1 (* Title: Pure/Isar/method.ML
3 Author: Markus Wenzel, TU Muenchen
8 signature BASIC_METHOD =
10 val FINDGOAL: (int -> thm -> 'a Seq.seq) -> thm -> 'a Seq.seq
11 val HEADGOAL: (int -> thm -> 'a Seq.seq) -> thm -> 'a Seq.seq
13 val trace_rules: bool ref
14 val print_methods: theory -> unit
20 val apply: Position.T -> (Proof.context -> method) -> Proof.context -> thm list -> cases_tactic
21 val RAW_METHOD_CASES: (thm list -> cases_tactic) -> method
22 val RAW_METHOD: (thm list -> tactic) -> method
23 val METHOD_CASES: (thm list -> cases_tactic) -> method
24 val METHOD: (thm list -> tactic) -> method
27 val insert_tac: thm list -> int -> tactic
28 val insert: thm list -> method
29 val insert_facts: method
30 val SIMPLE_METHOD: tactic -> method
31 val SIMPLE_METHOD': (int -> tactic) -> method
32 val SIMPLE_METHOD'': ((int -> tactic) -> tactic) -> (int -> tactic) -> method
33 val defer: int option -> method
34 val prefer: int -> method
35 val cheating: bool -> Proof.context -> method
36 val intro: thm list -> method
37 val elim: thm list -> method
38 val unfold: thm list -> Proof.context -> method
39 val fold: thm list -> Proof.context -> method
40 val atomize: bool -> method
42 val fact: thm list -> Proof.context -> method
43 val assumption: Proof.context -> method
44 val close: bool -> Proof.context -> method
45 val trace: Proof.context -> thm list -> unit
46 val rule_tac: thm list -> thm list -> int -> tactic
47 val some_rule_tac: thm list -> Proof.context -> thm list -> int -> tactic
48 val intros_tac: thm list -> thm list -> tactic
49 val rule: thm list -> method
50 val erule: int -> thm list -> method
51 val drule: int -> thm list -> method
52 val frule: int -> thm list -> method
53 val iprover_tac: Proof.context -> int option -> int -> tactic
54 val set_tactic: (Proof.context -> thm list -> tactic) -> unit
55 val tactic: string * Position.T -> Proof.context -> method
58 Basic of (Proof.context -> method) * Position.T |
65 SelectGoals of int * text
66 val primitive_text: (thm -> thm) -> text
67 val succeed_text: text
68 val default_text: text
71 val sorry_text: bool -> text
72 val finish_text: text option * bool -> Position.T -> text
73 val method: theory -> src -> Proof.context -> method
74 val method_i: theory -> src -> Proof.context -> method
75 val add_methods: (bstring * (src -> Proof.context -> method) * string) list
77 val add_method: bstring * (src -> Proof.context -> method) * string
79 val method_setup: bstring -> string * Position.T -> string -> theory -> theory
80 val syntax: (Context.generic * Args.T list -> 'a * (Context.generic * Args.T list))
81 -> src -> Proof.context -> 'a * Proof.context
82 val simple_args: (Args.T list -> 'a * Args.T list)
83 -> ('a -> Proof.context -> method) -> src -> Proof.context -> method
84 val ctxt_args: (Proof.context -> method) -> src -> Proof.context -> method
85 val no_args: method -> src -> Proof.context -> method
87 val sectioned_args: (Context.generic * Args.T list -> 'a * (Context.generic * Args.T list)) ->
88 (Args.T list -> modifier * Args.T list) list ->
89 ('a -> Proof.context -> 'b) -> src -> Proof.context -> 'b
90 val bang_sectioned_args:
91 (Args.T list -> modifier * Args.T list) list ->
92 (thm list -> Proof.context -> 'a) -> src -> Proof.context -> 'a
93 val bang_sectioned_args':
94 (Args.T list -> modifier * Args.T list) list ->
95 (Context.generic * Args.T list -> 'a * (Context.generic * Args.T list)) ->
96 ('a -> thm list -> Proof.context -> 'b) -> src -> Proof.context -> 'b
97 val only_sectioned_args:
98 (Args.T list -> modifier * Args.T list) list ->
99 (Proof.context -> 'a) -> src -> Proof.context -> 'a
100 val thms_ctxt_args: (thm list -> Proof.context -> 'a) -> src ->
102 val thms_args: (thm list -> 'a) -> src -> Proof.context -> 'a
103 val thm_args: (thm -> 'a) -> src -> Proof.context -> 'a
104 val goal_args: (Args.T list -> 'a * Args.T list) -> ('a -> int -> tactic)
105 -> src -> Proof.context -> method
106 val goal_args': (Context.generic * Args.T list -> 'a * (Context.generic * Args.T list))
107 -> ('a -> int -> tactic) -> src -> Proof.context -> method
108 val goal_args_ctxt: (Args.T list -> 'a * Args.T list) ->
109 (Proof.context -> 'a -> int -> tactic) -> src -> Proof.context -> method
110 val goal_args_ctxt': (Context.generic * Args.T list -> 'a * (Context.generic * Args.T list)) ->
111 (Proof.context -> 'a -> int -> tactic) -> src -> Proof.context -> method
112 val parse: OuterLex.token list -> text * OuterLex.token list
115 structure Method: METHOD =
118 (** generic tools **)
120 (* goal addressing *)
122 fun FINDGOAL tac st =
123 let fun find i n = if i > n then Seq.fail else Seq.APPEND (tac i, find (i + 1) n)
124 in find 1 (Thm.nprems_of st) st end;
126 fun HEADGOAL tac = tac 1;
130 (** proof methods **)
132 (* datatype method *)
134 datatype method = Meth of thm list -> cases_tactic;
136 fun apply pos meth_fun ctxt facts goal = Position.setmp_thread_data_seq pos
137 (fn () => let val Meth meth = meth_fun ctxt in meth facts goal end) ();
139 val RAW_METHOD_CASES = Meth;
141 fun RAW_METHOD tac = RAW_METHOD_CASES (NO_CASES o tac);
143 fun METHOD_CASES tac = RAW_METHOD_CASES (fn facts =>
144 Seq.THEN (ALLGOALS Goal.conjunction_tac, tac facts));
146 fun METHOD tac = RAW_METHOD (fn facts => ALLGOALS Goal.conjunction_tac THEN tac facts);
148 val fail = METHOD (K no_tac);
149 val succeed = METHOD (K all_tac);
156 fun cut_rule_tac rule =
157 Tactic.rtac (Drule.forall_intr_vars rule COMP_INCR revcut_rl);
161 fun insert_tac [] i = all_tac
162 | insert_tac facts i = EVERY (map (fn th => cut_rule_tac th i) facts);
164 val insert_facts = METHOD (ALLGOALS o insert_tac);
165 fun insert thms = METHOD (fn _ => ALLGOALS (insert_tac thms));
167 fun SIMPLE_METHOD tac = METHOD (fn facts => ALLGOALS (insert_tac facts) THEN tac);
168 fun SIMPLE_METHOD'' quant tac = METHOD (fn facts => quant (insert_tac facts THEN' tac));
169 val SIMPLE_METHOD' = SIMPLE_METHOD'' HEADGOAL;
174 (* shuffle subgoals *)
176 fun prefer i = METHOD (K (Tactic.defer_tac i THEN PRIMITIVE (Thm.permute_prems 0 ~1)));
177 fun defer opt_i = METHOD (K (Tactic.defer_tac (the_default 1 opt_i)));
182 fun cheating int ctxt = METHOD (K (setmp quick_and_dirty (int orelse ! quick_and_dirty)
183 (SkipProof.cheat_tac (ProofContext.theory_of ctxt))));
186 (* unfold intro/elim rules *)
188 fun intro ths = SIMPLE_METHOD' (CHANGED_PROP o REPEAT_ALL_NEW (Tactic.match_tac ths));
189 fun elim ths = SIMPLE_METHOD' (CHANGED_PROP o REPEAT_ALL_NEW (Tactic.ematch_tac ths));
192 (* unfold/fold definitions *)
194 fun unfold_meth ths ctxt = SIMPLE_METHOD (CHANGED_PROP (LocalDefs.unfold_tac ctxt ths));
195 fun fold_meth ths ctxt = SIMPLE_METHOD (CHANGED_PROP (LocalDefs.fold_tac ctxt ths));
198 (* atomize rule statements *)
200 fun atomize false = SIMPLE_METHOD' (CHANGED_PROP o ObjectLogic.atomize_prems_tac)
201 | atomize true = RAW_METHOD (K (HEADGOAL (CHANGED_PROP o ObjectLogic.full_atomize_tac)));
204 (* this -- resolve facts directly *)
206 val this = METHOD (EVERY o map (HEADGOAL o Tactic.rtac));
209 (* fact -- composition by facts from context *)
211 fun fact [] ctxt = SIMPLE_METHOD' (ProofContext.some_fact_tac ctxt)
212 | fact rules _ = SIMPLE_METHOD' (ProofContext.fact_tac rules);
219 fun cond_rtac cond rule = SUBGOAL (fn (prop, i) =>
220 if cond (Logic.strip_assums_concl prop)
221 then Tactic.rtac rule i else no_tac);
225 ("Implicit use of prems in assumption proof" ^ Position.str_of (Position.thread_data ()));
230 Goal.assume_rule_tac ctxt APPEND'
231 (CHANGED o solve_tac (Assumption.prems_of ctxt) THEN' K legacy_tac) APPEND'
232 cond_rtac (can Logic.dest_equals) Drule.reflexive_thm APPEND'
233 cond_rtac (can Logic.dest_term) Drule.termI;
237 fun assumption ctxt = METHOD (HEADGOAL o
238 (fn [] => assm_tac ctxt
239 | [fact] => solve_tac [fact]
242 fun close immed ctxt = METHOD (K
244 ((if immed then ALLGOALS (assm_tac ctxt) else all_tac) THEN flexflex_tac)));
249 (* rule etc. -- single-step refinements *)
251 val trace_rules = ref false;
253 fun trace ctxt rules =
254 if ! trace_rules andalso not (null rules) then
255 Pretty.big_list "rules:" (map (ProofContext.pretty_thm ctxt) rules)
256 |> Pretty.string_of |> tracing
261 fun gen_rule_tac tac rules facts =
263 if null facts then tac rules i st
264 else Seq.maps (fn rule => (tac o single) rule i st) (Drule.multi_resolves facts rules))
265 THEN_ALL_NEW Goal.norm_hhf_tac;
267 fun gen_arule_tac tac j rules facts =
268 EVERY' (gen_rule_tac tac rules facts :: replicate j Tactic.assume_tac);
270 fun gen_some_rule_tac tac arg_rules ctxt facts = SUBGOAL (fn (goal, i) =>
273 if not (null arg_rules) then arg_rules
274 else flat (ContextRules.find_rules false facts goal ctxt)
275 in trace ctxt rules; tac rules facts i end);
277 fun meth tac x = METHOD (HEADGOAL o tac x);
278 fun meth' tac x y = METHOD (HEADGOAL o tac x y);
282 val rule_tac = gen_rule_tac Tactic.resolve_tac;
283 val rule = meth rule_tac;
284 val some_rule_tac = gen_some_rule_tac rule_tac;
285 val some_rule = meth' some_rule_tac;
287 val erule = meth' (gen_arule_tac Tactic.eresolve_tac);
288 val drule = meth' (gen_arule_tac Tactic.dresolve_tac);
289 val frule = meth' (gen_arule_tac Tactic.forward_tac);
294 (* intros_tac -- pervasive search spanned by intro rules *)
296 fun intros_tac intros facts =
297 ALLGOALS (insert_tac facts THEN'
298 REPEAT_ALL_NEW (resolve_tac intros))
299 THEN Tactic.distinct_subgoals_tac;
302 (* iprover -- intuitionistic proof search *)
306 val remdups_tac = SUBGOAL (fn (g, i) =>
307 let val prems = Logic.strip_assums_hyp g in
308 REPEAT_DETERM_N (length prems - length (distinct op aconv prems))
309 (Tactic.ematch_tac [Drule.remdups_rl] i THEN Tactic.eq_assume_tac i)
312 fun REMDUPS tac = tac THEN_ALL_NEW remdups_tac;
314 val bires_tac = Tactic.biresolution_from_nets_tac ContextRules.orderlist;
316 fun safe_step_tac ctxt =
317 ContextRules.Swrap ctxt
318 (eq_assume_tac ORELSE'
319 bires_tac true (ContextRules.netpair_bang ctxt));
321 fun unsafe_step_tac ctxt =
322 ContextRules.wrap ctxt
324 bires_tac false (ContextRules.netpair_bang ctxt) APPEND'
325 bires_tac false (ContextRules.netpair ctxt));
327 fun step_tac ctxt i =
328 REPEAT_DETERM1 (REMDUPS (safe_step_tac ctxt) i) ORELSE
329 REMDUPS (unsafe_step_tac ctxt) i;
331 fun intprover_tac ctxt gs d lim = SUBGOAL (fn (g, i) => if d > lim then no_tac else
333 val ps = Logic.strip_assums_hyp g;
334 val c = Logic.strip_assums_concl g;
336 if member (fn ((ps1, c1), (ps2, c2)) =>
338 length ps1 = length ps2 andalso
339 gen_eq_set (op aconv) (ps1, ps2)) gs (ps, c) then no_tac
340 else (step_tac ctxt THEN_ALL_NEW intprover_tac ctxt ((ps, c) :: gs) (d + 1) lim) i
345 fun iprover_tac ctxt opt_lim =
346 SELECT_GOAL (DEEPEN (2, the_default 20 opt_lim) (intprover_tac ctxt [] 0) 4 1);
353 val tactic_ref = ref ((fn _ => raise Match): Proof.context -> thm list -> tactic);
354 fun set_tactic f = tactic_ref := f;
356 fun ml_tactic (txt, pos) ctxt = NAMED_CRITICAL "ML" (fn () =>
357 (ML_Context.eval_in (SOME (Context.Proof ctxt)) false pos
358 ("let fun tactic (ctxt: Proof.context) (facts: thm list) : tactic =\n"
359 ^ txt ^ "\nin Method.set_tactic tactic end");
360 Context.setmp_thread_data (SOME (Context.Proof ctxt)) (! tactic_ref ctxt)));
362 fun tactic txt ctxt = METHOD (ml_tactic txt ctxt);
363 fun raw_tactic txt ctxt = RAW_METHOD (ml_tactic txt ctxt);
367 (** method syntax **)
374 Basic of (Proof.context -> method) * Position.T |
378 Orelse of text list |
381 SelectGoals of int * text;
383 fun primitive_text r = Basic (K (SIMPLE_METHOD (PRIMITIVE r)), Position.none);
384 val succeed_text = Basic (K succeed, Position.none);
385 val default_text = Source (Args.src (("default", []), Position.none));
386 val this_text = Basic (K this, Position.none);
387 val done_text = Basic (K (SIMPLE_METHOD all_tac), Position.none);
388 fun sorry_text int = Basic (cheating int, Position.none);
390 fun finish_text (NONE, immed) pos = Basic (close immed, pos)
391 | finish_text (SOME txt, immed) pos = Then [txt, Basic (close immed, pos)];
394 (* method definitions *)
396 structure Methods = TheoryDataFun
398 type T = (((src -> Proof.context -> method) * string) * stamp) NameSpace.table;
399 val empty = NameSpace.empty_table;
402 fun merge _ tables : T = NameSpace.merge_tables (eq_snd (op =)) tables handle Symtab.DUP dup =>
403 error ("Attempt to merge different versions of method " ^ quote dup);
406 fun print_methods thy =
408 val meths = Methods.get thy;
409 fun prt_meth (name, ((_, comment), _)) = Pretty.block
410 [Pretty.str (name ^ ":"), Pretty.brk 2, Pretty.str comment];
412 [Pretty.big_list "methods:" (map prt_meth (NameSpace.extern_table meths))]
413 |> Pretty.chunks |> Pretty.writeln
421 val meths = #2 (Methods.get thy);
423 let val ((name, _), pos) = Args.dest_src src in
424 (case Symtab.lookup meths name of
425 NONE => error ("Unknown proof method: " ^ quote name ^ Position.str_of pos)
426 | SOME ((mth, _), _) => mth src)
430 fun method thy = method_i thy o Args.map_name (NameSpace.intern (#1 (Methods.get thy)));
435 fun add_methods raw_meths thy =
437 val new_meths = raw_meths |> map (fn (name, f, comment) =>
438 (name, ((f, comment), stamp ())));
440 fun add meths = NameSpace.extend_table (Sign.naming_of thy) new_meths meths
441 handle Symtab.DUP dup => error ("Duplicate declaration of method " ^ quote dup);
442 in Methods.map add thy end;
444 val add_method = add_methods o Library.single;
449 fun method_setup name (txt, pos) cmt =
450 ML_Context.expression pos
451 "val method: bstring * (Method.src -> Proof.context -> Proof.method) * string"
452 "Context.map_theory (Method.add_method method)"
453 ("(" ^ quote name ^ ", " ^ txt ^ ", " ^ quote cmt ^ ")")
454 |> Context.theory_map;
458 (** concrete syntax **)
462 fun syntax scan = Args.context_syntax "method" scan;
464 fun simple_args scan f src ctxt : method =
465 fst (syntax (Scan.lift (scan >> (fn x => f x ctxt))) src ctxt);
467 fun ctxt_args (f: Proof.context -> method) src ctxt =
468 fst (syntax (Scan.succeed (f ctxt)) src ctxt);
470 fun no_args m = ctxt_args (K m);
475 type modifier = (Proof.context -> Proof.context) * attribute;
479 fun thms ss = Scan.repeat (Scan.unless (Scan.lift (Scan.first ss)) Attrib.multi_thm) >> flat;
480 fun app (f, att) (context, ths) = foldl_map att (Context.map_proof f context, ths);
482 fun section ss = Scan.depend (fn context => (Scan.first ss -- Scan.pass context (thms ss)) :|--
483 (fn (m, ths) => Scan.succeed (app m (context, ths))));
485 fun sectioned args ss = args -- Scan.repeat (section ss);
489 fun sectioned_args args ss f src ctxt =
490 let val ((x, _), ctxt') = syntax (sectioned args ss) src ctxt
493 fun bang_sectioned_args ss f = sectioned_args Args.bang_facts ss f;
494 fun bang_sectioned_args' ss scan f =
495 sectioned_args (Args.bang_facts -- scan >> swap) ss (uncurry f);
496 fun only_sectioned_args ss f = sectioned_args (Scan.succeed ()) ss (fn () => f);
498 fun thms_ctxt_args f = sectioned_args (thms []) [] f;
499 fun thms_args f = thms_ctxt_args (K o f);
500 fun thm_args f = thms_args (fn [thm] => f thm | _ => error "Single theorem expected");
509 val introN = "intro";
514 fun modifier name kind kind' att =
515 Args.$$$ name |-- (kind >> K NONE || kind' |-- Args.nat --| Args.colon >> SOME)
516 >> (pair (I: Proof.context -> Proof.context) o att);
518 val iprover_modifiers =
519 [modifier destN Args.bang_colon Args.bang ContextRules.dest_bang,
520 modifier destN Args.colon (Scan.succeed ()) ContextRules.dest,
521 modifier elimN Args.bang_colon Args.bang ContextRules.elim_bang,
522 modifier elimN Args.colon (Scan.succeed ()) ContextRules.elim,
523 modifier introN Args.bang_colon Args.bang ContextRules.intro_bang,
524 modifier introN Args.colon (Scan.succeed ()) ContextRules.intro,
525 Args.del -- Args.colon >> K (I, ContextRules.rule_del)];
530 bang_sectioned_args' iprover_modifiers (Scan.lift (Scan.option Args.nat))
531 (fn n => fn prems => fn ctxt => METHOD (fn facts =>
532 HEADGOAL (insert_tac (prems @ facts) THEN'
533 ObjectLogic.atomize_prems_tac THEN' iprover_tac ctxt n)));
540 fun nat_thms_args f = uncurry f oo
541 (fst oo syntax (Scan.lift (Scan.optional (Args.parens Args.nat) 0) -- Attrib.thms));
543 fun goal_args' args tac src ctxt = fst (syntax (Args.goal_spec HEADGOAL -- args >>
544 (fn (quant, s) => SIMPLE_METHOD'' quant (tac s))) src ctxt);
546 fun goal_args args tac = goal_args' (Scan.lift args) tac;
548 fun goal_args_ctxt' args tac src ctxt =
549 fst (syntax (Args.goal_spec HEADGOAL -- args >>
550 (fn (quant, s) => SIMPLE_METHOD'' quant (tac ctxt s))) src ctxt);
552 fun goal_args_ctxt args tac = goal_args_ctxt' (Scan.lift args) tac;
557 val _ = Context.>> (add_methods
558 [("fail", no_args fail, "force failure"),
559 ("succeed", no_args succeed, "succeed"),
560 ("-", no_args insert_facts, "do nothing (insert current facts only)"),
561 ("insert", thms_args insert, "insert theorems, ignoring facts (improper)"),
562 ("intro", thms_args intro, "repeatedly apply introduction rules"),
563 ("elim", thms_args elim, "repeatedly apply elimination rules"),
564 ("unfold", thms_ctxt_args unfold_meth, "unfold definitions"),
565 ("fold", thms_ctxt_args fold_meth, "fold definitions"),
566 ("atomize", (atomize o fst) oo syntax (Args.mode "full"),
567 "present local premises as object-level statements"),
568 ("iprover", iprover_meth, "intuitionistic proof search"),
569 ("rule", thms_ctxt_args some_rule, "apply some intro/elim rule"),
570 ("erule", nat_thms_args erule, "apply rule in elimination manner (improper)"),
571 ("drule", nat_thms_args drule, "apply rule in destruct manner (improper)"),
572 ("frule", nat_thms_args frule, "apply rule in forward manner (improper)"),
573 ("this", no_args this, "apply current facts as rules"),
574 ("fact", thms_ctxt_args fact, "composition by facts from context"),
575 ("assumption", ctxt_args assumption, "proof by assumption, preferring facts"),
576 ("rename_tac", goal_args (Scan.repeat1 Args.name) Tactic.rename_params_tac,
577 "rename parameters of goal"),
578 ("rotate_tac", goal_args (Scan.optional Args.int 1) Tactic.rotate_tac,
579 "rotate assumptions of goal"),
580 ("tactic", simple_args (Args.position Args.name) tactic, "ML tactic as proof method"),
581 ("raw_tactic", simple_args (Args.position Args.name) raw_tactic, "ML tactic as raw proof method")]);
588 structure T = OuterLex;
589 structure P = OuterParse;
591 fun is_symid_meth s =
592 s <> "|" andalso s <> "?" andalso s <> "+" andalso T.is_sid s;
595 (P.position (P.xname >> rpair []) >> (Source o Args.src) ||
596 P.$$$ "(" |-- P.!!! (meth0 --| P.$$$ ")")) x
598 (meth4 --| P.$$$ "?" >> Try ||
599 meth4 --| P.$$$ "+" >> Repeat1 ||
600 meth4 -- (P.$$$ "[" |-- Scan.optional P.nat 1 --| P.$$$ "]") >> (SelectGoals o swap) ||
603 (P.position (P.xname -- P.args1 is_symid_meth false) >> (Source o Args.src) ||
605 and meth1 x = (P.enum1 "," meth2 >> (fn [m] => m | ms => Then ms)) x
606 and meth0 x = (P.enum1 "|" meth1 >> (fn [m] => m | ms => Orelse ms)) x;
608 in val parse = meth3 end;
611 (*final declarations of this structure!*)
612 val unfold = unfold_meth;
613 val fold = fold_meth;
617 structure BasicMethod: BASIC_METHOD = Method;