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_contexts: (context -> context) -> state -> state
20 val bind_terms: (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 show_main_goal: bool Unsynchronized.ref
33 val verbose: bool Unsynchronized.ref
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 goal_tac: thm -> int -> tactic
40 val refine_goals: (context -> thm -> unit) -> context -> thm list -> state -> state Seq.seq
41 val raw_goal: state -> {context: context, facts: thm list, goal: thm}
42 val goal: state -> {context: context, facts: thm list, goal: thm}
43 val simple_goal: state -> {context: context, goal: thm}
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 get_thmss_cmd: state -> (Facts.ref * Attrib.src list) list -> thm list
63 val note_thmss: (Thm.binding * (thm list * attribute list) list) list -> state -> state
64 val note_thmss_cmd: (Attrib.binding * (Facts.ref * Attrib.src list) list) list -> state -> state
65 val from_thmss: ((thm list * attribute list) list) list -> state -> state
66 val from_thmss_cmd: ((Facts.ref * Attrib.src list) list) list -> state -> state
67 val with_thmss: ((thm list * attribute list) list) list -> state -> state
68 val with_thmss_cmd: ((Facts.ref * Attrib.src list) list) list -> state -> state
69 val using: ((thm list * attribute list) list) list -> state -> state
70 val using_cmd: ((Facts.ref * Attrib.src list) list) list -> state -> state
71 val unfolding: ((thm list * attribute list) list) list -> state -> state
72 val unfolding_cmd: ((Facts.ref * Attrib.src list) list) list -> state -> state
73 val invoke_case: string * string option list * attribute list -> state -> state
74 val invoke_case_cmd: string * string option list * Attrib.src list -> state -> state
75 val begin_block: state -> state
76 val next_block: state -> state
77 val end_block: state -> state
78 val proof: Method.text option -> state -> state Seq.seq
79 val defer: int option -> state -> state Seq.seq
80 val prefer: int -> state -> state Seq.seq
81 val apply: Method.text -> state -> state Seq.seq
82 val apply_end: Method.text -> state -> state Seq.seq
83 val local_goal: (context -> ((string * string) * (string * thm list) list) -> unit) ->
84 (theory -> 'a -> attribute) ->
85 (context * 'b list -> context * (term list list * (context -> context))) ->
86 string -> Method.text option -> (thm list list -> state -> state) ->
87 ((binding * 'a list) * 'b) list -> state -> state
88 val local_qed: Method.text option * bool -> state -> state
89 val theorem: Method.text option -> (thm list list -> context -> context) ->
90 (term * term list) list list -> context -> state
91 val theorem_cmd: Method.text option -> (thm list list -> context -> context) ->
92 (string * string list) list list -> context -> state
93 val global_qed: Method.text option * bool -> state -> context
94 val local_terminal_proof: Method.text * Method.text option -> state -> state
95 val local_default_proof: state -> state
96 val local_immediate_proof: state -> state
97 val local_skip_proof: bool -> state -> state
98 val local_done_proof: state -> state
99 val global_terminal_proof: Method.text * Method.text option -> state -> context
100 val global_default_proof: state -> context
101 val global_immediate_proof: state -> context
102 val global_skip_proof: bool -> state -> context
103 val global_done_proof: state -> context
104 val have: Method.text option -> (thm list list -> state -> state) ->
105 (Thm.binding * (term * term list) list) list -> bool -> state -> state
106 val have_cmd: Method.text option -> (thm list list -> state -> state) ->
107 (Attrib.binding * (string * string list) list) list -> bool -> state -> state
108 val show: Method.text option -> (thm list list -> state -> state) ->
109 (Thm.binding * (term * term list) list) list -> bool -> state -> state
110 val show_cmd: Method.text option -> (thm list list -> state -> state) ->
111 (Attrib.binding * (string * string list) list) list -> bool -> state -> state
112 val schematic_goal: state -> bool
113 val is_relevant: state -> bool
114 val local_future_proof: (state -> ('a * state) Future.future) ->
115 state -> 'a Future.future * state
116 val global_future_proof: (state -> ('a * Proof.context) Future.future) ->
117 state -> 'a Future.future * context
118 val local_future_terminal_proof: Method.text * Method.text option -> bool -> state -> state
119 val global_future_terminal_proof: Method.text * Method.text option -> bool -> state -> context
122 structure Proof: PROOF =
125 type context = Proof.context;
126 type method = Method.method;
133 datatype mode = Forward | Chain | Backward;
136 State of node Stack.T
140 facts: thm list option,
145 {statement: (string * Position.T) * term list list * term,
146 (*goal kind and statement (starting with vars), initial proposition*)
147 messages: (unit -> Pretty.T) list, (*persistent messages (hints etc.)*)
148 using: thm list, (*goal facts*)
149 goal: thm, (*subgoals ==> statement*)
150 before_qed: Method.text option,
152 (thm list list -> state -> state) *
153 (thm list list -> context -> context)};
155 fun make_goal (statement, messages, using, goal, before_qed, after_qed) =
156 Goal {statement = statement, messages = messages, using = using, goal = goal,
157 before_qed = before_qed, after_qed = after_qed};
159 fun make_node (context, facts, mode, goal) =
160 Node {context = context, facts = facts, mode = mode, goal = goal};
162 fun map_node f (Node {context, facts, mode, goal}) =
163 make_node (f (context, facts, mode, goal));
166 ProofContext.set_stmt true #>
167 ProofContext.map_naming (K ProofContext.local_naming);
170 State (Stack.init (make_node (init_context ctxt, NONE, Forward, NONE)));
172 fun current (State st) = Stack.top st |> (fn Node node => node);
173 fun map_current f (State st) = State (Stack.map_top (map_node f) st);
174 fun map_all f (State st) = State (Stack.map_all (map_node f) st);
178 (** basic proof state operations **)
180 (* block structure *)
182 fun open_block (State st) = State (Stack.push st);
184 fun close_block (State st) = State (Stack.pop st)
185 handle Empty => error "Unbalanced block parentheses";
187 fun level (State st) = Stack.level st;
189 fun assert_bottom b state =
190 let val b' = (level state <= 2) in
191 if b andalso not b' then error "Not at bottom of proof!"
192 else if not b andalso b' then error "Already at bottom of proof!"
199 val context_of = #context o current;
200 val theory_of = ProofContext.theory_of o context_of;
203 map_current (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
205 fun map_context_result f state =
206 f (context_of state) ||> (fn ctxt => map_context (K ctxt) state);
208 fun map_contexts f = map_all (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
210 val bind_terms = map_context o ProofContext.bind_terms;
211 val put_thms = map_context oo ProofContext.put_thms;
216 val get_facts = #facts o current;
218 fun the_facts state =
219 (case get_facts state of SOME facts => facts
220 | NONE => error "No current facts available");
223 (case the_facts state of [thm] => thm
224 | _ => error "Single theorem expected");
226 fun put_facts facts =
227 map_current (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal)) #>
228 put_thms true (Auto_Bind.thisN, facts);
230 fun these_factss more_facts (named_factss, state) =
231 (named_factss, state |> put_facts (SOME (maps snd named_factss @ more_facts)));
233 fun export_facts inner outer =
234 (case get_facts inner of
235 NONE => put_facts NONE outer
238 |> ProofContext.export (context_of inner) (context_of outer)
239 |> (fn ths => put_facts (SOME ths) outer));
244 val get_mode = #mode o current;
245 fun put_mode mode = map_current (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));
247 val mode_name = (fn Forward => "state" | Chain => "chain" | Backward => "prove");
249 fun assert_mode pred state =
250 let val mode = get_mode state in
251 if pred mode then state
252 else error ("Illegal application of proof command in " ^ quote (mode_name mode) ^ " mode")
255 val assert_forward = assert_mode (fn mode => mode = Forward);
256 val assert_chain = assert_mode (fn mode => mode = Chain);
257 val assert_forward_or_chain = assert_mode (fn mode => mode = Forward orelse mode = Chain);
258 val assert_backward = assert_mode (fn mode => mode = Backward);
259 val assert_no_chain = assert_mode (fn mode => mode <> Chain);
261 val enter_forward = put_mode Forward;
262 val enter_chain = put_mode Chain;
263 val enter_backward = put_mode Backward;
268 fun current_goal state =
269 (case current state of
270 {context, goal = SOME (Goal goal), ...} => (context, goal)
271 | _ => error "No current goal!");
273 fun assert_current_goal g state =
274 let val g' = can current_goal state in
275 if g andalso not g' then error "No goal in this block!"
276 else if not g andalso g' then error "Goal present in this block!"
280 fun put_goal goal = map_current (fn (ctxt, using, mode, _) => (ctxt, using, mode, goal));
282 val before_qed = #before_qed o #2 o current_goal;
287 fun map_goal f g (State (Node {context, facts, mode, goal = SOME goal}, nodes)) =
289 val Goal {statement, messages, using, goal, before_qed, after_qed} = goal;
290 val goal' = make_goal (g (statement, messages, using, goal, before_qed, after_qed));
291 in State (make_node (f context, facts, mode, SOME goal'), nodes) end
292 | map_goal f g (State (nd, node :: nodes)) =
293 let val State (node', nodes') = map_goal f g (State (node, nodes))
294 in map_context f (State (nd, node' :: nodes')) end
295 | map_goal _ _ state = state;
297 fun set_goal goal = map_goal I (fn (statement, _, using, _, before_qed, after_qed) =>
298 (statement, [], using, goal, before_qed, after_qed));
300 fun goal_message msg = map_goal I (fn (statement, messages, using, goal, before_qed, after_qed) =>
301 (statement, msg :: messages, using, goal, before_qed, after_qed));
303 fun using_facts using = map_goal I (fn (statement, _, _, goal, before_qed, after_qed) =>
304 (statement, [], using, goal, before_qed, after_qed));
308 (case try current_goal state of
309 SOME (ctxt, goal) => (ctxt, (i, goal))
310 | NONE => find (i + 1) (close_block state handle ERROR _ => error "No goal present"));
311 in val find_goal = find 0 end;
314 let val (ctxt, (_, {using, goal, ...})) = find_goal state
315 in (ctxt, (using, goal)) end;
321 val show_main_goal = Unsynchronized.ref false;
322 val verbose = ProofContext.verbose;
324 fun pretty_facts _ _ NONE = []
325 | pretty_facts s ctxt (SOME ths) =
326 [Pretty.big_list (s ^ "this:") (map (Display.pretty_thm ctxt) ths), Pretty.str ""];
328 fun pretty_state nr state =
330 val {context, facts, mode, goal = _} = current state;
333 | levels_up 1 = "1 level up"
334 | levels_up i = string_of_int i ^ " levels up";
337 | subgoals 1 = "1 subgoal"
338 | subgoals n = string_of_int n ^ " subgoals";
340 fun description strs =
341 (case filter_out (fn s => s = "") strs of [] => ""
342 | strs' => enclose " (" ")" (commas strs'));
344 fun prt_goal (SOME (ctxt, (i,
345 {statement = ((_, pos), _, _), messages, using, goal, before_qed = _, after_qed = _}))) =
346 pretty_facts "using " ctxt
347 (if mode <> Backward orelse null using then NONE else SOME using) @
348 [Pretty.str ("goal" ^
349 description [levels_up (i div 2), subgoals (Thm.nprems_of goal)] ^ ":")] @
350 Goal_Display.pretty_goals ctxt
351 {total = true, main = ! show_main_goal, maxgoals = ! Display.goals_limit} goal @
352 (map (fn msg => Position.setmp_thread_data pos msg ()) (rev messages))
353 | prt_goal NONE = [];
356 if ! verbose orelse mode = Forward then ProofContext.pretty_context context
357 else if mode = Backward then ProofContext.pretty_ctxt context
360 [Pretty.str ("proof (" ^ mode_name mode ^ "): step " ^ string_of_int nr ^
361 (if ! verbose then ", depth " ^ string_of_int (level state div 2 - 1) else "")),
363 (if null prt_ctxt then [] else prt_ctxt @ [Pretty.str ""]) @
364 (if ! verbose orelse mode = Forward then
365 pretty_facts "" context facts @ prt_goal (try find_goal state)
366 else if mode = Chain then pretty_facts "picking " context facts
367 else prt_goal (try find_goal state))
370 fun pretty_goals main state =
371 let val (ctxt, (_, goal)) = get_goal state in
372 Goal_Display.pretty_goals ctxt
373 {total = false, main = main, maxgoals = ! Display.goals_limit} goal
380 (* refine via method *)
384 fun goalN i = "goal" ^ string_of_int i;
385 fun goals st = map goalN (1 upto Thm.nprems_of st);
387 fun no_goal_cases st = map (rpair NONE) (goals st);
390 Rule_Cases.make_common (Thm.theory_of_thm st, Thm.prop_of st) (map (rpair []) (goals st));
392 fun apply_method current_context meth state =
394 val (goal_ctxt, (_, {statement, messages = _, using, goal, before_qed, after_qed})) =
396 val ctxt = if current_context then context_of state else goal_ctxt;
398 Method.apply meth ctxt using goal |> Seq.map (fn (meth_cases, goal') =>
401 (ProofContext.add_cases false (no_goal_cases goal @ goal_cases goal') #>
402 ProofContext.add_cases true meth_cases)
403 (K (statement, [], using, goal', before_qed, after_qed)))
406 fun select_goals n meth state =
408 |> (#2 o #2 o get_goal)
409 |> ALLGOALS Goal.conjunction_tac
410 |> Seq.maps (fn goal =>
412 |> Seq.lift set_goal (Goal.extract 1 n goal |> Seq.maps (Goal.conjunction_tac 1))
414 |> Seq.maps (fn state' => state'
415 |> Seq.lift set_goal (Goal.retrofit 1 n (#2 (#2 (get_goal state'))) goal))
416 |> Seq.maps (apply_method true (K Method.succeed)));
418 fun apply_text cc text state =
420 val thy = theory_of state;
422 fun eval (Method.Basic m) = apply_method cc m
423 | eval (Method.Source src) = apply_method cc (Method.method thy src)
424 | eval (Method.Source_i src) = apply_method cc (Method.method_i thy src)
425 | eval (Method.Then txts) = Seq.EVERY (map eval txts)
426 | eval (Method.Orelse txts) = Seq.FIRST (map eval txts)
427 | eval (Method.Try txt) = Seq.TRY (eval txt)
428 | eval (Method.Repeat1 txt) = Seq.REPEAT1 (eval txt)
429 | eval (Method.SelectGoals (n, txt)) = select_goals n (eval txt);
430 in eval text state end;
434 val refine = apply_text true;
435 val refine_end = apply_text false;
436 fun refine_insert ths = Seq.hd o refine (Method.Basic (K (Method.insert ths)));
441 (* refine via sub-proof *)
443 fun finish_tac 0 = K all_tac
445 Goal.norm_hhf_tac THEN'
446 SUBGOAL (fn (goal, i) =>
447 if can Logic.unprotect (Logic.strip_assums_concl goal) then
448 Tactic.etac Drule.protectI i THEN finish_tac (n - 1) i
449 else finish_tac (n - 1) (i + 1));
452 Goal.norm_hhf_tac THEN'
453 Tactic.rtac rule THEN'
454 finish_tac (Thm.nprems_of rule);
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 = Display.string_of_thm ctxt;
475 val ngoals = Thm.nprems_of goal;
476 val _ = ngoals = 0 orelse error (Pretty.string_of (Pretty.chunks
477 (Goal_Display.pretty_goals ctxt
478 {total = true, main = ! show_main_goal, maxgoals = ! Display.goals_limit} goal @
479 [Pretty.str (string_of_int ngoals ^ " unsolved goal(s)!")])));
481 val extra_hyps = Assumption.extra_hyps ctxt goal;
482 val _ = null extra_hyps orelse
483 error ("Additional hypotheses:\n" ^ cat_lines (map string_of_term extra_hyps));
485 fun lost_structure () = error ("Lost goal structure:\n" ^ string_of_thm goal);
487 val th = Goal.conclude
488 (if length (flat propss) > 1 then Thm.norm_proof goal else goal)
489 handle THM _ => lost_structure ();
490 val goal_propss = filter_out null propss;
492 Conjunction.elim_balanced (length goal_propss) th
493 |> map2 Conjunction.elim_balanced (map length goal_propss)
494 handle THM _ => lost_structure ();
495 val _ = Unify.matches_list thy (flat goal_propss) (map Thm.prop_of (flat results)) orelse
496 error ("Proved a different theorem:\n" ^ string_of_thm th);
497 val _ = Thm.check_shyps (Variable.sorts_of ctxt) th;
499 fun recover_result ([] :: pss) thss = [] :: recover_result pss thss
500 | recover_result (_ :: pss) (ths :: thss) = ths :: recover_result pss thss
501 | recover_result [] [] = []
502 | recover_result _ _ = lost_structure ();
503 in recover_result propss results end;
506 (* goal views -- corresponding to methods *)
509 let val (ctxt, (facts, goal)) = get_goal state
510 in {context = ctxt, facts = facts, goal = goal} end;
512 val goal = raw_goal o refine_insert [];
514 fun simple_goal state =
516 val (_, (facts, _)) = get_goal state;
517 val (ctxt, (_, goal)) = get_goal (refine_insert facts state);
518 in {context = ctxt, goal = goal} end;
522 (*** structured proof commands ***)
524 (** context elements **)
530 fun gen_bind bind args state =
533 |> map_context (bind true args #> snd)
538 val let_bind = gen_bind ProofContext.match_bind_i;
539 val let_bind_cmd = gen_bind ProofContext.match_bind;
544 (* concrete syntax *)
548 fun gen_write prep_arg mode args =
550 #> map_context (fn ctxt => ctxt |> ProofContext.notation true mode (map (prep_arg ctxt) args))
555 val write = gen_write (K I);
558 gen_write (fn ctxt => fn (c, mx) =>
559 (ProofContext.read_const ctxt false (Syntax.mixfixT mx) c, mx));
568 fun gen_fix prep_vars args =
570 #> map_context (fn ctxt => snd (ProofContext.add_fixes (prep_vars ctxt args) ctxt))
575 val fix = gen_fix (K I);
576 val fix_cmd = gen_fix (fn ctxt => fn args => fst (ProofContext.read_vars args ctxt));
585 fun gen_assume asm prep_att exp args state =
588 |> map_context_result (asm exp (Attrib.map_specs (prep_att (theory_of state)) args))
589 |> these_factss [] |> #2;
593 val assm = gen_assume ProofContext.add_assms_i (K I);
594 val assm_cmd = gen_assume ProofContext.add_assms Attrib.attribute;
595 val assume = assm Assumption.assume_export;
596 val assume_cmd = assm_cmd Assumption.assume_export;
597 val presume = assm Assumption.presume_export;
598 val presume_cmd = assm_cmd Assumption.presume_export;
607 fun gen_def prep_att prep_vars prep_binds args state =
609 val _ = assert_forward state;
610 val thy = theory_of state;
612 val (raw_name_atts, (raw_vars, raw_rhss)) = args |> split_list ||> split_list;
613 val name_atts = map (apsnd (map (prep_att thy))) raw_name_atts;
616 |> map_context_result (prep_vars (map (fn (x, mx) => (x, NONE, mx)) raw_vars))
617 |>> map (fn (x, _, mx) => (x, mx))
619 map_context_result (prep_binds false (map swap raw_rhss))
620 #-> (fn rhss => map_context_result (Local_Defs.add_defs (vars ~~ (name_atts ~~ rhss)))))
621 |-> (put_facts o SOME o map (#2 o #2))
626 val def = gen_def (K I) ProofContext.cert_vars ProofContext.match_bind_i;
627 val def_cmd = gen_def Attrib.attribute ProofContext.read_vars ProofContext.match_bind;
637 fun clean_facts ctxt =
638 put_facts (SOME (filter_out Thm.is_dummy (the_facts ctxt))) ctxt;
645 fun chain_facts facts =
646 put_facts (SOME facts)
652 fun no_binding args = map (pair (Binding.empty, [])) args;
656 fun gen_thmss more_facts opt_chain opt_result prep_atts prep_fact args state =
659 |> map_context_result (ProofContext.note_thmss ""
660 (Attrib.map_facts_refs (prep_atts (theory_of state)) (prep_fact (context_of state)) args))
661 |> these_factss (more_facts state)
667 val note_thmss = gen_thmss (K []) I #2 (K I) (K I);
668 val note_thmss_cmd = gen_thmss (K []) I #2 Attrib.attribute ProofContext.get_fact;
670 val from_thmss = gen_thmss (K []) chain #2 (K I) (K I) o no_binding;
671 val from_thmss_cmd = gen_thmss (K []) chain #2 Attrib.attribute ProofContext.get_fact o no_binding;
673 val with_thmss = gen_thmss the_facts chain #2 (K I) (K I) o no_binding;
674 val with_thmss_cmd = gen_thmss the_facts chain #2 Attrib.attribute ProofContext.get_fact o no_binding;
676 val local_results = gen_thmss (K []) I I (K I) (K I) o map (apsnd Thm.simple_fact);
678 fun get_thmss_cmd state srcs = the_facts (note_thmss_cmd [((Binding.empty, []), srcs)] state);
683 (* using/unfolding *)
687 fun gen_using f g prep_atts prep_fact args state =
690 |> map_context_result
691 (ProofContext.note_thmss ""
692 (Attrib.map_facts_refs (prep_atts (theory_of state)) (prep_fact (context_of state))
694 |> (fn (named_facts, state') =>
695 state' |> map_goal I (fn (statement, _, using, goal, before_qed, after_qed) =>
697 val ctxt = context_of state';
698 val ths = maps snd named_facts;
699 in (statement, [], f ctxt ths using, g ctxt ths goal, before_qed, after_qed) end));
701 fun append_using _ ths using = using @ filter_out Thm.is_dummy ths;
702 fun unfold_using ctxt ths = map (Local_Defs.unfold ctxt ths);
703 val unfold_goals = Local_Defs.unfold_goals;
707 val using = gen_using append_using (K (K I)) (K I) (K I);
708 val using_cmd = gen_using append_using (K (K I)) Attrib.attribute ProofContext.get_fact;
709 val unfolding = gen_using unfold_using unfold_goals (K I) (K I);
710 val unfolding_cmd = gen_using unfold_using unfold_goals Attrib.attribute ProofContext.get_fact;
719 fun qualified_binding a =
720 Binding.qualify true (Long_Name.qualifier a) (Binding.name (Long_Name.base_name a));
722 fun gen_invoke_case prep_att (name, xs, raw_atts) state =
724 val atts = map (prep_att (theory_of state)) raw_atts;
725 val (asms, state') = state |> map_context_result (fn ctxt =>
726 ctxt |> ProofContext.apply_case (ProofContext.get_case ctxt name xs));
727 val assumptions = asms |> map (fn (a, ts) => ((qualified_binding a, atts), map (rpair []) ts));
730 |> assume assumptions
731 |> bind_terms Auto_Bind.no_facts
732 |> `the_facts |-> (fn thms => note_thmss [((Binding.name name, []), [(thms, [])])])
737 val invoke_case = gen_invoke_case (K I);
738 val invoke_case_cmd = gen_invoke_case Attrib.attribute;
744 (** proof structure **)
761 fun end_block state =
765 |> assert_current_goal false
767 |> export_facts state;
774 #> refine (the_default Method.default_text opt_text)
775 #> Seq.map (using_facts [] #> enter_forward);
777 fun end_proof bot txt state =
782 |> assert_current_goal true
784 |> `before_qed |-> (refine o the_default Method.succeed_text)
785 |> Seq.maps (refine (Method.finish_text txt));
787 fun check_result msg sq =
792 fun check_finish sq = check_result "Failed to finish proof" sq;
795 (* unstructured refinement *)
797 fun defer i = assert_no_chain #> refine (Method.Basic (K (Method.defer i)));
798 fun prefer i = assert_no_chain #> refine (Method.Basic (K (Method.prefer i)));
800 fun apply text = assert_backward #> refine text #> Seq.map (using_facts []);
801 fun apply_end text = assert_forward #> refine_end text;
812 can (dest_TVar o Logic.dest_type o Logic.dest_term) orf
813 can (dest_Var o Logic.dest_term);
815 fun implicit_vars props =
817 val (var_props, _) = take_prefix is_var props;
818 val explicit_vars = fold Term.add_vars var_props [];
819 val vars = filter_out (member (op =) explicit_vars) (fold Term.add_vars props []);
820 in map (Logic.mk_term o Var) vars end;
823 refine (Method.Basic (K (RAW_METHOD
824 (K (HEADGOAL (PRECISE_CONJUNCTS n
825 (HEADGOAL (CONJUNCTS (ALLGOALS (rtac Drule.termI))))))))))
830 fun generic_goal prepp kind before_qed after_qed raw_propp state =
832 val thy = theory_of state;
833 val cert = Thm.cterm_of thy;
834 val chaining = can assert_chain state;
835 val pos = Position.thread_data ();
837 val ((propss, after_ctxt), goal_state) =
839 |> assert_forward_or_chain
842 |> map_context_result (fn ctxt => swap (prepp (ctxt, raw_propp)));
843 val props = flat propss;
845 val vars = implicit_vars props;
846 val propss' = vars :: propss;
847 val goal_propss = filter_out null propss';
849 cert (Logic.mk_conjunction_balanced (map Logic.mk_conjunction_balanced goal_propss))
850 |> Thm.weaken_sorts (Variable.sorts_of (context_of goal_state));
851 val statement = ((kind, pos), propss', Thm.term_of goal);
852 val after_qed' = after_qed |>> (fn after_local =>
853 fn results => map_context after_ctxt #> after_local results);
856 |> map_context (init_context #> Variable.set_body true)
857 |> put_goal (SOME (make_goal (statement, [], [], Goal.init goal, before_qed, after_qed')))
858 |> map_context (ProofContext.auto_bind_goal props)
859 |> chaining ? (`the_facts #-> using_facts)
864 |> not (null vars) ? refine_terms (length goal_propss)
865 |> null props ? (refine (Method.Basic Method.assumption) #> Seq.hd)
868 fun generic_qed after_ctxt state =
870 val (goal_ctxt, {statement = (_, stmt, _), goal, after_qed, ...}) = current_goal state;
871 val outer_state = state |> close_block;
872 val outer_ctxt = context_of outer_state;
876 |> Variable.exportT_terms goal_ctxt outer_ctxt;
878 tl (conclude_goal goal_ctxt goal stmt)
879 |> burrow (ProofContext.export goal_ctxt outer_ctxt);
882 |> map_context (after_ctxt props)
883 |> pair (after_qed, results)
891 fun local_goal print_results prep_att prepp kind before_qed after_qed stmt state =
893 val thy = theory_of state;
894 val ((names, attss), propp) =
895 Attrib.map_specs (prep_att thy) stmt |> split_list |>> split_list;
897 fun after_qed' results =
898 local_results ((names ~~ attss) ~~ results)
899 #-> (fn res => tap (fn st => print_results (context_of st) ((kind, ""), res) : unit))
900 #> after_qed results;
903 |> generic_goal prepp kind before_qed (after_qed', K I) propp
904 |> tap (Variable.warn_extra_tfrees (context_of state) o context_of)
909 #> Seq.map (generic_qed ProofContext.auto_bind_facts #->
910 (fn ((after_qed, _), results) => after_qed results));
912 fun local_qed txt = local_qeds txt #> check_finish;
917 fun global_goal prepp before_qed after_qed propp ctxt =
919 |> generic_goal (prepp #> ProofContext.auto_fixes) "" before_qed (K I, after_qed) propp;
921 val theorem = global_goal ProofContext.bind_propp_schematic_i;
922 val theorem_cmd = global_goal ProofContext.bind_propp_schematic;
924 fun global_qeds txt =
926 #> Seq.map (generic_qed (K I) #> (fn (((_, after_qed), results), state) =>
927 after_qed results (context_of state)));
929 fun global_qed txt = global_qeds txt #> check_finish;
932 (* concluding steps *)
934 fun terminal_proof qed initial terminal =
935 proof (SOME initial) #> Seq.maps (qed terminal) #> check_finish;
937 fun local_terminal_proof (text, opt_text) = terminal_proof local_qeds text (opt_text, true);
938 val local_default_proof = local_terminal_proof (Method.default_text, NONE);
939 val local_immediate_proof = local_terminal_proof (Method.this_text, NONE);
940 fun local_skip_proof int = local_terminal_proof (Method.sorry_text int, NONE);
941 val local_done_proof = terminal_proof local_qeds Method.done_text (NONE, false);
943 fun global_terminal_proof (text, opt_text) = terminal_proof global_qeds text (opt_text, true);
944 val global_default_proof = global_terminal_proof (Method.default_text, NONE);
945 val global_immediate_proof = global_terminal_proof (Method.this_text, NONE);
946 fun global_skip_proof int = global_terminal_proof (Method.sorry_text int, NONE);
947 val global_done_proof = terminal_proof global_qeds Method.done_text (NONE, false);
950 (* common goal statements *)
954 fun gen_have prep_att prepp before_qed after_qed stmt int =
955 local_goal (Proof_Display.print_results int) prep_att prepp "have" before_qed after_qed stmt;
957 fun gen_show prep_att prepp before_qed after_qed stmt int state =
959 val testing = Unsynchronized.ref false;
960 val rule = Unsynchronized.ref (NONE: thm option);
962 "Local statement will fail to refine any pending goal" ::
963 (case ! rule of NONE => [] | SOME th => [Proof_Display.string_of_rule ctxt "Failed" th])
966 fun print_results ctxt res =
967 if ! testing then () else Proof_Display.print_results int ctxt res;
968 fun print_rule ctxt th =
969 if ! testing then rule := SOME th
970 else if int then priority (Proof_Display.string_of_rule ctxt "Successful" th)
973 try (local_skip_proof true)
974 |> setmp_noncritical testing true
977 fun after_qed' results =
978 refine_goals print_rule (context_of state) (flat results)
979 #> check_result "Failed to refine any pending goal"
980 #> after_qed results;
983 |> local_goal print_results prep_att prepp "show" before_qed after_qed' stmt
984 |> int ? (fn goal_state =>
985 (case test_proof goal_state of
986 Exn.Result (SOME _) => goal_state
987 | Exn.Result NONE => error (fail_msg (context_of goal_state))
988 | Exn.Exn Exn.Interrupt => raise Exn.Interrupt
989 | Exn.Exn exn => raise Exn.EXCEPTIONS ([exn, ERROR (fail_msg (context_of goal_state))])))
994 val have = gen_have (K I) ProofContext.bind_propp_i;
995 val have_cmd = gen_have Attrib.attribute ProofContext.bind_propp;
996 val show = gen_show (K I) ProofContext.bind_propp_i;
997 val show_cmd = gen_show Attrib.attribute ProofContext.bind_propp;
1003 (** future proofs **)
1005 (* relevant proof states *)
1007 fun is_schematic t =
1008 Term.exists_subterm Term.is_Var t orelse
1009 Term.exists_type (Term.exists_subtype Term.is_TVar) t;
1011 fun schematic_goal state =
1012 let val (_, (_, {statement = (_, _, prop), ...})) = find_goal state
1013 in is_schematic prop end;
1015 fun is_relevant state =
1016 (case try find_goal state of
1018 | SOME (_, (_, {statement = (_, _, prop), goal, ...})) =>
1019 is_schematic prop orelse not (Logic.protect prop aconv Thm.concl_of goal));
1026 fun future_proof done get_context fork_proof state =
1028 val _ = assert_backward state;
1029 val (goal_ctxt, (_, goal)) = find_goal state;
1030 val {statement as (kind, _, prop), messages, using, goal, before_qed, after_qed} = goal;
1031 val goal_txt = prop :: map Thm.term_of (Assumption.all_assms_of goal_ctxt);
1033 val _ = is_relevant state andalso error "Cannot fork relevant proof";
1035 val prop' = Logic.protect prop;
1036 val statement' = (kind, [[], [prop']], prop');
1037 val goal' = Thm.adjust_maxidx_thm (Thm.maxidx_of goal)
1038 (Drule.comp_no_flatten (goal, Thm.nprems_of goal) 1 Drule.protectI);
1040 fun after_local' [[th]] = put_thms false (Auto_Bind.thisN, SOME [th]);
1041 fun after_global' [[th]] = ProofContext.put_thms false (Auto_Bind.thisN, SOME [th]);
1042 val after_qed' = (after_local', after_global');
1043 val this_name = ProofContext.full_name goal_ctxt (Binding.name Auto_Bind.thisN);
1047 |> map_contexts (fold Variable.declare_term goal_txt)
1048 |> map_goal I (K (statement', messages, using, goal', before_qed, after_qed'))
1051 val future_thm = result_ctxt |> Future.map (fn (_, x) =>
1052 ProofContext.get_fact_single (get_context x) (Facts.named this_name));
1053 val finished_goal = Goal.future_result goal_ctxt future_thm prop';
1056 |> map_goal I (K (statement, messages, using, finished_goal, NONE, after_qed))
1058 in (Future.map #1 result_ctxt, state') end;
1062 fun local_future_proof x = future_proof local_done_proof context_of x;
1063 fun global_future_proof x = future_proof global_done_proof I x;
1068 (* terminal proofs *)
1072 fun future_terminal_proof proof1 proof2 meths int state =
1073 if int orelse is_relevant state orelse not (Goal.local_future_enabled ())
1074 then proof1 meths state
1075 else snd (proof2 (fn state' => Future.fork_pri ~1 (fn () => ((), proof1 meths state'))) state);
1079 fun local_future_terminal_proof x =
1080 future_terminal_proof local_terminal_proof local_future_proof x;
1082 fun global_future_terminal_proof x =
1083 future_terminal_proof global_terminal_proof global_future_proof x;