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 = Context.proof
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_contexts: (context -> context) -> state -> state
20 val add_binds_i: (indexname * term option) list -> state -> state
21 val put_thms: bool -> string * thm list option -> state -> state
22 val the_facts: state -> thm list
23 val the_fact: state -> thm
24 val put_facts: thm list option -> state -> state
25 val assert_forward: state -> state
26 val assert_chain: state -> state
27 val assert_forward_or_chain: state -> state
28 val assert_backward: state -> state
29 val assert_no_chain: state -> state
30 val enter_forward: state -> state
31 val goal_message: (unit -> Pretty.T) -> state -> state
32 val get_goal: state -> context * (thm list * thm)
33 val show_main_goal: bool ref
35 val pretty_state: int -> state -> Pretty.T list
36 val pretty_goals: bool -> state -> Pretty.T list
37 val refine: Method.text -> state -> state Seq.seq
38 val refine_end: Method.text -> state -> state Seq.seq
39 val refine_insert: thm list -> state -> state
40 val goal_tac: thm -> int -> tactic
41 val refine_goals: (context -> thm -> unit) -> context -> thm list -> state -> state Seq.seq
42 val match_bind: (string list * string) list -> state -> state
43 val match_bind_i: (term list * term) list -> state -> state
44 val let_bind: (string list * string) list -> state -> state
45 val let_bind_i: (term list * term) list -> state -> state
46 val fix: (binding * string option * mixfix) list -> state -> state
47 val fix_i: (binding * typ option * mixfix) list -> state -> state
48 val assm: Assumption.export ->
49 (Attrib.binding * (string * string list) list) list -> state -> state
50 val assm_i: Assumption.export ->
51 (Thm.binding * (term * term list) list) list -> state -> state
52 val assume: (Attrib.binding * (string * string list) list) list -> state -> state
53 val assume_i: (Thm.binding * (term * term list) list) list -> state -> state
54 val presume: (Attrib.binding * (string * string list) list) list -> state -> state
55 val presume_i: (Thm.binding * (term * term list) list) list -> state -> state
56 val def: (Attrib.binding * ((binding * mixfix) * (string * string list))) list -> state -> state
57 val def_i: (Thm.binding * ((binding * mixfix) * (term * term list))) list -> state -> state
58 val chain: state -> state
59 val chain_facts: thm list -> state -> state
60 val get_thmss: state -> (Facts.ref * Attrib.src list) list -> thm list
61 val note_thmss: (Attrib.binding * (Facts.ref * Attrib.src list) list) list -> state -> state
62 val note_thmss_i: (Thm.binding * (thm list * attribute list) list) list -> state -> state
63 val from_thmss: ((Facts.ref * Attrib.src list) list) list -> state -> state
64 val from_thmss_i: ((thm list * attribute list) list) list -> state -> state
65 val with_thmss: ((Facts.ref * Attrib.src list) list) list -> state -> state
66 val with_thmss_i: ((thm list * attribute list) list) list -> state -> state
67 val using: ((Facts.ref * Attrib.src list) list) list -> state -> state
68 val using_i: ((thm list * attribute list) list) list -> state -> state
69 val unfolding: ((Facts.ref * Attrib.src list) list) list -> state -> state
70 val unfolding_i: ((thm list * attribute list) list) list -> state -> state
71 val invoke_case: string * string option list * Attrib.src list -> state -> state
72 val invoke_case_i: string * string option list * attribute list -> state -> state
73 val begin_block: state -> state
74 val next_block: state -> state
75 val end_block: state -> state
76 val proof: Method.text option -> state -> state Seq.seq
77 val defer: int option -> state -> state Seq.seq
78 val prefer: int -> state -> state Seq.seq
79 val apply: Method.text -> state -> state Seq.seq
80 val apply_end: Method.text -> state -> state Seq.seq
81 val local_goal: (context -> ((string * string) * (string * thm list) list) -> unit) ->
82 (theory -> 'a -> attribute) ->
83 (context * 'b list -> context * (term list list * (context -> context))) ->
84 string -> Method.text option -> (thm list list -> state -> state) ->
85 ((binding * 'a list) * 'b) list -> state -> state
86 val local_qed: Method.text option * bool -> state -> state
87 val theorem: Method.text option -> (thm list list -> context -> context) ->
88 (string * string list) list list -> context -> state
89 val theorem_i: Method.text option -> (thm list list -> context -> context) ->
90 (term * term list) list list -> context -> state
91 val global_qed: Method.text option * bool -> state -> context
92 val local_terminal_proof: Method.text * Method.text option -> state -> state
93 val local_default_proof: state -> state
94 val local_immediate_proof: state -> state
95 val local_skip_proof: bool -> state -> state
96 val local_done_proof: state -> state
97 val global_terminal_proof: Method.text * Method.text option -> state -> context
98 val global_default_proof: state -> context
99 val global_immediate_proof: state -> context
100 val global_skip_proof: bool -> state -> context
101 val global_done_proof: state -> context
102 val have: Method.text option -> (thm list list -> state -> state) ->
103 (Attrib.binding * (string * string list) list) list -> bool -> state -> state
104 val have_i: Method.text option -> (thm list list -> state -> state) ->
105 (Thm.binding * (term * term list) list) list -> bool -> state -> state
106 val show: Method.text option -> (thm list list -> state -> state) ->
107 (Attrib.binding * (string * string list) list) list -> bool -> state -> state
108 val show_i: Method.text option -> (thm list list -> state -> state) ->
109 (Thm.binding * (term * term list) list) list -> bool -> state -> state
110 val schematic_goal: state -> bool
111 val is_relevant: state -> bool
112 val local_future_proof: (state -> ('a * state) Future.future) ->
113 state -> 'a Future.future * state
114 val global_future_proof: (state -> ('a * Proof.context) Future.future) ->
115 state -> 'a Future.future * context
116 val local_future_terminal_proof: Method.text * Method.text option -> bool -> state -> state
117 val global_future_terminal_proof: Method.text * Method.text option -> bool -> state -> context
120 structure Proof: PROOF =
123 type context = Context.proof;
124 type method = Method.method;
131 datatype mode = Forward | Chain | Backward;
134 State of node Stack.T
138 facts: thm list option,
143 {statement: (string * Position.T) * term list list * term,
144 (*goal kind and statement (starting with vars), initial proposition*)
145 messages: (unit -> Pretty.T) list, (*persistent messages (hints etc.)*)
146 using: thm list, (*goal facts*)
147 goal: thm, (*subgoals ==> statement*)
148 before_qed: Method.text option,
150 (thm list list -> state -> state) *
151 (thm list list -> context -> context)};
153 fun make_goal (statement, messages, using, goal, before_qed, after_qed) =
154 Goal {statement = statement, messages = messages, using = using, goal = goal,
155 before_qed = before_qed, after_qed = after_qed};
157 fun make_node (context, facts, mode, goal) =
158 Node {context = context, facts = facts, mode = mode, goal = goal};
160 fun map_node f (Node {context, facts, mode, goal}) =
161 make_node (f (context, facts, mode, goal));
164 ProofContext.set_stmt true #> ProofContext.reset_naming;
167 State (Stack.init (make_node (init_context ctxt, NONE, Forward, NONE)));
169 fun current (State st) = Stack.top st |> (fn Node node => node);
170 fun map_current f (State st) = State (Stack.map_top (map_node f) st);
171 fun map_all f (State st) = State (Stack.map_all (map_node f) st);
175 (** basic proof state operations **)
177 (* block structure *)
179 fun open_block (State st) = State (Stack.push st);
181 fun close_block (State st) = State (Stack.pop st)
182 handle Empty => error "Unbalanced block parentheses";
184 fun level (State st) = Stack.level st;
186 fun assert_bottom b state =
187 let val b' = (level state <= 2) in
188 if b andalso not b' then error "Not at bottom of proof!"
189 else if not b andalso b' then error "Already at bottom of proof!"
196 val context_of = #context o current;
197 val theory_of = ProofContext.theory_of o context_of;
200 map_current (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
202 fun map_context_result f state =
203 f (context_of state) ||> (fn ctxt => map_context (K ctxt) state);
205 fun map_contexts f = map_all (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
207 val add_binds_i = map_context o ProofContext.add_binds_i;
208 val put_thms = map_context oo ProofContext.put_thms;
213 val get_facts = #facts o current;
215 fun the_facts state =
216 (case get_facts state of SOME facts => facts
217 | NONE => error "No current facts available");
220 (case the_facts state of [thm] => thm
221 | _ => error "Single theorem expected");
223 fun put_facts facts =
224 map_current (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal)) #>
225 put_thms true (AutoBind.thisN, facts);
227 fun these_factss more_facts (named_factss, state) =
228 (named_factss, state |> put_facts (SOME (maps snd named_factss @ more_facts)));
230 fun export_facts inner outer =
231 (case get_facts inner of
232 NONE => put_facts NONE outer
235 |> ProofContext.export (context_of inner) (context_of outer)
236 |> (fn ths => put_facts (SOME ths) outer));
241 val get_mode = #mode o current;
242 fun put_mode mode = map_current (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));
244 val mode_name = (fn Forward => "state" | Chain => "chain" | Backward => "prove");
246 fun assert_mode pred state =
247 let val mode = get_mode state in
248 if pred mode then state
249 else error ("Illegal application of proof command in " ^ quote (mode_name mode) ^ " mode")
252 val assert_forward = assert_mode (fn mode => mode = Forward);
253 val assert_chain = assert_mode (fn mode => mode = Chain);
254 val assert_forward_or_chain = assert_mode (fn mode => mode = Forward orelse mode = Chain);
255 val assert_backward = assert_mode (fn mode => mode = Backward);
256 val assert_no_chain = assert_mode (fn mode => mode <> Chain);
258 val enter_forward = put_mode Forward;
259 val enter_chain = put_mode Chain;
260 val enter_backward = put_mode Backward;
265 fun current_goal state =
266 (case current state of
267 {context, goal = SOME (Goal goal), ...} => (context, goal)
268 | _ => error "No current goal!");
270 fun assert_current_goal g state =
271 let val g' = can current_goal state in
272 if g andalso not g' then error "No goal in this block!"
273 else if not g andalso g' then error "Goal present in this block!"
277 fun put_goal goal = map_current (fn (ctxt, using, mode, _) => (ctxt, using, mode, goal));
279 val before_qed = #before_qed o #2 o current_goal;
284 fun map_goal f g (State (Node {context, facts, mode, goal = SOME goal}, nodes)) =
286 val Goal {statement, messages, using, goal, before_qed, after_qed} = goal;
287 val goal' = make_goal (g (statement, messages, using, goal, before_qed, after_qed));
288 in State (make_node (f context, facts, mode, SOME goal'), nodes) end
289 | map_goal f g (State (nd, node :: nodes)) =
290 let val State (node', nodes') = map_goal f g (State (node, nodes))
291 in map_context f (State (nd, node' :: nodes')) end
292 | map_goal _ _ state = state;
294 fun set_goal goal = map_goal I (fn (statement, _, using, _, before_qed, after_qed) =>
295 (statement, [], using, goal, before_qed, after_qed));
297 fun goal_message msg = map_goal I (fn (statement, messages, using, goal, before_qed, after_qed) =>
298 (statement, msg :: messages, using, goal, before_qed, after_qed));
300 fun using_facts using = map_goal I (fn (statement, _, _, goal, before_qed, after_qed) =>
301 (statement, [], using, goal, before_qed, after_qed));
305 (case try current_goal state of
306 SOME (ctxt, goal) => (ctxt, (i, goal))
307 | NONE => find (i + 1) (close_block state handle ERROR _ => error "No goal present"));
308 in val find_goal = find 0 end;
311 let val (ctxt, (_, {using, goal, ...})) = find_goal state
312 in (ctxt, (using, goal)) end;
318 val show_main_goal = ref false;
319 val verbose = ProofContext.verbose;
321 val pretty_goals_local = Display.pretty_goals_aux o Syntax.pp;
323 fun pretty_facts _ _ NONE = []
324 | pretty_facts s ctxt (SOME ths) =
325 [Pretty.big_list (s ^ "this:") (map (ProofContext.pretty_thm ctxt) ths), Pretty.str ""];
327 fun pretty_state nr state =
329 val {context, facts, mode, goal = _} = current state;
332 | levels_up 1 = "1 level up"
333 | levels_up i = string_of_int i ^ " levels up";
336 | subgoals 1 = "1 subgoal"
337 | subgoals n = string_of_int n ^ " subgoals";
339 fun description strs =
340 (case filter_out (fn s => s = "") strs of [] => ""
341 | strs' => enclose " (" ")" (commas strs'));
343 fun prt_goal (SOME (ctxt, (i,
344 {statement = ((_, pos), _, _), messages, using, goal, before_qed = _, after_qed = _}))) =
345 pretty_facts "using " ctxt
346 (if mode <> Backward orelse null using then NONE else SOME using) @
347 [Pretty.str ("goal" ^
348 description [levels_up (i div 2), subgoals (Thm.nprems_of goal)] ^ ":")] @
349 pretty_goals_local ctxt Markup.subgoal
350 (true, ! show_main_goal) (! Display.goals_limit) goal @
351 (map (fn msg => Position.setmp_thread_data pos msg ()) (rev messages))
352 | prt_goal NONE = [];
355 if ! verbose orelse mode = Forward then ProofContext.pretty_context context
356 else if mode = Backward then ProofContext.pretty_ctxt context
359 [Pretty.str ("proof (" ^ mode_name mode ^ "): step " ^ string_of_int nr ^
360 (if ! verbose then ", depth " ^ string_of_int (level state div 2 - 1) else "")),
362 (if null prt_ctxt then [] else prt_ctxt @ [Pretty.str ""]) @
363 (if ! verbose orelse mode = Forward then
364 pretty_facts "" context facts @ prt_goal (try find_goal state)
365 else if mode = Chain then pretty_facts "picking " context facts
366 else prt_goal (try find_goal state))
369 fun pretty_goals main state =
370 let val (ctxt, (_, goal)) = get_goal state
371 in pretty_goals_local ctxt Markup.none (false, main) (! Display.goals_limit) goal end;
377 (* refine via method *)
381 fun goalN i = "goal" ^ string_of_int i;
382 fun goals st = map goalN (1 upto Thm.nprems_of st);
384 fun no_goal_cases st = map (rpair NONE) (goals st);
387 RuleCases.make_common true (Thm.theory_of_thm st, Thm.prop_of st) (map (rpair []) (goals st));
389 fun apply_method current_context pos meth state =
391 val (goal_ctxt, (_, {statement, messages = _, using, goal, before_qed, after_qed})) =
393 val ctxt = if current_context then context_of state else goal_ctxt;
395 Method.apply pos meth ctxt using goal |> Seq.map (fn (meth_cases, goal') =>
398 (ProofContext.add_cases false (no_goal_cases goal @ goal_cases goal') #>
399 ProofContext.add_cases true meth_cases)
400 (K (statement, [], using, goal', before_qed, after_qed)))
403 fun select_goals n meth state =
405 |> (#2 o #2 o get_goal)
406 |> ALLGOALS Goal.conjunction_tac
407 |> Seq.maps (fn goal =>
409 |> Seq.lift set_goal (Goal.extract 1 n goal |> Seq.maps (Goal.conjunction_tac 1))
411 |> Seq.maps (fn state' => state'
412 |> Seq.lift set_goal (Goal.retrofit 1 n (#2 (#2 (get_goal state'))) goal))
413 |> Seq.maps (apply_method true Position.none (K Method.succeed)));
415 fun apply_text cc text state =
417 val thy = theory_of state;
418 val pos_of = #2 o Args.dest_src;
420 fun eval (Method.Basic (m, pos)) = apply_method cc pos m
421 | eval (Method.Source src) = apply_method cc (pos_of src) (Method.method thy src)
422 | eval (Method.Source_i src) = apply_method cc (pos_of src) (Method.method_i thy src)
423 | eval (Method.Then txts) = Seq.EVERY (map eval txts)
424 | eval (Method.Orelse txts) = Seq.FIRST (map eval txts)
425 | eval (Method.Try txt) = Seq.TRY (eval txt)
426 | eval (Method.Repeat1 txt) = Seq.REPEAT1 (eval txt)
427 | eval (Method.SelectGoals (n, txt)) = select_goals n (eval txt);
428 in eval text state end;
432 val refine = apply_text true;
433 val refine_end = apply_text false;
435 fun refine_insert [] = I
436 | refine_insert ths = Seq.hd o refine (Method.Basic (K (Method.insert ths), Position.none));
441 (* refine via sub-proof *)
444 Goal.norm_hhf_tac THEN' Tactic.rtac rule THEN_ALL_NEW
445 (Goal.norm_hhf_tac THEN' (SUBGOAL (fn (goal, i) =>
446 if can Logic.unprotect (Logic.strip_assums_concl goal) then
447 Tactic.etac Drule.protectI i
450 fun refine_goals print_rule inner raw_rules state =
452 val (outer, (_, goal)) = get_goal state;
453 fun refine rule st = (print_rule outer rule; FINDGOAL (goal_tac rule) st);
456 |> ProofContext.goal_export inner outer
457 |> (fn rules => Seq.lift set_goal (EVERY (map refine rules) goal) state)
463 fun conclude_goal ctxt goal propss =
465 val thy = ProofContext.theory_of ctxt;
466 val string_of_term = Syntax.string_of_term ctxt;
467 val string_of_thm = ProofContext.string_of_thm ctxt;
469 val ngoals = Thm.nprems_of goal;
470 val _ = ngoals = 0 orelse error (Pretty.string_of (Pretty.chunks
471 (pretty_goals_local ctxt Markup.none (true, ! show_main_goal) (! Display.goals_limit) goal @
472 [Pretty.str (string_of_int ngoals ^ " unsolved goal(s)!")])));
474 val extra_hyps = Assumption.extra_hyps ctxt goal;
475 val _ = null extra_hyps orelse
476 error ("Additional hypotheses:\n" ^ cat_lines (map string_of_term extra_hyps));
478 fun lost_structure () = error ("Lost goal structure:\n" ^ string_of_thm goal);
480 val th = Goal.conclude
481 (if length (flat propss) > 1 then Thm.norm_proof goal else goal)
482 handle THM _ => lost_structure ();
483 val goal_propss = filter_out null propss;
485 Conjunction.elim_balanced (length goal_propss) th
486 |> map2 Conjunction.elim_balanced (map length goal_propss)
487 handle THM _ => lost_structure ();
488 val _ = Unify.matches_list thy (flat goal_propss) (map Thm.prop_of (flat results)) orelse
489 error ("Proved a different theorem:\n" ^ string_of_thm th);
490 val _ = Thm.check_shyps (Variable.sorts_of ctxt) th;
492 fun recover_result ([] :: pss) thss = [] :: recover_result pss thss
493 | recover_result (_ :: pss) (ths :: thss) = ths :: recover_result pss thss
494 | recover_result [] [] = []
495 | recover_result _ _ = lost_structure ();
496 in recover_result propss results end;
500 (*** structured proof commands ***)
502 (** context elements **)
508 fun gen_bind bind args state =
511 |> map_context (bind args #> snd)
516 val match_bind = gen_bind (ProofContext.match_bind false);
517 val match_bind_i = gen_bind (ProofContext.match_bind_i false);
518 val let_bind = gen_bind (ProofContext.match_bind true);
519 val let_bind_i = gen_bind (ProofContext.match_bind_i true);
528 fun gen_fix add_fixes args =
530 #> map_context (snd o add_fixes args)
535 val fix = gen_fix ProofContext.add_fixes;
536 val fix_i = gen_fix ProofContext.add_fixes_i;
545 fun gen_assume asm prep_att exp args state =
548 |> map_context_result (asm exp (Attrib.map_specs (prep_att (theory_of state)) args))
549 |> these_factss [] |> #2;
553 val assm = gen_assume ProofContext.add_assms Attrib.attribute;
554 val assm_i = gen_assume ProofContext.add_assms_i (K I);
555 val assume = assm Assumption.assume_export;
556 val assume_i = assm_i Assumption.assume_export;
557 val presume = assm Assumption.presume_export;
558 val presume_i = assm_i Assumption.presume_export;
567 fun gen_def prep_att prep_vars prep_binds args state =
569 val _ = assert_forward state;
570 val thy = theory_of state;
571 val ctxt = context_of state;
573 val (raw_name_atts, (raw_vars, raw_rhss)) = args |> split_list ||> split_list;
574 val name_atts = map (apsnd (map (prep_att thy))) raw_name_atts;
577 |> map_context_result (prep_vars (map (fn (x, mx) => (x, NONE, mx)) raw_vars))
578 |>> map (fn (x, _, mx) => (x, mx))
580 map_context_result (prep_binds false (map swap raw_rhss))
581 #-> (fn rhss => map_context_result (LocalDefs.add_defs (vars ~~ (name_atts ~~ rhss)))))
582 |-> (put_facts o SOME o map (#2 o #2))
587 val def = gen_def Attrib.attribute ProofContext.read_vars ProofContext.match_bind;
588 val def_i = gen_def (K I) ProofContext.cert_vars ProofContext.match_bind_i;
598 fun clean_facts ctxt =
599 put_facts (SOME (filter_out Thm.is_dummy (the_facts ctxt))) ctxt;
606 fun chain_facts facts =
607 put_facts (SOME facts)
613 fun no_binding args = map (pair (Binding.empty, [])) args;
617 fun gen_thmss note_ctxt more_facts opt_chain opt_result prep_atts args state =
620 |> map_context_result (note_ctxt (Attrib.map_facts (prep_atts (theory_of state)) args))
621 |> these_factss (more_facts state)
627 val note_thmss = gen_thmss (ProofContext.note_thmss "") (K []) I #2 Attrib.attribute;
628 val note_thmss_i = gen_thmss (ProofContext.note_thmss_i "") (K []) I #2 (K I);
631 gen_thmss (ProofContext.note_thmss "") (K []) chain #2 Attrib.attribute o no_binding;
632 val from_thmss_i = gen_thmss (ProofContext.note_thmss_i "") (K []) chain #2 (K I) o no_binding;
635 gen_thmss (ProofContext.note_thmss "") the_facts chain #2 Attrib.attribute o no_binding;
636 val with_thmss_i = gen_thmss (ProofContext.note_thmss_i "") the_facts chain #2 (K I) o no_binding;
639 gen_thmss (ProofContext.note_thmss_i "") (K []) I I (K I) o map (apsnd Thm.simple_fact);
641 fun get_thmss state srcs = the_facts (note_thmss [((Binding.empty, []), srcs)] state);
646 (* using/unfolding *)
650 fun gen_using f g note prep_atts args state =
653 |> map_context_result
654 (note "" (Attrib.map_facts (prep_atts (theory_of state)) (no_binding args)))
655 |> (fn (named_facts, state') =>
656 state' |> map_goal I (fn (statement, _, using, goal, before_qed, after_qed) =>
658 val ctxt = context_of state';
659 val ths = maps snd named_facts;
660 in (statement, [], f ctxt ths using, g ctxt ths goal, before_qed, after_qed) end));
662 fun append_using _ ths using = using @ filter_out Thm.is_dummy ths;
663 fun unfold_using ctxt ths = map (LocalDefs.unfold ctxt ths);
664 val unfold_goals = LocalDefs.unfold_goals;
668 val using = gen_using append_using (K (K I)) ProofContext.note_thmss Attrib.attribute;
669 val using_i = gen_using append_using (K (K I)) ProofContext.note_thmss_i (K I);
670 val unfolding = gen_using unfold_using unfold_goals ProofContext.note_thmss Attrib.attribute;
671 val unfolding_i = gen_using unfold_using unfold_goals ProofContext.note_thmss_i (K I);
680 fun qualified_binding a =
681 Binding.qualify true (Long_Name.qualifier a) (Binding.name (Long_Name.base_name a));
683 fun gen_invoke_case prep_att (name, xs, raw_atts) state =
685 val atts = map (prep_att (theory_of state)) raw_atts;
686 val (asms, state') = state |> map_context_result (fn ctxt =>
687 ctxt |> ProofContext.apply_case (ProofContext.get_case ctxt name xs));
688 val assumptions = asms |> map (fn (a, ts) => ((qualified_binding a, atts), map (rpair []) ts));
691 |> assume_i assumptions
692 |> add_binds_i AutoBind.no_facts
693 |> `the_facts |-> (fn thms => note_thmss_i [((Binding.name name, []), [(thms, [])])])
698 val invoke_case = gen_invoke_case Attrib.attribute;
699 val invoke_case_i = gen_invoke_case (K I);
705 (** proof structure **)
722 fun end_block state =
726 |> assert_current_goal false
728 |> export_facts state;
735 #> refine (the_default Method.default_text opt_text)
736 #> Seq.map (using_facts [] #> enter_forward);
738 fun end_proof bot txt state =
743 |> assert_current_goal true
745 |> `before_qed |-> (refine o the_default Method.succeed_text)
746 |> Seq.maps (refine (Method.finish_text txt (Position.thread_data ())));
748 fun check_result msg sq =
753 fun check_finish sq = check_result "Failed to finish proof" sq;
756 (* unstructured refinement *)
758 fun defer i = assert_no_chain #> refine (Method.Basic (K (Method.defer i), Position.none));
759 fun prefer i = assert_no_chain #> refine (Method.Basic (K (Method.prefer i), Position.none));
761 fun apply text = assert_backward #> refine text #> Seq.map (using_facts []);
762 fun apply_end text = assert_forward #> refine_end text;
772 fun implicit_vars dest add props =
774 val (explicit_vars, props') = take_prefix (can dest) props |>> map dest;
775 val vars = rev (subtract (op =) explicit_vars (fold add props []));
778 else warning ("Goal statement contains unbound schematic variable(s): " ^
779 commas_quote (map (Term.string_of_vname o fst) vars));
780 in (rev vars, props') end;
783 refine (Method.Basic (K (RAW_METHOD
784 (K (HEADGOAL (PRECISE_CONJUNCTS n
785 (HEADGOAL (CONJUNCTS (ALLGOALS (rtac Drule.termI)))))))), Position.none))
790 fun generic_goal prepp kind before_qed after_qed raw_propp state =
792 val thy = theory_of state;
793 val cert = Thm.cterm_of thy;
794 val chaining = can assert_chain state;
795 val pos = Position.thread_data ();
797 val ((propss, after_ctxt), goal_state) =
799 |> assert_forward_or_chain
802 |> map_context_result (fn ctxt => swap (prepp (ctxt, raw_propp)));
803 val props = flat propss;
806 implicit_vars (dest_TVar o Logic.dest_type o Logic.dest_term) Term.add_tvars props;
807 val (vars, _) = implicit_vars (dest_Var o Logic.dest_term) Term.add_vars props';
809 val propss' = map (Logic.mk_term o Var) vars :: propss;
810 val goal_propss = filter_out null propss';
812 cert (Logic.mk_conjunction_balanced (map Logic.mk_conjunction_balanced goal_propss))
813 |> Thm.weaken_sorts (Variable.sorts_of (context_of goal_state));
814 val statement = ((kind, pos), propss', Thm.term_of goal);
815 val after_qed' = after_qed |>> (fn after_local =>
816 fn results => map_context after_ctxt #> after_local results);
819 |> map_context (init_context #> Variable.set_body true)
820 |> put_goal (SOME (make_goal (statement, [], [], Goal.init goal, before_qed, after_qed')))
821 |> map_context (ProofContext.auto_bind_goal props)
822 |> chaining ? (`the_facts #-> using_facts)
827 |> not (null vars) ? refine_terms (length goal_propss)
828 |> null props ? (refine (Method.Basic (Method.assumption, Position.none)) #> Seq.hd)
831 fun generic_qed after_ctxt state =
833 val (goal_ctxt, {statement, goal, after_qed, ...}) = current_goal state;
834 val outer_state = state |> close_block;
835 val outer_ctxt = context_of outer_state;
837 val ((_, pos), stmt, _) = statement;
840 |> Variable.exportT_terms goal_ctxt outer_ctxt;
842 tl (conclude_goal goal_ctxt goal stmt)
843 |> burrow (ProofContext.export goal_ctxt outer_ctxt);
845 val (after_local, after_global) = after_qed;
846 fun after_local' x y = Position.setmp_thread_data pos (fn () => after_local x y) ();
847 fun after_global' x y = Position.setmp_thread_data pos (fn () => after_global x y) ();
850 |> map_context (after_ctxt props)
851 |> pair ((after_local', after_global'), results)
859 fun local_goal print_results prep_att prepp kind before_qed after_qed stmt state =
861 val thy = theory_of state;
862 val ((names, attss), propp) =
863 Attrib.map_specs (prep_att thy) stmt |> split_list |>> split_list;
865 fun after_qed' results =
866 local_results ((names ~~ attss) ~~ results)
867 #-> (fn res => tap (fn st => print_results (context_of st) ((kind, ""), res) : unit))
868 #> after_qed results;
871 |> generic_goal prepp kind before_qed (after_qed', K I) propp
872 |> tap (Variable.warn_extra_tfrees (context_of state) o context_of)
877 #> Seq.map (generic_qed ProofContext.auto_bind_facts #->
878 (fn ((after_qed, _), results) => after_qed results));
880 fun local_qed txt = local_qeds txt #> check_finish;
885 fun global_goal prepp before_qed after_qed propp ctxt =
887 |> generic_goal (prepp #> ProofContext.auto_fixes) "" before_qed (K I, after_qed) propp;
889 val theorem = global_goal ProofContext.bind_propp_schematic;
890 val theorem_i = global_goal ProofContext.bind_propp_schematic_i;
892 fun global_qeds txt =
894 #> Seq.map (generic_qed (K I) #> (fn (((_, after_qed), results), state) =>
895 after_qed results (context_of state)));
897 fun global_qed txt = global_qeds txt #> check_finish;
900 (* concluding steps *)
902 fun terminal_proof qed initial terminal =
903 proof (SOME initial) #> Seq.maps (qed terminal) #> check_finish;
905 fun local_terminal_proof (text, opt_text) = terminal_proof local_qeds text (opt_text, true);
906 val local_default_proof = local_terminal_proof (Method.default_text, NONE);
907 val local_immediate_proof = local_terminal_proof (Method.this_text, NONE);
908 fun local_skip_proof int = local_terminal_proof (Method.sorry_text int, NONE);
909 val local_done_proof = terminal_proof local_qeds Method.done_text (NONE, false);
911 fun global_terminal_proof (text, opt_text) = terminal_proof global_qeds text (opt_text, true);
912 val global_default_proof = global_terminal_proof (Method.default_text, NONE);
913 val global_immediate_proof = global_terminal_proof (Method.this_text, NONE);
914 fun global_skip_proof int = global_terminal_proof (Method.sorry_text int, NONE);
915 val global_done_proof = terminal_proof global_qeds Method.done_text (NONE, false);
918 (* common goal statements *)
922 fun gen_have prep_att prepp before_qed after_qed stmt int =
923 local_goal (ProofDisplay.print_results int) prep_att prepp "have" before_qed after_qed stmt;
925 fun gen_show prep_att prepp before_qed after_qed stmt int state =
927 val testing = ref false;
928 val rule = ref (NONE: thm option);
930 "Local statement will fail to refine any pending goal" ::
931 (case ! rule of NONE => [] | SOME th => [ProofDisplay.string_of_rule ctxt "Failed" th])
934 fun print_results ctxt res =
935 if ! testing then () else ProofDisplay.print_results int ctxt res;
936 fun print_rule ctxt th =
937 if ! testing then rule := SOME th
938 else if int then priority (ProofDisplay.string_of_rule ctxt "Successful" th)
941 try (local_skip_proof true)
942 |> setmp_noncritical testing true
945 fun after_qed' results =
946 refine_goals print_rule (context_of state) (flat results)
947 #> check_result "Failed to refine any pending goal"
948 #> after_qed results;
951 |> local_goal print_results prep_att prepp "show" before_qed after_qed' stmt
952 |> int ? (fn goal_state =>
953 (case test_proof goal_state of
954 Exn.Result (SOME _) => goal_state
955 | Exn.Result NONE => error (fail_msg (context_of goal_state))
956 | Exn.Exn Exn.Interrupt => raise Exn.Interrupt
957 | Exn.Exn exn => raise Exn.EXCEPTIONS ([exn, ERROR (fail_msg (context_of goal_state))])))
962 val have = gen_have Attrib.attribute ProofContext.bind_propp;
963 val have_i = gen_have (K I) ProofContext.bind_propp_i;
964 val show = gen_show Attrib.attribute ProofContext.bind_propp;
965 val show_i = gen_show (K I) ProofContext.bind_propp_i;
971 (** future proofs **)
973 (* relevant proof states *)
976 Term.exists_subterm Term.is_Var t orelse
977 Term.exists_type (Term.exists_subtype Term.is_TVar) t;
979 fun schematic_goal state =
980 let val (_, (_, {statement = (_, _, prop), ...})) = find_goal state
981 in is_schematic prop end;
983 fun is_relevant state =
984 (case try find_goal state of
986 | SOME (_, (_, {statement = (_, _, prop), goal, ...})) =>
987 is_schematic prop orelse not (Logic.protect prop aconv Thm.concl_of goal));
994 fun future_proof done get_context fork_proof state =
996 val _ = assert_backward state;
997 val (goal_ctxt, (_, goal)) = find_goal state;
998 val {statement as (kind, propss, prop), messages, using, goal, before_qed, after_qed} = goal;
1000 val _ = is_relevant state andalso error "Cannot fork relevant proof";
1002 val prop' = Logic.protect prop;
1003 val statement' = (kind, [[], [prop']], prop');
1004 val goal' = Thm.adjust_maxidx_thm (Thm.maxidx_of goal)
1005 (Drule.comp_no_flatten (goal, Thm.nprems_of goal) 1 Drule.protectI);
1007 fun after_local' [[th]] = put_thms false (AutoBind.thisN, SOME [th]);
1008 fun after_global' [[th]] = ProofContext.put_thms false (AutoBind.thisN, SOME [th]);
1009 val after_qed' = (after_local', after_global');
1010 val this_name = ProofContext.full_name goal_ctxt (Binding.name AutoBind.thisN);
1014 |> map_contexts (Variable.declare_term prop)
1015 |> map_goal I (K (statement', messages, using, goal', before_qed, after_qed'))
1018 val future_thm = result_ctxt |> Future.map (fn (_, x) =>
1019 ProofContext.get_fact_single (get_context x) (Facts.named this_name));
1020 val finished_goal = exception_trace (fn () => Goal.future_result goal_ctxt future_thm prop');
1023 |> map_goal I (K (statement, messages, using, finished_goal, NONE, after_qed))
1025 in (Future.map #1 result_ctxt, state') end;
1029 fun local_future_proof x = future_proof local_done_proof context_of x;
1030 fun global_future_proof x = future_proof global_done_proof I x;
1035 (* terminal proofs *)
1039 fun future_terminal_proof proof1 proof2 meths int state =
1040 if int orelse is_relevant state orelse not (Goal.future_enabled ())
1041 then proof1 meths state
1042 else snd (state |> proof2 (fn state' => Future.fork_pri ~1 (fn () => ((), proof1 meths state'))));
1046 fun local_future_terminal_proof x =
1047 future_terminal_proof local_terminal_proof local_future_proof x;
1049 fun global_future_terminal_proof x =
1050 future_terminal_proof global_terminal_proof global_future_proof x;