1 (* Title: Pure/Isar/proof.ML
3 Author: Markus Wenzel, TU Muenchen
5 The Isar/VM proof language interpreter: maintains a structured flow of
6 context elements, goals, refinements, and facts.
11 type context = Context.proof
12 type method = Method.method
14 val init: context -> state
15 val level: state -> int
16 val assert_bottom: bool -> state -> state
17 val context_of: state -> context
18 val theory_of: state -> theory
19 val map_context: (context -> context) -> state -> state
20 val add_binds_i: (indexname * term option) list -> state -> state
21 val put_thms: 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 get_goal: state -> context * (thm list * thm)
32 val schematic_goal: state -> bool
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: (string * string option * mixfix) list -> state -> state
47 val fix_i: (string * typ option * mixfix) list -> state -> state
48 val assm: Assumption.export ->
49 ((string * Attrib.src list) * (string * string list) list) list -> state -> state
50 val assm_i: Assumption.export ->
51 ((string * attribute list) * (term * term list) list) list -> state -> state
52 val assume: ((string * Attrib.src list) * (string * string list) list) list -> state -> state
53 val assume_i: ((string * attribute list) * (term * term list) list) list -> state -> state
54 val presume: ((string * Attrib.src list) * (string * string list) list) list -> state -> state
55 val presume_i: ((string * attribute list) * (term * term list) list) list -> state -> state
56 val def: ((string * Attrib.src list) *
57 ((string * mixfix) * (string * string list))) list -> state -> state
58 val def_i: ((string * attribute list) *
59 ((string * mixfix) * (term * term list))) list -> state -> state
60 val chain: state -> state
61 val chain_facts: thm list -> state -> state
62 val get_thmss: state -> (thmref * Attrib.src list) list -> thm list
63 val note_thmss: ((string * Attrib.src list) *
64 (thmref * Attrib.src list) list) list -> state -> state
65 val note_thmss_i: ((string * attribute list) *
66 (thm list * attribute list) list) list -> state -> state
67 val from_thmss: ((thmref * Attrib.src list) list) list -> state -> state
68 val from_thmss_i: ((thm list * attribute list) list) list -> state -> state
69 val with_thmss: ((thmref * Attrib.src list) list) list -> state -> state
70 val with_thmss_i: ((thm list * attribute list) list) list -> state -> state
71 val using: ((thmref * Attrib.src list) list) list -> state -> state
72 val using_i: ((thm list * attribute list) list) list -> state -> state
73 val unfolding: ((thmref * Attrib.src list) list) list -> state -> state
74 val unfolding_i: ((thm list * attribute list) list) list -> state -> state
75 val invoke_case: string * string option list * Attrib.src list -> state -> state
76 val invoke_case_i: string * string option list * attribute list -> state -> state
77 val begin_block: state -> state
78 val next_block: state -> state
79 val end_block: state -> state
80 val proof: Method.text option -> state -> state Seq.seq
81 val defer: int option -> state -> state Seq.seq
82 val prefer: int -> state -> state Seq.seq
83 val apply: Method.text -> state -> state Seq.seq
84 val apply_end: Method.text -> state -> state Seq.seq
85 val local_goal: (context -> ((string * string) * (string * thm list) list) -> unit) ->
86 (theory -> 'a -> attribute) ->
87 (context * 'b list -> context * (term list list * (context -> context))) ->
88 string -> Method.text option -> (thm list list -> state -> state Seq.seq) ->
89 ((string * 'a list) * 'b) list -> state -> state
90 val local_qed: Method.text option * bool -> state -> state Seq.seq
91 val theorem: Method.text option -> (thm list list -> context -> context) ->
92 (string * string list) list list -> context -> state
93 val theorem_i: Method.text option -> (thm list list -> context -> context) ->
94 (term * term list) list list -> context -> state
95 val global_qed: Method.text option * bool -> state -> context
96 val local_terminal_proof: Method.text * Method.text option -> state -> state Seq.seq
97 val local_default_proof: state -> state Seq.seq
98 val local_immediate_proof: state -> state Seq.seq
99 val local_done_proof: state -> state Seq.seq
100 val local_skip_proof: bool -> state -> state Seq.seq
101 val global_terminal_proof: Method.text * Method.text option -> state -> context
102 val global_default_proof: state -> context
103 val global_immediate_proof: state -> context
104 val global_done_proof: state -> context
105 val global_skip_proof: bool -> state -> context
106 val have: Method.text option -> (thm list list -> state -> state Seq.seq) ->
107 ((string * Attrib.src list) * (string * string list) list) list -> bool -> state -> state
108 val have_i: Method.text option -> (thm list list -> state -> state Seq.seq) ->
109 ((string * attribute list) * (term * term list) list) list -> bool -> state -> state
110 val show: Method.text option -> (thm list list -> state -> state Seq.seq) ->
111 ((string * Attrib.src list) * (string * string list) list) list -> bool -> state -> state
112 val show_i: Method.text option -> (thm list list -> state -> state Seq.seq) ->
113 ((string * attribute list) * (term * term list) list) list -> bool -> state -> state
116 structure Proof: PROOF =
119 type context = Context.proof;
120 type method = Method.method;
127 datatype mode = Forward | Chain | Backward;
130 State of node Stack.T
134 facts: thm list option,
139 {statement: string * term list list, (*goal kind and statement, starting with vars*)
140 using: thm list, (*goal facts*)
141 goal: thm, (*subgoals ==> statement*)
142 before_qed: Method.text option,
144 (thm list list -> state -> state Seq.seq) *
145 (thm list list -> context -> context)};
147 fun make_goal (statement, using, goal, before_qed, after_qed) =
148 Goal {statement = statement, using = using, goal = goal,
149 before_qed = before_qed, after_qed = after_qed};
151 fun make_node (context, facts, mode, goal) =
152 Node {context = context, facts = facts, mode = mode, goal = goal};
154 fun map_node f (Node {context, facts, mode, goal}) =
155 make_node (f (context, facts, mode, goal));
158 ProofContext.set_stmt true #> ProofContext.reset_naming;
161 State (Stack.init (make_node (init_context ctxt, NONE, Forward, NONE)));
163 fun current (State st) = Stack.top st |> (fn Node node => node);
164 fun map_current f (State st) = State (Stack.map_top (map_node f) st);
168 (** basic proof state operations **)
170 (* block structure *)
172 fun open_block (State st) = State (Stack.push st);
174 fun close_block (State st) = State (Stack.pop st)
175 handle Empty => error "Unbalanced block parentheses";
177 fun level (State st) = Stack.level st;
179 fun assert_bottom b state =
180 let val b' = (level state <= 2) in
181 if b andalso not b' then error "Not at bottom of proof!"
182 else if not b andalso b' then error "Already at bottom of proof!"
189 val context_of = #context o current;
190 val theory_of = ProofContext.theory_of o context_of;
193 map_current (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
195 fun map_context_result f state =
196 f (context_of state) ||> (fn ctxt => map_context (K ctxt) state);
198 val add_binds_i = map_context o ProofContext.add_binds_i;
199 val put_thms = map_context o ProofContext.put_thms;
204 val get_facts = #facts o current;
206 fun the_facts state =
207 (case get_facts state of SOME facts => facts
208 | NONE => error "No current facts available");
211 (case the_facts state of [thm] => thm
212 | _ => error "Single theorem expected");
214 fun put_facts facts =
215 map_current (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal)) #>
216 put_thms (AutoBind.thisN, facts);
218 fun these_factss more_facts (named_factss, state) =
219 (named_factss, state |> put_facts (SOME (maps snd named_factss @ more_facts)));
221 fun export_facts inner outer =
222 (case get_facts inner of
223 NONE => put_facts NONE outer
226 |> ProofContext.export (context_of inner) (context_of outer)
227 |> (fn ths => put_facts (SOME ths) outer));
232 val get_mode = #mode o current;
233 fun put_mode mode = map_current (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));
235 val mode_name = (fn Forward => "state" | Chain => "chain" | Backward => "prove");
237 fun assert_mode pred state =
238 let val mode = get_mode state in
239 if pred mode then state
240 else error ("Illegal application of proof command in " ^ quote (mode_name mode) ^ " mode")
243 val assert_forward = assert_mode (fn mode => mode = Forward);
244 val assert_chain = assert_mode (fn mode => mode = Chain);
245 val assert_forward_or_chain = assert_mode (fn mode => mode = Forward orelse mode = Chain);
246 val assert_backward = assert_mode (fn mode => mode = Backward);
247 val assert_no_chain = assert_mode (fn mode => mode <> Chain);
249 val enter_forward = put_mode Forward;
250 val enter_chain = put_mode Chain;
251 val enter_backward = put_mode Backward;
256 fun current_goal state =
257 (case current state of
258 {context, goal = SOME (Goal goal), ...} => (context, goal)
259 | _ => error "No current goal!");
261 fun assert_current_goal g state =
262 let val g' = can current_goal state in
263 if g andalso not g' then error "No goal in this block!"
264 else if not g andalso g' then error "Goal present in this block!"
268 fun put_goal goal = map_current (fn (ctxt, using, mode, _) => (ctxt, using, mode, goal));
270 val before_qed = #before_qed o #2 o current_goal;
275 fun map_goal f g (State (Node {context, facts, mode, goal = SOME goal}, nodes)) =
277 val Goal {statement, using, goal, before_qed, after_qed} = goal;
278 val goal' = make_goal (g (statement, using, goal, before_qed, after_qed));
279 in State (make_node (f context, facts, mode, SOME goal'), nodes) end
280 | map_goal f g (State (nd, node :: nodes)) =
281 let val State (node', nodes') = map_goal f g (State (node, nodes))
282 in map_context f (State (nd, node' :: nodes')) end
283 | map_goal _ _ state = state;
285 fun set_goal goal = map_goal I (fn (statement, using, _, before_qed, after_qed) =>
286 (statement, using, goal, before_qed, after_qed));
288 fun using_facts using = map_goal I (fn (statement, _, goal, before_qed, after_qed) =>
289 (statement, using, goal, before_qed, after_qed));
293 (case try current_goal state of
294 SOME (ctxt, goal) => (ctxt, (i, goal))
295 | NONE => find (i + 1) (close_block state handle ERROR _ => error "No goal present"));
296 in val find_goal = find 0 end;
299 let val (ctxt, (_, {using, goal, ...})) = find_goal state
300 in (ctxt, (using, goal)) end;
302 fun schematic_goal state =
303 let val (_, (_, {statement = (_, propss), ...})) = find_goal state in
304 exists (exists (Term.exists_subterm Term.is_Var)) propss orelse
305 exists (exists (Term.exists_type (Term.exists_subtype Term.is_TVar))) propss
312 val show_main_goal = ref false;
313 val verbose = ProofContext.verbose;
315 val pretty_goals_local = Display.pretty_goals_aux o ProofContext.pp;
317 fun pretty_facts _ _ NONE = []
318 | pretty_facts s ctxt (SOME ths) =
319 [Pretty.big_list (s ^ "this:") (map (ProofContext.pretty_thm ctxt) ths), Pretty.str ""];
321 fun pretty_state nr state =
323 val {context, facts, mode, goal = _} = current state;
326 | levels_up 1 = "1 level up"
327 | levels_up i = string_of_int i ^ " levels up";
330 | subgoals 1 = "1 subgoal"
331 | subgoals n = string_of_int n ^ " subgoals";
333 fun description strs =
334 (case filter_out (equal "") strs of [] => ""
335 | strs' => enclose " (" ")" (commas strs'));
337 fun prt_goal (SOME (ctxt, (i, {statement = _, using, goal, before_qed, after_qed}))) =
338 pretty_facts "using " ctxt
339 (if mode <> Backward orelse null using then NONE else SOME using) @
340 [Pretty.str ("goal" ^
341 description [levels_up (i div 2), subgoals (Thm.nprems_of goal)] ^ ":")] @
342 pretty_goals_local ctxt Markup.subgoal
343 (true, ! show_main_goal) (! Display.goals_limit) goal
344 | prt_goal NONE = [];
347 if ! verbose orelse mode = Forward then ProofContext.pretty_context context
348 else if mode = Backward then ProofContext.pretty_ctxt context
351 [Pretty.str ("proof (" ^ mode_name mode ^ "): step " ^ string_of_int nr ^
352 (if ! verbose then ", depth " ^ string_of_int (level state div 2 - 1) else "")),
354 (if null prt_ctxt then [] else prt_ctxt @ [Pretty.str ""]) @
355 (if ! verbose orelse mode = Forward then
356 pretty_facts "" context facts @ prt_goal (try find_goal state)
357 else if mode = Chain then pretty_facts "picking " context facts
358 else prt_goal (try find_goal state))
361 fun pretty_goals main state =
362 let val (ctxt, (_, goal)) = get_goal state
363 in pretty_goals_local ctxt Markup.none (false, main) (! Display.goals_limit) goal end;
369 (* refine via method *)
373 fun goalN i = "goal" ^ string_of_int i;
374 fun goals st = map goalN (1 upto Thm.nprems_of st);
376 fun no_goal_cases st = map (rpair NONE) (goals st);
379 RuleCases.make_common true (Thm.theory_of_thm st, Thm.prop_of st) (map (rpair []) (goals st));
381 fun apply_method current_context pos meth_fun state =
383 val (goal_ctxt, (_, {statement, using, goal, before_qed, after_qed})) = find_goal state;
384 val ctxt = ContextPosition.put pos (if current_context then context_of state else goal_ctxt);
385 val meth = meth_fun ctxt;
387 Method.apply meth using goal |> Seq.map (fn (meth_cases, goal') =>
390 (ProofContext.add_cases false (no_goal_cases goal @ goal_cases goal') #>
391 ProofContext.add_cases true meth_cases)
392 (K (statement, using, goal', before_qed, after_qed)))
395 fun select_goals n meth state =
397 |> (#2 o #2 o get_goal)
398 |> ALLGOALS Goal.conjunction_tac
399 |> Seq.maps (fn goal =>
401 |> Seq.lift set_goal (Goal.extract 1 n goal |> Seq.maps (Goal.conjunction_tac 1))
403 |> Seq.maps (fn state' => state'
404 |> Seq.lift set_goal (Goal.retrofit 1 n (#2 (#2 (get_goal state'))) goal))
405 |> Seq.maps (apply_method true Position.none (K Method.succeed)));
407 fun apply_text cc text state =
409 val thy = theory_of state;
410 val pos_of = #2 o Args.dest_src;
412 fun eval (Method.Basic (m, pos)) = apply_method cc pos m
413 | eval (Method.Source src) = apply_method cc (pos_of src) (Method.method thy src)
414 | eval (Method.Source_i src) = apply_method cc (pos_of src) (Method.method_i thy src)
415 | eval (Method.Then txts) = Seq.EVERY (map eval txts)
416 | eval (Method.Orelse txts) = Seq.FIRST (map eval txts)
417 | eval (Method.Try txt) = Seq.TRY (eval txt)
418 | eval (Method.Repeat1 txt) = Seq.REPEAT1 (eval txt)
419 | eval (Method.SelectGoals (n, txt)) = select_goals n (eval txt);
420 in eval text state end;
424 val refine = apply_text true;
425 val refine_end = apply_text false;
427 fun refine_insert [] = I
428 | refine_insert ths = Seq.hd o refine (Method.Basic (K (Method.insert ths), Position.none));
433 (* refine via sub-proof *)
436 Goal.norm_hhf_tac THEN' Tactic.rtac rule THEN_ALL_NEW
437 (Goal.norm_hhf_tac THEN' (SUBGOAL (fn (goal, i) =>
438 if can Logic.unprotect (Logic.strip_assums_concl goal) then
439 Tactic.etac Drule.protectI i
442 fun refine_goals print_rule inner raw_rules state =
444 val (outer, (_, goal)) = get_goal state;
445 fun refine rule st = (print_rule outer rule; FINDGOAL (goal_tac rule) st);
448 |> ProofContext.goal_export inner outer
449 |> (fn rules => Seq.lift set_goal (EVERY (map refine rules) goal) state)
455 fun conclude_goal state goal propss =
457 val thy = theory_of state;
458 val ctxt = context_of state;
459 val string_of_term = ProofContext.string_of_term ctxt;
460 val string_of_thm = ProofContext.string_of_thm ctxt;
462 val ngoals = Thm.nprems_of goal;
463 val _ = ngoals = 0 orelse error (Pretty.string_of (Pretty.chunks
464 (pretty_goals_local ctxt Markup.none (true, ! show_main_goal) (! Display.goals_limit) goal @
465 [Pretty.str (string_of_int ngoals ^ " unsolved goal(s)!")])));
467 val extra_hyps = Assumption.extra_hyps ctxt goal;
468 val _ = null extra_hyps orelse
469 error ("Additional hypotheses:\n" ^ cat_lines (map string_of_term extra_hyps));
471 fun lost_structure () = error ("Lost goal structure:\n" ^ string_of_thm goal);
473 val th = Goal.conclude
474 (if length (flat propss) > 1 then Thm.norm_proof goal else goal)
475 handle THM _ => lost_structure ();
476 val goal_propss = filter_out null propss;
478 Conjunction.elim_balanced (length goal_propss) th
479 |> map2 Conjunction.elim_balanced (map length goal_propss)
480 handle THM _ => lost_structure ();
481 val _ = Unify.matches_list thy (flat goal_propss) (map Thm.prop_of (flat results)) orelse
482 error ("Proved a different theorem:\n" ^ string_of_thm th);
484 fun recover_result ([] :: pss) thss = [] :: recover_result pss thss
485 | recover_result (_ :: pss) (ths :: thss) = ths :: recover_result pss thss
486 | recover_result [] [] = []
487 | recover_result _ _ = lost_structure ();
488 in recover_result propss results end;
492 (*** structured proof commands ***)
494 (** context elements **)
500 fun gen_bind bind args state =
503 |> map_context (bind args #> snd)
508 val match_bind = gen_bind (ProofContext.match_bind false);
509 val match_bind_i = gen_bind (ProofContext.match_bind_i false);
510 val let_bind = gen_bind (ProofContext.match_bind true);
511 val let_bind_i = gen_bind (ProofContext.match_bind_i true);
520 fun gen_fix add_fixes args =
522 #> map_context (snd o add_fixes args)
527 val fix = gen_fix ProofContext.add_fixes;
528 val fix_i = gen_fix ProofContext.add_fixes_i;
537 fun gen_assume asm prep_att exp args state =
540 |> map_context_result (asm exp (Attrib.map_specs (prep_att (theory_of state)) args))
541 |> these_factss [] |> #2;
545 val assm = gen_assume ProofContext.add_assms Attrib.attribute;
546 val assm_i = gen_assume ProofContext.add_assms_i (K I);
547 val assume = assm Assumption.assume_export;
548 val assume_i = assm_i Assumption.assume_export;
549 val presume = assm Assumption.presume_export;
550 val presume_i = assm_i Assumption.presume_export;
559 fun gen_def prep_att prep_vars prep_binds args state =
561 val _ = assert_forward state;
562 val thy = theory_of state;
563 val ctxt = context_of state;
565 val (raw_name_atts, (raw_vars, raw_rhss)) = args |> split_list ||> split_list;
566 val name_atts = map (apsnd (map (prep_att thy))) raw_name_atts;
569 |> map_context_result (prep_vars (map (fn (x, mx) => (x, NONE, mx)) raw_vars))
570 |>> map (fn (x, _, mx) => (x, mx))
572 map_context_result (prep_binds false (map swap raw_rhss))
573 #-> (fn rhss => map_context_result (LocalDefs.add_defs (vars ~~ (name_atts ~~ rhss)))))
574 |-> (put_facts o SOME o map (#2 o #2))
579 val def = gen_def Attrib.attribute ProofContext.read_vars ProofContext.match_bind;
580 val def_i = gen_def (K I) ProofContext.cert_vars ProofContext.match_bind_i;
595 fun chain_facts facts =
596 put_facts (SOME facts)
602 fun no_binding args = map (pair ("", [])) args;
606 fun gen_thmss note_ctxt more_facts opt_chain opt_result prep_atts args state =
609 |> map_context_result (note_ctxt (Attrib.map_facts (prep_atts (theory_of state)) args))
610 |> these_factss (more_facts state)
616 val note_thmss = gen_thmss (ProofContext.note_thmss "") (K []) I #2 Attrib.attribute;
617 val note_thmss_i = gen_thmss (ProofContext.note_thmss_i "") (K []) I #2 (K I);
620 gen_thmss (ProofContext.note_thmss "") (K []) chain #2 Attrib.attribute o no_binding;
621 val from_thmss_i = gen_thmss (ProofContext.note_thmss_i "") (K []) chain #2 (K I) o no_binding;
624 gen_thmss (ProofContext.note_thmss "") the_facts chain #2 Attrib.attribute o no_binding;
625 val with_thmss_i = gen_thmss (ProofContext.note_thmss_i "") the_facts chain #2 (K I) o no_binding;
628 gen_thmss (ProofContext.note_thmss_i "") (K []) I I (K I) o map (apsnd Thm.simple_fact);
630 fun get_thmss state srcs = the_facts (note_thmss [(("", []), srcs)] state);
635 (* using/unfolding *)
639 fun gen_using f g note prep_atts args state =
642 |> map_context_result
643 (note "" (Attrib.map_facts (prep_atts (theory_of state)) (no_binding args)))
644 |> (fn (named_facts, state') =>
645 state' |> map_goal I (fn (statement, using, goal, before_qed, after_qed) =>
647 val ctxt = context_of state';
648 val ths = maps snd named_facts;
649 in (statement, f ctxt ths using, g ctxt ths goal, before_qed, after_qed) end));
651 fun append_using _ ths using = using @ ths;
652 fun unfold_using ctxt ths = map (LocalDefs.unfold ctxt ths);
653 val unfold_goals = LocalDefs.unfold_goals;
657 val using = gen_using append_using (K (K I)) ProofContext.note_thmss Attrib.attribute;
658 val using_i = gen_using append_using (K (K I)) ProofContext.note_thmss_i (K I);
659 val unfolding = gen_using unfold_using unfold_goals ProofContext.note_thmss Attrib.attribute;
660 val unfolding_i = gen_using unfold_using unfold_goals ProofContext.note_thmss_i (K I);
669 fun gen_invoke_case prep_att (name, xs, raw_atts) state =
671 val atts = map (prep_att (theory_of state)) raw_atts;
672 val (asms, state') = state |> map_context_result (fn ctxt =>
673 ctxt |> ProofContext.apply_case (ProofContext.get_case ctxt name xs));
674 val assumptions = asms |> map (fn (a, ts) => ((a, atts), map (rpair []) ts));
677 |> map_context (ProofContext.qualified_names #> ProofContext.no_base_names)
678 |> assume_i assumptions
679 |> add_binds_i AutoBind.no_facts
680 |> map_context (ProofContext.restore_naming (context_of state))
681 |> `the_facts |-> (fn thms => note_thmss_i [((name, []), [(thms, [])])])
686 val invoke_case = gen_invoke_case Attrib.attribute;
687 val invoke_case_i = gen_invoke_case (K I);
693 (** proof structure **)
710 fun end_block state =
714 |> assert_current_goal false
716 |> export_facts state;
723 #> refine (the_default Method.default_text opt_text)
724 #> Seq.map (using_facts [] #> enter_forward);
726 fun end_proof bot txt state =
731 |> assert_current_goal true
733 |> `before_qed |-> (refine o the_default Method.succeed_text)
734 |> Seq.maps (refine (Method.finish_text txt (ContextPosition.get (context_of state))));
737 (* unstructured refinement *)
739 fun defer i = assert_no_chain #> refine (Method.Basic (K (Method.defer i), Position.none));
740 fun prefer i = assert_no_chain #> refine (Method.Basic (K (Method.prefer i), Position.none));
742 fun apply text = assert_backward #> refine text #> Seq.map (using_facts []);
743 fun apply_end text = assert_forward #> refine_end text;
753 fun implicit_vars dest add props =
755 val (explicit_vars, props') = take_prefix (can dest) props |>> map dest;
756 val vars = rev (subtract (op =) explicit_vars (fold add props []));
759 else warning ("Goal statement contains unbound schematic variable(s): " ^
760 commas_quote (map (Term.string_of_vname o fst) vars));
761 in (rev vars, props') end;
764 refine (Method.Basic (K (Method.RAW_METHOD
765 (K (HEADGOAL (PRECISE_CONJUNCTS n
766 (HEADGOAL (CONJUNCTS (ALLGOALS (rtac Drule.termI)))))))), Position.none))
771 fun generic_goal prepp kind before_qed after_qed raw_propp state =
773 val thy = theory_of state;
774 val cert = Thm.cterm_of thy;
775 val chaining = can assert_chain state;
777 val ((propss, after_ctxt), goal_state) =
779 |> assert_forward_or_chain
782 |> map_context_result (fn ctxt => swap (prepp (ctxt, raw_propp)));
783 val props = flat propss;
786 implicit_vars (dest_TVar o Logic.dest_type o Logic.dest_term) Term.add_tvars props;
787 val (vars, _) = implicit_vars (dest_Var o Logic.dest_term) Term.add_vars props';
789 val propss' = map (Logic.mk_term o Var) vars :: propss;
790 val goal_propss = filter_out null propss';
791 val goal = Goal.init (cert
792 (Logic.mk_conjunction_balanced (map Logic.mk_conjunction_balanced goal_propss)));
793 val after_qed' = after_qed |>> (fn after_local =>
794 fn results => map_context after_ctxt #> after_local results);
797 |> map_context (init_context #> Variable.set_body true)
798 |> put_goal (SOME (make_goal ((kind, propss'), [], goal, before_qed, after_qed')))
799 |> map_context (ProofContext.add_cases false (AutoBind.cases thy props))
800 |> map_context (ProofContext.auto_bind_goal props)
801 |> chaining ? (`the_facts #-> using_facts)
806 |> not (null vars) ? refine_terms (length goal_propss)
807 |> null props ? (refine (Method.Basic (Method.assumption, Position.none)) #> Seq.hd)
810 fun generic_qed state =
812 val (goal_ctxt, {statement = (_, stmt), using = _, goal, before_qed = _, after_qed}) =
814 val outer_state = state |> close_block;
815 val outer_ctxt = context_of outer_state;
819 |> Variable.exportT_terms goal_ctxt outer_ctxt;
821 tl (conclude_goal state goal stmt)
822 |> burrow (ProofContext.export goal_ctxt outer_ctxt);
825 |> map_context (ProofContext.auto_bind_facts props)
826 |> pair (after_qed, results)
834 fun local_goal print_results prep_att prepp kind before_qed after_qed stmt state =
836 val thy = theory_of state;
837 val ((names, attss), propp) =
838 Attrib.map_specs (prep_att thy) stmt |> split_list |>> split_list;
840 fun after_qed' results =
841 local_results ((names ~~ attss) ~~ results)
842 #-> (fn res => tap (fn st => print_results (context_of st) ((kind, ""), res) : unit))
843 #> after_qed results;
846 |> generic_goal prepp kind before_qed (after_qed', K I) propp
847 |> tap (Variable.warn_extra_tfrees (context_of state) o context_of)
851 end_proof false txt #>
852 Seq.maps (generic_qed #-> (fn ((after_qed, _), results) => after_qed results));
857 fun global_goal prepp before_qed after_qed propp ctxt =
859 |> generic_goal (prepp #> ProofContext.auto_fixes) ""
860 before_qed (K Seq.single, after_qed) propp;
862 val theorem = global_goal ProofContext.bind_propp_schematic;
863 val theorem_i = global_goal ProofContext.bind_propp_schematic_i;
865 fun check_result msg sq =
868 | SOME (s', sq') => Seq.cons s' sq');
870 fun global_qeds txt =
872 #> Seq.map (generic_qed #> (fn (((_, after_qed), results), state) =>
873 after_qed results (context_of state)))
874 |> Seq.DETERM; (*backtracking may destroy theory!*)
878 #> check_result "Failed to finish proof"
882 (* concluding steps *)
884 fun local_terminal_proof (text, opt_text) =
885 proof (SOME text) #> Seq.maps (local_qed (opt_text, true));
887 val local_default_proof = local_terminal_proof (Method.default_text, NONE);
888 val local_immediate_proof = local_terminal_proof (Method.this_text, NONE);
889 val local_done_proof = proof (SOME Method.done_text) #> Seq.maps (local_qed (NONE, false));
890 fun local_skip_proof int = local_terminal_proof (Method.sorry_text int, NONE);
892 fun global_term_proof immed (text, opt_text) =
894 #> check_result "Terminal proof method failed"
895 #> Seq.maps (global_qeds (opt_text, immed))
896 #> check_result "Failed to finish proof (after successful terminal method)"
899 val global_terminal_proof = global_term_proof true;
900 val global_default_proof = global_terminal_proof (Method.default_text, NONE);
901 val global_immediate_proof = global_terminal_proof (Method.this_text, NONE);
902 val global_done_proof = global_term_proof false (Method.done_text, NONE);
903 fun global_skip_proof int = global_terminal_proof (Method.sorry_text int, NONE);
906 (* common goal statements *)
910 fun gen_have prep_att prepp before_qed after_qed stmt int =
911 local_goal (ProofDisplay.print_results int) prep_att prepp "have" before_qed after_qed stmt;
913 fun gen_show prep_att prepp before_qed after_qed stmt int state =
915 val testing = ref false;
916 val rule = ref (NONE: thm option);
918 "Local statement will fail to solve any pending goal" ::
919 (case ! rule of NONE => [] | SOME th => [ProofDisplay.string_of_rule ctxt "Failed" th])
922 fun print_results ctxt res =
923 if ! testing then () else ProofDisplay.print_results int ctxt res;
924 fun print_rule ctxt th =
925 if ! testing then rule := SOME th
926 else if int then priority (ProofDisplay.string_of_rule ctxt "Successful" th)
929 (Seq.pull oo local_skip_proof) true
930 |> setmp testing true
934 fun after_qed' results =
935 refine_goals print_rule (context_of state) (flat results)
936 #> Seq.maps (after_qed results);
939 |> local_goal print_results prep_att prepp "show" before_qed after_qed' stmt
940 |> int ? (fn goal_state =>
941 (case test_proof goal_state of
942 Result (SOME _) => goal_state
943 | Result NONE => error (fail_msg (context_of goal_state))
944 | Exn Interrupt => raise Interrupt
945 | Exn exn => raise EXCEPTION (exn, fail_msg (context_of goal_state))))
950 val have = gen_have Attrib.attribute ProofContext.bind_propp;
951 val have_i = gen_have (K I) ProofContext.bind_propp_i;
952 val show = gen_show Attrib.attribute ProofContext.bind_propp;
953 val show_i = gen_show (K I) ProofContext.bind_propp_i;