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 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: (string * string option * mixfix) list -> state -> state
48 val fix_i: (string * typ option * mixfix) list -> state -> state
49 val assm: Assumption.export ->
50 ((string * Attrib.src list) * (string * string list) list) list -> state -> state
51 val assm_i: Assumption.export ->
52 ((string * attribute list) * (term * term list) list) list -> state -> state
53 val assume: ((string * Attrib.src list) * (string * string list) list) list -> state -> state
54 val assume_i: ((string * attribute list) * (term * term list) list) list -> state -> state
55 val presume: ((string * Attrib.src list) * (string * string list) list) list -> state -> state
56 val presume_i: ((string * attribute list) * (term * term list) list) list -> state -> state
57 val def: ((string * Attrib.src list) *
58 ((string * mixfix) * (string * string list))) list -> state -> state
59 val def_i: ((string * attribute list) *
60 ((string * mixfix) * (term * term list))) list -> state -> state
61 val chain: state -> state
62 val chain_facts: thm list -> state -> state
63 val get_thmss: state -> (thmref * Attrib.src list) list -> thm list
64 val note_thmss: ((string * Attrib.src list) *
65 (thmref * Attrib.src list) list) list -> state -> state
66 val note_thmss_i: ((string * attribute list) *
67 (thm list * attribute list) list) list -> state -> state
68 val from_thmss: ((thmref * Attrib.src list) list) list -> state -> state
69 val from_thmss_i: ((thm list * attribute list) list) list -> state -> state
70 val with_thmss: ((thmref * Attrib.src list) list) list -> state -> state
71 val with_thmss_i: ((thm list * attribute list) list) list -> state -> state
72 val using: ((thmref * Attrib.src list) list) list -> state -> state
73 val using_i: ((thm list * attribute list) list) list -> state -> state
74 val unfolding: ((thmref * Attrib.src list) list) list -> state -> state
75 val unfolding_i: ((thm list * attribute list) list) list -> state -> state
76 val invoke_case: string * string option list * Attrib.src list -> state -> state
77 val invoke_case_i: string * string option list * attribute list -> state -> state
78 val begin_block: state -> state
79 val next_block: state -> state
80 val end_block: state -> state
81 val proof: Method.text option -> state -> state Seq.seq
82 val defer: int option -> state -> state Seq.seq
83 val prefer: int -> state -> state Seq.seq
84 val apply: Method.text -> state -> state Seq.seq
85 val apply_end: Method.text -> state -> state Seq.seq
86 val local_goal: (context -> ((string * string) * (string * thm list) list) -> unit) ->
87 (theory -> 'a -> attribute) ->
88 (context * 'b list -> context * (term list list * (context -> context))) ->
89 string -> Method.text option -> (thm list list -> state -> state Seq.seq) ->
90 ((string * 'a list) * 'b) list -> state -> state
91 val local_qed: Method.text option * bool -> state -> state Seq.seq
92 val theorem: Method.text option -> (thm list list -> context -> context) ->
93 (string * string list) list list -> context -> state
94 val theorem_i: Method.text option -> (thm list list -> context -> context) ->
95 (term * term list) list list -> context -> state
96 val global_qed: Method.text option * bool -> state -> context
97 val local_terminal_proof: Method.text * Method.text option -> state -> state Seq.seq
98 val local_default_proof: state -> state Seq.seq
99 val local_immediate_proof: state -> state Seq.seq
100 val local_done_proof: state -> state Seq.seq
101 val local_skip_proof: bool -> state -> state Seq.seq
102 val global_terminal_proof: Method.text * Method.text option -> state -> context
103 val global_default_proof: state -> context
104 val global_immediate_proof: state -> context
105 val global_done_proof: state -> context
106 val global_skip_proof: bool -> state -> context
107 val have: Method.text option -> (thm list list -> state -> state Seq.seq) ->
108 ((string * Attrib.src list) * (string * string list) list) list -> bool -> state -> state
109 val have_i: Method.text option -> (thm list list -> state -> state Seq.seq) ->
110 ((string * attribute list) * (term * term list) list) list -> bool -> state -> state
111 val show: Method.text option -> (thm list list -> state -> state Seq.seq) ->
112 ((string * Attrib.src list) * (string * string list) list) list -> bool -> state -> state
113 val show_i: Method.text option -> (thm list list -> state -> state Seq.seq) ->
114 ((string * attribute list) * (term * term list) list) list -> bool -> state -> state
117 structure Proof: PROOF =
120 type context = Context.proof;
121 type method = Method.method;
128 datatype mode = Forward | Chain | Backward;
131 State of node Stack.T
135 facts: thm list option,
140 {statement: string * term list list, (*goal kind and statement, starting with vars*)
141 messages: (unit -> Pretty.T) list, (*persistent messages (hints etc.)*)
142 using: thm list, (*goal facts*)
143 goal: thm, (*subgoals ==> statement*)
144 before_qed: Method.text option,
146 (thm list list -> state -> state Seq.seq) *
147 (thm list list -> context -> context)};
149 fun make_goal (statement, messages, using, goal, before_qed, after_qed) =
150 Goal {statement = statement, messages = messages, using = using, goal = goal,
151 before_qed = before_qed, after_qed = after_qed};
153 fun make_node (context, facts, mode, goal) =
154 Node {context = context, facts = facts, mode = mode, goal = goal};
156 fun map_node f (Node {context, facts, mode, goal}) =
157 make_node (f (context, facts, mode, goal));
160 ProofContext.set_stmt true #> ProofContext.reset_naming;
163 State (Stack.init (make_node (init_context ctxt, NONE, Forward, NONE)));
165 fun current (State st) = Stack.top st |> (fn Node node => node);
166 fun map_current f (State st) = State (Stack.map_top (map_node f) st);
170 (** basic proof state operations **)
172 (* block structure *)
174 fun open_block (State st) = State (Stack.push st);
176 fun close_block (State st) = State (Stack.pop st)
177 handle Empty => error "Unbalanced block parentheses";
179 fun level (State st) = Stack.level st;
181 fun assert_bottom b state =
182 let val b' = (level state <= 2) in
183 if b andalso not b' then error "Not at bottom of proof!"
184 else if not b andalso b' then error "Already at bottom of proof!"
191 val context_of = #context o current;
192 val theory_of = ProofContext.theory_of o context_of;
195 map_current (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));
197 fun map_context_result f state =
198 f (context_of state) ||> (fn ctxt => map_context (K ctxt) state);
200 val add_binds_i = map_context o ProofContext.add_binds_i;
201 val put_thms = map_context o ProofContext.put_thms;
206 val get_facts = #facts o current;
208 fun the_facts state =
209 (case get_facts state of SOME facts => facts
210 | NONE => error "No current facts available");
213 (case the_facts state of [thm] => thm
214 | _ => error "Single theorem expected");
216 fun put_facts facts =
217 map_current (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal)) #>
218 put_thms (AutoBind.thisN, facts);
220 fun these_factss more_facts (named_factss, state) =
221 (named_factss, state |> put_facts (SOME (maps snd named_factss @ more_facts)));
223 fun export_facts inner outer =
224 (case get_facts inner of
225 NONE => put_facts NONE outer
228 |> ProofContext.export (context_of inner) (context_of outer)
229 |> (fn ths => put_facts (SOME ths) outer));
234 val get_mode = #mode o current;
235 fun put_mode mode = map_current (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));
237 val mode_name = (fn Forward => "state" | Chain => "chain" | Backward => "prove");
239 fun assert_mode pred state =
240 let val mode = get_mode state in
241 if pred mode then state
242 else error ("Illegal application of proof command in " ^ quote (mode_name mode) ^ " mode")
245 val assert_forward = assert_mode (fn mode => mode = Forward);
246 val assert_chain = assert_mode (fn mode => mode = Chain);
247 val assert_forward_or_chain = assert_mode (fn mode => mode = Forward orelse mode = Chain);
248 val assert_backward = assert_mode (fn mode => mode = Backward);
249 val assert_no_chain = assert_mode (fn mode => mode <> Chain);
251 val enter_forward = put_mode Forward;
252 val enter_chain = put_mode Chain;
253 val enter_backward = put_mode Backward;
258 fun current_goal state =
259 (case current state of
260 {context, goal = SOME (Goal goal), ...} => (context, goal)
261 | _ => error "No current goal!");
263 fun assert_current_goal g state =
264 let val g' = can current_goal state in
265 if g andalso not g' then error "No goal in this block!"
266 else if not g andalso g' then error "Goal present in this block!"
270 fun put_goal goal = map_current (fn (ctxt, using, mode, _) => (ctxt, using, mode, goal));
272 val before_qed = #before_qed o #2 o current_goal;
277 fun map_goal f g (State (Node {context, facts, mode, goal = SOME goal}, nodes)) =
279 val Goal {statement, messages, using, goal, before_qed, after_qed} = goal;
280 val goal' = make_goal (g (statement, messages, using, goal, before_qed, after_qed));
281 in State (make_node (f context, facts, mode, SOME goal'), nodes) end
282 | map_goal f g (State (nd, node :: nodes)) =
283 let val State (node', nodes') = map_goal f g (State (node, nodes))
284 in map_context f (State (nd, node' :: nodes')) end
285 | map_goal _ _ state = state;
287 fun set_goal goal = map_goal I (fn (statement, _, using, _, before_qed, after_qed) =>
288 (statement, [], using, goal, before_qed, after_qed));
290 fun goal_message msg = map_goal I (fn (statement, messages, using, goal, before_qed, after_qed) =>
291 (statement, msg :: messages, using, goal, before_qed, after_qed));
293 fun using_facts using = map_goal I (fn (statement, _, _, goal, before_qed, after_qed) =>
294 (statement, [], using, goal, before_qed, after_qed));
298 (case try current_goal state of
299 SOME (ctxt, goal) => (ctxt, (i, goal))
300 | NONE => find (i + 1) (close_block state handle ERROR _ => error "No goal present"));
301 in val find_goal = find 0 end;
304 let val (ctxt, (_, {using, goal, ...})) = find_goal state
305 in (ctxt, (using, goal)) end;
307 fun schematic_goal state =
308 let val (_, (_, {statement = (_, propss), ...})) = find_goal state in
309 exists (exists (Term.exists_subterm Term.is_Var)) propss orelse
310 exists (exists (Term.exists_type (Term.exists_subtype Term.is_TVar))) propss
317 val show_main_goal = ref false;
318 val verbose = ProofContext.verbose;
320 val pretty_goals_local = Display.pretty_goals_aux o ProofContext.pp;
322 fun pretty_facts _ _ NONE = []
323 | pretty_facts s ctxt (SOME ths) =
324 [Pretty.big_list (s ^ "this:") (map (ProofContext.pretty_thm ctxt) ths), Pretty.str ""];
326 fun pretty_state nr state =
328 val {context, facts, mode, goal = _} = current state;
331 | levels_up 1 = "1 level up"
332 | levels_up i = string_of_int i ^ " levels up";
335 | subgoals 1 = "1 subgoal"
336 | subgoals n = string_of_int n ^ " subgoals";
338 fun description strs =
339 (case filter_out (equal "") strs of [] => ""
340 | strs' => enclose " (" ")" (commas strs'));
342 fun prt_goal (SOME (ctxt, (i,
343 {statement = _, messages, using, goal, before_qed, after_qed}))) =
344 pretty_facts "using " ctxt
345 (if mode <> Backward orelse null using then NONE else SOME using) @
346 [Pretty.str ("goal" ^
347 description [levels_up (i div 2), subgoals (Thm.nprems_of goal)] ^ ":")] @
348 pretty_goals_local ctxt Markup.subgoal
349 (true, ! show_main_goal) (! Display.goals_limit) goal @
350 (map (fn msg => msg ()) (rev messages))
351 | prt_goal NONE = [];
354 if ! verbose orelse mode = Forward then ProofContext.pretty_context context
355 else if mode = Backward then ProofContext.pretty_ctxt context
358 [Pretty.str ("proof (" ^ mode_name mode ^ "): step " ^ string_of_int nr ^
359 (if ! verbose then ", depth " ^ string_of_int (level state div 2 - 1) else "")),
361 (if null prt_ctxt then [] else prt_ctxt @ [Pretty.str ""]) @
362 (if ! verbose orelse mode = Forward then
363 pretty_facts "" context facts @ prt_goal (try find_goal state)
364 else if mode = Chain then pretty_facts "picking " context facts
365 else prt_goal (try find_goal state))
368 fun pretty_goals main state =
369 let val (ctxt, (_, goal)) = get_goal state
370 in pretty_goals_local ctxt Markup.none (false, main) (! Display.goals_limit) goal end;
376 (* refine via method *)
380 fun goalN i = "goal" ^ string_of_int i;
381 fun goals st = map goalN (1 upto Thm.nprems_of st);
383 fun no_goal_cases st = map (rpair NONE) (goals st);
386 RuleCases.make_common true (Thm.theory_of_thm st, Thm.prop_of st) (map (rpair []) (goals st));
388 fun apply_method current_context pos meth_fun state =
390 val (goal_ctxt, (_, {statement, messages = _, using, goal, before_qed, after_qed})) =
392 val ctxt = ContextPosition.put_ctxt pos
393 (if current_context then context_of state else goal_ctxt);
394 val meth = meth_fun ctxt;
396 Method.apply meth using goal |> Seq.map (fn (meth_cases, goal') =>
399 (ProofContext.add_cases false (no_goal_cases goal @ goal_cases goal') #>
400 ProofContext.add_cases true meth_cases)
401 (K (statement, [], using, goal', before_qed, after_qed)))
404 fun select_goals n meth state =
406 |> (#2 o #2 o get_goal)
407 |> ALLGOALS Goal.conjunction_tac
408 |> Seq.maps (fn goal =>
410 |> Seq.lift set_goal (Goal.extract 1 n goal |> Seq.maps (Goal.conjunction_tac 1))
412 |> Seq.maps (fn state' => state'
413 |> Seq.lift set_goal (Goal.retrofit 1 n (#2 (#2 (get_goal state'))) goal))
414 |> Seq.maps (apply_method true Position.none (K Method.succeed)));
416 fun apply_text cc text state =
418 val thy = theory_of state;
419 val pos_of = #2 o Args.dest_src;
421 fun eval (Method.Basic (m, pos)) = apply_method cc pos m
422 | eval (Method.Source src) = apply_method cc (pos_of src) (Method.method thy src)
423 | eval (Method.Source_i src) = apply_method cc (pos_of src) (Method.method_i thy src)
424 | eval (Method.Then txts) = Seq.EVERY (map eval txts)
425 | eval (Method.Orelse txts) = Seq.FIRST (map eval txts)
426 | eval (Method.Try txt) = Seq.TRY (eval txt)
427 | eval (Method.Repeat1 txt) = Seq.REPEAT1 (eval txt)
428 | eval (Method.SelectGoals (n, txt)) = select_goals n (eval txt);
429 in eval text state end;
433 val refine = apply_text true;
434 val refine_end = apply_text false;
436 fun refine_insert [] = I
437 | refine_insert ths = Seq.hd o refine (Method.Basic (K (Method.insert ths), Position.none));
442 (* refine via sub-proof *)
445 Goal.norm_hhf_tac THEN' Tactic.rtac rule THEN_ALL_NEW
446 (Goal.norm_hhf_tac THEN' (SUBGOAL (fn (goal, i) =>
447 if can Logic.unprotect (Logic.strip_assums_concl goal) then
448 Tactic.etac Drule.protectI i
451 fun refine_goals print_rule inner raw_rules state =
453 val (outer, (_, goal)) = get_goal state;
454 fun refine rule st = (print_rule outer rule; FINDGOAL (goal_tac rule) st);
457 |> ProofContext.goal_export inner outer
458 |> (fn rules => Seq.lift set_goal (EVERY (map refine rules) goal) state)
464 fun conclude_goal state goal propss =
466 val thy = theory_of state;
467 val ctxt = context_of state;
468 val string_of_term = Syntax.string_of_term ctxt;
469 val string_of_thm = ProofContext.string_of_thm ctxt;
471 val ngoals = Thm.nprems_of goal;
472 val _ = ngoals = 0 orelse error (Pretty.string_of (Pretty.chunks
473 (pretty_goals_local ctxt Markup.none (true, ! show_main_goal) (! Display.goals_limit) goal @
474 [Pretty.str (string_of_int ngoals ^ " unsolved goal(s)!")])));
476 val extra_hyps = Assumption.extra_hyps ctxt goal;
477 val _ = null extra_hyps orelse
478 error ("Additional hypotheses:\n" ^ cat_lines (map string_of_term extra_hyps));
480 fun lost_structure () = error ("Lost goal structure:\n" ^ string_of_thm goal);
482 val th = Goal.conclude
483 (if length (flat propss) > 1 then Thm.norm_proof goal else goal)
484 handle THM _ => lost_structure ();
485 val goal_propss = filter_out null propss;
487 Conjunction.elim_balanced (length goal_propss) th
488 |> map2 Conjunction.elim_balanced (map length goal_propss)
489 handle THM _ => lost_structure ();
490 val _ = Unify.matches_list thy (flat goal_propss) (map Thm.prop_of (flat results)) orelse
491 error ("Proved a different theorem:\n" ^ string_of_thm th);
493 fun recover_result ([] :: pss) thss = [] :: recover_result pss thss
494 | recover_result (_ :: pss) (ths :: thss) = ths :: recover_result pss thss
495 | recover_result [] [] = []
496 | recover_result _ _ = lost_structure ();
497 in recover_result propss results end;
501 (*** structured proof commands ***)
503 (** context elements **)
509 fun gen_bind bind args state =
512 |> map_context (bind args #> snd)
517 val match_bind = gen_bind (ProofContext.match_bind false);
518 val match_bind_i = gen_bind (ProofContext.match_bind_i false);
519 val let_bind = gen_bind (ProofContext.match_bind true);
520 val let_bind_i = gen_bind (ProofContext.match_bind_i true);
529 fun gen_fix add_fixes args =
531 #> map_context (snd o add_fixes args)
536 val fix = gen_fix ProofContext.add_fixes;
537 val fix_i = gen_fix ProofContext.add_fixes_i;
546 fun gen_assume asm prep_att exp args state =
549 |> map_context_result (asm exp (Attrib.map_specs (prep_att (theory_of state)) args))
550 |> these_factss [] |> #2;
554 val assm = gen_assume ProofContext.add_assms Attrib.attribute;
555 val assm_i = gen_assume ProofContext.add_assms_i (K I);
556 val assume = assm Assumption.assume_export;
557 val assume_i = assm_i Assumption.assume_export;
558 val presume = assm Assumption.presume_export;
559 val presume_i = assm_i Assumption.presume_export;
568 fun gen_def prep_att prep_vars prep_binds args state =
570 val _ = assert_forward state;
571 val thy = theory_of state;
572 val ctxt = context_of state;
574 val (raw_name_atts, (raw_vars, raw_rhss)) = args |> split_list ||> split_list;
575 val name_atts = map (apsnd (map (prep_att thy))) raw_name_atts;
578 |> map_context_result (prep_vars (map (fn (x, mx) => (x, NONE, mx)) raw_vars))
579 |>> map (fn (x, _, mx) => (x, mx))
581 map_context_result (prep_binds false (map swap raw_rhss))
582 #-> (fn rhss => map_context_result (LocalDefs.add_defs (vars ~~ (name_atts ~~ rhss)))))
583 |-> (put_facts o SOME o map (#2 o #2))
588 val def = gen_def Attrib.attribute ProofContext.read_vars ProofContext.match_bind;
589 val def_i = gen_def (K I) ProofContext.cert_vars ProofContext.match_bind_i;
599 fun clean_facts ctxt =
600 put_facts (SOME (filter_out Thm.is_dummy (the_facts ctxt))) ctxt;
607 fun chain_facts facts =
608 put_facts (SOME facts)
614 fun no_binding args = map (pair ("", [])) args;
618 fun gen_thmss note_ctxt more_facts opt_chain opt_result prep_atts args state =
621 |> map_context_result (note_ctxt (Attrib.map_facts (prep_atts (theory_of state)) args))
622 |> these_factss (more_facts state)
628 val note_thmss = gen_thmss (ProofContext.note_thmss "") (K []) I #2 Attrib.attribute;
629 val note_thmss_i = gen_thmss (ProofContext.note_thmss_i "") (K []) I #2 (K I);
632 gen_thmss (ProofContext.note_thmss "") (K []) chain #2 Attrib.attribute o no_binding;
633 val from_thmss_i = gen_thmss (ProofContext.note_thmss_i "") (K []) chain #2 (K I) o no_binding;
636 gen_thmss (ProofContext.note_thmss "") the_facts chain #2 Attrib.attribute o no_binding;
637 val with_thmss_i = gen_thmss (ProofContext.note_thmss_i "") the_facts chain #2 (K I) o no_binding;
640 gen_thmss (ProofContext.note_thmss_i "") (K []) I I (K I) o map (apsnd Thm.simple_fact);
642 fun get_thmss state srcs = the_facts (note_thmss [(("", []), srcs)] state);
647 (* using/unfolding *)
651 fun gen_using f g note prep_atts args state =
654 |> map_context_result
655 (note "" (Attrib.map_facts (prep_atts (theory_of state)) (no_binding args)))
656 |> (fn (named_facts, state') =>
657 state' |> map_goal I (fn (statement, _, using, goal, before_qed, after_qed) =>
659 val ctxt = context_of state';
660 val ths = maps snd named_facts;
661 in (statement, [], f ctxt ths using, g ctxt ths goal, before_qed, after_qed) end));
663 fun append_using _ ths using = using @ filter_out Thm.is_dummy ths;
664 fun unfold_using ctxt ths = map (LocalDefs.unfold ctxt ths);
665 val unfold_goals = LocalDefs.unfold_goals;
669 val using = gen_using append_using (K (K I)) ProofContext.note_thmss Attrib.attribute;
670 val using_i = gen_using append_using (K (K I)) ProofContext.note_thmss_i (K I);
671 val unfolding = gen_using unfold_using unfold_goals ProofContext.note_thmss Attrib.attribute;
672 val unfolding_i = gen_using unfold_using unfold_goals ProofContext.note_thmss_i (K I);
681 fun gen_invoke_case prep_att (name, xs, raw_atts) state =
683 val atts = map (prep_att (theory_of state)) raw_atts;
684 val (asms, state') = state |> map_context_result (fn ctxt =>
685 ctxt |> ProofContext.apply_case (ProofContext.get_case ctxt name xs));
686 val assumptions = asms |> map (fn (a, ts) => ((a, atts), map (rpair []) ts));
689 |> map_context (ProofContext.qualified_names #> ProofContext.no_base_names)
690 |> assume_i assumptions
691 |> add_binds_i AutoBind.no_facts
692 |> map_context (ProofContext.restore_naming (context_of state))
693 |> `the_facts |-> (fn thms => note_thmss_i [((name, []), [(thms, [])])])
698 val invoke_case = gen_invoke_case Attrib.attribute;
699 val invoke_case_i = gen_invoke_case (K I);
705 (** proof structure **)
722 fun end_block state =
726 |> assert_current_goal false
728 |> export_facts state;
735 #> refine (the_default Method.default_text opt_text)
736 #> Seq.map (using_facts [] #> enter_forward);
738 fun end_proof bot txt state =
743 |> assert_current_goal true
745 |> `before_qed |-> (refine o the_default Method.succeed_text)
746 |> Seq.maps (refine (Method.finish_text txt (ContextPosition.get (context_of state))));
749 (* unstructured refinement *)
751 fun defer i = assert_no_chain #> refine (Method.Basic (K (Method.defer i), Position.none));
752 fun prefer i = assert_no_chain #> refine (Method.Basic (K (Method.prefer i), Position.none));
754 fun apply text = assert_backward #> refine text #> Seq.map (using_facts []);
755 fun apply_end text = assert_forward #> refine_end text;
765 fun implicit_vars dest add props =
767 val (explicit_vars, props') = take_prefix (can dest) props |>> map dest;
768 val vars = rev (subtract (op =) explicit_vars (fold add props []));
771 else warning ("Goal statement contains unbound schematic variable(s): " ^
772 commas_quote (map (Term.string_of_vname o fst) vars));
773 in (rev vars, props') end;
776 refine (Method.Basic (K (Method.RAW_METHOD
777 (K (HEADGOAL (PRECISE_CONJUNCTS n
778 (HEADGOAL (CONJUNCTS (ALLGOALS (rtac Drule.termI)))))))), Position.none))
783 fun generic_goal prepp kind before_qed after_qed raw_propp state =
785 val thy = theory_of state;
786 val cert = Thm.cterm_of thy;
787 val chaining = can assert_chain state;
789 val ((propss, after_ctxt), goal_state) =
791 |> assert_forward_or_chain
794 |> map_context_result (fn ctxt => swap (prepp (ctxt, raw_propp)));
795 val props = flat propss;
798 implicit_vars (dest_TVar o Logic.dest_type o Logic.dest_term) Term.add_tvars props;
799 val (vars, _) = implicit_vars (dest_Var o Logic.dest_term) Term.add_vars props';
801 val propss' = map (Logic.mk_term o Var) vars :: propss;
802 val goal_propss = filter_out null propss';
803 val goal = Goal.init (cert
804 (Logic.mk_conjunction_balanced (map Logic.mk_conjunction_balanced goal_propss)));
805 val after_qed' = after_qed |>> (fn after_local =>
806 fn results => map_context after_ctxt #> after_local results);
809 |> map_context (init_context #> Variable.set_body true)
810 |> put_goal (SOME (make_goal ((kind, propss'), [], [], goal, before_qed, after_qed')))
811 |> map_context (ProofContext.add_cases false (AutoBind.cases thy props))
812 |> map_context (ProofContext.auto_bind_goal props)
813 |> chaining ? (`the_facts #-> using_facts)
818 |> not (null vars) ? refine_terms (length goal_propss)
819 |> null props ? (refine (Method.Basic (Method.assumption, Position.none)) #> Seq.hd)
822 fun generic_qed state =
824 val (goal_ctxt, {statement = (_, stmt), goal, after_qed, ...}) = current_goal state;
825 val outer_state = state |> close_block;
826 val outer_ctxt = context_of outer_state;
830 |> Variable.exportT_terms goal_ctxt outer_ctxt;
832 tl (conclude_goal state goal stmt)
833 |> burrow (ProofContext.export goal_ctxt outer_ctxt);
836 |> map_context (ProofContext.auto_bind_facts props)
837 |> pair (after_qed, results)
845 fun local_goal print_results prep_att prepp kind before_qed after_qed stmt state =
847 val thy = theory_of state;
848 val ((names, attss), propp) =
849 Attrib.map_specs (prep_att thy) stmt |> split_list |>> split_list;
851 fun after_qed' results =
852 local_results ((names ~~ attss) ~~ results)
853 #-> (fn res => tap (fn st => print_results (context_of st) ((kind, ""), res) : unit))
854 #> after_qed results;
857 |> generic_goal prepp kind before_qed (after_qed', K I) propp
858 |> tap (Variable.warn_extra_tfrees (context_of state) o context_of)
862 end_proof false txt #>
863 Seq.maps (generic_qed #-> (fn ((after_qed, _), results) => after_qed results));
868 fun global_goal prepp before_qed after_qed propp ctxt =
870 |> generic_goal (prepp #> ProofContext.auto_fixes) ""
871 before_qed (K Seq.single, after_qed) propp;
873 val theorem = global_goal ProofContext.bind_propp_schematic;
874 val theorem_i = global_goal ProofContext.bind_propp_schematic_i;
876 fun check_result msg sq =
879 | SOME (s', sq') => Seq.cons s' sq');
881 fun global_qeds txt =
883 #> Seq.map (generic_qed #> (fn (((_, after_qed), results), state) =>
884 after_qed results (context_of state)))
885 |> Seq.DETERM; (*backtracking may destroy theory!*)
889 #> check_result "Failed to finish proof"
893 (* concluding steps *)
895 fun local_terminal_proof (text, opt_text) =
896 proof (SOME text) #> Seq.maps (local_qed (opt_text, true));
898 val local_default_proof = local_terminal_proof (Method.default_text, NONE);
899 val local_immediate_proof = local_terminal_proof (Method.this_text, NONE);
900 val local_done_proof = proof (SOME Method.done_text) #> Seq.maps (local_qed (NONE, false));
901 fun local_skip_proof int = local_terminal_proof (Method.sorry_text int, NONE);
903 fun global_term_proof immed (text, opt_text) =
905 #> check_result "Terminal proof method failed"
906 #> Seq.maps (global_qeds (opt_text, immed))
907 #> check_result "Failed to finish proof (after successful terminal method)"
910 val global_terminal_proof = global_term_proof true;
911 val global_default_proof = global_terminal_proof (Method.default_text, NONE);
912 val global_immediate_proof = global_terminal_proof (Method.this_text, NONE);
913 val global_done_proof = global_term_proof false (Method.done_text, NONE);
914 fun global_skip_proof int = global_terminal_proof (Method.sorry_text int, NONE);
917 (* common goal statements *)
921 fun gen_have prep_att prepp before_qed after_qed stmt int =
922 local_goal (ProofDisplay.print_results int) prep_att prepp "have" before_qed after_qed stmt;
924 fun gen_show prep_att prepp before_qed after_qed stmt int state =
926 val testing = ref false;
927 val rule = ref (NONE: thm option);
929 "Local statement will fail to solve any pending goal" ::
930 (case ! rule of NONE => [] | SOME th => [ProofDisplay.string_of_rule ctxt "Failed" th])
933 fun print_results ctxt res =
934 if ! testing then () else ProofDisplay.print_results int ctxt res;
935 fun print_rule ctxt th =
936 if ! testing then rule := SOME th
937 else if int then priority (ProofDisplay.string_of_rule ctxt "Successful" th)
940 (Seq.pull oo local_skip_proof) true
941 |> setmp testing true
945 fun after_qed' results =
946 refine_goals print_rule (context_of state) (flat results)
947 #> Seq.maps (after_qed results);
950 |> local_goal print_results prep_att prepp "show" before_qed after_qed' stmt
951 |> int ? (fn goal_state =>
952 (case test_proof goal_state of
953 Exn.Result (SOME _) => goal_state
954 | Exn.Result NONE => error (fail_msg (context_of goal_state))
955 | Exn.Exn Interrupt => raise Interrupt
956 | Exn.Exn exn => raise Exn.EXCEPTIONS ([exn], fail_msg (context_of goal_state))))
961 val have = gen_have Attrib.attribute ProofContext.bind_propp;
962 val have_i = gen_have (K I) ProofContext.bind_propp_i;
963 val show = gen_show Attrib.attribute ProofContext.bind_propp;
964 val show_i = gen_show (K I) ProofContext.bind_propp_i;