1 (* Title: Pure/Isar/proof_context.ML
2 Author: Markus Wenzel, TU Muenchen
4 The key concept of Isar proof contexts: elevates primitive local
5 reasoning Gamma |- phi to a structured concept, with generic context
6 elements. See also structure Variable and Assumption.
9 signature PROOF_CONTEXT =
11 val theory_of: Proof.context -> theory
12 val init_global: theory -> Proof.context
14 val mode_default: mode
16 val mode_pattern: mode
17 val mode_schematic: mode
19 val set_mode: mode -> Proof.context -> Proof.context
20 val get_mode: Proof.context -> mode
21 val restore_mode: Proof.context -> Proof.context -> Proof.context
22 val abbrev_mode: Proof.context -> bool
23 val set_stmt: bool -> Proof.context -> Proof.context
24 val local_naming: Name_Space.naming
25 val map_naming: (Name_Space.naming -> Name_Space.naming) -> Proof.context -> Proof.context
26 val naming_of: Proof.context -> Name_Space.naming
27 val restore_naming: Proof.context -> Proof.context -> Proof.context
28 val full_name: Proof.context -> binding -> string
29 val syntax_of: Proof.context -> Local_Syntax.T
30 val syn_of: Proof.context -> Syntax.syntax
31 val tsig_of: Proof.context -> Type.tsig
32 val set_defsort: sort -> Proof.context -> Proof.context
33 val default_sort: Proof.context -> indexname -> sort
34 val consts_of: Proof.context -> Consts.T
35 val the_const_constraint: Proof.context -> string -> typ
36 val set_syntax_mode: Syntax.mode -> Proof.context -> Proof.context
37 val restore_syntax_mode: Proof.context -> Proof.context -> Proof.context
38 val facts_of: Proof.context -> Facts.T
39 val cases_of: Proof.context -> (string * (Rule_Cases.T * bool)) list
40 val class_space: Proof.context -> Name_Space.T
41 val type_space: Proof.context -> Name_Space.T
42 val const_space: Proof.context -> Name_Space.T
43 val intern_class: Proof.context -> xstring -> string
44 val intern_type: Proof.context -> xstring -> string
45 val intern_const: Proof.context -> xstring -> string
46 val extern_class: Proof.context -> string -> xstring
47 val extern_type: Proof.context -> string -> xstring
48 val extern_const: Proof.context -> string -> xstring
49 val transfer_syntax: theory -> Proof.context -> Proof.context
50 val transfer: theory -> Proof.context -> Proof.context
51 val background_theory: (theory -> theory) -> Proof.context -> Proof.context
52 val background_theory_result: (theory -> 'a * theory) -> Proof.context -> 'a * Proof.context
53 val extern_fact: Proof.context -> string -> xstring
54 val pretty_term_abbrev: Proof.context -> term -> Pretty.T
55 val pretty_fact_aux: Proof.context -> bool -> string * thm list -> Pretty.T
56 val pretty_fact: Proof.context -> string * thm list -> Pretty.T
57 val read_class: Proof.context -> xstring -> class
58 val read_arity: Proof.context -> xstring * string list * string -> arity
59 val cert_arity: Proof.context -> arity -> arity
60 val read_typ: Proof.context -> string -> typ
61 val read_typ_syntax: Proof.context -> string -> typ
62 val read_typ_abbrev: Proof.context -> string -> typ
63 val cert_typ: Proof.context -> typ -> typ
64 val cert_typ_syntax: Proof.context -> typ -> typ
65 val cert_typ_abbrev: Proof.context -> typ -> typ
66 val infer_type: Proof.context -> string * typ -> typ
67 val inferred_param: string -> Proof.context -> typ * Proof.context
68 val inferred_fixes: Proof.context -> (string * typ) list * Proof.context
69 val read_type_name: Proof.context -> bool -> string -> typ
70 val read_type_name_proper: Proof.context -> bool -> string -> typ
71 val read_const_proper: Proof.context -> bool -> string -> term
72 val read_const: Proof.context -> bool -> typ -> string -> term
73 val allow_dummies: Proof.context -> Proof.context
74 val prepare_sorts: Proof.context -> typ list -> typ list
75 val check_tfree: Proof.context -> string * sort -> string * sort
76 val intern_skolem: Proof.context -> string -> string option
77 val read_term_pattern: Proof.context -> string -> term
78 val read_term_schematic: Proof.context -> string -> term
79 val read_term_abbrev: Proof.context -> string -> term
80 val show_abbrevs_raw: Config.raw
81 val show_abbrevs: bool Config.T
82 val expand_abbrevs: Proof.context -> term -> term
83 val cert_term: Proof.context -> term -> term
84 val cert_prop: Proof.context -> term -> term
85 val def_type: Proof.context -> indexname -> typ option
86 val standard_typ_check: Proof.context -> typ list -> typ list
87 val standard_term_check_finish: Proof.context -> term list -> term list
88 val standard_term_uncheck: Proof.context -> term list -> term list
89 val goal_export: Proof.context -> Proof.context -> thm list -> thm list
90 val export: Proof.context -> Proof.context -> thm list -> thm list
91 val export_morphism: Proof.context -> Proof.context -> morphism
92 val norm_export_morphism: Proof.context -> Proof.context -> morphism
93 val bind_terms: (indexname * term option) list -> Proof.context -> Proof.context
94 val auto_bind_goal: term list -> Proof.context -> Proof.context
95 val auto_bind_facts: term list -> Proof.context -> Proof.context
96 val match_bind: bool -> (string list * string) list -> Proof.context -> term list * Proof.context
97 val match_bind_i: bool -> (term list * term) list -> Proof.context -> term list * Proof.context
98 val read_propp: (string * string list) list list -> Proof.context ->
99 (term * term list) list list * Proof.context
100 val cert_propp: (term * term list) list list -> Proof.context ->
101 (term * term list) list list * Proof.context
102 val read_propp_schematic: (string * string list) list list -> Proof.context ->
103 (term * term list) list list * Proof.context
104 val cert_propp_schematic: (term * term list) list list -> Proof.context ->
105 (term * term list) list list * Proof.context
106 val bind_propp: (string * string list) list list -> Proof.context ->
107 (term list list * (Proof.context -> Proof.context)) * Proof.context
108 val bind_propp_i: (term * term list) list list -> Proof.context ->
109 (term list list * (Proof.context -> Proof.context)) * Proof.context
110 val bind_propp_schematic: (string * string list) list list -> Proof.context ->
111 (term list list * (Proof.context -> Proof.context)) * Proof.context
112 val bind_propp_schematic_i: (term * term list) list list -> Proof.context ->
113 (term list list * (Proof.context -> Proof.context)) * Proof.context
114 val fact_tac: thm list -> int -> tactic
115 val some_fact_tac: Proof.context -> int -> tactic
116 val get_fact: Proof.context -> Facts.ref -> thm list
117 val get_fact_single: Proof.context -> Facts.ref -> thm
118 val get_thms: Proof.context -> xstring -> thm list
119 val get_thm: Proof.context -> xstring -> thm
120 val note_thmss: string -> (Thm.binding * (thm list * attribute list) list) list ->
121 Proof.context -> (string * thm list) list * Proof.context
122 val put_thms: bool -> string * thm list option -> Proof.context -> Proof.context
123 val read_vars: (binding * string option * mixfix) list -> Proof.context ->
124 (binding * typ option * mixfix) list * Proof.context
125 val cert_vars: (binding * typ option * mixfix) list -> Proof.context ->
126 (binding * typ option * mixfix) list * Proof.context
127 val add_fixes: (binding * typ option * mixfix) list -> Proof.context ->
128 string list * Proof.context
129 val add_assms: Assumption.export ->
130 (Thm.binding * (string * string list) list) list ->
131 Proof.context -> (string * thm list) list * Proof.context
132 val add_assms_i: Assumption.export ->
133 (Thm.binding * (term * term list) list) list ->
134 Proof.context -> (string * thm list) list * Proof.context
135 val add_cases: bool -> (string * Rule_Cases.T option) list -> Proof.context -> Proof.context
136 val apply_case: Rule_Cases.T -> Proof.context -> (string * term list) list * Proof.context
137 val get_case: Proof.context -> string -> binding option list -> Rule_Cases.T
138 val type_notation: bool -> Syntax.mode -> (typ * mixfix) list -> Proof.context -> Proof.context
139 val notation: bool -> Syntax.mode -> (term * mixfix) list -> Proof.context -> Proof.context
140 val target_type_notation: bool -> Syntax.mode -> (typ * mixfix) list -> morphism ->
141 Context.generic -> Context.generic
142 val target_notation: bool -> Syntax.mode -> (term * mixfix) list -> morphism ->
143 Context.generic -> Context.generic
144 val class_alias: binding -> class -> Proof.context -> Proof.context
145 val type_alias: binding -> string -> Proof.context -> Proof.context
146 val const_alias: binding -> string -> Proof.context -> Proof.context
147 val add_const_constraint: string * typ option -> Proof.context -> Proof.context
148 val add_abbrev: string -> binding * term -> Proof.context -> (term * term) * Proof.context
149 val revert_abbrev: string -> string -> Proof.context -> Proof.context
150 val print_syntax: Proof.context -> unit
151 val print_abbrevs: Proof.context -> unit
152 val print_binds: Proof.context -> unit
153 val print_lthms: Proof.context -> unit
154 val print_cases: Proof.context -> unit
155 val debug: bool Config.T
156 val verbose: bool Config.T
157 val pretty_ctxt: Proof.context -> Pretty.T list
158 val pretty_context: Proof.context -> Pretty.T list
161 structure Proof_Context: PROOF_CONTEXT =
164 val theory_of = Proof_Context.theory_of;
165 val init_global = Proof_Context.init_global;
169 (** inner syntax mode **)
173 {stmt: bool, (*inner statement mode*)
174 pattern: bool, (*pattern binding schematic variables*)
175 schematic: bool, (*term referencing loose schematic variables*)
176 abbrev: bool}; (*abbrev mode -- no normalization*)
178 fun make_mode (stmt, pattern, schematic, abbrev) =
179 Mode {stmt = stmt, pattern = pattern, schematic = schematic, abbrev = abbrev};
181 val mode_default = make_mode (false, false, false, false);
182 val mode_stmt = make_mode (true, false, false, false);
183 val mode_pattern = make_mode (false, true, false, false);
184 val mode_schematic = make_mode (false, false, true, false);
185 val mode_abbrev = make_mode (false, false, false, true);
189 (** Isar proof context information **)
193 {mode: mode, (*inner syntax mode*)
194 naming: Name_Space.naming, (*local naming conventions*)
195 syntax: Local_Syntax.T, (*local syntax*)
196 tsig: Type.tsig * Type.tsig, (*local/global type signature -- local name space / defsort only*)
197 consts: Consts.T * Consts.T, (*local/global consts -- local name space / abbrevs only*)
198 facts: Facts.T, (*local facts*)
199 cases: (string * (Rule_Cases.T * bool)) list}; (*named case contexts*)
201 fun make_data (mode, naming, syntax, tsig, consts, facts, cases) =
202 Data {mode = mode, naming = naming, syntax = syntax,
203 tsig = tsig, consts = consts, facts = facts, cases = cases};
205 val local_naming = Name_Space.default_naming |> Name_Space.add_path "local";
207 structure Data = Proof_Data
211 make_data (mode_default, local_naming, Local_Syntax.init thy,
212 (Sign.tsig_of thy, Sign.tsig_of thy),
213 (Sign.consts_of thy, Sign.consts_of thy), Facts.empty, []);
216 fun rep_data ctxt = Data.get ctxt |> (fn Data rep => rep);
219 Data.map (fn Data {mode, naming, syntax, tsig, consts, facts, cases} =>
220 make_data (f (mode, naming, syntax, tsig, consts, facts, cases)));
222 fun set_mode mode = map_data (fn (_, naming, syntax, tsig, consts, facts, cases) =>
223 (mode, naming, syntax, tsig, consts, facts, cases));
226 map_data (fn (Mode {stmt, pattern, schematic, abbrev}, naming, syntax, tsig, consts, facts, cases) =>
227 (make_mode (f (stmt, pattern, schematic, abbrev)), naming, syntax, tsig, consts, facts, cases));
230 map_data (fn (mode, naming, syntax, tsig, consts, facts, cases) =>
231 (mode, f naming, syntax, tsig, consts, facts, cases));
234 map_data (fn (mode, naming, syntax, tsig, consts, facts, cases) =>
235 (mode, naming, f syntax, tsig, consts, facts, cases));
238 map_data (fn (mode, naming, syntax, tsig, consts, facts, cases) =>
239 (mode, naming, syntax, f tsig, consts, facts, cases));
242 map_data (fn (mode, naming, syntax, tsig, consts, facts, cases) =>
243 (mode, naming, syntax, tsig, f consts, facts, cases));
246 map_data (fn (mode, naming, syntax, tsig, consts, facts, cases) =>
247 (mode, naming, syntax, tsig, consts, f facts, cases));
250 map_data (fn (mode, naming, syntax, tsig, consts, facts, cases) =>
251 (mode, naming, syntax, tsig, consts, facts, f cases));
253 val get_mode = #mode o rep_data;
254 val restore_mode = set_mode o get_mode;
255 val abbrev_mode = get_mode #> (fn Mode {abbrev, ...} => abbrev);
258 map_mode (fn (_, pattern, schematic, abbrev) => (stmt, pattern, schematic, abbrev));
260 val naming_of = #naming o rep_data;
261 val restore_naming = map_naming o K o naming_of
262 val full_name = Name_Space.full_name o naming_of;
264 val syntax_of = #syntax o rep_data;
265 val syn_of = Local_Syntax.syn_of o syntax_of;
266 val set_syntax_mode = map_syntax o Local_Syntax.set_mode;
267 val restore_syntax_mode = map_syntax o Local_Syntax.restore_mode o syntax_of;
269 val tsig_of = #1 o #tsig o rep_data;
270 val set_defsort = map_tsig o apfst o Type.set_defsort;
271 fun default_sort ctxt = the_default (Type.defaultS (tsig_of ctxt)) o Variable.def_sort ctxt;
273 val consts_of = #1 o #consts o rep_data;
274 val the_const_constraint = Consts.the_constraint o consts_of;
276 val facts_of = #facts o rep_data;
277 val cases_of = #cases o rep_data;
282 val class_space = Type.class_space o tsig_of;
283 val type_space = Type.type_space o tsig_of;
284 val const_space = Consts.space_of o consts_of;
286 val intern_class = Name_Space.intern o class_space;
287 val intern_type = Name_Space.intern o type_space;
288 val intern_const = Name_Space.intern o const_space;
290 fun extern_class ctxt = Name_Space.extern ctxt (class_space ctxt);
291 fun extern_type ctxt = Name_Space.extern ctxt (type_space ctxt);
292 fun extern_const ctxt = Name_Space.extern ctxt (const_space ctxt);
295 (* theory transfer *)
297 fun transfer_syntax thy ctxt = ctxt |>
298 map_syntax (Local_Syntax.rebuild thy) |>
299 map_tsig (fn tsig as (local_tsig, global_tsig) =>
300 let val thy_tsig = Sign.tsig_of thy in
301 if Type.eq_tsig (thy_tsig, global_tsig) then tsig
302 else (Type.merge_tsig ctxt (local_tsig, thy_tsig), thy_tsig)
304 map_consts (fn consts as (local_consts, global_consts) =>
305 let val thy_consts = Sign.consts_of thy in
306 if Consts.eq_consts (thy_consts, global_consts) then consts
307 else (Consts.merge (local_consts, thy_consts), thy_consts)
310 fun transfer thy = Context.raw_transfer thy #> transfer_syntax thy;
312 fun background_theory f ctxt = transfer (f (theory_of ctxt)) ctxt;
314 fun background_theory_result f ctxt =
315 let val (res, thy') = f (theory_of ctxt)
316 in (res, ctxt |> transfer thy') end;
320 (** pretty printing **)
324 fun which_facts ctxt name =
326 val local_facts = facts_of ctxt;
327 val global_facts = Global_Theory.facts_of (theory_of ctxt);
329 if is_some (Facts.lookup (Context.Proof ctxt) local_facts name)
330 then local_facts else global_facts
333 fun markup_fact ctxt name = Name_Space.markup (Facts.space_of (which_facts ctxt name)) name;
335 fun extern_fact ctxt name = Facts.extern ctxt (which_facts ctxt name) name;
340 fun pretty_term_abbrev ctxt = Syntax.pretty_term (set_mode mode_abbrev ctxt);
342 fun pretty_fact_name ctxt a =
343 Pretty.block [Pretty.mark_str (markup_fact ctxt a, extern_fact ctxt a), Pretty.str ":"];
345 fun pretty_fact_aux ctxt flag ("", ths) =
346 Display.pretty_thms_aux ctxt flag ths
347 | pretty_fact_aux ctxt flag (a, [th]) = Pretty.block
348 [pretty_fact_name ctxt a, Pretty.brk 1, Display.pretty_thm_aux ctxt flag th]
349 | pretty_fact_aux ctxt flag (a, ths) = Pretty.block
350 (Pretty.fbreaks (pretty_fact_name ctxt a :: map (Display.pretty_thm_aux ctxt flag) ths));
352 fun pretty_fact ctxt = pretty_fact_aux ctxt true;
356 (** prepare types **)
360 fun read_class ctxt text =
362 val tsig = tsig_of ctxt;
363 val (syms, pos) = Syntax.read_token text;
364 val c = Type.cert_class tsig (Type.intern_class tsig (Symbol_Pos.content syms))
365 handle TYPE (msg, _, _) => error (msg ^ Position.str_of pos);
366 val _ = Context_Position.report ctxt pos (Name_Space.markup (Type.class_space tsig) c);
374 fun prep_arity prep_tycon prep_sort ctxt (t, Ss, S) =
375 let val arity = (prep_tycon ctxt t, map (prep_sort ctxt) Ss, prep_sort ctxt S)
376 in Type.add_arity ctxt arity (tsig_of ctxt); arity end;
380 val read_arity = prep_arity intern_type Syntax.read_sort;
381 val cert_arity = prep_arity (K I) (Type.cert_sort o tsig_of);
388 fun read_typ_mode mode ctxt s =
389 Syntax.read_typ (Type.set_mode mode ctxt) s;
391 val read_typ = read_typ_mode Type.mode_default;
392 val read_typ_syntax = read_typ_mode Type.mode_syntax;
393 val read_typ_abbrev = read_typ_mode Type.mode_abbrev;
396 fun cert_typ_mode mode ctxt T =
397 Type.cert_typ_mode mode (tsig_of ctxt) T
398 handle TYPE (msg, _, _) => error msg;
400 val cert_typ = cert_typ_mode Type.mode_default;
401 val cert_typ_syntax = cert_typ_mode Type.mode_syntax;
402 val cert_typ_abbrev = cert_typ_mode Type.mode_abbrev;
406 (** prepare variables **)
408 (* check Skolem constants *)
410 fun no_skolem internal x =
411 if can Name.dest_skolem x then
412 error ("Illegal reference to internal Skolem constant: " ^ quote x)
413 else if not internal andalso can Name.dest_internal x then
414 error ("Illegal reference to internal variable: " ^ quote x)
419 (** prepare terms and propositions **)
421 (* inferred types of parameters *)
423 fun infer_type ctxt x =
424 Term.fastype_of (singleton (Syntax.check_terms (set_mode mode_schematic ctxt)) (Free x));
426 fun inferred_param x ctxt =
427 let val T = infer_type ctxt (x, dummyT)
428 in (T, ctxt |> Variable.declare_term (Free (x, T))) end;
430 fun inferred_fixes ctxt =
432 val xs = map #2 (Variable.dest_fixes ctxt);
433 val (Ts, ctxt') = fold_map inferred_param xs ctxt;
434 in (xs ~~ Ts, ctxt') end;
437 (* type and constant names *)
441 val token_content = Syntax.read_token #>> Symbol_Pos.content;
443 fun prep_const_proper ctxt strict (c, pos) =
445 fun err msg = error (msg ^ Position.str_of pos);
446 val consts = consts_of ctxt;
447 val t as Const (d, _) =
448 (case Variable.lookup_const ctxt c of
450 Const (d, Consts.type_scheme (consts_of ctxt) d handle TYPE (msg, _, _) => err msg)
451 | NONE => Consts.read_const consts (c, pos));
453 if strict then ignore (Consts.the_const consts d) handle TYPE (msg, _, _) => err msg
455 val _ = Context_Position.report ctxt pos (Name_Space.markup (Consts.space_of consts) d);
460 fun read_type_name ctxt strict text =
462 val tsig = tsig_of ctxt;
463 val (c, pos) = token_content text;
465 if Lexicon.is_tid c then
466 (Context_Position.report ctxt pos Isabelle_Markup.tfree;
467 TFree (c, default_sort ctxt (c, ~1)))
470 val d = intern_type ctxt c;
471 val decl = Type.the_decl tsig (d, pos);
472 fun err () = error ("Bad type name: " ^ quote d ^ Position.str_of pos);
475 Type.LogicalType n => n
476 | Type.Abbreviation (vs, _, _) => if strict then err () else length vs
477 | Type.Nonterminal => if strict then err () else 0);
478 val _ = Context_Position.report ctxt pos (Name_Space.markup (Type.type_space tsig) d);
479 in Type (d, replicate args dummyT) end
482 fun read_type_name_proper ctxt strict text =
483 (case read_type_name ctxt strict text of
485 | T => error ("Not a type constructor: " ^ Syntax.string_of_typ ctxt T));
488 fun read_const_proper ctxt strict = prep_const_proper ctxt strict o token_content;
490 fun read_const ctxt strict ty text =
492 val (c, pos) = token_content text;
493 val _ = no_skolem false c;
495 (case (Variable.lookup_fixed ctxt c, Variable.is_const ctxt c) of
497 (Context_Position.report ctxt pos
499 (if can Name.dest_skolem x then Isabelle_Markup.skolem else Isabelle_Markup.free));
500 Free (x, infer_type ctxt (x, ty)))
501 | _ => prep_const_proper ctxt strict (c, pos))
507 (* skolem variables *)
509 fun intern_skolem ctxt x =
511 val _ = no_skolem false x;
512 val sko = Variable.lookup_fixed ctxt x;
513 val is_const = can (read_const_proper ctxt false) x orelse Long_Name.is_qualified x;
514 val is_declared = is_some (Variable.def_type ctxt false (x, ~1));
516 if Variable.is_const ctxt x then NONE
517 else if is_some sko then sko
518 else if not is_const orelse is_declared then SOME x
525 fun read_term_mode mode ctxt = Syntax.read_term (set_mode mode ctxt);
527 val read_term_pattern = read_term_mode mode_pattern;
528 val read_term_schematic = read_term_mode mode_schematic;
529 val read_term_abbrev = read_term_mode mode_abbrev;
532 (* local abbreviations *)
536 fun certify_consts ctxt = Consts.certify (Context.pretty ctxt) (tsig_of ctxt)
537 (not (abbrev_mode ctxt)) (consts_of ctxt);
539 fun expand_binds ctxt =
541 val Mode {pattern, schematic, ...} = get_mode ctxt;
543 fun reject_schematic (t as Var _) =
544 error ("Unbound schematic variable: " ^ Syntax.string_of_term ctxt t)
545 | reject_schematic (Abs (_, _, t)) = reject_schematic t
546 | reject_schematic (t $ u) = (reject_schematic t; reject_schematic u)
547 | reject_schematic _ = ();
550 else Variable.expand_binds ctxt #> (if schematic then I else tap reject_schematic)
555 fun expand_abbrevs ctxt = certify_consts ctxt #> expand_binds ctxt;
559 val show_abbrevs_raw = Config.declare "show_abbrevs" (fn _ => Config.Bool true);
560 val show_abbrevs = Config.bool show_abbrevs_raw;
562 fun contract_abbrevs ctxt t =
564 val thy = theory_of ctxt;
565 val consts = consts_of ctxt;
566 val Mode {abbrev, ...} = get_mode ctxt;
567 val retrieve = Consts.retrieve_abbrevs consts (print_mode_value () @ [""]);
568 fun match_abbrev u = Option.map #1 (get_first (Pattern.match_rew thy u) (retrieve u));
570 if abbrev orelse not (Config.get ctxt show_abbrevs) orelse not (can Term.type_of t) then t
571 else Pattern.rewrite_term_top thy [] [match_abbrev] t
577 fun prepare_patternT ctxt T =
579 val Mode {pattern, schematic, ...} = get_mode ctxt;
581 pattern orelse schematic orelse
582 T |> Term.exists_subtype
583 (fn T as TVar (xi, _) =>
584 not (Type_Infer.is_param xi) andalso
585 error ("Illegal schematic type variable: " ^ Syntax.string_of_typ ctxt T)
592 val dummies = Config.bool (Config.declare "Proof_Context.dummies" (K (Config.Bool false)));
594 fun check_dummies ctxt t =
595 if Config.get ctxt dummies then t
596 else Term.no_dummy_patterns t handle TERM _ => error "Illegal dummy pattern(s) in term";
598 fun prepare_dummies ts = #1 (fold_map Term.replace_dummy_patterns ts 1);
602 val allow_dummies = Config.put dummies true;
604 fun prepare_patterns ctxt =
605 let val Mode {pattern, ...} = get_mode ctxt in
606 Type_Infer.fixate ctxt #>
607 pattern ? Variable.polymorphic ctxt #>
608 (map o Term.map_types) (prepare_patternT ctxt) #>
609 (if pattern then prepare_dummies else map (check_dummies ctxt))
615 (* sort constraints *)
617 fun prepare_sorts ctxt tys =
619 val tsig = tsig_of ctxt;
620 val defaultS = Type.defaultS tsig;
622 fun constraint (xi, S) env =
623 if S = dummyS then env
625 Vartab.insert (op =) (xi, Type.minimize_sort tsig S) env
626 handle Vartab.DUP _ =>
627 error ("Inconsistent sort constraints for type variable " ^
628 quote (Term.string_of_vname' xi));
631 (fn TFree (x, S) => constraint ((x, ~1), S)
632 | TVar v => constraint v
633 | _ => I) tys Vartab.empty;
636 (case (Vartab.lookup env xi, Variable.def_sort ctxt xi) of
637 (NONE, NONE) => defaultS
638 | (NONE, SOME S) => S
639 | (SOME S, NONE) => S
640 | (SOME S, SOME S') =>
641 if Type.eq_sort tsig (S, S') then S'
643 error ("Sort constraint " ^ Syntax.string_of_sort ctxt S ^
644 " inconsistent with default " ^ Syntax.string_of_sort ctxt S' ^
645 " for type variable " ^ quote (Term.string_of_vname' xi)));
649 if Term_Position.is_positionT T then T
652 TFree (x, _) => TFree (x, get_sort (x, ~1))
653 | TVar (xi, _) => TVar (xi, get_sort xi)
657 fun check_tfree ctxt v = dest_TFree (singleton (prepare_sorts ctxt) (TFree v));
664 fun gen_cert prop ctxt t =
666 |> expand_abbrevs ctxt
668 #1 (Sign.certify' prop (Context.pretty ctxt) false (consts_of ctxt) (theory_of ctxt) t')
669 handle TYPE (msg, _, _) => error msg | TERM (msg, _) => error msg);
673 val cert_term = gen_cert false;
674 val cert_prop = gen_cert true;
682 let val Mode {pattern, ...} = get_mode ctxt
683 in Variable.def_type ctxt pattern end;
685 fun standard_typ_check ctxt =
686 map (cert_typ_mode (Type.get_mode ctxt) ctxt #> prepare_patternT ctxt);
688 val standard_term_check_finish = prepare_patterns;
690 fun standard_term_uncheck ctxt = map (contract_abbrevs ctxt);
694 (** export results **)
696 fun common_export is_goal inner outer =
697 map (Assumption.export is_goal inner outer) #>
698 Variable.export inner outer;
700 val goal_export = common_export true;
701 val export = common_export false;
703 fun export_morphism inner outer =
704 Assumption.export_morphism inner outer $>
705 Variable.export_morphism inner outer;
707 fun norm_export_morphism inner outer =
708 export_morphism inner outer $>
709 Morphism.thm_morphism Goal.norm_result;
713 (** term bindings **)
717 fun simult_matches ctxt (t, pats) =
718 (case Seq.pull (Unify.matchers (theory_of ctxt) (map (rpair t) pats)) of
719 NONE => error "Pattern match failed!"
720 | SOME (env, _) => Vartab.fold (fn (v, (_, t)) => cons (v, t)) (Envir.term_env env) []);
725 val bind_terms = fold (fn (xi, t) => fn ctxt =>
727 |> Variable.bind_term (xi, Option.map (cert_term (set_mode mode_default ctxt)) t));
732 fun drop_schematic (b as (xi, SOME t)) = if Term.exists_subterm is_Var t then (xi, NONE) else b
733 | drop_schematic b = b;
735 fun auto_bind f ts ctxt = ctxt |> bind_terms (map drop_schematic (f (theory_of ctxt) ts));
737 val auto_bind_goal = auto_bind Auto_Bind.goal;
738 val auto_bind_facts = auto_bind Auto_Bind.facts;
745 fun gen_bind prep_terms gen raw_binds ctxt =
747 fun prep_bind (raw_pats, t) ctxt1 =
749 val T = Term.fastype_of t;
750 val ctxt2 = Variable.declare_term t ctxt1;
751 val pats = prep_terms (set_mode mode_pattern ctxt2) T raw_pats;
752 val binds = simult_matches ctxt2 (t, pats);
753 in (binds, ctxt2) end;
755 val ts = prep_terms ctxt dummyT (map snd raw_binds);
756 val (binds, ctxt') = apfst flat (fold_map prep_bind (map fst raw_binds ~~ ts) ctxt);
758 if gen then map #1 binds ~~ Variable.exportT_terms ctxt' ctxt (map #2 binds)
760 val binds'' = map (apsnd SOME) binds';
762 tap (Variable.warn_extra_tfrees ctxt)
764 ctxt (*sic!*) |> fold Variable.declare_term (map #2 binds') |> bind_terms binds''
765 else ctxt' |> bind_terms binds'');
770 fun read_terms ctxt T =
771 map (Syntax.parse_term ctxt #> Type.constraint T) #> Syntax.check_terms ctxt;
773 val match_bind = gen_bind read_terms;
774 val match_bind_i = gen_bind (fn ctxt => fn _ => map (cert_term ctxt));
779 (* propositions with patterns *)
783 fun prep_propp mode prep_props args context =
785 fun prep (_, raw_pats) (ctxt, prop :: props) =
786 let val ctxt' = Variable.declare_term prop ctxt
787 in ((prop, prep_props (set_mode mode_pattern ctxt') raw_pats), (ctxt', props)) end;
789 val (propp, (context', _)) =
790 (fold_map o fold_map) prep args
791 (context, prep_props (set_mode mode context) (maps (map fst) args));
792 in (propp, context') end;
794 fun gen_bind_propp mode parse_prop raw_args ctxt =
796 val (args, ctxt') = prep_propp mode parse_prop raw_args ctxt;
797 val binds = flat (flat (map (map (simult_matches ctxt')) args));
798 val propss = map (map #1) args;
799 fun gen_binds ctxt0 = ctxt0
800 |> bind_terms (map #1 binds ~~
801 map (SOME o Term.close_schematic_term) (Variable.export_terms ctxt' ctxt0 (map #2 binds)));
802 in ((propss, gen_binds), ctxt' |> bind_terms (map (apsnd SOME) binds)) end;
806 val read_propp = prep_propp mode_default Syntax.read_props;
807 val cert_propp = prep_propp mode_default (map o cert_prop);
808 val read_propp_schematic = prep_propp mode_schematic Syntax.read_props;
809 val cert_propp_schematic = prep_propp mode_schematic (map o cert_prop);
811 val bind_propp = gen_bind_propp mode_default Syntax.read_props;
812 val bind_propp_i = gen_bind_propp mode_default (map o cert_prop);
813 val bind_propp_schematic = gen_bind_propp mode_schematic Syntax.read_props;
814 val bind_propp_schematic_i = gen_bind_propp mode_schematic (map o cert_prop);
824 fun comp_incr_tac [] _ = no_tac
825 | comp_incr_tac (th :: ths) i =
826 (fn st => Goal.compose_hhf_tac (Drule.incr_indexes st th) i st) APPEND comp_incr_tac ths i;
828 fun fact_tac facts = Goal.norm_hhf_tac THEN' comp_incr_tac facts;
830 fun potential_facts ctxt prop =
831 Facts.could_unify (facts_of ctxt) (Term.strip_all_body prop);
833 fun some_fact_tac ctxt = SUBGOAL (fn (goal, i) => fact_tac (potential_facts ctxt goal) i);
840 fun retrieve_thms pick ctxt (Facts.Fact s) =
842 val pos = Syntax.read_token_pos s;
844 Syntax.read_prop (ctxt |> set_mode mode_default |> allow_dummies) s
845 |> singleton (Variable.polymorphic ctxt);
846 fun err msg = error (msg ^ Position.str_of pos ^ ":\n" ^ Syntax.string_of_term ctxt prop);
848 val (prop', _) = Term.replace_dummy_patterns prop (Variable.maxidx_of ctxt + 1);
850 Goal.prove ctxt [] [] prop' (K (ALLGOALS (fact_tac [th])));
851 val results = map_filter (try prove_fact) (potential_facts ctxt prop');
853 (case distinct Thm.eq_thm_prop results of
855 | [] => err "Failed to retrieve literal fact"
856 | _ => err "Ambiguous specification of literal fact");
858 | retrieve_thms pick ctxt xthmref =
860 val thy = theory_of ctxt;
861 val local_facts = facts_of ctxt;
862 val thmref = Facts.map_name_of_ref (Facts.intern local_facts) xthmref;
863 val name = Facts.name_of_ref thmref;
864 val pos = Facts.pos_of_ref xthmref;
866 if name = "" then [Thm.transfer thy Drule.dummy_thm]
868 (case Facts.lookup (Context.Proof ctxt) local_facts name of
870 (Context_Position.report ctxt pos
871 (Name_Space.markup (Facts.space_of local_facts) name);
872 map (Thm.transfer thy) (Facts.select thmref ths))
873 | NONE => Global_Theory.get_fact (Context.Proof ctxt) thy xthmref);
874 in pick name thms end;
878 val get_fact = retrieve_thms (K I);
879 val get_fact_single = retrieve_thms Facts.the_single;
881 fun get_thms ctxt = get_fact ctxt o Facts.named;
882 fun get_thm ctxt = get_fact_single ctxt o Facts.named;
891 fun update_thms _ (b, NONE) ctxt = ctxt |> map_facts (Facts.del (full_name ctxt b))
892 | update_thms do_props (b, SOME ths) ctxt = ctxt |> map_facts
893 (Facts.add_local ctxt do_props (naming_of ctxt) (b, ths) #> snd);
897 fun note_thmss kind = fold_map (fn ((b, more_atts), raw_facts) => fn ctxt =>
899 val name = full_name ctxt b;
900 val facts = Global_Theory.name_thmss false name raw_facts;
901 fun app (ths, atts) =
902 fold_map (Thm.proof_attributes (surround (Thm.kind kind) (atts @ more_atts))) ths;
903 val (res, ctxt') = fold_map app facts ctxt;
904 val thms = Global_Theory.name_thms false false name (flat res);
905 val Mode {stmt, ...} = get_mode ctxt;
906 in ((name, thms), ctxt' |> update_thms stmt (b, SOME thms)) end);
908 fun put_thms do_props thms ctxt = ctxt
909 |> map_naming (K local_naming)
910 |> Context_Position.set_visible false
911 |> update_thms do_props (apfst Binding.name thms)
912 |> Context_Position.restore_visible ctxt
913 |> restore_naming ctxt;
919 (** basic logical entities **)
923 fun declare_var (x, opt_T, mx) ctxt =
924 let val T = (case opt_T of SOME T => T | NONE => Mixfix.mixfixT mx)
925 in ((x, T, mx), ctxt |> Variable.declare_constraints (Free (x, T))) end;
929 fun prep_vars prep_typ internal =
930 fold_map (fn (b, raw_T, mx) => fn ctxt =>
932 val x = Variable.check_name b;
933 val _ = Lexicon.is_identifier (no_skolem internal x) orelse
934 error ("Illegal variable name: " ^ Binding.print b);
938 else Type.no_tvars T handle TYPE (msg, _, _) => error msg;
939 val opt_T = Option.map (cond_tvars o cert_typ ctxt o prep_typ ctxt) raw_T;
940 val (_, ctxt') = ctxt |> declare_var (x, opt_T, mx);
941 in ((b, opt_T, mx), ctxt') end);
945 val read_vars = prep_vars Syntax.read_typ false;
946 val cert_vars = prep_vars (K I) true;
955 fun type_syntax (Type (c, args), mx) =
956 SOME (Local_Syntax.Type, (Lexicon.mark_type c, Mixfix.make_type (length args), mx))
957 | type_syntax _ = NONE;
959 fun const_syntax _ (Free (x, T), mx) = SOME (Local_Syntax.Fixed, (x, T, mx))
960 | const_syntax ctxt (Const (c, _), mx) =
961 (case try (Consts.type_scheme (consts_of ctxt)) c of
962 SOME T => SOME (Local_Syntax.Const, (Lexicon.mark_const c, T, mx))
964 | const_syntax _ _ = NONE;
966 fun gen_notation syntax add mode args ctxt =
968 (Local_Syntax.update_modesyntax (theory_of ctxt) add mode (map_filter (syntax ctxt) args));
972 val type_notation = gen_notation (K type_syntax);
973 val notation = gen_notation const_syntax;
975 fun target_type_notation add mode args phi =
977 val args' = args |> map_filter (fn (T, mx) =>
979 val T' = Morphism.typ phi T;
980 val similar = (case (T, T') of (Type (c, _), Type (c', _)) => c = c' | _ => false);
981 in if similar then SOME (T', mx) else NONE end);
982 in Context.mapping (Sign.type_notation add mode args') (type_notation add mode args') end;
984 fun target_notation add mode args phi =
986 val args' = args |> map_filter (fn (t, mx) =>
987 let val t' = Morphism.term phi t
988 in if Term.aconv_untyped (t, t') then SOME (t', mx) else NONE end);
989 in Context.mapping (Sign.notation add mode args') (notation add mode args') end;
996 fun class_alias b c ctxt = (map_tsig o apfst) (Type.class_alias (naming_of ctxt) b c) ctxt;
997 fun type_alias b c ctxt = (map_tsig o apfst) (Type.type_alias (naming_of ctxt) b c) ctxt;
998 fun const_alias b c ctxt = (map_consts o apfst) (Consts.alias (naming_of ctxt) b c) ctxt;
1001 (* local constants *)
1003 fun add_const_constraint (c, opt_T) ctxt =
1006 let val T = cert_typ ctxt raw_T
1007 in cert_term ctxt (Const (c, T)); T end;
1008 in ctxt |> (map_consts o apfst) (Consts.constrain (c, Option.map prepT opt_T)) end;
1010 fun add_abbrev mode (b, raw_t) ctxt =
1012 val t0 = cert_term (ctxt |> set_mode mode_abbrev) raw_t
1013 handle ERROR msg => cat_error msg ("in constant abbreviation " ^ Binding.print b);
1014 val [t] = Variable.exportT_terms (Variable.declare_term t0 ctxt) ctxt [t0];
1015 val ((lhs, rhs), consts') = consts_of ctxt
1016 |> Consts.abbreviate ctxt (tsig_of ctxt) (naming_of ctxt) mode (b, t);
1019 |> (map_consts o apfst) (K consts')
1020 |> Variable.declare_term rhs
1024 fun revert_abbrev mode c = (map_consts o apfst) (Consts.revert_abbrev mode c);
1029 fun add_fixes raw_vars ctxt =
1031 val thy = theory_of ctxt;
1032 val vars = #1 (cert_vars raw_vars ctxt);
1035 |> Variable.add_fixes_binding (map #1 vars)
1037 fold_map declare_var (map2 (fn x => fn (_, T, mx) => (x, T, mx)) xs vars)
1038 #-> (map_syntax o Local_Syntax.add_syntax thy o map (pair Local_Syntax.Fixed))
1048 fun gen_assms prepp exp args ctxt =
1050 val cert = Thm.cterm_of (theory_of ctxt);
1051 val ((propss, _), ctxt1) = prepp (map snd args) ctxt;
1052 val _ = Variable.warn_extra_tfrees ctxt ctxt1;
1053 val (premss, ctxt2) = fold_burrow (Assumption.add_assms exp o map cert) propss ctxt1;
1056 |> auto_bind_facts (flat propss)
1057 |> note_thmss "" (map fst args ~~ map (map (fn th => ([th], []))) premss)
1062 val add_assms = gen_assms bind_propp;
1063 val add_assms_i = gen_assms bind_propp_i;
1073 fun rem_case name = remove (fn (x: string, (y, _)) => x = y) name;
1075 fun add_case _ ("", _) cases = cases
1076 | add_case _ (name, NONE) cases = rem_case name cases
1077 | add_case is_proper (name, SOME c) cases = (name, (c, is_proper)) :: rem_case name cases;
1079 fun prep_case name fxs c =
1081 fun replace (opt_x :: xs) ((y, T) :: ys) = (the_default y opt_x, T) :: replace xs ys
1082 | replace [] ys = ys
1083 | replace (_ :: _) [] = error ("Too many parameters for case " ^ quote name);
1084 val Rule_Cases.Case {fixes, assumes, binds, cases} = c;
1085 val fixes' = replace fxs fixes;
1086 val binds' = map drop_schematic binds;
1088 if null (fold (Term.add_tvarsT o snd) fixes []) andalso
1089 null (fold (fold Term.add_vars o snd) assumes []) then
1090 Rule_Cases.Case {fixes = fixes', assumes = assumes, binds = binds', cases = cases}
1091 else error ("Illegal schematic variable(s) in case " ^ quote name)
1094 fun fix (b, T) ctxt =
1095 let val ([x], ctxt') = add_fixes [(b, SOME T, NoSyn)] ctxt
1096 in (Free (x, T), ctxt') end;
1100 fun add_cases is_proper = map_cases o fold (add_case is_proper);
1102 fun case_result c ctxt =
1104 val Rule_Cases.Case {fixes, ...} = c;
1105 val (ts, ctxt') = ctxt |> fold_map fix fixes;
1106 val Rule_Cases.Case {assumes, binds, cases, ...} = Rule_Cases.apply ts c;
1109 |> bind_terms (map drop_schematic binds)
1110 |> add_cases true (map (apsnd SOME) cases)
1111 |> pair (assumes, (binds, cases))
1114 val apply_case = apfst fst oo case_result;
1116 fun get_case ctxt name xs =
1117 (case AList.lookup (op =) (cases_of ctxt) name of
1118 NONE => error ("Unknown case: " ^ quote name)
1119 | SOME (c, _) => prep_case name xs c);
1125 (** print context information **)
1129 val print_syntax = Syntax.print_syntax o syn_of;
1134 fun pretty_abbrevs show_globals ctxt =
1136 val ((space, consts), (_, globals)) =
1137 pairself (#constants o Consts.dest) (#consts (rep_data ctxt));
1138 fun add_abbr (_, (_, NONE)) = I
1139 | add_abbr (c, (T, SOME t)) =
1140 if not show_globals andalso Symtab.defined globals c then I
1141 else cons (c, Logic.mk_equals (Const (c, T), t));
1143 Name_Space.extern_table ctxt (space, Symtab.make (Symtab.fold add_abbr consts []));
1145 if null abbrevs then []
1146 else [Pretty.big_list "abbreviations:" (map (pretty_term_abbrev ctxt o #2) abbrevs)]
1149 val print_abbrevs = Pretty.writeln o Pretty.chunks o pretty_abbrevs true;
1154 fun pretty_binds ctxt =
1156 val binds = Variable.binds_of ctxt;
1157 fun prt_bind (xi, (T, t)) = pretty_term_abbrev ctxt (Logic.mk_equals (Var (xi, T), t));
1159 if Vartab.is_empty binds then []
1160 else [Pretty.big_list "term bindings:" (map prt_bind (Vartab.dest binds))]
1163 val print_binds = Pretty.writeln o Pretty.chunks o pretty_binds;
1166 (* local theorems *)
1168 fun pretty_lthms ctxt =
1170 val local_facts = facts_of ctxt;
1171 val props = Facts.props local_facts;
1173 (if null props then [] else [("<unnamed>", props)]) @
1174 Facts.dest_static [] local_facts;
1176 if null facts then []
1177 else [Pretty.big_list "facts:" (map #1 (sort_wrt (#1 o #2) (map (`(pretty_fact ctxt)) facts)))]
1180 val print_lthms = Pretty.writeln o Pretty.chunks o pretty_lthms;
1183 (* local contexts *)
1187 fun pretty_case (name, (fixes, ((asms, (lets, cs)), ctxt))) =
1189 val prt_term = Syntax.pretty_term ctxt;
1191 fun prt_let (xi, t) = Pretty.block
1192 [Pretty.quote (prt_term (Var (xi, Term.fastype_of t))), Pretty.str " =", Pretty.brk 1,
1193 Pretty.quote (prt_term t)];
1195 fun prt_asm (a, ts) = Pretty.block (Pretty.breaks
1196 ((if a = "" then [] else [Pretty.str (a ^ ":")]) @ map (Pretty.quote o prt_term) ts));
1198 fun prt_sect _ _ _ [] = []
1199 | prt_sect s sep prt xs =
1200 [Pretty.block (Pretty.breaks (Pretty.str s ::
1201 flat (separate sep (map (single o prt) xs))))];
1203 Pretty.block (Pretty.fbreaks
1204 (Pretty.str (name ^ ":") ::
1205 prt_sect "fix" [] (Pretty.str o Binding.name_of o fst) fixes @
1206 prt_sect "let" [Pretty.str "and"] prt_let
1207 (map_filter (fn (xi, SOME t) => SOME (xi, t) | _ => NONE) lets) @
1208 (if forall (null o #2) asms then []
1209 else prt_sect "assume" [Pretty.str "and"] prt_asm asms) @
1210 prt_sect "subcases:" [] (Pretty.str o fst) cs))
1215 fun pretty_cases ctxt =
1217 fun add_case (_, (_, false)) = I
1218 | add_case (name, (c as Rule_Cases.Case {fixes, ...}, true)) =
1219 cons (name, (fixes, case_result c ctxt));
1220 val cases = fold add_case (cases_of ctxt) [];
1222 if null cases then []
1223 else [Pretty.big_list "cases:" (map pretty_case cases)]
1226 val print_cases = Pretty.writeln o Pretty.chunks o pretty_cases;
1233 val debug = Config.bool (Config.declare "Proof_Context.debug" (K (Config.Bool false)));
1234 val verbose = Config.bool (Config.declare "Proof_Context.verbose" (K (Config.Bool false)));
1236 fun pretty_ctxt ctxt =
1237 if not (Config.get ctxt debug) then []
1240 val prt_term = Syntax.pretty_term ctxt;
1243 val {structs, ...} = Local_Syntax.idents_of (syntax_of ctxt);
1245 if null structs then []
1246 else [Pretty.block (Pretty.str "structures:" :: Pretty.brk 1 ::
1247 Pretty.commas (map Pretty.str structs))];
1250 fun prt_fix (x, x') =
1251 if x = x' then Pretty.str x
1252 else Pretty.block [Pretty.str x, Pretty.str " =", Pretty.brk 1, prt_term (Syntax.free x')];
1254 filter_out ((can Name.dest_internal orf member (op =) structs) o #1)
1255 (Variable.dest_fixes ctxt);
1257 if null fixes then []
1258 else [Pretty.block (Pretty.str "fixed variables:" :: Pretty.brk 1 ::
1259 Pretty.commas (map prt_fix fixes))];
1262 val prems = Assumption.all_prems_of ctxt;
1264 if null prems then []
1265 else [Pretty.big_list "prems:" (map (Display.pretty_thm ctxt) prems)];
1266 in prt_structs @ prt_fixes @ prt_prems end;
1271 fun pretty_context ctxt =
1273 val verbose = Config.get ctxt verbose;
1274 fun verb f x = if verbose then f (x ()) else [];
1276 val prt_term = Syntax.pretty_term ctxt;
1277 val prt_typ = Syntax.pretty_typ ctxt;
1278 val prt_sort = Syntax.pretty_sort ctxt;
1281 val pretty_thy = Pretty.block
1282 [Pretty.str "theory:", Pretty.brk 1, Context.pretty_thy (theory_of ctxt)];
1285 fun prt_atom prt prtT (x, X) = Pretty.block
1286 [prt x, Pretty.str " ::", Pretty.brk 1, prtT X];
1288 fun prt_var (x, ~1) = prt_term (Syntax.free x)
1289 | prt_var xi = prt_term (Syntax.var xi);
1291 fun prt_varT (x, ~1) = prt_typ (TFree (x, []))
1292 | prt_varT xi = prt_typ (TVar (xi, []));
1294 val prt_defT = prt_atom prt_var prt_typ;
1295 val prt_defS = prt_atom prt_varT prt_sort;
1297 val (types, sorts) = Variable.constraints_of ctxt;
1299 verb single (K pretty_thy) @
1301 verb (pretty_abbrevs false) (K ctxt) @
1302 verb pretty_binds (K ctxt) @
1303 verb pretty_lthms (K ctxt) @
1304 verb pretty_cases (K ctxt) @
1305 verb single (fn () => Pretty.big_list "type constraints:" (map prt_defT (Vartab.dest types))) @
1306 verb single (fn () => Pretty.big_list "default sorts:" (map prt_defS (Vartab.dest sorts)))
1311 val show_abbrevs = Proof_Context.show_abbrevs;