src/Pure/goal.ML
author wenzelm
Thu Mar 12 15:54:58 2009 +0100 (2009-03-12)
changeset 30473 e0b66c11e7e4
parent 29448 34b9652b2f45
child 32056 f4b74cbecdaf
permissions -rw-r--r--
Assumption.all_prems_of, Assumption.all_assms_of;
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@29435
     9
  val parallel_proofs: bool 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@17980
    21
  val finish: thm -> thm
wenzelm@21604
    22
  val norm_result: thm -> thm
wenzelm@29448
    23
  val future_enabled: unit -> bool
wenzelm@28973
    24
  val future_result: Proof.context -> thm future -> term -> thm
wenzelm@23356
    25
  val prove_internal: cterm list -> cterm -> (thm list -> tactic) -> thm
wenzelm@20290
    26
  val prove_multi: Proof.context -> string list -> term list -> term list ->
wenzelm@20290
    27
    ({prems: thm list, context: Proof.context} -> tactic) -> thm list
wenzelm@28446
    28
  val prove_future: Proof.context -> string list -> term list -> term ->
wenzelm@28340
    29
    ({prems: thm list, context: Proof.context} -> tactic) -> thm
wenzelm@20290
    30
  val prove: Proof.context -> string list -> term list -> term ->
wenzelm@20290
    31
    ({prems: thm list, context: Proof.context} -> tactic) -> thm
wenzelm@26713
    32
  val prove_global: theory -> string list -> term list -> term ->
wenzelm@26713
    33
    ({prems: thm list, context: Proof.context} -> tactic) -> thm
wenzelm@19184
    34
  val extract: int -> int -> thm -> thm Seq.seq
wenzelm@19184
    35
  val retrofit: int -> int -> thm -> thm -> thm Seq.seq
wenzelm@23418
    36
  val conjunction_tac: int -> tactic
wenzelm@23414
    37
  val precise_conjunction_tac: int -> int -> tactic
wenzelm@23418
    38
  val recover_conjunction_tac: tactic
wenzelm@21687
    39
  val norm_hhf_tac: int -> tactic
wenzelm@21687
    40
  val compose_hhf_tac: thm -> int -> tactic
wenzelm@23237
    41
  val assume_rule_tac: Proof.context -> int -> tactic
wenzelm@17980
    42
end;
wenzelm@17980
    43
wenzelm@17980
    44
structure Goal: GOAL =
wenzelm@17980
    45
struct
wenzelm@17980
    46
wenzelm@18027
    47
(** goals **)
wenzelm@18027
    48
wenzelm@18027
    49
(*
wenzelm@18027
    50
  -------- (init)
wenzelm@18027
    51
  C ==> #C
wenzelm@18027
    52
*)
wenzelm@20290
    53
val init =
wenzelm@22902
    54
  let val A = #1 (Thm.dest_implies (Thm.cprop_of Drule.protectI))
wenzelm@20290
    55
  in fn C => Thm.instantiate ([], [(A, C)]) Drule.protectI end;
wenzelm@17980
    56
wenzelm@17980
    57
(*
wenzelm@18119
    58
   C
wenzelm@18119
    59
  --- (protect)
wenzelm@18119
    60
  #C
wenzelm@17980
    61
*)
wenzelm@29345
    62
fun protect th = Drule.comp_no_flatten (th, 0) 1 Drule.protectI;
wenzelm@17980
    63
wenzelm@17980
    64
(*
wenzelm@18027
    65
  A ==> ... ==> #C
wenzelm@18027
    66
  ---------------- (conclude)
wenzelm@17980
    67
  A ==> ... ==> C
wenzelm@17980
    68
*)
wenzelm@29345
    69
fun conclude th = Drule.comp_no_flatten (th, Thm.nprems_of th) 1 Drule.protectD;
wenzelm@17980
    70
wenzelm@17980
    71
(*
wenzelm@18027
    72
  #C
wenzelm@18027
    73
  --- (finish)
wenzelm@18027
    74
   C
wenzelm@17983
    75
*)
wenzelm@17980
    76
fun finish th =
wenzelm@17980
    77
  (case Thm.nprems_of th of
wenzelm@17980
    78
    0 => conclude th
wenzelm@17980
    79
  | n => raise THM ("Proof failed.\n" ^
wenzelm@17980
    80
      Pretty.string_of (Pretty.chunks (Display.pretty_goals n th)) ^
wenzelm@17980
    81
      ("\n" ^ string_of_int n ^ " unsolved goal(s)!"), 0, [th]));
wenzelm@17980
    82
wenzelm@17980
    83
wenzelm@18027
    84
wenzelm@18027
    85
(** results **)
wenzelm@18027
    86
wenzelm@28340
    87
(* normal form *)
wenzelm@28340
    88
wenzelm@21604
    89
val norm_result =
wenzelm@21604
    90
  Drule.flexflex_unique
wenzelm@21604
    91
  #> MetaSimplifier.norm_hhf_protect
wenzelm@21604
    92
  #> Thm.strip_shyps
wenzelm@21604
    93
  #> Drule.zero_var_indexes;
wenzelm@21604
    94
wenzelm@21604
    95
wenzelm@29448
    96
(* future_enabled *)
wenzelm@29448
    97
wenzelm@29448
    98
val parallel_proofs = ref true;
wenzelm@29448
    99
wenzelm@29448
   100
fun future_enabled () =
wenzelm@29448
   101
  Future.enabled () andalso ! parallel_proofs andalso is_some (Future.thread_data ());
wenzelm@29448
   102
wenzelm@29448
   103
wenzelm@28446
   104
(* future_result *)
wenzelm@28340
   105
wenzelm@28446
   106
fun future_result ctxt result prop =
wenzelm@28340
   107
  let
wenzelm@28340
   108
    val thy = ProofContext.theory_of ctxt;
wenzelm@28340
   109
    val _ = Context.reject_draft thy;
wenzelm@28340
   110
    val cert = Thm.cterm_of thy;
wenzelm@28340
   111
    val certT = Thm.ctyp_of thy;
wenzelm@28340
   112
wenzelm@30473
   113
    val assms = Assumption.all_assms_of ctxt;
wenzelm@28340
   114
    val As = map Thm.term_of assms;
wenzelm@28340
   115
wenzelm@28340
   116
    val xs = map Free (fold Term.add_frees (prop :: As) []);
wenzelm@28340
   117
    val fixes = map cert xs;
wenzelm@28340
   118
wenzelm@28340
   119
    val tfrees = fold Term.add_tfrees (prop :: As) [];
wenzelm@28340
   120
    val instT = map (fn (a, S) => (certT (TVar ((a, 0), S)), certT (TFree (a, S)))) tfrees;
wenzelm@28340
   121
wenzelm@28340
   122
    val global_prop =
wenzelm@28340
   123
      Term.map_types Logic.varifyT (fold_rev Logic.all xs (Logic.list_implies (As, prop)));
wenzelm@28973
   124
    val global_result = result |> Future.map
wenzelm@28973
   125
      (Thm.adjust_maxidx_thm ~1 #>
wenzelm@28973
   126
        Drule.implies_intr_list assms #>
wenzelm@28973
   127
        Drule.forall_intr_list fixes #>
wenzelm@28973
   128
        Thm.generalize (map #1 tfrees, []) 0);
wenzelm@28340
   129
    val local_result =
wenzelm@28446
   130
      Thm.future global_result (cert global_prop)
wenzelm@28340
   131
      |> Thm.instantiate (instT, [])
wenzelm@28340
   132
      |> Drule.forall_elim_list fixes
wenzelm@28340
   133
      |> fold (Thm.elim_implies o Thm.assume) assms;
wenzelm@28340
   134
  in local_result end;
wenzelm@28340
   135
wenzelm@28340
   136
wenzelm@18027
   137
wenzelm@18027
   138
(** tactical theorem proving **)
wenzelm@18027
   139
wenzelm@23356
   140
(* prove_internal -- minimal checks, no normalization of result! *)
wenzelm@20250
   141
wenzelm@23356
   142
fun prove_internal casms cprop tac =
wenzelm@20250
   143
  (case SINGLE (tac (map Assumption.assume casms)) (init cprop) of
wenzelm@20250
   144
    SOME th => Drule.implies_intr_list casms (finish th)
wenzelm@20250
   145
  | NONE => error "Tactic failed.");
wenzelm@20250
   146
wenzelm@20250
   147
wenzelm@28340
   148
(* prove_common etc. *)
wenzelm@17986
   149
wenzelm@28340
   150
fun prove_common immediate ctxt xs asms props tac =
wenzelm@17980
   151
  let
wenzelm@21516
   152
    val thy = ProofContext.theory_of ctxt;
wenzelm@26939
   153
    val string_of_term = Syntax.string_of_term ctxt;
wenzelm@20056
   154
wenzelm@28355
   155
    val pos = Position.thread_data ();
wenzelm@20250
   156
    fun err msg = cat_error msg
wenzelm@20250
   157
      ("The error(s) above occurred for the goal statement:\n" ^
wenzelm@28355
   158
        string_of_term (Logic.list_implies (asms, Logic.mk_conjunction_list props)) ^
wenzelm@28355
   159
        (case Position.str_of pos of "" => "" | s => "\n" ^ s));
wenzelm@17980
   160
wenzelm@20250
   161
    fun cert_safe t = Thm.cterm_of thy (Envir.beta_norm (Term.no_dummy_patterns t))
wenzelm@17980
   162
      handle TERM (msg, _) => err msg | TYPE (msg, _, _) => err msg;
wenzelm@20250
   163
    val casms = map cert_safe asms;
wenzelm@20250
   164
    val cprops = map cert_safe props;
wenzelm@17980
   165
wenzelm@20250
   166
    val (prems, ctxt') = ctxt
wenzelm@20250
   167
      |> Variable.add_fixes_direct xs
wenzelm@27218
   168
      |> fold Variable.declare_term (asms @ props)
wenzelm@26713
   169
      |> Assumption.add_assumes casms
wenzelm@26713
   170
      ||> Variable.set_body true;
wenzelm@28619
   171
    val sorts = Variable.sorts_of ctxt';
wenzelm@17980
   172
wenzelm@28619
   173
    val stmt = Thm.weaken_sorts sorts (Conjunction.mk_conjunction_balanced cprops);
wenzelm@28340
   174
wenzelm@28340
   175
    fun result () =
wenzelm@28340
   176
      (case SINGLE (tac {prems = prems, context = ctxt'}) (init stmt) of
wenzelm@19774
   177
        NONE => err "Tactic failed."
wenzelm@28340
   178
      | SOME st =>
wenzelm@28340
   179
          let val res = finish st handle THM (msg, _, _) => err msg in
wenzelm@28619
   180
            if Unify.matches_list thy [Thm.term_of stmt] [Thm.prop_of res]
wenzelm@28619
   181
            then Thm.check_shyps sorts res
wenzelm@28340
   182
            else err ("Proved a different theorem: " ^ string_of_term (Thm.prop_of res))
wenzelm@28340
   183
          end);
wenzelm@28340
   184
    val res =
wenzelm@29448
   185
      if immediate orelse #maxidx (Thm.rep_cterm stmt) >= 0 orelse not (future_enabled ())
wenzelm@29088
   186
      then result ()
wenzelm@29343
   187
      else future_result ctxt' (Future.fork_pri ~1 result) (Thm.term_of stmt);
wenzelm@17980
   188
  in
wenzelm@28340
   189
    Conjunction.elim_balanced (length props) res
wenzelm@20290
   190
    |> map (Assumption.export false ctxt' ctxt)
wenzelm@20056
   191
    |> Variable.export ctxt' ctxt
wenzelm@20250
   192
    |> map Drule.zero_var_indexes
wenzelm@17980
   193
  end;
wenzelm@17980
   194
wenzelm@28341
   195
val prove_multi = prove_common true;
wenzelm@17980
   196
wenzelm@28446
   197
fun prove_future ctxt xs asms prop tac = hd (prove_common false ctxt xs asms [prop] tac);
wenzelm@28340
   198
fun prove ctxt xs asms prop tac = hd (prove_common true ctxt xs asms [prop] tac);
wenzelm@20056
   199
wenzelm@20056
   200
fun prove_global thy xs asms prop tac =
wenzelm@26713
   201
  Drule.standard (prove (ProofContext.init thy) xs asms prop tac);
wenzelm@18027
   202
wenzelm@18027
   203
wenzelm@17980
   204
wenzelm@21687
   205
(** goal structure **)
wenzelm@21687
   206
wenzelm@21687
   207
(* nested goals *)
wenzelm@18207
   208
wenzelm@19184
   209
fun extract i n st =
wenzelm@19184
   210
  (if i < 1 orelse n < 1 orelse i + n - 1 > Thm.nprems_of st then Seq.empty
wenzelm@19184
   211
   else if n = 1 then Seq.single (Thm.cprem_of st i)
wenzelm@23418
   212
   else
wenzelm@23418
   213
     Seq.single (Conjunction.mk_conjunction_balanced (map (Thm.cprem_of st) (i upto i + n - 1))))
wenzelm@20260
   214
  |> Seq.map (Thm.adjust_maxidx_cterm ~1 #> init);
wenzelm@17980
   215
wenzelm@19221
   216
fun retrofit i n st' st =
wenzelm@19221
   217
  (if n = 1 then st
wenzelm@23418
   218
   else st |> Drule.with_subgoal i (Conjunction.uncurry_balanced n))
wenzelm@19221
   219
  |> Thm.compose_no_flatten false (conclude st', Thm.nprems_of st') i;
wenzelm@18207
   220
wenzelm@17980
   221
fun SELECT_GOAL tac i st =
wenzelm@19191
   222
  if Thm.nprems_of st = 1 andalso i = 1 then tac st
wenzelm@19184
   223
  else Seq.lifts (retrofit i 1) (Seq.maps tac (extract i 1 st)) st;
wenzelm@17980
   224
wenzelm@21687
   225
wenzelm@21687
   226
(* multiple goals *)
wenzelm@21687
   227
wenzelm@23418
   228
fun precise_conjunction_tac 0 i = eq_assume_tac i
wenzelm@23418
   229
  | precise_conjunction_tac 1 i = SUBGOAL (K all_tac) i
wenzelm@23418
   230
  | precise_conjunction_tac n i = PRIMITIVE (Drule.with_subgoal i (Conjunction.curry_balanced n));
wenzelm@23414
   231
wenzelm@23418
   232
val adhoc_conjunction_tac = REPEAT_ALL_NEW
wenzelm@23418
   233
  (SUBGOAL (fn (goal, i) =>
wenzelm@23418
   234
    if can Logic.dest_conjunction goal then rtac Conjunction.conjunctionI i
wenzelm@23418
   235
    else no_tac));
wenzelm@21687
   236
wenzelm@23418
   237
val conjunction_tac = SUBGOAL (fn (goal, i) =>
wenzelm@23418
   238
  precise_conjunction_tac (length (Logic.dest_conjunctions goal)) i ORELSE
wenzelm@23418
   239
  TRY (adhoc_conjunction_tac i));
wenzelm@21687
   240
wenzelm@23418
   241
val recover_conjunction_tac = PRIMITIVE (fn th =>
wenzelm@23418
   242
  Conjunction.uncurry_balanced (Thm.nprems_of th) th);
wenzelm@23414
   243
wenzelm@23414
   244
fun PRECISE_CONJUNCTS n tac =
wenzelm@23414
   245
  SELECT_GOAL (precise_conjunction_tac n 1
wenzelm@23414
   246
    THEN tac
wenzelm@23418
   247
    THEN recover_conjunction_tac);
wenzelm@23414
   248
wenzelm@21687
   249
fun CONJUNCTS tac =
wenzelm@21687
   250
  SELECT_GOAL (conjunction_tac 1
wenzelm@21687
   251
    THEN tac
wenzelm@23418
   252
    THEN recover_conjunction_tac);
wenzelm@21687
   253
wenzelm@21687
   254
wenzelm@21687
   255
(* hhf normal form *)
wenzelm@21687
   256
wenzelm@21687
   257
val norm_hhf_tac =
wenzelm@21687
   258
  rtac Drule.asm_rl  (*cheap approximation -- thanks to builtin Logic.flatten_params*)
wenzelm@21687
   259
  THEN' SUBGOAL (fn (t, i) =>
wenzelm@21687
   260
    if Drule.is_norm_hhf t then all_tac
wenzelm@28619
   261
    else MetaSimplifier.rewrite_goal_tac Drule.norm_hhf_eqs i);
wenzelm@21687
   262
wenzelm@25301
   263
fun compose_hhf_tac th i st =
wenzelm@25301
   264
  PRIMSEQ (Thm.bicompose false (false, Drule.lift_all (Thm.cprem_of st i) th, 0) i) st;
wenzelm@21687
   265
wenzelm@23237
   266
wenzelm@23237
   267
(* non-atomic goal assumptions *)
wenzelm@23237
   268
wenzelm@23356
   269
fun non_atomic (Const ("==>", _) $ _ $ _) = true
wenzelm@23356
   270
  | non_atomic (Const ("all", _) $ _) = true
wenzelm@23356
   271
  | non_atomic _ = false;
wenzelm@23356
   272
wenzelm@23237
   273
fun assume_rule_tac ctxt = norm_hhf_tac THEN' CSUBGOAL (fn (goal, i) =>
wenzelm@23237
   274
  let
wenzelm@23237
   275
    val ((_, goal'), ctxt') = Variable.focus goal ctxt;
wenzelm@23237
   276
    val goal'' = Drule.cterm_rule (singleton (Variable.export ctxt' ctxt)) goal';
wenzelm@23356
   277
    val Rs = filter (non_atomic o Thm.term_of) (Drule.strip_imp_prems goal'');
wenzelm@23237
   278
    val tacs = Rs |> map (fn R =>
wenzelm@23237
   279
      Tactic.etac (MetaSimplifier.norm_hhf (Thm.trivial R)) THEN_ALL_NEW assume_tac);
wenzelm@23237
   280
  in fold_rev (curry op APPEND') tacs (K no_tac) i end);
wenzelm@23237
   281
wenzelm@18207
   282
end;
wenzelm@18207
   283
wenzelm@17980
   284
structure BasicGoal: BASIC_GOAL = Goal;
wenzelm@17980
   285
open BasicGoal;