt';
593 val types = Symtab.fold (fn (a, _) => if Symtab.defined occs a then I else cons a) occs' [];
594 val idx = maxidx_of ctxt' + 1;
595 val Ts' = (fold o fold_types o fold_atyps)
597 (case Term_Subst.generalizeT types idx T of TVar v => insert (op =) v | _ => I)
599 val ts' = map (Term_Subst.generalize (types, []) idx) ts;
600 in (rev Ts', ts') end;
602 fun polymorphic ctxt ts = snd (polymorphic_types ctxt ts);