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 schematic_goal: state -> bool
34 val show_main_goal: bool ref
36 val pretty_state: int -> state -> Pretty.T list
37 val pretty_goals: bool -> state -> Pretty.T list
38 val refine: Method.text -> state -> state Seq.seq
39 val refine_end: Method.text -> state -> state Seq.seq
40 val refine_insert: thm list -> state -> state
41 val goal_tac: thm -> int -> tactic
42 val refine_goals: (context -> thm -> unit) -> context -> thm list -> state -> state Seq.seq
43 val match_bind: (string list * string) list -> state -> state
44 val match_bind_i: (term list * term) list -> state -> state
45 val let_bind: (string list * string) list -> state -> state
46 val let_bind_i: (term list * term) list -> state -> state
47 val fix: (Binding.T * string option * mixfix) list -> state -> state
48 val fix_i: (Binding.T * typ option * mixfix) list -> state -> state
49 val assm: Assumption.export ->
50 (Attrib.binding * (string * string list) list) list -> state -> state
51 val assm_i: Assumption.export ->
52 ((Binding.T * attribute list) * (term * term list) list) list -> state -> state
53 val assume: (Attrib.binding * (string * string list) list) list -> state -> state
54 val assume_i: ((Binding.T * attribute list) * (term * term list) list) list ->
56 val presume: (Attrib.binding * (string * string list) list) list -> state -> state
57 val presume_i: ((Binding.T * attribute list) * (term * term list) list) list ->
59 val def: (Attrib.binding * ((Binding.T * mixfix) * (string * string list))) list ->
61 val def_i: ((Binding.T * attribute list) *
62 ((Binding.T * mixfix) * (term * term list))) list -> state -> state
63 val chain: state -> state
64 val chain_facts: thm list -> state -> state
65 val get_thmss: state -> (Facts.ref * Attrib.src list) list -> thm list
66 val note_thmss: (Attrib.binding * (Facts.ref * Attrib.src list) list) list -> state -> state
67 val note_thmss_i: ((Binding.T * attribute list) *
68 (thm list * attribute list) list) list -> state -> state
69 val from_thmss: ((Facts.ref * Attrib.src list) list) list -> state -> state
70 val from_thmss_i: ((thm list * attribute list) list) list -> state -> state
71 val with_thmss: ((Facts.ref * Attrib.src list) list) list -> state -> state
72 val with_thmss_i: ((thm list * attribute list) list) list -> state -> state
73 val using: ((Facts.ref * Attrib.src list) list) list -> state -> state
74 val using_i: ((thm list * attribute list) list) list -> state -> state
75 val unfolding: ((Facts.ref * Attrib.src list) list) list -> state -> state
76 val unfolding_i: ((thm list * attribute list) list) list -> state -> state
77 val invoke_case: string * string option list * Attrib.src list -> state -> state
78 val invoke_case_i: string * string option list * attribute list -> state -> state
79 val begin_block: state -> state
80 val next_block: state -> state
81 val end_block: state -> state
82 val proof: Method.text option -> state -> state Seq.seq
83 val defer: int option -> state -> state Seq.seq
84 val prefer: int -> state -> state Seq.seq
85 val apply: Method.text -> state -> state Seq.seq
86 val apply_end: Method.text -> state -> state Seq.seq
87 val local_goal: (context -> ((string * string) * (string * thm list) list) -> unit) ->
88 (theory -> 'a -> attribute) ->
89 (context * 'b list -> context * (term list list * (context -> context))) ->
90 string -> Method.text option -> (thm list list -> state -> state) ->
91 ((Binding.T * 'a list) * 'b) list -> state -> state
92 val local_qed: Method.text option * bool -> state -> state
93 val theorem: Method.text option -> (thm list list -> context -> context) ->
94 (string * string list) list list -> context -> state
95 val theorem_i: Method.text option -> (thm list list -> context -> context) ->
96 (term * term list) list list -> context -> state
97 val global_qed: Method.text option * bool -> state -> context
98 val local_terminal_proof: Method.text * Method.text option -> state -> state
99 val local_default_proof: state -> state
100 val local_immediate_proof: state -> state
101 val local_skip_proof: bool -> state -> state
102 val local_done_proof: state -> state
103 val global_terminal_proof: Method.text * Method.text option -> state -> context
104 val global_default_proof: state -> context
105 val global_immediate_proof: state -> context
106 val global_skip_proof: bool -> state -> context
107 val global_done_proof: state -> context
108 val have: Method.text option -> (thm list list -> state -> state) ->
109 (Attrib.binding * (string * string list) list) list -> bool -> state -> state
110 val have_i: Method.text option -> (thm list list -> state -> state) ->
111 ((Binding.T * attribute list) * (term * term list) list) list -> bool -> state -> state
112 val show: Method.text option -> (thm list list -> state -> state) ->
113 (Attrib.binding * (string * string list) list) list -> bool -> state -> state
114 val show_i: Method.text option -> (thm list list -> state -> state) ->
115 ((Binding.T * attribute list) * (term * term list) list) list -> bool -> state -> state
116 val is_relevant: state -> bool
117 val future_proof: (state -> ('a * context) future) -> state -> 'a future * context
118 val future_terminal_proof: Method.text * Method.text option -> bool -> state -> context
121 structure Proof: PROOF =
124 type context = Context.proof;
125 type method = Method.method;
132 datatype mode = Forward | Chain | Backward;
135 State of node Stack.T
139 facts: thm list option,
144 {statement: (string * Position.T) * term list list * term,
145 (*goal kind and statement (starting with vars), initial proposition*)
146 messages: (unit -> Pretty.T) list, (*persistent messages (hints etc.)*)
147 using: thm list, (*goal facts*)
148 goal: thm, (*subgoals ==> statement*)
149 before_qed: Method.text option,
151 (thm list list -> state -> state) *
152 (thm list list -> context -> context)};
154 fun make_goal (statement, messages, using, goal, before_qed, after_qed) =
155 Goal {statement = statement, messages = messages, using = using, goal = goal,
156 before_qed = before_qed, after_qed = after_qed};
158 fun make_node (context, facts, mode, goal) =
159 Node {context = context, facts = facts, mode = mode, goal = goal};
161 fun map_node f (Node {context, facts, mode, goal}) =
162 make_node (f (context, facts, mode, goal));
165 ProofContext.set_stmt true #> ProofContext.reset_naming;
168 State (Stack.init (make_node (init_context ctxt, NONE, Forward, NONE)));
170 fun current (State st) = Stack.top st |> (fn Node node => node);
171 fun map_current f (State st) = State (Stack.map_top (map_node f) st);
172 fun map_all f (State st) = State (Stack.map_all (map_node f) st);
176 (** basic proof state operations **)
178 (* block structure *)
180 fun open_block (State st) = State (Stack.push st);
182 fun close_block (State st) = State (Stack.pop st)
183 handle Empty => error "Unbalanced block parentheses";
185 fun level (State st) = Stack.level st;
187 fun assert_bottom b state =
188 let val b' = (level state <= 2) in
189 if b andalso not b' then error "Not at bottom of proof!"
190 else if not b andalso b' then error "Already at bottom of proof!"
197 val context_of = #context o current;
198 val theory_of = ProofContext.theory_of o context_of;
201 map_current (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
203 fun map_context_result f state =
204 f (context_of state) ||> (fn ctxt => map_context (K ctxt) state);
206 fun map_contexts f = map_all (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
208 val add_binds_i = map_context o ProofContext.add_binds_i;
209 val put_thms = map_context oo ProofContext.put_thms;
214 val get_facts = #facts o current;
216 fun the_facts state =
217 (case get_facts state of SOME facts => facts
218 | NONE => error "No current facts available");
221 (case the_facts state of [thm] => thm
222 | _ => error "Single theorem expected");
224 fun put_facts facts =
225 map_current (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal)) #>
226 put_thms true (AutoBind.thisN, facts);
228 fun these_factss more_facts (named_factss, state) =
229 (named_factss, state |> put_facts (SOME (maps snd named_factss @ more_facts)));
231 fun export_facts inner outer =
232 (case get_facts inner of
233 NONE => put_facts NONE outer
236 |> ProofContext.export (context_of inner) (context_of outer)
237 |> (fn ths => put_facts (SOME ths) outer));
242 val get_mode = #mode o current;
243 fun put_mode mode = map_current (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));
245 val mode_name = (fn Forward => "state" | Chain => "chain" | Backward => "prove");
247 fun assert_mode pred state =
248 let val mode = get_mode state in
249 if pred mode then state
250 else error ("Illegal application of proof command in " ^ quote (mode_name mode) ^ " mode")
253 val assert_forward = assert_mode (fn mode => mode = Forward);
254 val assert_chain = assert_mode (fn mode => mode = Chain);
255 val assert_forward_or_chain = assert_mode (fn mode => mode = Forward orelse mode = Chain);
256 val assert_backward = assert_mode (fn mode => mode = Backward);
257 val assert_no_chain = assert_mode (fn mode => mode <> Chain);
259 val enter_forward = put_mode Forward;
260 val enter_chain = put_mode Chain;
261 val enter_backward = put_mode Backward;
266 fun current_goal state =
267 (case current state of
268 {context, goal = SOME (Goal goal), ...} => (context, goal)
269 | _ => error "No current goal!");
271 fun assert_current_goal g state =
272 let val g' = can current_goal state in
273 if g andalso not g' then error "No goal in this block!"
274 else if not g andalso g' then error "Goal present in this block!"
278 fun put_goal goal = map_current (fn (ctxt, using, mode, _) => (ctxt, using, mode, goal));
280 val before_qed = #before_qed o #2 o current_goal;
285 fun map_goal f g (State (Node {context, facts, mode, goal = SOME goal}, nodes)) =
287 val Goal {statement, messages, using, goal, before_qed, after_qed} = goal;
288 val goal' = make_goal (g (statement, messages, using, goal, before_qed, after_qed));
289 in State (make_node (f context, facts, mode, SOME goal'), nodes) end
290 | map_goal f g (State (nd, node :: nodes)) =
291 let val State (node', nodes') = map_goal f g (State (node, nodes))
292 in map_context f (State (nd, node' :: nodes')) end
293 | map_goal _ _ state = state;
295 fun set_goal goal = map_goal I (fn (statement, _, using, _, before_qed, after_qed) =>
296 (statement, [], using, goal, before_qed, after_qed));
298 fun goal_message msg = map_goal I (fn (statement, messages, using, goal, before_qed, after_qed) =>
299 (statement, msg :: messages, using, goal, before_qed, after_qed));
301 fun using_facts using = map_goal I (fn (statement, _, _, goal, before_qed, after_qed) =>
302 (statement, [], using, goal, before_qed, after_qed));
306 (case try current_goal state of
307 SOME (ctxt, goal) => (ctxt, (i, goal))
308 | NONE => find (i + 1) (close_block state handle ERROR _ => error "No goal present"));
309 in val find_goal = find 0 end;
312 let val (ctxt, (_, {using, goal, ...})) = find_goal state
313 in (ctxt, (using, goal)) end;
315 fun schematic_goal state =
316 let val (_, (_, {statement = (_, _, prop), ...})) = find_goal state in
317 Term.exists_subterm Term.is_Var prop orelse
318 Term.exists_type (Term.exists_subtype Term.is_TVar) prop
325 val show_main_goal = ref false;
326 val verbose = ProofContext.verbose;
328 val pretty_goals_local = Display.pretty_goals_aux o Syntax.pp;
330 fun pretty_facts _ _ NONE = []
331 | pretty_facts s ctxt (SOME ths) =
332 [Pretty.big_list (s ^ "this:") (map (ProofContext.pretty_thm ctxt) ths), Pretty.str ""];
334 fun pretty_state nr state =
336 val {context, facts, mode, goal = _} = current state;
339 | levels_up 1 = "1 level up"
340 | levels_up i = string_of_int i ^ " levels up";
343 | subgoals 1 = "1 subgoal"
344 | subgoals n = string_of_int n ^ " subgoals";
346 fun description strs =
347 (case filter_out (fn s => s = "") strs of [] => ""
348 | strs' => enclose " (" ")" (commas strs'));
350 fun prt_goal (SOME (ctxt, (i, {statement = ((_, pos), _, _), messages, using, goal, ...}))) =
351 pretty_facts "using " ctxt
352 (if mode <> Backward orelse null using then NONE else SOME using) @
353 [Pretty.str ("goal" ^
354 description [levels_up (i div 2), subgoals (Thm.nprems_of goal)] ^ ":")] @
355 pretty_goals_local ctxt Markup.subgoal
356 (true, ! show_main_goal) (! Display.goals_limit) goal @
357 (map (fn msg => Position.setmp_thread_data pos msg ()) (rev messages))
358 | prt_goal NONE = [];
361 if ! verbose orelse mode = Forward then ProofContext.pretty_context context
362 else if mode = Backward then ProofContext.pretty_ctxt context
365 [Pretty.str ("proof (" ^ mode_name mode ^ "): step " ^ string_of_int nr ^
366 (if ! verbose then ", depth " ^ string_of_int (level state div 2 - 1) else "")),
368 (if null prt_ctxt then [] else prt_ctxt @ [Pretty.str ""]) @
369 (if ! verbose orelse mode = Forward then
370 pretty_facts "" context facts @ prt_goal (try find_goal state)
371 else if mode = Chain then pretty_facts "picking " context facts
372 else prt_goal (try find_goal state))
375 fun pretty_goals main state =
376 let val (ctxt, (_, goal)) = get_goal state
377 in pretty_goals_local ctxt Markup.none (false, main) (! Display.goals_limit) 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 RuleCases.make_common true (Thm.theory_of_thm st, Thm.prop_of st) (map (rpair []) (goals st));
395 fun apply_method current_context pos 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 pos meth ctxt using goal |> Seq.map (fn (meth_cases, goal') =>
404 (ProofContext.add_cases false (no_goal_cases goal @ goal_cases goal') #>
405 ProofContext.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 Position.none (K Method.succeed)));
421 fun apply_text cc text state =
423 val thy = theory_of state;
424 val pos_of = #2 o Args.dest_src;
426 fun eval (Method.Basic (m, pos)) = apply_method cc pos m
427 | eval (Method.Source src) = apply_method cc (pos_of src) (Method.method thy src)
428 | eval (Method.Source_i src) = apply_method cc (pos_of src) (Method.method_i thy src)
429 | eval (Method.Then txts) = Seq.EVERY (map eval txts)
430 | eval (Method.Orelse txts) = Seq.FIRST (map eval txts)
431 | eval (Method.Try txt) = Seq.TRY (eval txt)
432 | eval (Method.Repeat1 txt) = Seq.REPEAT1 (eval txt)
433 | eval (Method.SelectGoals (n, txt)) = select_goals n (eval txt);
434 in eval text state end;
438 val refine = apply_text true;
439 val refine_end = apply_text false;
441 fun refine_insert [] = I
442 | refine_insert ths = Seq.hd o refine (Method.Basic (K (Method.insert ths), Position.none));
447 (* refine via sub-proof *)
450 Goal.norm_hhf_tac THEN' Tactic.rtac rule THEN_ALL_NEW
451 (Goal.norm_hhf_tac THEN' (SUBGOAL (fn (goal, i) =>
452 if can Logic.unprotect (Logic.strip_assums_concl goal) then
453 Tactic.etac Drule.protectI i
456 fun refine_goals print_rule inner raw_rules state =
458 val (outer, (_, goal)) = get_goal state;
459 fun refine rule st = (print_rule outer rule; FINDGOAL (goal_tac rule) st);
462 |> ProofContext.goal_export inner outer
463 |> (fn rules => Seq.lift set_goal (EVERY (map refine rules) goal) state)
469 fun conclude_goal ctxt goal propss =
471 val thy = ProofContext.theory_of ctxt;
472 val string_of_term = Syntax.string_of_term ctxt;
473 val string_of_thm = ProofContext.string_of_thm ctxt;
475 val ngoals = Thm.nprems_of goal;
476 val _ = ngoals = 0 orelse error (Pretty.string_of (Pretty.chunks
477 (pretty_goals_local ctxt Markup.none (true, ! show_main_goal) (! Display.goals_limit) goal @
478 [Pretty.str (string_of_int ngoals ^ " unsolved goal(s)!")])));
480 val extra_hyps = Assumption.extra_hyps ctxt goal;
481 val _ = null extra_hyps orelse
482 error ("Additional hypotheses:\n" ^ cat_lines (map string_of_term extra_hyps));
484 fun lost_structure () = error ("Lost goal structure:\n" ^ string_of_thm goal);
486 val th = Goal.conclude
487 (if length (flat propss) > 1 then Thm.norm_proof goal else goal)
488 handle THM _ => lost_structure ();
489 val goal_propss = filter_out null propss;
491 Conjunction.elim_balanced (length goal_propss) th
492 |> map2 Conjunction.elim_balanced (map length goal_propss)
493 handle THM _ => lost_structure ();
494 val _ = Unify.matches_list thy (flat goal_propss) (map Thm.prop_of (flat results)) orelse
495 error ("Proved a different theorem:\n" ^ string_of_thm th);
496 val _ = Thm.check_shyps (Variable.sorts_of ctxt) th;
498 fun recover_result ([] :: pss) thss = [] :: recover_result pss thss
499 | recover_result (_ :: pss) (ths :: thss) = ths :: recover_result pss thss
500 | recover_result [] [] = []
501 | recover_result _ _ = lost_structure ();
502 in recover_result propss results end;
506 (*** structured proof commands ***)
508 (** context elements **)
514 fun gen_bind bind args state =
517 |> map_context (bind args #> snd)
522 val match_bind = gen_bind (ProofContext.match_bind false);
523 val match_bind_i = gen_bind (ProofContext.match_bind_i false);
524 val let_bind = gen_bind (ProofContext.match_bind true);
525 val let_bind_i = gen_bind (ProofContext.match_bind_i true);
534 fun gen_fix add_fixes args =
536 #> map_context (snd o add_fixes args)
541 val fix = gen_fix ProofContext.add_fixes;
542 val fix_i = gen_fix ProofContext.add_fixes_i;
551 fun gen_assume asm prep_att exp args state =
554 |> map_context_result (asm exp (Attrib.map_specs (prep_att (theory_of state)) args))
555 |> these_factss [] |> #2;
559 val assm = gen_assume ProofContext.add_assms Attrib.attribute;
560 val assm_i = gen_assume ProofContext.add_assms_i (K I);
561 val assume = assm Assumption.assume_export;
562 val assume_i = assm_i Assumption.assume_export;
563 val presume = assm Assumption.presume_export;
564 val presume_i = assm_i Assumption.presume_export;
573 fun gen_def prep_att prep_vars prep_binds args state =
575 val _ = assert_forward state;
576 val thy = theory_of state;
577 val ctxt = context_of state;
579 val (raw_name_atts, (raw_vars, raw_rhss)) = args |> split_list ||> split_list;
580 val name_atts = map (apsnd (map (prep_att thy))) raw_name_atts;
583 |> map_context_result (prep_vars (map (fn (x, mx) => (x, NONE, mx)) raw_vars))
584 |>> map (fn (x, _, mx) => (x, mx))
586 map_context_result (prep_binds false (map swap raw_rhss))
587 #-> (fn rhss => map_context_result (LocalDefs.add_defs (vars ~~ (name_atts ~~ rhss)))))
588 |-> (put_facts o SOME o map (#2 o #2))
593 val def = gen_def Attrib.attribute ProofContext.read_vars ProofContext.match_bind;
594 val def_i = gen_def (K I) ProofContext.cert_vars ProofContext.match_bind_i;
604 fun clean_facts ctxt =
605 put_facts (SOME (filter_out Thm.is_dummy (the_facts ctxt))) ctxt;
612 fun chain_facts facts =
613 put_facts (SOME facts)
619 fun no_binding args = map (pair (Binding.empty, [])) args;
623 fun gen_thmss note_ctxt more_facts opt_chain opt_result prep_atts args state =
626 |> map_context_result (note_ctxt (Attrib.map_facts (prep_atts (theory_of state)) args))
627 |> these_factss (more_facts state)
633 val note_thmss = gen_thmss (ProofContext.note_thmss "") (K []) I #2 Attrib.attribute;
634 val note_thmss_i = gen_thmss (ProofContext.note_thmss_i "") (K []) I #2 (K I);
637 gen_thmss (ProofContext.note_thmss "") (K []) chain #2 Attrib.attribute o no_binding;
638 val from_thmss_i = gen_thmss (ProofContext.note_thmss_i "") (K []) chain #2 (K I) o no_binding;
641 gen_thmss (ProofContext.note_thmss "") the_facts chain #2 Attrib.attribute o no_binding;
642 val with_thmss_i = gen_thmss (ProofContext.note_thmss_i "") the_facts chain #2 (K I) o no_binding;
645 gen_thmss (ProofContext.note_thmss_i "") (K []) I I (K I) o map (apsnd Thm.simple_fact);
647 fun get_thmss state srcs = the_facts (note_thmss [((Binding.empty, []), srcs)] state);
652 (* using/unfolding *)
656 fun gen_using f g note prep_atts args state =
659 |> map_context_result
660 (note "" (Attrib.map_facts (prep_atts (theory_of state)) (no_binding args)))
661 |> (fn (named_facts, state') =>
662 state' |> map_goal I (fn (statement, _, using, goal, before_qed, after_qed) =>
664 val ctxt = context_of state';
665 val ths = maps snd named_facts;
666 in (statement, [], f ctxt ths using, g ctxt ths goal, before_qed, after_qed) end));
668 fun append_using _ ths using = using @ filter_out Thm.is_dummy ths;
669 fun unfold_using ctxt ths = map (LocalDefs.unfold ctxt ths);
670 val unfold_goals = LocalDefs.unfold_goals;
674 val using = gen_using append_using (K (K I)) ProofContext.note_thmss Attrib.attribute;
675 val using_i = gen_using append_using (K (K I)) ProofContext.note_thmss_i (K I);
676 val unfolding = gen_using unfold_using unfold_goals ProofContext.note_thmss Attrib.attribute;
677 val unfolding_i = gen_using unfold_using unfold_goals ProofContext.note_thmss_i (K I);
686 fun gen_invoke_case prep_att (name, xs, raw_atts) state =
688 val atts = map (prep_att (theory_of state)) raw_atts;
689 val (asms, state') = state |> map_context_result (fn ctxt =>
690 ctxt |> ProofContext.apply_case (ProofContext.get_case ctxt name xs));
691 val assumptions = asms |> map (fn (a, ts) => ((Binding.name a, atts), map (rpair []) ts));
694 |> map_context (ProofContext.qualified_names #> ProofContext.no_base_names)
695 |> assume_i assumptions
696 |> add_binds_i AutoBind.no_facts
697 |> map_context (ProofContext.restore_naming (context_of state))
698 |> `the_facts |-> (fn thms => note_thmss_i [((Binding.name name, []), [(thms, [])])])
703 val invoke_case = gen_invoke_case Attrib.attribute;
704 val invoke_case_i = gen_invoke_case (K I);
710 (** proof structure **)
727 fun end_block state =
731 |> assert_current_goal false
733 |> export_facts state;
740 #> refine (the_default Method.default_text opt_text)
741 #> Seq.map (using_facts [] #> enter_forward);
743 fun end_proof bot txt state =
748 |> assert_current_goal true
750 |> `before_qed |-> (refine o the_default Method.succeed_text)
751 |> Seq.maps (refine (Method.finish_text txt (Position.thread_data ())));
753 fun check_result msg sq =
758 fun check_finish sq = check_result "Failed to finish proof" sq;
761 (* unstructured refinement *)
763 fun defer i = assert_no_chain #> refine (Method.Basic (K (Method.defer i), Position.none));
764 fun prefer i = assert_no_chain #> refine (Method.Basic (K (Method.prefer i), Position.none));
766 fun apply text = assert_backward #> refine text #> Seq.map (using_facts []);
767 fun apply_end text = assert_forward #> refine_end text;
777 fun implicit_vars dest add props =
779 val (explicit_vars, props') = take_prefix (can dest) props |>> map dest;
780 val vars = rev (subtract (op =) explicit_vars (fold add props []));
783 else warning ("Goal statement contains unbound schematic variable(s): " ^
784 commas_quote (map (Term.string_of_vname o fst) vars));
785 in (rev vars, props') end;
788 refine (Method.Basic (K (Method.RAW_METHOD
789 (K (HEADGOAL (PRECISE_CONJUNCTS n
790 (HEADGOAL (CONJUNCTS (ALLGOALS (rtac Drule.termI)))))))), Position.none))
795 fun generic_goal prepp kind before_qed after_qed raw_propp state =
797 val thy = theory_of state;
798 val cert = Thm.cterm_of thy;
799 val chaining = can assert_chain state;
800 val pos = Position.thread_data ();
802 val ((propss, after_ctxt), goal_state) =
804 |> assert_forward_or_chain
807 |> map_context_result (fn ctxt => swap (prepp (ctxt, raw_propp)));
808 val props = flat propss;
811 implicit_vars (dest_TVar o Logic.dest_type o Logic.dest_term) Term.add_tvars props;
812 val (vars, _) = implicit_vars (dest_Var o Logic.dest_term) Term.add_vars props';
814 val propss' = map (Logic.mk_term o Var) vars :: propss;
815 val goal_propss = filter_out null propss';
817 cert (Logic.mk_conjunction_balanced (map Logic.mk_conjunction_balanced goal_propss))
818 |> Thm.weaken_sorts (Variable.sorts_of (context_of goal_state));
819 val statement = ((kind, pos), propss', Thm.term_of goal);
820 val after_qed' = after_qed |>> (fn after_local =>
821 fn results => map_context after_ctxt #> after_local results);
824 |> map_context (init_context #> Variable.set_body true)
825 |> put_goal (SOME (make_goal (statement, [], [], Goal.init goal, before_qed, after_qed')))
826 |> map_context (ProofContext.auto_bind_goal props)
827 |> chaining ? (`the_facts #-> using_facts)
832 |> not (null vars) ? refine_terms (length goal_propss)
833 |> null props ? (refine (Method.Basic (Method.assumption, Position.none)) #> Seq.hd)
836 fun generic_qed after_ctxt state =
838 val (goal_ctxt, {statement, goal, after_qed, ...}) = current_goal state;
839 val outer_state = state |> close_block;
840 val outer_ctxt = context_of outer_state;
842 val ((_, pos), stmt, _) = statement;
845 |> Variable.exportT_terms goal_ctxt outer_ctxt;
847 tl (conclude_goal goal_ctxt goal stmt)
848 |> burrow (ProofContext.export goal_ctxt outer_ctxt);
850 val (after_local, after_global) = after_qed;
851 fun after_local' x y = Position.setmp_thread_data pos (fn () => after_local x y) ();
852 fun after_global' x y = Position.setmp_thread_data pos (fn () => after_global x y) ();
855 |> map_context (after_ctxt props)
856 |> pair ((after_local', after_global'), results)
864 fun local_goal print_results prep_att prepp kind before_qed after_qed stmt state =
866 val thy = theory_of state;
867 val ((names, attss), propp) =
868 Attrib.map_specs (prep_att thy) stmt |> split_list |>> split_list;
870 fun after_qed' results =
871 local_results ((names ~~ attss) ~~ results)
872 #-> (fn res => tap (fn st => print_results (context_of st) ((kind, ""), res) : unit))
873 #> after_qed results;
876 |> generic_goal prepp kind before_qed (after_qed', K I) propp
877 |> tap (Variable.warn_extra_tfrees (context_of state) o context_of)
882 #> Seq.map (generic_qed ProofContext.auto_bind_facts #->
883 (fn ((after_qed, _), results) => after_qed results));
885 fun local_qed txt = local_qeds txt #> check_finish;
890 fun global_goal prepp before_qed after_qed propp ctxt =
892 |> generic_goal (prepp #> ProofContext.auto_fixes) "" before_qed (K I, after_qed) propp;
894 val theorem = global_goal ProofContext.bind_propp_schematic;
895 val theorem_i = global_goal ProofContext.bind_propp_schematic_i;
897 fun global_qeds txt =
899 #> Seq.map (generic_qed (K I) #> (fn (((_, after_qed), results), state) =>
900 after_qed results (context_of state)));
902 fun global_qed txt = global_qeds txt #> check_finish;
905 (* concluding steps *)
907 fun terminal_proof qed initial terminal =
908 proof (SOME initial) #> Seq.maps (qed terminal) #> check_finish;
910 fun local_terminal_proof (text, opt_text) = terminal_proof local_qeds text (opt_text, true);
911 val local_default_proof = local_terminal_proof (Method.default_text, NONE);
912 val local_immediate_proof = local_terminal_proof (Method.this_text, NONE);
913 fun local_skip_proof int = local_terminal_proof (Method.sorry_text int, NONE);
914 val local_done_proof = terminal_proof local_qeds Method.done_text (NONE, false);
916 fun global_terminal_proof (text, opt_text) = terminal_proof global_qeds text (opt_text, true);
917 val global_default_proof = global_terminal_proof (Method.default_text, NONE);
918 val global_immediate_proof = global_terminal_proof (Method.this_text, NONE);
919 fun global_skip_proof int = global_terminal_proof (Method.sorry_text int, NONE);
920 val global_done_proof = terminal_proof global_qeds Method.done_text (NONE, false);
923 (* common goal statements *)
927 fun gen_have prep_att prepp before_qed after_qed stmt int =
928 local_goal (ProofDisplay.print_results int) prep_att prepp "have" before_qed after_qed stmt;
930 fun gen_show prep_att prepp before_qed after_qed stmt int state =
932 val testing = ref false;
933 val rule = ref (NONE: thm option);
935 "Local statement will fail to refine any pending goal" ::
936 (case ! rule of NONE => [] | SOME th => [ProofDisplay.string_of_rule ctxt "Failed" th])
939 fun print_results ctxt res =
940 if ! testing then () else ProofDisplay.print_results int ctxt res;
941 fun print_rule ctxt th =
942 if ! testing then rule := SOME th
943 else if int then priority (ProofDisplay.string_of_rule ctxt "Successful" th)
946 try (local_skip_proof true)
947 |> setmp_noncritical testing true
950 fun after_qed' results =
951 refine_goals print_rule (context_of state) (flat results)
952 #> check_result "Failed to refine any pending goal"
953 #> after_qed results;
956 |> local_goal print_results prep_att prepp "show" before_qed after_qed' stmt
957 |> int ? (fn goal_state =>
958 (case test_proof goal_state of
959 Exn.Result (SOME _) => goal_state
960 | Exn.Result NONE => error (fail_msg (context_of goal_state))
961 | Exn.Exn Exn.Interrupt => raise Exn.Interrupt
962 | Exn.Exn exn => raise Exn.EXCEPTIONS ([exn, ERROR (fail_msg (context_of goal_state))])))
967 val have = gen_have Attrib.attribute ProofContext.bind_propp;
968 val have_i = gen_have (K I) ProofContext.bind_propp_i;
969 val show = gen_show Attrib.attribute ProofContext.bind_propp;
970 val show_i = gen_show (K I) ProofContext.bind_propp_i;
975 (* fork global proofs *)
979 fun is_original state =
980 (case try find_goal state of
982 | SOME (_, (_, {statement = (_, _, prop), goal, ...})) =>
983 Logic.protect prop aconv Thm.concl_of goal);
987 fun is_relevant state =
988 can (assert_bottom false) state orelse
989 not (is_original state) orelse
990 schematic_goal state;
992 fun future_proof fork_proof state =
994 val _ = assert_backward state;
995 val (goal_ctxt, (_, goal)) = find_goal state;
996 val {statement as (kind, propss, prop), messages, using, goal, before_qed, after_qed} = goal;
998 val _ = is_relevant state andalso error "Cannot fork relevant proof";
1000 val prop' = Logic.protect prop;
1001 val statement' = (kind, [[], [prop']], prop');
1002 val goal' = Thm.adjust_maxidx_thm (Thm.maxidx_of goal)
1003 (Drule.comp_no_flatten (goal, Thm.nprems_of goal) 1 Drule.protectI);
1004 fun after_qed' [[th]] = ProofContext.put_thms false (AutoBind.thisN, SOME [th]);
1005 val this_name = ProofContext.full_bname goal_ctxt AutoBind.thisN;
1009 |> map_contexts (Variable.auto_fixes prop)
1010 |> map_goal I (K (statement', messages, using, goal', before_qed, (#1 after_qed, after_qed')))
1013 val future_thm = result_ctxt |> Future.map (fn (_, ctxt) =>
1014 ProofContext.get_fact_single ctxt (Facts.named this_name));
1015 val finished_goal = Goal.future_result goal_ctxt future_thm prop';
1018 |> map_goal I (K (statement, messages, using, finished_goal, NONE, after_qed))
1019 |> global_done_proof;
1020 in (Future.map #1 result_ctxt, state') end;
1024 fun future_terminal_proof meths int state =
1025 if int orelse is_relevant state orelse not (Future.enabled ())
1026 then global_terminal_proof meths state
1027 else #2 (state |> future_proof (fn state' =>
1028 Future.fork_pri ~1 (fn () => ((), global_terminal_proof meths state'))));