src/Pure/goal.ML
author wenzelm
Sun Jul 26 13:12:52 2009 +0200 (2009-07-26)
changeset 32197 bc341bbe4417
parent 32187 cca43ca13f4f
child 32255 d302f1c9e356
permissions -rw-r--r--
Goal.finish: explicit context for printing;
wenzelm@17980
     1
(*  Title:      Pure/goal.ML
wenzelm@29345
     2
    Author:     Makarius
wenzelm@17980
     3
wenzelm@18139
     4
Goals in tactical theorem proving.
wenzelm@17980
     5
*)
wenzelm@17980
     6
wenzelm@17980
     7
signature BASIC_GOAL =
wenzelm@17980
     8
sig
wenzelm@32061
     9
  val parallel_proofs: int ref
wenzelm@17980
    10
  val SELECT_GOAL: tactic -> int -> tactic
wenzelm@23418
    11
  val CONJUNCTS: tactic -> int -> tactic
wenzelm@23414
    12
  val PRECISE_CONJUNCTS: int -> tactic -> int -> tactic
wenzelm@17980
    13
end;
wenzelm@17980
    14
wenzelm@17980
    15
signature GOAL =
wenzelm@17980
    16
sig
wenzelm@17980
    17
  include BASIC_GOAL
wenzelm@17980
    18
  val init: cterm -> thm
wenzelm@18027
    19
  val protect: thm -> thm
wenzelm@17980
    20
  val conclude: thm -> thm
wenzelm@32197
    21
  val check_finished: Proof.context -> thm -> unit
wenzelm@32197
    22
  val finish: Proof.context -> thm -> thm
wenzelm@21604
    23
  val norm_result: thm -> thm
wenzelm@29448
    24
  val future_enabled: unit -> bool
wenzelm@32061
    25
  val local_future_enabled: unit -> bool
wenzelm@28973
    26
  val future_result: Proof.context -> thm future -> term -> thm
wenzelm@23356
    27
  val prove_internal: cterm list -> cterm -> (thm list -> tactic) -> thm
wenzelm@20290
    28
  val prove_multi: Proof.context -> string list -> term list -> term list ->
wenzelm@20290
    29
    ({prems: thm list, context: Proof.context} -> tactic) -> thm list
wenzelm@28446
    30
  val prove_future: Proof.context -> string list -> term list -> term ->
wenzelm@28340
    31
    ({prems: thm list, context: Proof.context} -> tactic) -> thm
wenzelm@20290
    32
  val prove: Proof.context -> string list -> term list -> term ->
wenzelm@20290
    33
    ({prems: thm list, context: Proof.context} -> tactic) -> thm
wenzelm@26713
    34
  val prove_global: theory -> string list -> term list -> term ->
wenzelm@26713
    35
    ({prems: thm list, context: Proof.context} -> tactic) -> thm
wenzelm@19184
    36
  val extract: int -> int -> thm -> thm Seq.seq
wenzelm@19184
    37
  val retrofit: int -> int -> thm -> thm -> thm Seq.seq
wenzelm@23418
    38
  val conjunction_tac: int -> tactic
wenzelm@23414
    39
  val precise_conjunction_tac: int -> int -> tactic
wenzelm@23418
    40
  val recover_conjunction_tac: tactic
wenzelm@21687
    41
  val norm_hhf_tac: int -> tactic
wenzelm@21687
    42
  val compose_hhf_tac: thm -> int -> tactic
wenzelm@23237
    43
  val assume_rule_tac: Proof.context -> int -> tactic
wenzelm@17980
    44
end;
wenzelm@17980
    45
wenzelm@17980
    46
structure Goal: GOAL =
wenzelm@17980
    47
struct
wenzelm@17980
    48
wenzelm@18027
    49
(** goals **)
wenzelm@18027
    50
wenzelm@18027
    51
(*
wenzelm@18027
    52
  -------- (init)
wenzelm@18027
    53
  C ==> #C
wenzelm@18027
    54
*)
wenzelm@20290
    55
val init =
wenzelm@22902
    56
  let val A = #1 (Thm.dest_implies (Thm.cprop_of Drule.protectI))
wenzelm@20290
    57
  in fn C => Thm.instantiate ([], [(A, C)]) Drule.protectI end;
wenzelm@17980
    58
wenzelm@17980
    59
(*
wenzelm@18119
    60
   C
wenzelm@18119
    61
  --- (protect)
wenzelm@18119
    62
  #C
wenzelm@17980
    63
*)
wenzelm@29345
    64
fun protect th = Drule.comp_no_flatten (th, 0) 1 Drule.protectI;
wenzelm@17980
    65
wenzelm@17980
    66
(*
wenzelm@18027
    67
  A ==> ... ==> #C
wenzelm@18027
    68
  ---------------- (conclude)
wenzelm@17980
    69
  A ==> ... ==> C
wenzelm@17980
    70
*)
wenzelm@29345
    71
fun conclude th = Drule.comp_no_flatten (th, Thm.nprems_of th) 1 Drule.protectD;
wenzelm@17980
    72
wenzelm@17980
    73
(*
wenzelm@18027
    74
  #C
wenzelm@18027
    75
  --- (finish)
wenzelm@18027
    76
   C
wenzelm@17983
    77
*)
wenzelm@32197
    78
fun check_finished ctxt th =
wenzelm@17980
    79
  (case Thm.nprems_of th of
wenzelm@32197
    80
    0 => ()
wenzelm@17980
    81
  | n => raise THM ("Proof failed.\n" ^
wenzelm@32197
    82
      Pretty.string_of (Pretty.chunks
wenzelm@32197
    83
        (Goal_Display.pretty_goals ctxt {total = true, main = true, maxgoals = n} th)) ^
wenzelm@32197
    84
      "\n" ^ string_of_int n ^ " unsolved goal(s)!", 0, [th]));
wenzelm@32197
    85
wenzelm@32197
    86
fun finish ctxt th = (check_finished ctxt th; conclude th);
wenzelm@17980
    87
wenzelm@17980
    88
wenzelm@18027
    89
wenzelm@18027
    90
(** results **)
wenzelm@18027
    91
wenzelm@28340
    92
(* normal form *)
wenzelm@28340
    93
wenzelm@21604
    94
val norm_result =
wenzelm@21604
    95
  Drule.flexflex_unique
wenzelm@21604
    96
  #> MetaSimplifier.norm_hhf_protect
wenzelm@21604
    97
  #> Thm.strip_shyps
wenzelm@21604
    98
  #> Drule.zero_var_indexes;
wenzelm@21604
    99
wenzelm@21604
   100
wenzelm@29448
   101
(* future_enabled *)
wenzelm@29448
   102
wenzelm@32061
   103
val parallel_proofs = ref 1;
wenzelm@29448
   104
wenzelm@29448
   105
fun future_enabled () =
wenzelm@32061
   106
  Future.enabled () andalso Future.is_worker () andalso ! parallel_proofs >= 1;
wenzelm@32061
   107
wenzelm@32061
   108
fun local_future_enabled () = future_enabled () andalso ! parallel_proofs >= 2;
wenzelm@29448
   109
wenzelm@29448
   110
wenzelm@28446
   111
(* future_result *)
wenzelm@28340
   112
wenzelm@28446
   113
fun future_result ctxt result prop =
wenzelm@28340
   114
  let
wenzelm@28340
   115
    val thy = ProofContext.theory_of ctxt;
wenzelm@28340
   116
    val _ = Context.reject_draft thy;
wenzelm@28340
   117
    val cert = Thm.cterm_of thy;
wenzelm@28340
   118
    val certT = Thm.ctyp_of thy;
wenzelm@28340
   119
wenzelm@30473
   120
    val assms = Assumption.all_assms_of ctxt;
wenzelm@28340
   121
    val As = map Thm.term_of assms;
wenzelm@28340
   122
wenzelm@28340
   123
    val xs = map Free (fold Term.add_frees (prop :: As) []);
wenzelm@28340
   124
    val fixes = map cert xs;
wenzelm@28340
   125
wenzelm@28340
   126
    val tfrees = fold Term.add_tfrees (prop :: As) [];
wenzelm@28340
   127
    val instT = map (fn (a, S) => (certT (TVar ((a, 0), S)), certT (TFree (a, S)))) tfrees;
wenzelm@28340
   128
wenzelm@28340
   129
    val global_prop =
wenzelm@32056
   130
      cert (Term.map_types Logic.varifyT (fold_rev Logic.all xs (Logic.list_implies (As, prop))))
wenzelm@32056
   131
      |> Thm.weaken_sorts (Variable.sorts_of ctxt);
wenzelm@28973
   132
    val global_result = result |> Future.map
wenzelm@28973
   133
      (Thm.adjust_maxidx_thm ~1 #>
wenzelm@28973
   134
        Drule.implies_intr_list assms #>
wenzelm@28973
   135
        Drule.forall_intr_list fixes #>
wenzelm@28973
   136
        Thm.generalize (map #1 tfrees, []) 0);
wenzelm@28340
   137
    val local_result =
wenzelm@32056
   138
      Thm.future global_result global_prop
wenzelm@28340
   139
      |> Thm.instantiate (instT, [])
wenzelm@28340
   140
      |> Drule.forall_elim_list fixes
wenzelm@28340
   141
      |> fold (Thm.elim_implies o Thm.assume) assms;
wenzelm@28340
   142
  in local_result end;
wenzelm@28340
   143
wenzelm@28340
   144
wenzelm@18027
   145
wenzelm@18027
   146
(** tactical theorem proving **)
wenzelm@18027
   147
wenzelm@23356
   148
(* prove_internal -- minimal checks, no normalization of result! *)
wenzelm@20250
   149
wenzelm@23356
   150
fun prove_internal casms cprop tac =
wenzelm@20250
   151
  (case SINGLE (tac (map Assumption.assume casms)) (init cprop) of
wenzelm@32197
   152
    SOME th => Drule.implies_intr_list casms
wenzelm@32197
   153
      (finish (Syntax.init_pretty_global (Thm.theory_of_thm th)) th)
wenzelm@20250
   154
  | NONE => error "Tactic failed.");
wenzelm@20250
   155
wenzelm@20250
   156
wenzelm@28340
   157
(* prove_common etc. *)
wenzelm@17986
   158
wenzelm@28340
   159
fun prove_common immediate ctxt xs asms props tac =
wenzelm@17980
   160
  let
wenzelm@21516
   161
    val thy = ProofContext.theory_of ctxt;
wenzelm@26939
   162
    val string_of_term = Syntax.string_of_term ctxt;
wenzelm@20056
   163
wenzelm@28355
   164
    val pos = Position.thread_data ();
wenzelm@20250
   165
    fun err msg = cat_error msg
wenzelm@20250
   166
      ("The error(s) above occurred for the goal statement:\n" ^
wenzelm@28355
   167
        string_of_term (Logic.list_implies (asms, Logic.mk_conjunction_list props)) ^
wenzelm@28355
   168
        (case Position.str_of pos of "" => "" | s => "\n" ^ s));
wenzelm@17980
   169
wenzelm@20250
   170
    fun cert_safe t = Thm.cterm_of thy (Envir.beta_norm (Term.no_dummy_patterns t))
wenzelm@17980
   171
      handle TERM (msg, _) => err msg | TYPE (msg, _, _) => err msg;
wenzelm@20250
   172
    val casms = map cert_safe asms;
wenzelm@20250
   173
    val cprops = map cert_safe props;
wenzelm@17980
   174
wenzelm@20250
   175
    val (prems, ctxt') = ctxt
wenzelm@20250
   176
      |> Variable.add_fixes_direct xs
wenzelm@27218
   177
      |> fold Variable.declare_term (asms @ props)
wenzelm@26713
   178
      |> Assumption.add_assumes casms
wenzelm@26713
   179
      ||> Variable.set_body true;
wenzelm@28619
   180
    val sorts = Variable.sorts_of ctxt';
wenzelm@17980
   181
wenzelm@28619
   182
    val stmt = Thm.weaken_sorts sorts (Conjunction.mk_conjunction_balanced cprops);
wenzelm@28340
   183
wenzelm@28340
   184
    fun result () =
wenzelm@28340
   185
      (case SINGLE (tac {prems = prems, context = ctxt'}) (init stmt) of
wenzelm@19774
   186
        NONE => err "Tactic failed."
wenzelm@28340
   187
      | SOME st =>
wenzelm@32197
   188
          let val res = finish ctxt' st handle THM (msg, _, _) => err msg in
wenzelm@28619
   189
            if Unify.matches_list thy [Thm.term_of stmt] [Thm.prop_of res]
wenzelm@28619
   190
            then Thm.check_shyps sorts res
wenzelm@28340
   191
            else err ("Proved a different theorem: " ^ string_of_term (Thm.prop_of res))
wenzelm@28340
   192
          end);
wenzelm@28340
   193
    val res =
wenzelm@29448
   194
      if immediate orelse #maxidx (Thm.rep_cterm stmt) >= 0 orelse not (future_enabled ())
wenzelm@29088
   195
      then result ()
wenzelm@32062
   196
      else future_result ctxt' (Future.fork_pri ~1 result) (Thm.term_of stmt);
wenzelm@17980
   197
  in
wenzelm@28340
   198
    Conjunction.elim_balanced (length props) res
wenzelm@20290
   199
    |> map (Assumption.export false ctxt' ctxt)
wenzelm@20056
   200
    |> Variable.export ctxt' ctxt
wenzelm@20250
   201
    |> map Drule.zero_var_indexes
wenzelm@17980
   202
  end;
wenzelm@17980
   203
wenzelm@28341
   204
val prove_multi = prove_common true;
wenzelm@17980
   205
wenzelm@28446
   206
fun prove_future ctxt xs asms prop tac = hd (prove_common false ctxt xs asms [prop] tac);
wenzelm@28340
   207
fun prove ctxt xs asms prop tac = hd (prove_common true ctxt xs asms [prop] tac);
wenzelm@20056
   208
wenzelm@20056
   209
fun prove_global thy xs asms prop tac =
wenzelm@26713
   210
  Drule.standard (prove (ProofContext.init thy) xs asms prop tac);
wenzelm@18027
   211
wenzelm@18027
   212
wenzelm@17980
   213
wenzelm@21687
   214
(** goal structure **)
wenzelm@21687
   215
wenzelm@21687
   216
(* nested goals *)
wenzelm@18207
   217
wenzelm@19184
   218
fun extract i n st =
wenzelm@19184
   219
  (if i < 1 orelse n < 1 orelse i + n - 1 > Thm.nprems_of st then Seq.empty
wenzelm@19184
   220
   else if n = 1 then Seq.single (Thm.cprem_of st i)
wenzelm@23418
   221
   else
wenzelm@23418
   222
     Seq.single (Conjunction.mk_conjunction_balanced (map (Thm.cprem_of st) (i upto i + n - 1))))
wenzelm@20260
   223
  |> Seq.map (Thm.adjust_maxidx_cterm ~1 #> init);
wenzelm@17980
   224
wenzelm@19221
   225
fun retrofit i n st' st =
wenzelm@19221
   226
  (if n = 1 then st
wenzelm@23418
   227
   else st |> Drule.with_subgoal i (Conjunction.uncurry_balanced n))
wenzelm@19221
   228
  |> Thm.compose_no_flatten false (conclude st', Thm.nprems_of st') i;
wenzelm@18207
   229
wenzelm@17980
   230
fun SELECT_GOAL tac i st =
wenzelm@19191
   231
  if Thm.nprems_of st = 1 andalso i = 1 then tac st
wenzelm@19184
   232
  else Seq.lifts (retrofit i 1) (Seq.maps tac (extract i 1 st)) st;
wenzelm@17980
   233
wenzelm@21687
   234
wenzelm@21687
   235
(* multiple goals *)
wenzelm@21687
   236
wenzelm@23418
   237
fun precise_conjunction_tac 0 i = eq_assume_tac i
wenzelm@23418
   238
  | precise_conjunction_tac 1 i = SUBGOAL (K all_tac) i
wenzelm@23418
   239
  | precise_conjunction_tac n i = PRIMITIVE (Drule.with_subgoal i (Conjunction.curry_balanced n));
wenzelm@23414
   240
wenzelm@23418
   241
val adhoc_conjunction_tac = REPEAT_ALL_NEW
wenzelm@23418
   242
  (SUBGOAL (fn (goal, i) =>
wenzelm@23418
   243
    if can Logic.dest_conjunction goal then rtac Conjunction.conjunctionI i
wenzelm@23418
   244
    else no_tac));
wenzelm@21687
   245
wenzelm@23418
   246
val conjunction_tac = SUBGOAL (fn (goal, i) =>
wenzelm@23418
   247
  precise_conjunction_tac (length (Logic.dest_conjunctions goal)) i ORELSE
wenzelm@23418
   248
  TRY (adhoc_conjunction_tac i));
wenzelm@21687
   249
wenzelm@23418
   250
val recover_conjunction_tac = PRIMITIVE (fn th =>
wenzelm@23418
   251
  Conjunction.uncurry_balanced (Thm.nprems_of th) th);
wenzelm@23414
   252
wenzelm@23414
   253
fun PRECISE_CONJUNCTS n tac =
wenzelm@23414
   254
  SELECT_GOAL (precise_conjunction_tac n 1
wenzelm@23414
   255
    THEN tac
wenzelm@23418
   256
    THEN recover_conjunction_tac);
wenzelm@23414
   257
wenzelm@21687
   258
fun CONJUNCTS tac =
wenzelm@21687
   259
  SELECT_GOAL (conjunction_tac 1
wenzelm@21687
   260
    THEN tac
wenzelm@23418
   261
    THEN recover_conjunction_tac);
wenzelm@21687
   262
wenzelm@21687
   263
wenzelm@21687
   264
(* hhf normal form *)
wenzelm@21687
   265
wenzelm@21687
   266
val norm_hhf_tac =
wenzelm@21687
   267
  rtac Drule.asm_rl  (*cheap approximation -- thanks to builtin Logic.flatten_params*)
wenzelm@21687
   268
  THEN' SUBGOAL (fn (t, i) =>
wenzelm@21687
   269
    if Drule.is_norm_hhf t then all_tac
wenzelm@28619
   270
    else MetaSimplifier.rewrite_goal_tac Drule.norm_hhf_eqs i);
wenzelm@21687
   271
wenzelm@25301
   272
fun compose_hhf_tac th i st =
wenzelm@25301
   273
  PRIMSEQ (Thm.bicompose false (false, Drule.lift_all (Thm.cprem_of st i) th, 0) i) st;
wenzelm@21687
   274
wenzelm@23237
   275
wenzelm@23237
   276
(* non-atomic goal assumptions *)
wenzelm@23237
   277
wenzelm@23356
   278
fun non_atomic (Const ("==>", _) $ _ $ _) = true
wenzelm@23356
   279
  | non_atomic (Const ("all", _) $ _) = true
wenzelm@23356
   280
  | non_atomic _ = false;
wenzelm@23356
   281
wenzelm@23237
   282
fun assume_rule_tac ctxt = norm_hhf_tac THEN' CSUBGOAL (fn (goal, i) =>
wenzelm@23237
   283
  let
wenzelm@23237
   284
    val ((_, goal'), ctxt') = Variable.focus goal ctxt;
wenzelm@23237
   285
    val goal'' = Drule.cterm_rule (singleton (Variable.export ctxt' ctxt)) goal';
wenzelm@23356
   286
    val Rs = filter (non_atomic o Thm.term_of) (Drule.strip_imp_prems goal'');
wenzelm@23237
   287
    val tacs = Rs |> map (fn R =>
wenzelm@23237
   288
      Tactic.etac (MetaSimplifier.norm_hhf (Thm.trivial R)) THEN_ALL_NEW assume_tac);
wenzelm@23237
   289
  in fold_rev (curry op APPEND') tacs (K no_tac) i end);
wenzelm@23237
   290
wenzelm@18207
   291
end;
wenzelm@18207
   292
wenzelm@17980
   293
structure BasicGoal: BASIC_GOAL = Goal;
wenzelm@17980
   294
open BasicGoal;