src/Pure/tactic.ML
author wenzelm
Tue Oct 16 17:47:23 2012 +0200 (2012-10-16)
changeset 49865 eeaf1ec7eac2
parent 46704 f800eb467515
child 50081 9b92ee8dec98
permissions -rw-r--r--
clarified defer/prefer: more specific errors;
wenzelm@10805
     1
(*  Title:      Pure/tactic.ML
wenzelm@10805
     2
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
clasohm@0
     3
wenzelm@29276
     4
Fundamental tactics.
clasohm@0
     5
*)
clasohm@0
     6
wenzelm@11774
     7
signature BASIC_TACTIC =
wenzelm@11774
     8
sig
wenzelm@23223
     9
  val trace_goalno_tac: (int -> tactic) -> int -> tactic
wenzelm@36546
    10
  val rule_by_tactic: Proof.context -> tactic -> thm -> thm
wenzelm@23223
    11
  val assume_tac: int -> tactic
wenzelm@23223
    12
  val eq_assume_tac: int -> tactic
wenzelm@23223
    13
  val compose_tac: (bool * thm * int) -> int -> tactic
wenzelm@23223
    14
  val make_elim: thm -> thm
wenzelm@23223
    15
  val biresolve_tac: (bool * thm) list -> int -> tactic
wenzelm@23223
    16
  val resolve_tac: thm list -> int -> tactic
wenzelm@23223
    17
  val eresolve_tac: thm list -> int -> tactic
wenzelm@23223
    18
  val forward_tac: thm list -> int -> tactic
wenzelm@23223
    19
  val dresolve_tac: thm list -> int -> tactic
wenzelm@23223
    20
  val atac: int -> tactic
wenzelm@23223
    21
  val rtac: thm -> int -> tactic
haftmann@31251
    22
  val dtac: thm -> int -> tactic
haftmann@31251
    23
  val etac: thm -> int -> tactic
haftmann@31251
    24
  val ftac: thm -> int -> tactic
wenzelm@23223
    25
  val ares_tac: thm list -> int -> tactic
wenzelm@23223
    26
  val solve_tac: thm list -> int -> tactic
wenzelm@23223
    27
  val bimatch_tac: (bool * thm) list -> int -> tactic
wenzelm@23223
    28
  val match_tac: thm list -> int -> tactic
wenzelm@23223
    29
  val ematch_tac: thm list -> int -> tactic
wenzelm@23223
    30
  val dmatch_tac: thm list -> int -> tactic
wenzelm@23223
    31
  val flexflex_tac: tactic
wenzelm@23223
    32
  val distinct_subgoal_tac: int -> tactic
wenzelm@23223
    33
  val distinct_subgoals_tac: tactic
wenzelm@46704
    34
  val cut_tac: thm -> int -> tactic
wenzelm@23223
    35
  val cut_rules_tac: thm list -> int -> tactic
wenzelm@23223
    36
  val cut_facts_tac: thm list -> int -> tactic
wenzelm@23223
    37
  val filter_thms: (term * term -> bool) -> int * term * thm list -> thm list
wenzelm@23223
    38
  val biresolution_from_nets_tac: ('a list -> (bool * thm) list) ->
wenzelm@23223
    39
    bool -> 'a Net.net * 'a Net.net -> int -> tactic
wenzelm@23223
    40
  val biresolve_from_nets_tac: (int * (bool * thm)) Net.net * (int * (bool * thm)) Net.net ->
wenzelm@23223
    41
    int -> tactic
wenzelm@23223
    42
  val bimatch_from_nets_tac: (int * (bool * thm)) Net.net * (int * (bool * thm)) Net.net ->
wenzelm@23223
    43
    int -> tactic
wenzelm@23223
    44
  val net_biresolve_tac: (bool * thm) list -> int -> tactic
wenzelm@23223
    45
  val net_bimatch_tac: (bool * thm) list -> int -> tactic
wenzelm@23223
    46
  val filt_resolve_tac: thm list -> int -> int -> tactic
wenzelm@23223
    47
  val resolve_from_net_tac: (int * thm) Net.net -> int -> tactic
wenzelm@23223
    48
  val match_from_net_tac: (int * thm) Net.net -> int -> tactic
wenzelm@23223
    49
  val net_resolve_tac: thm list -> int -> tactic
wenzelm@23223
    50
  val net_match_tac: thm list -> int -> tactic
wenzelm@23223
    51
  val subgoals_of_brl: bool * thm -> int
wenzelm@23223
    52
  val lessb: (bool * thm) * (bool * thm) -> bool
wenzelm@27243
    53
  val rename_tac: string list -> int -> tactic
wenzelm@23223
    54
  val rotate_tac: int -> int -> tactic
wenzelm@23223
    55
  val defer_tac: int -> tactic
wenzelm@49865
    56
  val prefer_tac: int -> tactic
wenzelm@23223
    57
  val filter_prems_tac: (term -> bool) -> int -> tactic
wenzelm@11774
    58
end;
clasohm@0
    59
wenzelm@11774
    60
signature TACTIC =
wenzelm@11774
    61
sig
wenzelm@11774
    62
  include BASIC_TACTIC
wenzelm@23223
    63
  val insert_tagged_brl: 'a * (bool * thm) ->
wenzelm@23223
    64
    ('a * (bool * thm)) Net.net * ('a * (bool * thm)) Net.net ->
wenzelm@23223
    65
      ('a * (bool * thm)) Net.net * ('a * (bool * thm)) Net.net
wenzelm@23223
    66
  val build_netpair: (int * (bool * thm)) Net.net * (int * (bool * thm)) Net.net ->
wenzelm@23223
    67
    (bool * thm) list -> (int * (bool * thm)) Net.net * (int * (bool * thm)) Net.net
wenzelm@23223
    68
  val delete_tagged_brl: bool * thm ->
wenzelm@23223
    69
    ('a * (bool * thm)) Net.net * ('a * (bool * thm)) Net.net ->
wenzelm@23223
    70
      ('a * (bool * thm)) Net.net * ('a * (bool * thm)) Net.net
wenzelm@23223
    71
  val eq_kbrl: ('a * (bool * thm)) * ('a * (bool * thm)) -> bool
wenzelm@32971
    72
  val build_net: thm list -> (int * thm) Net.net
wenzelm@11774
    73
end;
clasohm@0
    74
wenzelm@11774
    75
structure Tactic: TACTIC =
clasohm@0
    76
struct
clasohm@0
    77
paulson@1501
    78
(*Discover which goal is chosen:  SOMEGOAL(trace_goalno_tac tac) *)
wenzelm@10817
    79
fun trace_goalno_tac tac i st =
wenzelm@4270
    80
    case Seq.pull(tac i st) of
skalberg@15531
    81
        NONE    => Seq.empty
wenzelm@12262
    82
      | seqcell => (tracing ("Subgoal " ^ string_of_int i ^ " selected");
wenzelm@10805
    83
                         Seq.make(fn()=> seqcell));
clasohm@0
    84
clasohm@0
    85
(*Makes a rule by applying a tactic to an existing rule*)
wenzelm@36546
    86
fun rule_by_tactic ctxt tac rl =
wenzelm@19925
    87
  let
wenzelm@36546
    88
    val ctxt' = Variable.declare_thm rl ctxt;
wenzelm@36546
    89
    val ((_, [st]), ctxt'') = Variable.import true [rl] ctxt';
wenzelm@19925
    90
  in
wenzelm@19925
    91
    (case Seq.pull (tac st) of
wenzelm@19925
    92
      NONE => raise THM ("rule_by_tactic", 0, [rl])
wenzelm@36546
    93
    | SOME (st', _) => zero_var_indexes (singleton (Variable.export ctxt'' ctxt') st'))
paulson@2688
    94
  end;
wenzelm@10817
    95
wenzelm@19925
    96
clasohm@0
    97
(*** Basic tactics ***)
clasohm@0
    98
clasohm@0
    99
(*** The following fail if the goal number is out of range:
clasohm@0
   100
     thus (REPEAT (resolve_tac rules i)) stops once subgoal i disappears. *)
clasohm@0
   101
clasohm@0
   102
(*Solve subgoal i by assumption*)
wenzelm@31945
   103
fun assume_tac i = PRIMSEQ (Thm.assumption i);
clasohm@0
   104
clasohm@0
   105
(*Solve subgoal i by assumption, using no unification*)
wenzelm@31945
   106
fun eq_assume_tac i = PRIMITIVE (Thm.eq_assumption i);
clasohm@0
   107
wenzelm@23223
   108
clasohm@0
   109
(** Resolution/matching tactics **)
clasohm@0
   110
clasohm@0
   111
(*The composition rule/state: no lifting or var renaming.
wenzelm@31945
   112
  The arg = (bires_flg, orule, m);  see Thm.bicompose for explanation.*)
wenzelm@31945
   113
fun compose_tac arg i = PRIMSEQ (Thm.bicompose false arg i);
clasohm@0
   114
clasohm@0
   115
(*Converts a "destruct" rule like P&Q==>P to an "elimination" rule
clasohm@0
   116
  like [| P&Q; P==>R |] ==> R *)
clasohm@0
   117
fun make_elim rl = zero_var_indexes (rl RS revcut_rl);
clasohm@0
   118
clasohm@0
   119
(*Attack subgoal i by resolution, using flags to indicate elimination rules*)
wenzelm@31945
   120
fun biresolve_tac brules i = PRIMSEQ (Thm.biresolution false brules i);
clasohm@0
   121
clasohm@0
   122
(*Resolution: the simple case, works for introduction rules*)
clasohm@0
   123
fun resolve_tac rules = biresolve_tac (map (pair false) rules);
clasohm@0
   124
clasohm@0
   125
(*Resolution with elimination rules only*)
clasohm@0
   126
fun eresolve_tac rules = biresolve_tac (map (pair true) rules);
clasohm@0
   127
clasohm@0
   128
(*Forward reasoning using destruction rules.*)
clasohm@0
   129
fun forward_tac rls = resolve_tac (map make_elim rls) THEN' assume_tac;
clasohm@0
   130
clasohm@0
   131
(*Like forward_tac, but deletes the assumption after use.*)
clasohm@0
   132
fun dresolve_tac rls = eresolve_tac (map make_elim rls);
clasohm@0
   133
clasohm@0
   134
(*Shorthand versions: for resolution with a single theorem*)
oheimb@7491
   135
val atac    =   assume_tac;
oheimb@7491
   136
fun rtac rl =  resolve_tac [rl];
oheimb@7491
   137
fun dtac rl = dresolve_tac [rl];
clasohm@1460
   138
fun etac rl = eresolve_tac [rl];
oheimb@7491
   139
fun ftac rl =  forward_tac [rl];
clasohm@0
   140
clasohm@0
   141
(*Use an assumption or some rules ... A popular combination!*)
clasohm@0
   142
fun ares_tac rules = assume_tac  ORELSE'  resolve_tac rules;
clasohm@0
   143
wenzelm@5263
   144
fun solve_tac rules = resolve_tac rules THEN_ALL_NEW assume_tac;
wenzelm@5263
   145
clasohm@0
   146
(*Matching tactics -- as above, but forbid updating of state*)
wenzelm@31945
   147
fun bimatch_tac brules i = PRIMSEQ (Thm.biresolution true brules i);
clasohm@0
   148
fun match_tac rules  = bimatch_tac (map (pair false) rules);
clasohm@0
   149
fun ematch_tac rules = bimatch_tac (map (pair true) rules);
clasohm@0
   150
fun dmatch_tac rls   = ematch_tac (map make_elim rls);
clasohm@0
   151
clasohm@0
   152
(*Smash all flex-flex disagreement pairs in the proof state.*)
wenzelm@36944
   153
val flexflex_tac = PRIMSEQ Thm.flexflex_rule;
clasohm@0
   154
wenzelm@19056
   155
(*Remove duplicate subgoals.*)
paulson@22560
   156
val perm_tac = PRIMITIVE oo Thm.permute_prems;
paulson@22560
   157
paulson@22560
   158
fun distinct_tac (i, k) =
paulson@22560
   159
  perm_tac 0 (i - 1) THEN
paulson@22560
   160
  perm_tac 1 (k - 1) THEN
paulson@22560
   161
  DETERM (PRIMSEQ (fn st =>
paulson@22560
   162
    Thm.compose_no_flatten false (st, 0) 1
paulson@22560
   163
      (Drule.incr_indexes st Drule.distinct_prems_rl))) THEN
paulson@22560
   164
  perm_tac 1 (1 - k) THEN
paulson@22560
   165
  perm_tac 0 (1 - i);
paulson@22560
   166
paulson@22560
   167
fun distinct_subgoal_tac i st =
haftmann@33957
   168
  (case drop (i - 1) (Thm.prems_of st) of
paulson@22560
   169
    [] => no_tac st
paulson@22560
   170
  | A :: Bs =>
paulson@22560
   171
      st |> EVERY (fold (fn (B, k) =>
wenzelm@23223
   172
        if A aconv B then cons (distinct_tac (i, k)) else I) (Bs ~~ (1 upto length Bs)) []));
paulson@22560
   173
wenzelm@10817
   174
fun distinct_subgoals_tac state =
wenzelm@19056
   175
  let
wenzelm@19056
   176
    val goals = Thm.prems_of state;
wenzelm@19056
   177
    val dups = distinct (eq_fst (op aconv)) (goals ~~ (1 upto length goals));
wenzelm@19056
   178
  in EVERY (rev (map (distinct_subgoal_tac o snd) dups)) state end;
paulson@3409
   179
paulson@1951
   180
lcp@270
   181
(*** Applications of cut_rl ***)
clasohm@0
   182
clasohm@0
   183
(*The conclusion of the rule gets assumed in subgoal i,
clasohm@0
   184
  while subgoal i+1,... are the premises of the rule.*)
wenzelm@46704
   185
fun cut_tac rule i = rtac cut_rl i THEN rtac rule (i + 1);
clasohm@0
   186
paulson@13650
   187
(*"Cut" a list of rules into the goal.  Their premises will become new
paulson@13650
   188
  subgoals.*)
wenzelm@46704
   189
fun cut_rules_tac ths i = EVERY (map (fn th => cut_tac th i) ths);
paulson@13650
   190
paulson@13650
   191
(*As above, but inserts only facts (unconditional theorems);
paulson@13650
   192
  generates no additional subgoals. *)
wenzelm@20232
   193
fun cut_facts_tac ths = cut_rules_tac (filter Thm.no_prems ths);
clasohm@0
   194
clasohm@0
   195
clasohm@0
   196
(**** Indexing and filtering of theorems ****)
clasohm@0
   197
clasohm@0
   198
(*Returns the list of potentially resolvable theorems for the goal "prem",
wenzelm@10805
   199
        using the predicate  could(subgoal,concl).
clasohm@0
   200
  Resulting list is no longer than "limit"*)
clasohm@0
   201
fun filter_thms could (limit, prem, ths) =
clasohm@0
   202
  let val pb = Logic.strip_assums_concl prem;   (*delete assumptions*)
clasohm@0
   203
      fun filtr (limit, []) = []
wenzelm@10805
   204
        | filtr (limit, th::ths) =
wenzelm@10805
   205
            if limit=0 then  []
wenzelm@10805
   206
            else if could(pb, concl_of th)  then th :: filtr(limit-1, ths)
wenzelm@10805
   207
            else filtr(limit,ths)
clasohm@0
   208
  in  filtr(limit,ths)  end;
clasohm@0
   209
clasohm@0
   210
clasohm@0
   211
(*** biresolution and resolution using nets ***)
clasohm@0
   212
clasohm@0
   213
(** To preserve the order of the rules, tag them with increasing integers **)
clasohm@0
   214
clasohm@0
   215
(*insert one tagged brl into the pair of nets*)
wenzelm@23178
   216
fun insert_tagged_brl (kbrl as (k, (eres, th))) (inet, enet) =
wenzelm@12320
   217
  if eres then
wenzelm@12320
   218
    (case try Thm.major_prem_of th of
wenzelm@16809
   219
      SOME prem => (inet, Net.insert_term (K false) (prem, kbrl) enet)
skalberg@15531
   220
    | NONE => error "insert_tagged_brl: elimination rule with no premises")
wenzelm@16809
   221
  else (Net.insert_term (K false) (concl_of th, kbrl) inet, enet);
clasohm@0
   222
clasohm@0
   223
(*build a pair of nets for biresolution*)
wenzelm@10817
   224
fun build_netpair netpair brls =
wenzelm@30558
   225
    fold_rev insert_tagged_brl (tag_list 1 brls) netpair;
clasohm@0
   226
wenzelm@12320
   227
(*delete one kbrl from the pair of nets*)
wenzelm@22360
   228
fun eq_kbrl ((_, (_, th)), (_, (_, th'))) = Thm.eq_thm_prop (th, th')
wenzelm@16809
   229
wenzelm@23178
   230
fun delete_tagged_brl (brl as (eres, th)) (inet, enet) =
paulson@13925
   231
  (if eres then
wenzelm@12320
   232
    (case try Thm.major_prem_of th of
wenzelm@16809
   233
      SOME prem => (inet, Net.delete_term eq_kbrl (prem, ((), brl)) enet)
skalberg@15531
   234
    | NONE => (inet, enet))  (*no major premise: ignore*)
wenzelm@16809
   235
  else (Net.delete_term eq_kbrl (Thm.concl_of th, ((), brl)) inet, enet))
paulson@13925
   236
  handle Net.DELETE => (inet,enet);
paulson@1801
   237
paulson@1801
   238
wenzelm@10817
   239
(*biresolution using a pair of nets rather than rules.
paulson@3706
   240
    function "order" must sort and possibly filter the list of brls.
paulson@3706
   241
    boolean "match" indicates matching or unification.*)
paulson@3706
   242
fun biresolution_from_nets_tac order match (inet,enet) =
clasohm@0
   243
  SUBGOAL
clasohm@0
   244
    (fn (prem,i) =>
clasohm@0
   245
      let val hyps = Logic.strip_assums_hyp prem
wenzelm@10817
   246
          and concl = Logic.strip_assums_concl prem
wenzelm@19482
   247
          val kbrls = Net.unify_term inet concl @ maps (Net.unify_term enet) hyps
wenzelm@31945
   248
      in PRIMSEQ (Thm.biresolution match (order kbrls) i) end);
clasohm@0
   249
paulson@3706
   250
(*versions taking pre-built nets.  No filtering of brls*)
wenzelm@30558
   251
val biresolve_from_nets_tac = biresolution_from_nets_tac order_list false;
wenzelm@30558
   252
val bimatch_from_nets_tac   = biresolution_from_nets_tac order_list true;
clasohm@0
   253
clasohm@0
   254
(*fast versions using nets internally*)
lcp@670
   255
val net_biresolve_tac =
lcp@670
   256
    biresolve_from_nets_tac o build_netpair(Net.empty,Net.empty);
lcp@670
   257
lcp@670
   258
val net_bimatch_tac =
lcp@670
   259
    bimatch_from_nets_tac o build_netpair(Net.empty,Net.empty);
clasohm@0
   260
clasohm@0
   261
(*** Simpler version for resolve_tac -- only one net, and no hyps ***)
clasohm@0
   262
clasohm@0
   263
(*insert one tagged rl into the net*)
wenzelm@23178
   264
fun insert_krl (krl as (k,th)) =
wenzelm@23178
   265
  Net.insert_term (K false) (concl_of th, krl);
clasohm@0
   266
clasohm@0
   267
(*build a net of rules for resolution*)
wenzelm@10817
   268
fun build_net rls =
wenzelm@30558
   269
  fold_rev insert_krl (tag_list 1 rls) Net.empty;
clasohm@0
   270
clasohm@0
   271
(*resolution using a net rather than rules; pred supports filt_resolve_tac*)
clasohm@0
   272
fun filt_resolution_from_net_tac match pred net =
clasohm@0
   273
  SUBGOAL
clasohm@0
   274
    (fn (prem,i) =>
clasohm@0
   275
      let val krls = Net.unify_term net (Logic.strip_assums_concl prem)
wenzelm@10817
   276
      in
wenzelm@10817
   277
         if pred krls
clasohm@0
   278
         then PRIMSEQ
wenzelm@31945
   279
                (Thm.biresolution match (map (pair false) (order_list krls)) i)
clasohm@0
   280
         else no_tac
clasohm@0
   281
      end);
clasohm@0
   282
clasohm@0
   283
(*Resolve the subgoal using the rules (making a net) unless too flexible,
clasohm@0
   284
   which means more than maxr rules are unifiable.      *)
wenzelm@10817
   285
fun filt_resolve_tac rules maxr =
clasohm@0
   286
    let fun pred krls = length krls <= maxr
clasohm@0
   287
    in  filt_resolution_from_net_tac false pred (build_net rules)  end;
clasohm@0
   288
clasohm@0
   289
(*versions taking pre-built nets*)
clasohm@0
   290
val resolve_from_net_tac = filt_resolution_from_net_tac false (K true);
clasohm@0
   291
val match_from_net_tac = filt_resolution_from_net_tac true (K true);
clasohm@0
   292
clasohm@0
   293
(*fast versions using nets internally*)
clasohm@0
   294
val net_resolve_tac = resolve_from_net_tac o build_net;
clasohm@0
   295
val net_match_tac = match_from_net_tac o build_net;
clasohm@0
   296
clasohm@0
   297
clasohm@0
   298
(*** For Natural Deduction using (bires_flg, rule) pairs ***)
clasohm@0
   299
clasohm@0
   300
(*The number of new subgoals produced by the brule*)
lcp@1077
   301
fun subgoals_of_brl (true,rule)  = nprems_of rule - 1
lcp@1077
   302
  | subgoals_of_brl (false,rule) = nprems_of rule;
clasohm@0
   303
clasohm@0
   304
(*Less-than test: for sorting to minimize number of new subgoals*)
clasohm@0
   305
fun lessb (brl1,brl2) = subgoals_of_brl brl1 < subgoals_of_brl brl2;
clasohm@0
   306
clasohm@0
   307
wenzelm@27243
   308
(*Renaming of parameters in a subgoal*)
wenzelm@27243
   309
fun rename_tac xs i =
wenzelm@42290
   310
  case Library.find_first (not o Lexicon.is_identifier) xs of
skalberg@15531
   311
      SOME x => error ("Not an identifier: " ^ x)
wenzelm@31945
   312
    | NONE => PRIMITIVE (Thm.rename_params_rule (xs, i));
wenzelm@9535
   313
paulson@1501
   314
(*rotate_tac n i: rotate the assumptions of subgoal i by n positions, from
paulson@1501
   315
  right to left if n is positive, and from left to right if n is negative.*)
paulson@2672
   316
fun rotate_tac 0 i = all_tac
wenzelm@31945
   317
  | rotate_tac k i = PRIMITIVE (Thm.rotate_rule k i);
nipkow@1209
   318
paulson@7248
   319
(*Rotates the given subgoal to be the last.*)
wenzelm@31945
   320
fun defer_tac i = PRIMITIVE (Thm.permute_prems (i - 1) 1);
paulson@7248
   321
wenzelm@49865
   322
(*Rotates the given subgoal to be the first.*)
wenzelm@49865
   323
fun prefer_tac i = PRIMITIVE (Thm.permute_prems (i - 1) 1 #> Thm.permute_prems 0 ~1);
wenzelm@49865
   324
nipkow@5974
   325
(* remove premises that do not satisfy p; fails if all prems satisfy p *)
nipkow@5974
   326
fun filter_prems_tac p =
skalberg@15531
   327
  let fun Then NONE tac = SOME tac
skalberg@15531
   328
        | Then (SOME tac) tac' = SOME(tac THEN' tac');
wenzelm@19473
   329
      fun thins H (tac,n) =
nipkow@5974
   330
        if p H then (tac,n+1)
nipkow@5974
   331
        else (Then tac (rotate_tac n THEN' etac thin_rl),0);
nipkow@5974
   332
  in SUBGOAL(fn (subg,n) =>
nipkow@5974
   333
       let val Hs = Logic.strip_assums_hyp subg
wenzelm@19473
   334
       in case fst(fold thins Hs (NONE,0)) of
skalberg@15531
   335
            NONE => no_tac | SOME tac => tac n
nipkow@5974
   336
       end)
nipkow@5974
   337
  end;
nipkow@5974
   338
clasohm@0
   339
end;
paulson@1501
   340
wenzelm@32971
   341
structure Basic_Tactic: BASIC_TACTIC = Tactic;
wenzelm@32971
   342
open Basic_Tactic;