maintain generic context naming in structure Name_Space (NB: empty = default_naming, init = local_naming);
more explicit Context.generic for Name_Space.declare/define and derivatives (NB: naming changed after Proof_Context.init_global);
prefer Context.pretty in low-level operations of structure Sorts/Type (defer full Syntax.init_pretty until error output);
simplified signatures;
1 (* Title: Pure/Isar/proof.ML
2 Author: Markus Wenzel, TU Muenchen
4 The Isar/VM proof language interpreter: maintains a structured flow of
5 context elements, goals, refinements, and facts.
10 type context = Proof.context
11 type method = Method.method
13 val init: context -> state
14 val level: state -> int
15 val assert_bottom: bool -> state -> state
16 val context_of: state -> context
17 val theory_of: state -> theory
18 val map_context: (context -> context) -> state -> state
19 val map_context_result : (context -> 'a * context) -> state -> 'a * state
20 val map_contexts: (context -> context) -> state -> state
21 val propagate_ml_env: state -> state
22 val bind_terms: (indexname * term option) list -> state -> state
23 val put_thms: bool -> string * thm list option -> state -> state
24 val the_facts: state -> thm list
25 val the_fact: state -> thm
26 val put_facts: thm list option -> state -> state
27 val assert_forward: state -> state
28 val assert_chain: state -> state
29 val assert_forward_or_chain: state -> state
30 val assert_backward: state -> state
31 val assert_no_chain: state -> state
32 val enter_forward: state -> state
33 val goal_message: (unit -> Pretty.T) -> state -> state
34 val pretty_state: int -> state -> Pretty.T list
35 val pretty_goals: bool -> state -> Pretty.T list
36 val refine: Method.text -> state -> state Seq.seq
37 val refine_end: Method.text -> state -> state Seq.seq
38 val refine_insert: thm list -> state -> state
39 val refine_goals: (context -> thm -> unit) -> context -> thm list -> state -> state Seq.seq
40 val raw_goal: state -> {context: context, facts: thm list, goal: thm}
41 val goal: state -> {context: context, facts: thm list, goal: thm}
42 val simple_goal: state -> {context: context, goal: thm}
43 val status_markup: state -> Markup.T
44 val let_bind: (term list * term) list -> state -> state
45 val let_bind_cmd: (string list * string) list -> state -> state
46 val write: Syntax.mode -> (term * mixfix) list -> state -> state
47 val write_cmd: Syntax.mode -> (string * mixfix) list -> state -> state
48 val fix: (binding * typ option * mixfix) list -> state -> state
49 val fix_cmd: (binding * string option * mixfix) list -> state -> state
50 val assm: Assumption.export ->
51 (Thm.binding * (term * term list) list) list -> state -> state
52 val assm_cmd: Assumption.export ->
53 (Attrib.binding * (string * string list) list) list -> state -> state
54 val assume: (Thm.binding * (term * term list) list) list -> state -> state
55 val assume_cmd: (Attrib.binding * (string * string list) list) list -> state -> state
56 val presume: (Thm.binding * (term * term list) list) list -> state -> state
57 val presume_cmd: (Attrib.binding * (string * string list) list) list -> state -> state
58 val def: (Thm.binding * ((binding * mixfix) * (term * term list))) list -> state -> state
59 val def_cmd: (Attrib.binding * ((binding * mixfix) * (string * string list))) list -> state -> state
60 val chain: state -> state
61 val chain_facts: thm list -> state -> state
62 val note_thmss: (Thm.binding * (thm list * attribute list) list) list -> state -> state
63 val note_thmss_cmd: (Attrib.binding * (Facts.ref * Attrib.src list) list) list -> state -> state
64 val from_thmss: ((thm list * attribute list) list) list -> state -> state
65 val from_thmss_cmd: ((Facts.ref * Attrib.src list) list) list -> state -> state
66 val with_thmss: ((thm list * attribute list) list) list -> state -> state
67 val with_thmss_cmd: ((Facts.ref * Attrib.src list) list) list -> state -> state
68 val using: ((thm list * attribute list) list) list -> state -> state
69 val using_cmd: ((Facts.ref * Attrib.src list) list) list -> state -> state
70 val unfolding: ((thm list * attribute list) list) list -> state -> state
71 val unfolding_cmd: ((Facts.ref * Attrib.src list) list) list -> state -> state
72 val invoke_case: string * binding option list * attribute list -> state -> state
73 val invoke_case_cmd: string * binding option list * Attrib.src list -> state -> state
74 val begin_block: state -> state
75 val next_block: state -> state
76 val end_block: state -> state
77 val begin_notepad: Proof.context -> state
78 val end_notepad: state -> Proof.context
79 val proof: Method.text option -> state -> state Seq.seq
80 val defer: int option -> state -> state Seq.seq
81 val prefer: int -> state -> state Seq.seq
82 val apply: Method.text -> state -> state Seq.seq
83 val apply_end: Method.text -> state -> state Seq.seq
84 val local_goal: (context -> ((string * string) * (string * thm list) list) -> unit) ->
85 (theory -> 'a -> attribute) ->
86 ('b list -> context -> (term list list * (context -> context)) * context) ->
87 string -> Method.text option -> (thm list list -> state -> state) ->
88 ((binding * 'a list) * 'b) list -> state -> state
89 val local_qed: Method.text option * bool -> state -> state
90 val theorem: Method.text option -> (thm list list -> context -> context) ->
91 (term * term list) list list -> context -> state
92 val theorem_cmd: Method.text option -> (thm list list -> context -> context) ->
93 (string * string list) list list -> context -> state
94 val global_qed: Method.text option * bool -> state -> context
95 val local_terminal_proof: Method.text * Method.text option -> state -> state
96 val local_default_proof: state -> state
97 val local_immediate_proof: state -> state
98 val local_skip_proof: bool -> state -> state
99 val local_done_proof: state -> state
100 val global_terminal_proof: Method.text * Method.text option -> state -> context
101 val global_default_proof: state -> context
102 val global_immediate_proof: state -> context
103 val global_skip_proof: bool -> state -> context
104 val global_done_proof: state -> context
105 val have: Method.text option -> (thm list list -> state -> state) ->
106 (Thm.binding * (term * term list) list) list -> bool -> state -> state
107 val have_cmd: Method.text option -> (thm list list -> state -> state) ->
108 (Attrib.binding * (string * string list) list) list -> bool -> state -> state
109 val show: Method.text option -> (thm list list -> state -> state) ->
110 (Thm.binding * (term * term list) list) list -> bool -> state -> state
111 val show_cmd: Method.text option -> (thm list list -> state -> state) ->
112 (Attrib.binding * (string * string list) list) list -> bool -> state -> state
113 val schematic_goal: state -> bool
114 val is_relevant: state -> bool
115 val local_future_proof: (state -> ('a * state) Future.future) ->
116 state -> 'a Future.future * state
117 val global_future_proof: (state -> ('a * Proof.context) Future.future) ->
118 state -> 'a Future.future * context
119 val local_future_terminal_proof: Method.text * Method.text option -> bool -> state -> state
120 val global_future_terminal_proof: Method.text * Method.text option -> bool -> state -> context
123 structure Proof: PROOF =
126 type context = Proof.context;
127 type method = Method.method;
134 datatype mode = Forward | Chain | Backward;
137 State of node Stack.T
141 facts: thm list option,
146 {statement: (string * Position.T) * term list list * term,
147 (*goal kind and statement (starting with vars), initial proposition*)
148 messages: (unit -> Pretty.T) list, (*persistent messages (hints etc.)*)
149 using: thm list, (*goal facts*)
150 goal: thm, (*subgoals ==> statement*)
151 before_qed: Method.text option,
153 (thm list list -> state -> state) *
154 (thm list list -> context -> context)};
156 fun make_goal (statement, messages, using, goal, before_qed, after_qed) =
157 Goal {statement = statement, messages = messages, using = using, goal = goal,
158 before_qed = before_qed, after_qed = after_qed};
160 fun make_node (context, facts, mode, goal) =
161 Node {context = context, facts = facts, mode = mode, goal = goal};
163 fun map_node f (Node {context, facts, mode, goal}) =
164 make_node (f (context, facts, mode, goal));
167 Proof_Context.set_stmt true #>
168 Proof_Context.map_naming (K Name_Space.local_naming);
171 State (Stack.init (make_node (init_context ctxt, NONE, Forward, NONE)));
173 fun current (State st) = Stack.top st |> (fn Node node => node);
174 fun map_current f (State st) = State (Stack.map_top (map_node f) st);
175 fun map_all f (State st) = State (Stack.map_all (map_node f) st);
179 (** basic proof state operations **)
181 (* block structure *)
183 fun open_block (State st) = State (Stack.push st);
185 fun close_block (State st) = State (Stack.pop st)
186 handle Empty => error "Unbalanced block parentheses";
188 fun level (State st) = Stack.level st;
190 fun assert_bottom b state =
191 let val b' = (level state <= 2) in
192 if b andalso not b' then error "Not at bottom of proof!"
193 else if not b andalso b' then error "Already at bottom of proof!"
200 val context_of = #context o current;
201 val theory_of = Proof_Context.theory_of o context_of;
204 map_current (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
206 fun map_context_result f state =
207 f (context_of state) ||> (fn ctxt => map_context (K ctxt) state);
209 fun map_contexts f = map_all (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
211 fun propagate_ml_env state = map_contexts
212 (Context.proof_map (ML_Env.inherit (Context.Proof (context_of state)))) state;
214 val bind_terms = map_context o Proof_Context.bind_terms;
215 val put_thms = map_context oo Proof_Context.put_thms;
220 val get_facts = #facts o current;
222 fun the_facts state =
223 (case get_facts state of SOME facts => facts
224 | NONE => error "No current facts available");
227 (case the_facts state of [thm] => thm
228 | _ => error "Single theorem expected");
230 fun put_facts facts =
231 map_current (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal)) #>
232 put_thms true (Auto_Bind.thisN, facts);
234 fun these_factss more_facts (named_factss, state) =
235 (named_factss, state |> put_facts (SOME (maps snd named_factss @ more_facts)));
237 fun export_facts inner outer =
238 (case get_facts inner of
239 NONE => put_facts NONE outer
242 |> Proof_Context.export (context_of inner) (context_of outer)
243 |> (fn ths => put_facts (SOME ths) outer));
248 val get_mode = #mode o current;
249 fun put_mode mode = map_current (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));
251 val mode_name = (fn Forward => "state" | Chain => "chain" | Backward => "prove");
253 fun assert_mode pred state =
254 let val mode = get_mode state in
255 if pred mode then state
256 else error ("Illegal application of proof command in " ^ quote (mode_name mode) ^ " mode")
259 val assert_forward = assert_mode (fn mode => mode = Forward);
260 val assert_chain = assert_mode (fn mode => mode = Chain);
261 val assert_forward_or_chain = assert_mode (fn mode => mode = Forward orelse mode = Chain);
262 val assert_backward = assert_mode (fn mode => mode = Backward);
263 val assert_no_chain = assert_mode (fn mode => mode <> Chain);
265 val enter_forward = put_mode Forward;
266 val enter_chain = put_mode Chain;
267 val enter_backward = put_mode Backward;
272 fun current_goal state =
273 (case current state of
274 {context, goal = SOME (Goal goal), ...} => (context, goal)
275 | _ => error "No current goal!");
277 fun assert_current_goal g state =
278 let val g' = can current_goal state in
279 if g andalso not g' then error "No goal in this block!"
280 else if not g andalso g' then error "Goal present in this block!"
284 fun put_goal goal = map_current (fn (ctxt, using, mode, _) => (ctxt, using, mode, goal));
286 val before_qed = #before_qed o #2 o current_goal;
291 fun map_goal f g (State (Node {context, facts, mode, goal = SOME goal}, nodes)) =
293 val Goal {statement, messages, using, goal, before_qed, after_qed} = goal;
294 val goal' = make_goal (g (statement, messages, using, goal, before_qed, after_qed));
295 in State (make_node (f context, facts, mode, SOME goal'), nodes) end
296 | map_goal f g (State (nd, node :: nodes)) =
297 let val State (node', nodes') = map_goal f g (State (node, nodes))
298 in map_context f (State (nd, node' :: nodes')) end
299 | map_goal _ _ state = state;
301 fun set_goal goal = map_goal I (fn (statement, _, using, _, before_qed, after_qed) =>
302 (statement, [], using, goal, before_qed, after_qed));
304 fun goal_message msg = map_goal I (fn (statement, messages, using, goal, before_qed, after_qed) =>
305 (statement, msg :: messages, using, goal, before_qed, after_qed));
307 fun using_facts using = map_goal I (fn (statement, _, _, goal, before_qed, after_qed) =>
308 (statement, [], using, goal, before_qed, after_qed));
312 (case try current_goal state of
313 SOME (ctxt, goal) => (ctxt, (i, goal))
314 | NONE => find (i + 1) (close_block state handle ERROR _ => error "No goal present"));
315 in val find_goal = find 0 end;
318 let val (ctxt, (_, {using, goal, ...})) = find_goal state
319 in (ctxt, (using, goal)) end;
325 fun pretty_facts _ _ NONE = []
326 | pretty_facts s ctxt (SOME ths) =
327 [Pretty.big_list (s ^ "this:") (map (Display.pretty_thm ctxt) ths), Pretty.str ""];
329 fun pretty_state nr state =
331 val {context = ctxt, facts, mode, goal = _} = current state;
332 val verbose = Config.get ctxt Proof_Context.verbose;
335 | levels_up 1 = "1 level up"
336 | levels_up i = string_of_int i ^ " levels up";
339 | subgoals 1 = "1 subgoal"
340 | subgoals n = string_of_int n ^ " subgoals";
342 fun description strs =
343 (case filter_out (fn s => s = "") strs of [] => ""
344 | strs' => enclose " (" ")" (commas strs'));
346 fun prt_goal (SOME (_, (i,
347 {statement = ((_, pos), _, _), messages, using, goal, before_qed = _, after_qed = _}))) =
348 pretty_facts "using " ctxt
349 (if mode <> Backward orelse null using then NONE else SOME using) @
350 [Pretty.str ("goal" ^
351 description [levels_up (i div 2), subgoals (Thm.nprems_of goal)] ^ ":")] @
352 Goal_Display.pretty_goals ctxt goal @
353 (map (fn msg => Position.setmp_thread_data pos msg ()) (rev messages))
354 | prt_goal NONE = [];
357 if verbose orelse mode = Forward then Proof_Context.pretty_context ctxt
358 else if mode = Backward then Proof_Context.pretty_ctxt ctxt
361 [Pretty.str ("proof (" ^ mode_name mode ^ "): step " ^ string_of_int nr ^
362 (if verbose then ", depth " ^ string_of_int (level state div 2 - 1) else "")),
364 (if null prt_ctxt then [] else prt_ctxt @ [Pretty.str ""]) @
365 (if verbose orelse mode = Forward then
366 pretty_facts "" ctxt facts @ prt_goal (try find_goal state)
367 else if mode = Chain then pretty_facts "picking " ctxt facts
368 else prt_goal (try find_goal state))
371 fun pretty_goals main state =
373 val (_, (_, goal)) = get_goal state;
374 val ctxt = context_of state
375 |> Config.put Goal_Display.show_main_goal main
376 |> Config.put Goal_Display.goals_total false;
377 in Goal_Display.pretty_goals ctxt goal end;
383 (* refine via method *)
387 fun goalN i = "goal" ^ string_of_int i;
388 fun goals st = map goalN (1 upto Thm.nprems_of st);
390 fun no_goal_cases st = map (rpair NONE) (goals st);
393 Rule_Cases.make_common (Thm.theory_of_thm st, Thm.prop_of st) (map (rpair [] o rpair []) (goals st));
395 fun apply_method current_context meth state =
397 val (goal_ctxt, (_, {statement, messages = _, using, goal, before_qed, after_qed})) =
399 val ctxt = if current_context then context_of state else goal_ctxt;
401 Method.apply meth ctxt using goal |> Seq.map (fn (meth_cases, goal') =>
404 (Proof_Context.add_cases false (no_goal_cases goal @ goal_cases goal') #>
405 Proof_Context.add_cases true meth_cases)
406 (K (statement, [], using, goal', before_qed, after_qed)))
409 fun select_goals n meth state =
411 |> (#2 o #2 o get_goal)
412 |> ALLGOALS Goal.conjunction_tac
413 |> Seq.maps (fn goal =>
415 |> Seq.lift set_goal (Goal.extract 1 n goal |> Seq.maps (Goal.conjunction_tac 1))
417 |> Seq.maps (fn state' => state'
418 |> Seq.lift set_goal (Goal.retrofit 1 n (#2 (#2 (get_goal state'))) goal))
419 |> Seq.maps (apply_method true (K Method.succeed)));
421 fun apply_text cc text state =
423 val thy = theory_of state;
425 fun eval (Method.Basic m) = apply_method cc m
426 | eval (Method.Source src) = apply_method cc (Method.method thy src)
427 | eval (Method.Source_i src) = apply_method cc (Method.method_i thy src)
428 | eval (Method.Then txts) = Seq.EVERY (map eval txts)
429 | eval (Method.Orelse txts) = Seq.FIRST (map eval txts)
430 | eval (Method.Try txt) = Seq.TRY (eval txt)
431 | eval (Method.Repeat1 txt) = Seq.REPEAT1 (eval txt)
432 | eval (Method.SelectGoals (n, txt)) = select_goals n (eval txt);
433 in eval text state end;
437 val refine = apply_text true;
438 val refine_end = apply_text false;
439 fun refine_insert ths = Seq.hd o refine (Method.Basic (K (Method.insert ths)));
444 (* refine via sub-proof *)
448 fun finish_tac 0 = K all_tac
450 Goal.norm_hhf_tac THEN'
451 SUBGOAL (fn (goal, i) =>
452 if can Logic.unprotect (Logic.strip_assums_concl goal) then
453 Tactic.etac Drule.protectI i THEN finish_tac (n - 1) i
454 else finish_tac (n - 1) (i + 1));
457 Goal.norm_hhf_tac THEN'
458 Tactic.rtac rule THEN'
459 finish_tac (Thm.nprems_of rule);
461 fun FINDGOAL tac st =
462 let fun find i n = if i > n then Seq.fail else Seq.APPEND (tac i, find (i + 1) n)
463 in find 1 (Thm.nprems_of st) st end;
467 fun refine_goals print_rule inner raw_rules state =
469 val (outer, (_, goal)) = get_goal state;
470 fun refine rule st = (print_rule outer rule; FINDGOAL (goal_tac rule) st);
473 |> Proof_Context.goal_export inner outer
474 |> (fn rules => Seq.lift set_goal (EVERY (map refine rules) goal) state)
482 fun conclude_goal ctxt goal propss =
484 val thy = Proof_Context.theory_of ctxt;
485 val string_of_term = Syntax.string_of_term ctxt;
486 val string_of_thm = Display.string_of_thm ctxt;
488 val ngoals = Thm.nprems_of goal;
489 val _ = ngoals = 0 orelse error (Pretty.string_of (Pretty.chunks
490 (Goal_Display.pretty_goals ctxt goal @
491 [Pretty.str (string_of_int ngoals ^ " unsolved goal(s)!")])));
493 val extra_hyps = Assumption.extra_hyps ctxt goal;
494 val _ = null extra_hyps orelse
495 error ("Additional hypotheses:\n" ^ cat_lines (map string_of_term extra_hyps));
497 fun lost_structure () = error ("Lost goal structure:\n" ^ string_of_thm goal);
499 val th = Goal.conclude
500 (if length (flat propss) > 1 then Thm.norm_proof goal else goal)
501 handle THM _ => lost_structure ();
502 val goal_propss = filter_out null propss;
504 Conjunction.elim_balanced (length goal_propss) th
505 |> map2 Conjunction.elim_balanced (map length goal_propss)
506 handle THM _ => lost_structure ();
507 val _ = Unify.matches_list thy (flat goal_propss) (map Thm.prop_of (flat results)) orelse
508 error ("Proved a different theorem:\n" ^ string_of_thm th);
509 val _ = Thm.check_shyps (Variable.sorts_of ctxt) th;
511 fun recover_result ([] :: pss) thss = [] :: recover_result pss thss
512 | recover_result (_ :: pss) (ths :: thss) = ths :: recover_result pss thss
513 | recover_result [] [] = []
514 | recover_result _ _ = lost_structure ();
515 in recover_result propss results end;
518 (* goal views -- corresponding to methods *)
521 let val (ctxt, (facts, goal)) = get_goal state
522 in {context = ctxt, facts = facts, goal = goal} end;
524 val goal = raw_goal o refine_insert [];
526 fun simple_goal state =
528 val (_, (facts, _)) = get_goal state;
529 val (ctxt, (_, goal)) = get_goal (refine_insert facts state);
530 in {context = ctxt, goal = goal} end;
532 fun status_markup state =
533 (case try goal state of
534 SOME {goal, ...} => Isabelle_Markup.proof_state (Thm.nprems_of goal)
535 | NONE => Markup.empty);
539 (*** structured proof commands ***)
541 (** context elements **)
547 fun gen_bind bind args state =
550 |> map_context (bind true args #> snd)
555 val let_bind = gen_bind Proof_Context.match_bind_i;
556 val let_bind_cmd = gen_bind Proof_Context.match_bind;
561 (* concrete syntax *)
565 fun gen_write prep_arg mode args =
567 #> map_context (fn ctxt => ctxt |> Proof_Context.notation true mode (map (prep_arg ctxt) args))
572 val write = gen_write (K I);
575 gen_write (fn ctxt => fn (c, mx) =>
576 (Proof_Context.read_const ctxt false (Mixfix.mixfixT mx) c, mx));
585 fun gen_fix prep_vars args =
587 #> map_context (fn ctxt => snd (Proof_Context.add_fixes (fst (prep_vars args ctxt)) ctxt))
592 val fix = gen_fix Proof_Context.cert_vars;
593 val fix_cmd = gen_fix Proof_Context.read_vars;
602 fun gen_assume asm prep_att exp args state =
605 |> map_context_result (asm exp (Attrib.map_specs (map (prep_att (theory_of state))) args))
606 |> these_factss [] |> #2;
610 val assm = gen_assume Proof_Context.add_assms_i (K I);
611 val assm_cmd = gen_assume Proof_Context.add_assms Attrib.attribute;
612 val assume = assm Assumption.assume_export;
613 val assume_cmd = assm_cmd Assumption.assume_export;
614 val presume = assm Assumption.presume_export;
615 val presume_cmd = assm_cmd Assumption.presume_export;
624 fun gen_def prep_att prep_vars prep_binds args state =
626 val _ = assert_forward state;
627 val thy = theory_of state;
629 val (raw_name_atts, (raw_vars, raw_rhss)) = args |> split_list ||> split_list;
630 val name_atts = map (apsnd (map (prep_att thy))) raw_name_atts;
633 |> map_context_result (prep_vars (map (fn (x, mx) => (x, NONE, mx)) raw_vars))
634 |>> map (fn (x, _, mx) => (x, mx))
636 map_context_result (prep_binds false (map swap raw_rhss))
637 #-> (fn rhss => map_context_result (Local_Defs.add_defs (vars ~~ (name_atts ~~ rhss)))))
638 |-> (put_facts o SOME o map (#2 o #2))
643 val def = gen_def (K I) Proof_Context.cert_vars Proof_Context.match_bind_i;
644 val def_cmd = gen_def Attrib.attribute Proof_Context.read_vars Proof_Context.match_bind;
654 fun clean_facts ctxt =
655 put_facts (SOME (filter_out Thm.is_dummy (the_facts ctxt))) ctxt;
662 fun chain_facts facts =
663 put_facts (SOME facts)
669 fun no_binding args = map (pair (Binding.empty, [])) args;
673 fun gen_thmss more_facts opt_chain opt_result prep_atts prep_fact args state =
676 |> map_context_result (Proof_Context.note_thmss ""
677 (Attrib.map_facts_refs
678 (map (prep_atts (theory_of state)))
679 (prep_fact (context_of state)) args))
680 |> these_factss (more_facts state)
686 val note_thmss = gen_thmss (K []) I #2 (K I) (K I);
687 val note_thmss_cmd = gen_thmss (K []) I #2 Attrib.attribute Proof_Context.get_fact;
689 val from_thmss = gen_thmss (K []) chain #2 (K I) (K I) o no_binding;
690 val from_thmss_cmd = gen_thmss (K []) chain #2 Attrib.attribute Proof_Context.get_fact o no_binding;
692 val with_thmss = gen_thmss the_facts chain #2 (K I) (K I) o no_binding;
693 val with_thmss_cmd = gen_thmss the_facts chain #2 Attrib.attribute Proof_Context.get_fact o no_binding;
695 val local_results = gen_thmss (K []) I I (K I) (K I) o map (apsnd Thm.simple_fact);
700 (* using/unfolding *)
704 fun gen_using f g prep_att prep_fact args state =
707 |> map_context_result
708 (Proof_Context.note_thmss ""
709 (Attrib.map_facts_refs (map (prep_att (theory_of state))) (prep_fact (context_of state))
711 |> (fn (named_facts, state') =>
712 state' |> map_goal I (fn (statement, _, using, goal, before_qed, after_qed) =>
714 val ctxt = context_of state';
715 val ths = maps snd named_facts;
716 in (statement, [], f ctxt ths using, g ctxt ths goal, before_qed, after_qed) end));
718 fun append_using _ ths using = using @ filter_out Thm.is_dummy ths;
719 fun unfold_using ctxt ths = map (Local_Defs.unfold ctxt ths);
720 val unfold_goals = Local_Defs.unfold_goals;
724 val using = gen_using append_using (K (K I)) (K I) (K I);
725 val using_cmd = gen_using append_using (K (K I)) Attrib.attribute Proof_Context.get_fact;
726 val unfolding = gen_using unfold_using unfold_goals (K I) (K I);
727 val unfolding_cmd = gen_using unfold_using unfold_goals Attrib.attribute Proof_Context.get_fact;
736 fun qualified_binding a =
737 Binding.qualify true (Long_Name.qualifier a) (Binding.name (Long_Name.base_name a));
739 fun gen_invoke_case prep_att (name, xs, raw_atts) state =
741 val atts = map (prep_att (theory_of state)) raw_atts;
742 val (asms, state') = state |> map_context_result (fn ctxt =>
743 ctxt |> Proof_Context.apply_case (Proof_Context.get_case ctxt name xs));
744 val assumptions = asms |> map (fn (a, ts) => ((qualified_binding a, atts), map (rpair []) ts));
747 |> assume assumptions
748 |> bind_terms Auto_Bind.no_facts
749 |> `the_facts |-> (fn thms => note_thmss [((Binding.name name, []), [(thms, [])])])
754 val invoke_case = gen_invoke_case (K I);
755 val invoke_case_cmd = gen_invoke_case Attrib.attribute;
761 (** proof structure **)
778 fun end_block state =
781 |> assert_bottom false
783 |> assert_current_goal false
785 |> export_facts state;
793 #> map_context (Variable.set_body true)
798 #> assert_bottom true
800 #> assert_current_goal false
809 #> refine (the_default Method.default_text opt_text)
810 #> Seq.map (using_facts [] #> enter_forward);
812 fun end_proof bot txt state =
817 |> assert_current_goal true
819 |> `before_qed |-> (refine o the_default Method.succeed_text)
820 |> Seq.maps (refine (Method.finish_text txt));
822 fun check_result msg sq =
827 fun check_finish sq = check_result "Failed to finish proof" sq;
830 (* unstructured refinement *)
832 fun defer i = assert_no_chain #> refine (Method.Basic (K (Method.defer i)));
833 fun prefer i = assert_no_chain #> refine (Method.Basic (K (Method.prefer i)));
835 fun apply text = assert_backward #> refine text #> Seq.map (using_facts []);
836 fun apply_end text = assert_forward #> refine_end text;
847 can (dest_TVar o Logic.dest_type o Logic.dest_term) orf
848 can (dest_Var o Logic.dest_term);
850 fun implicit_vars props =
852 val (var_props, _) = take_prefix is_var props;
853 val explicit_vars = fold Term.add_vars var_props [];
854 val vars = filter_out (member (op =) explicit_vars) (fold Term.add_vars props []);
855 in map (Logic.mk_term o Var) vars end;
858 refine (Method.Basic (K (RAW_METHOD
859 (K (HEADGOAL (PRECISE_CONJUNCTS n
860 (HEADGOAL (CONJUNCTS (ALLGOALS (rtac Drule.termI))))))))))
865 fun generic_goal prepp kind before_qed after_qed raw_propp state =
867 val thy = theory_of state;
868 val cert = Thm.cterm_of thy;
869 val chaining = can assert_chain state;
870 val pos = Position.thread_data ();
872 val ((propss, after_ctxt), goal_state) =
874 |> assert_forward_or_chain
877 |> map_context_result (prepp raw_propp);
878 val props = flat propss;
880 val vars = implicit_vars props;
881 val propss' = vars :: propss;
882 val goal_propss = filter_out null propss';
884 cert (Logic.mk_conjunction_balanced (map Logic.mk_conjunction_balanced goal_propss))
885 |> Thm.weaken_sorts (Variable.sorts_of (context_of goal_state));
886 val statement = ((kind, pos), propss', Thm.term_of goal);
887 val after_qed' = after_qed |>> (fn after_local =>
888 fn results => map_context after_ctxt #> after_local results);
891 |> map_context (init_context #> Variable.set_body true)
892 |> put_goal (SOME (make_goal (statement, [], [], Goal.init goal, before_qed, after_qed')))
893 |> map_context (Proof_Context.auto_bind_goal props)
894 |> chaining ? (`the_facts #-> using_facts)
899 |> not (null vars) ? refine_terms (length goal_propss)
900 |> null props ? (refine (Method.Basic Method.assumption) #> Seq.hd)
903 fun generic_qed after_ctxt state =
905 val (goal_ctxt, {statement = (_, stmt, _), goal, after_qed, ...}) = current_goal state;
906 val outer_state = state |> close_block;
907 val outer_ctxt = context_of outer_state;
911 |> Variable.exportT_terms goal_ctxt outer_ctxt;
913 tl (conclude_goal goal_ctxt goal stmt)
914 |> burrow (Proof_Context.export goal_ctxt outer_ctxt);
917 |> map_context (after_ctxt props)
918 |> pair (after_qed, results)
926 fun local_goal print_results prep_att prepp kind before_qed after_qed stmt state =
928 val thy = theory_of state;
929 val ((names, attss), propp) =
930 Attrib.map_specs (map (prep_att thy)) stmt |> split_list |>> split_list;
932 fun after_qed' results =
933 local_results ((names ~~ attss) ~~ results)
934 #-> (fn res => tap (fn st => print_results (context_of st) ((kind, ""), res) : unit))
935 #> after_qed results;
938 |> generic_goal prepp kind before_qed (after_qed', K I) propp
939 |> tap (Variable.warn_extra_tfrees (context_of state) o context_of)
944 #> Seq.map (generic_qed Proof_Context.auto_bind_facts #->
945 (fn ((after_qed, _), results) => after_qed results));
947 fun local_qed txt = local_qeds txt #> check_finish;
952 fun prepp_auto_fixes prepp args =
954 (fn ((propss, a), ctxt) => ((propss, a), (fold o fold) Variable.auto_fixes propss ctxt));
956 fun global_goal prepp before_qed after_qed propp =
958 generic_goal (prepp_auto_fixes prepp) "" before_qed (K I, after_qed) propp;
960 val theorem = global_goal Proof_Context.bind_propp_schematic_i;
961 val theorem_cmd = global_goal Proof_Context.bind_propp_schematic;
963 fun global_qeds txt =
965 #> Seq.map (generic_qed (K I) #> (fn (((_, after_qed), results), state) =>
966 after_qed results (context_of state)));
968 fun global_qed txt = global_qeds txt #> check_finish;
971 (* concluding steps *)
973 fun terminal_proof qed initial terminal =
974 proof (SOME initial) #> Seq.maps (qed terminal) #> check_finish;
976 fun local_terminal_proof (text, opt_text) = terminal_proof local_qeds text (opt_text, true);
977 val local_default_proof = local_terminal_proof (Method.default_text, NONE);
978 val local_immediate_proof = local_terminal_proof (Method.this_text, NONE);
979 fun local_skip_proof int = local_terminal_proof (Method.sorry_text int, NONE);
980 val local_done_proof = terminal_proof local_qeds Method.done_text (NONE, false);
982 fun global_terminal_proof (text, opt_text) = terminal_proof global_qeds text (opt_text, true);
983 val global_default_proof = global_terminal_proof (Method.default_text, NONE);
984 val global_immediate_proof = global_terminal_proof (Method.this_text, NONE);
985 fun global_skip_proof int = global_terminal_proof (Method.sorry_text int, NONE);
986 val global_done_proof = terminal_proof global_qeds Method.done_text (NONE, false);
989 (* common goal statements *)
993 fun gen_have prep_att prepp before_qed after_qed stmt int =
994 local_goal (Proof_Display.print_results Isabelle_Markup.state int)
995 prep_att prepp "have" before_qed after_qed stmt;
997 fun gen_show prep_att prepp before_qed after_qed stmt int state =
999 val testing = Unsynchronized.ref false;
1000 val rule = Unsynchronized.ref (NONE: thm option);
1002 "Local statement will fail to refine any pending goal" ::
1003 (case ! rule of NONE => [] | SOME th => [Proof_Display.string_of_rule ctxt "Failed" th])
1006 fun print_results ctxt res =
1007 if ! testing then ()
1008 else Proof_Display.print_results Isabelle_Markup.state int ctxt res;
1009 fun print_rule ctxt th =
1010 if ! testing then rule := SOME th
1013 (Markup.markup Isabelle_Markup.state (Proof_Display.string_of_rule ctxt "Successful" th))
1016 try (local_skip_proof true)
1017 |> Unsynchronized.setmp testing true
1018 |> Exn.interruptible_capture;
1020 fun after_qed' results =
1021 refine_goals print_rule (context_of state) (flat results)
1022 #> check_result "Failed to refine any pending goal"
1023 #> after_qed results;
1026 |> local_goal print_results prep_att prepp "show" before_qed after_qed' stmt
1027 |> int ? (fn goal_state =>
1028 (case test_proof goal_state of
1029 Exn.Res (SOME _) => goal_state
1030 | Exn.Res NONE => error (fail_msg (context_of goal_state))
1031 | Exn.Exn exn => raise Exn.EXCEPTIONS ([exn, ERROR (fail_msg (context_of goal_state))])))
1036 val have = gen_have (K I) Proof_Context.bind_propp_i;
1037 val have_cmd = gen_have Attrib.attribute Proof_Context.bind_propp;
1038 val show = gen_show (K I) Proof_Context.bind_propp_i;
1039 val show_cmd = gen_show Attrib.attribute Proof_Context.bind_propp;
1045 (** future proofs **)
1047 (* relevant proof states *)
1049 fun is_schematic t =
1050 Term.exists_subterm Term.is_Var t orelse
1051 Term.exists_type (Term.exists_subtype Term.is_TVar) t;
1053 fun schematic_goal state =
1054 let val (_, (_, {statement = (_, _, prop), ...})) = find_goal state
1055 in is_schematic prop end;
1057 fun is_relevant state =
1058 (case try find_goal state of
1060 | SOME (_, (_, {statement = (_, _, prop), goal, ...})) =>
1061 is_schematic prop orelse not (Logic.protect prop aconv Thm.concl_of goal));
1068 fun future_proof done get_context fork_proof state =
1070 val _ = assert_backward state;
1071 val (goal_ctxt, (_, goal)) = find_goal state;
1072 val {statement as (kind, _, prop), messages, using, goal, before_qed, after_qed} = goal;
1073 val goal_txt = prop :: map Thm.term_of (Assumption.all_assms_of goal_ctxt);
1075 val _ = is_relevant state andalso error "Cannot fork relevant proof";
1077 val prop' = Logic.protect prop;
1078 val statement' = (kind, [[], [prop']], prop');
1079 val goal' = Thm.adjust_maxidx_thm (Thm.maxidx_of goal)
1080 (Drule.comp_no_flatten (goal, Thm.nprems_of goal) 1 Drule.protectI);
1082 fun after_local' [[th]] = put_thms false (Auto_Bind.thisN, SOME [th]);
1083 fun after_global' [[th]] = Proof_Context.put_thms false (Auto_Bind.thisN, SOME [th]);
1084 val after_qed' = (after_local', after_global');
1085 val this_name = Proof_Context.full_name goal_ctxt (Binding.name Auto_Bind.thisN);
1089 |> map_contexts (fold Variable.declare_term goal_txt)
1090 |> map_goal I (K (statement', messages, using, goal', before_qed, after_qed'))
1093 val future_thm = result_ctxt |> Future.map (fn (_, x) =>
1094 Proof_Context.get_fact_single (get_context x) (Facts.named this_name));
1095 val finished_goal = Goal.future_result goal_ctxt future_thm prop';
1098 |> map_goal I (K (statement, messages, using, finished_goal, NONE, after_qed))
1100 in (Future.map #1 result_ctxt, state') end;
1104 fun local_future_proof x = future_proof local_done_proof context_of x;
1105 fun global_future_proof x = future_proof global_done_proof I x;
1110 (* terminal proofs *)
1114 fun future_terminal_proof proof1 proof2 meths int state =
1115 if int orelse is_relevant state orelse not (Goal.local_future_enabled ())
1116 then proof1 meths state
1117 else snd (proof2 (fn state' =>
1118 Goal.fork_name "Proof.future_terminal_proof" (fn () => ((), proof1 meths state'))) state);
1122 fun local_future_terminal_proof x =
1123 future_terminal_proof local_terminal_proof local_future_proof x;
1125 fun global_future_terminal_proof x =
1126 future_terminal_proof global_terminal_proof global_future_proof x;