src/Pure/tactic.ML
author wenzelm
Wed Jul 23 10:22:30 1997 +0200 (1997-07-23)
changeset 3554 b1013660aeff
parent 3538 ed9de44032e0
child 3575 4e9beacb5339
permissions -rw-r--r--
tuned apsome;
clasohm@1460
     1
(*  Title: 	tactic
clasohm@0
     2
    ID:         $Id$
clasohm@1460
     3
    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
clasohm@0
     4
    Copyright   1991  University of Cambridge
clasohm@0
     5
clasohm@0
     6
Tactics 
clasohm@0
     7
*)
clasohm@0
     8
clasohm@0
     9
signature TACTIC =
paulson@1501
    10
  sig
paulson@3409
    11
  val ares_tac		: thm list -> int -> tactic
clasohm@0
    12
  val asm_rewrite_goal_tac:
nipkow@214
    13
        bool*bool -> (meta_simpset -> tactic) -> meta_simpset -> int -> tactic
paulson@3409
    14
  val assume_tac	: int -> tactic
paulson@3409
    15
  val atac	: int ->tactic
lcp@670
    16
  val bimatch_from_nets_tac: 
paulson@1501
    17
      (int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net -> int -> tactic
paulson@3409
    18
  val bimatch_tac	: (bool*thm)list -> int -> tactic
lcp@670
    19
  val biresolve_from_nets_tac: 
paulson@1501
    20
      (int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net -> int -> tactic
paulson@3409
    21
  val biresolve_tac	: (bool*thm)list -> int -> tactic
paulson@3409
    22
  val build_net	: thm list -> (int*thm) Net.net
paulson@1501
    23
  val build_netpair:    (int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net ->
paulson@1501
    24
      (bool*thm)list -> (int*(bool*thm)) Net.net * (int*(bool*thm)) Net.net
paulson@3409
    25
  val compose_inst_tac	: (string*string)list -> (bool*thm*int) -> 
paulson@3409
    26
                          int -> tactic
paulson@3409
    27
  val compose_tac	: (bool * thm * int) -> int -> tactic 
paulson@3409
    28
  val cut_facts_tac	: thm list -> int -> tactic
paulson@3409
    29
  val cut_inst_tac	: (string*string)list -> thm -> int -> tactic   
paulson@3409
    30
  val defer_tac 	: int -> tactic
paulson@3409
    31
  val distinct_subgoals_tac	: tactic
paulson@3409
    32
  val dmatch_tac	: thm list -> int -> tactic
paulson@3409
    33
  val dresolve_tac	: thm list -> int -> tactic
paulson@3409
    34
  val dres_inst_tac	: (string*string)list -> thm -> int -> tactic   
paulson@3409
    35
  val dtac		: thm -> int ->tactic
paulson@3409
    36
  val etac		: thm -> int ->tactic
paulson@3409
    37
  val eq_assume_tac	: int -> tactic   
paulson@3409
    38
  val ematch_tac	: thm list -> int -> tactic
paulson@3409
    39
  val eresolve_tac	: thm list -> int -> tactic
paulson@3409
    40
  val eres_inst_tac	: (string*string)list -> thm -> int -> tactic   
paulson@3409
    41
  val filter_thms	: (term*term->bool) -> int*term*thm list -> thm list
paulson@3409
    42
  val filt_resolve_tac	: thm list -> int -> int -> tactic
paulson@3409
    43
  val flexflex_tac	: tactic
paulson@3409
    44
  val fold_goals_tac	: thm list -> tactic
paulson@3409
    45
  val fold_tac		: thm list -> tactic
paulson@3409
    46
  val forward_tac	: thm list -> int -> tactic   
paulson@3409
    47
  val forw_inst_tac	: (string*string)list -> thm -> int -> tactic
paulson@3409
    48
  val freeze_thaw	: thm -> thm * (thm -> thm)
paulson@3409
    49
  val insert_tagged_brl : ('a*(bool*thm)) * 
paulson@3409
    50
                          (('a*(bool*thm))Net.net * ('a*(bool*thm))Net.net) ->
paulson@3409
    51
                          ('a*(bool*thm))Net.net * ('a*(bool*thm))Net.net
paulson@3409
    52
  val delete_tagged_brl	: (bool*thm) * 
paulson@3409
    53
                         ((int*(bool*thm))Net.net * (int*(bool*thm))Net.net) ->
paulson@1801
    54
                    (int*(bool*thm))Net.net * (int*(bool*thm))Net.net
paulson@3409
    55
  val is_fact		: thm -> bool
paulson@3409
    56
  val lessb		: (bool * thm) * (bool * thm) -> bool
paulson@3409
    57
  val lift_inst_rule	: thm * int * (string*string)list * thm -> thm
paulson@3409
    58
  val make_elim		: thm -> thm
paulson@3409
    59
  val match_from_net_tac	: (int*thm) Net.net -> int -> tactic
paulson@3409
    60
  val match_tac	: thm list -> int -> tactic
paulson@3409
    61
  val metacut_tac	: thm -> int -> tactic   
paulson@3409
    62
  val net_bimatch_tac	: (bool*thm) list -> int -> tactic
paulson@3409
    63
  val net_biresolve_tac	: (bool*thm) list -> int -> tactic
paulson@3409
    64
  val net_match_tac	: thm list -> int -> tactic
paulson@3409
    65
  val net_resolve_tac	: thm list -> int -> tactic
paulson@3409
    66
  val orderlist		: (int * 'a) list -> 'a list
paulson@3409
    67
  val PRIMITIVE		: (thm -> thm) -> tactic  
paulson@3409
    68
  val PRIMSEQ		: (thm -> thm Sequence.seq) -> tactic  
paulson@3409
    69
  val prune_params_tac	: tactic
paulson@3409
    70
  val rename_tac	: string -> int -> tactic
paulson@3409
    71
  val rename_last_tac	: string -> string list -> int -> tactic
paulson@3409
    72
  val resolve_from_net_tac	: (int*thm) Net.net -> int -> tactic
paulson@3409
    73
  val resolve_tac	: thm list -> int -> tactic
paulson@3409
    74
  val res_inst_tac	: (string*string)list -> thm -> int -> tactic   
paulson@3409
    75
  val rewrite_goals_tac	: thm list -> tactic
paulson@3409
    76
  val rewrite_tac	: thm list -> tactic
paulson@3409
    77
  val rewtac		: thm -> tactic
paulson@3409
    78
  val rotate_tac	: int -> int -> tactic
paulson@3409
    79
  val rtac		: thm -> int -> tactic
paulson@3409
    80
  val rule_by_tactic	: tactic -> thm -> thm
paulson@3409
    81
  val subgoal_tac	: string -> int -> tactic
paulson@3409
    82
  val subgoals_tac	: string list -> int -> tactic
paulson@3409
    83
  val subgoals_of_brl	: bool * thm -> int
paulson@3409
    84
  val term_lift_inst_rule	:
nipkow@1975
    85
      thm * int * (indexname*typ)list * ((indexname*typ)*term)list  * thm
nipkow@1975
    86
      -> thm
paulson@3409
    87
  val thin_tac		: string -> int -> tactic
paulson@3409
    88
  val trace_goalno_tac	: (int -> tactic) -> int -> tactic
paulson@1501
    89
  end;
clasohm@0
    90
clasohm@0
    91
paulson@1501
    92
structure Tactic : TACTIC = 
clasohm@0
    93
struct
clasohm@0
    94
paulson@1501
    95
(*Discover which goal is chosen:  SOMEGOAL(trace_goalno_tac tac) *)
paulson@1501
    96
fun trace_goalno_tac tac i st =  
paulson@1501
    97
    case Sequence.pull(tac i st) of
clasohm@1460
    98
	None    => Sequence.null
clasohm@0
    99
      | seqcell => (prs("Subgoal " ^ string_of_int i ^ " selected\n"); 
paulson@1501
   100
    			 Sequence.seqof(fn()=> seqcell));
clasohm@0
   101
clasohm@0
   102
paulson@2029
   103
(*Convert all Vars in a theorem to Frees.  Also return a function for 
paulson@3409
   104
  reversing that operation.  DOES NOT WORK FOR TYPE VARIABLES.
paulson@3409
   105
  Similar code in type/freeze_thaw*)
paulson@3409
   106
fun freeze_thaw th =
paulson@3409
   107
  let val fth = freezeT th
paulson@3409
   108
      val {prop,sign,...} = rep_thm fth
paulson@3409
   109
      val used = add_term_names (prop, [])
paulson@3409
   110
      and vars = term_vars prop
paulson@3409
   111
      fun newName (Var(ix,_), (pairs,used)) = 
paulson@3409
   112
	    let val v = variant used (string_of_indexname ix)
paulson@3409
   113
	    in  ((ix,v)::pairs, v::used)  end;
paulson@3409
   114
      val (alist, _) = foldr newName (vars, ([], used))
paulson@3409
   115
      fun mk_inst (Var(v,T)) = 
paulson@3409
   116
	  (cterm_of sign (Var(v,T)),
paulson@3409
   117
	   cterm_of sign (Free(the (assoc(alist,v)), T)))
paulson@3409
   118
      val insts = map mk_inst vars
paulson@3409
   119
      fun thaw th' = 
paulson@3409
   120
	  th' |> forall_intr_list (map #2 insts)
paulson@3409
   121
	      |> forall_elim_list (map #1 insts)
paulson@3409
   122
  in  (instantiate ([],insts) fth, thaw)  end;
paulson@2029
   123
paulson@2029
   124
paulson@2029
   125
(*Rotates the given subgoal to be the last.  Useful when re-playing
paulson@2029
   126
  an old proof script, when the proof of an early subgoal fails.
paulson@2029
   127
  DOES NOT WORK FOR TYPE VARIABLES.*)
paulson@2029
   128
fun defer_tac i state = 
paulson@2029
   129
    let val (state',thaw) = freeze_thaw state
paulson@2029
   130
	val hyps = Drule.strip_imp_prems (adjust_maxidx (cprop_of state'))
paulson@2580
   131
	val hyp::hyps' = List.drop(hyps, i-1)
paulson@2029
   132
    in  implies_intr hyp (implies_elim_list state' (map assume hyps)) 
paulson@2580
   133
        |> implies_intr_list (List.take(hyps, i-1) @ hyps')
paulson@2029
   134
        |> thaw
paulson@2029
   135
        |> Sequence.single
paulson@2029
   136
    end
paulson@2029
   137
    handle _ => Sequence.null;
paulson@2029
   138
clasohm@0
   139
clasohm@0
   140
(*Makes a rule by applying a tactic to an existing rule*)
paulson@1501
   141
fun rule_by_tactic tac rl =
paulson@2688
   142
  let val (st, thaw) = freeze_thaw (zero_var_indexes rl)
paulson@2688
   143
  in case Sequence.pull (tac st)  of
clasohm@1460
   144
	None        => raise THM("rule_by_tactic", 0, [rl])
paulson@2688
   145
      | Some(st',_) => Thm.varifyT (thaw st')
paulson@2688
   146
  end;
clasohm@0
   147
 
clasohm@0
   148
(*** Basic tactics ***)
clasohm@0
   149
clasohm@0
   150
(*Makes a tactic whose effect on a state is given by thmfun: thm->thm seq.*)
paulson@1501
   151
fun PRIMSEQ thmfun st =  thmfun st handle THM _ => Sequence.null;
clasohm@0
   152
clasohm@0
   153
(*Makes a tactic whose effect on a state is given by thmfun: thm->thm.*)
clasohm@0
   154
fun PRIMITIVE thmfun = PRIMSEQ (Sequence.single o thmfun);
clasohm@0
   155
clasohm@0
   156
(*** The following fail if the goal number is out of range:
clasohm@0
   157
     thus (REPEAT (resolve_tac rules i)) stops once subgoal i disappears. *)
clasohm@0
   158
clasohm@0
   159
(*Solve subgoal i by assumption*)
clasohm@0
   160
fun assume_tac i = PRIMSEQ (assumption i);
clasohm@0
   161
clasohm@0
   162
(*Solve subgoal i by assumption, using no unification*)
clasohm@0
   163
fun eq_assume_tac i = PRIMITIVE (eq_assumption i);
clasohm@0
   164
clasohm@0
   165
(** Resolution/matching tactics **)
clasohm@0
   166
clasohm@0
   167
(*The composition rule/state: no lifting or var renaming.
clasohm@0
   168
  The arg = (bires_flg, orule, m) ;  see bicompose for explanation.*)
clasohm@0
   169
fun compose_tac arg i = PRIMSEQ (bicompose false arg i);
clasohm@0
   170
clasohm@0
   171
(*Converts a "destruct" rule like P&Q==>P to an "elimination" rule
clasohm@0
   172
  like [| P&Q; P==>R |] ==> R *)
clasohm@0
   173
fun make_elim rl = zero_var_indexes (rl RS revcut_rl);
clasohm@0
   174
clasohm@0
   175
(*Attack subgoal i by resolution, using flags to indicate elimination rules*)
clasohm@0
   176
fun biresolve_tac brules i = PRIMSEQ (biresolution false brules i);
clasohm@0
   177
clasohm@0
   178
(*Resolution: the simple case, works for introduction rules*)
clasohm@0
   179
fun resolve_tac rules = biresolve_tac (map (pair false) rules);
clasohm@0
   180
clasohm@0
   181
(*Resolution with elimination rules only*)
clasohm@0
   182
fun eresolve_tac rules = biresolve_tac (map (pair true) rules);
clasohm@0
   183
clasohm@0
   184
(*Forward reasoning using destruction rules.*)
clasohm@0
   185
fun forward_tac rls = resolve_tac (map make_elim rls) THEN' assume_tac;
clasohm@0
   186
clasohm@0
   187
(*Like forward_tac, but deletes the assumption after use.*)
clasohm@0
   188
fun dresolve_tac rls = eresolve_tac (map make_elim rls);
clasohm@0
   189
clasohm@0
   190
(*Shorthand versions: for resolution with a single theorem*)
clasohm@1460
   191
fun rtac rl = resolve_tac [rl];
clasohm@1460
   192
fun etac rl = eresolve_tac [rl];
clasohm@1460
   193
fun dtac rl = dresolve_tac [rl];
clasohm@0
   194
val atac = assume_tac;
clasohm@0
   195
clasohm@0
   196
(*Use an assumption or some rules ... A popular combination!*)
clasohm@0
   197
fun ares_tac rules = assume_tac  ORELSE'  resolve_tac rules;
clasohm@0
   198
clasohm@0
   199
(*Matching tactics -- as above, but forbid updating of state*)
clasohm@0
   200
fun bimatch_tac brules i = PRIMSEQ (biresolution true brules i);
clasohm@0
   201
fun match_tac rules  = bimatch_tac (map (pair false) rules);
clasohm@0
   202
fun ematch_tac rules = bimatch_tac (map (pair true) rules);
clasohm@0
   203
fun dmatch_tac rls   = ematch_tac (map make_elim rls);
clasohm@0
   204
clasohm@0
   205
(*Smash all flex-flex disagreement pairs in the proof state.*)
clasohm@0
   206
val flexflex_tac = PRIMSEQ flexflex_rule;
clasohm@0
   207
paulson@3409
   208
paulson@3409
   209
(*Remove duplicate subgoals.  By Mark Staples*)
paulson@3409
   210
local
paulson@3409
   211
fun cterm_aconv (a,b) = #t (rep_cterm a) aconv #t (rep_cterm b);
paulson@3409
   212
in
paulson@3409
   213
fun distinct_subgoals_tac state = 
paulson@3409
   214
    let val (frozth,thawfn) = freeze_thaw state
paulson@3409
   215
	val froz_prems = cprems_of frozth
paulson@3409
   216
	val assumed = implies_elim_list frozth (map assume froz_prems)
paulson@3409
   217
	val implied = implies_intr_list (gen_distinct cterm_aconv froz_prems)
paulson@3409
   218
					assumed;
paulson@3409
   219
    in  Sequence.single (thawfn implied)  end
paulson@3409
   220
end; 
paulson@3409
   221
paulson@3409
   222
clasohm@0
   223
(*Lift and instantiate a rule wrt the given state and subgoal number *)
paulson@1501
   224
fun lift_inst_rule (st, i, sinsts, rule) =
paulson@1501
   225
let val {maxidx,sign,...} = rep_thm st
paulson@1501
   226
    val (_, _, Bi, _) = dest_state(st,i)
clasohm@1460
   227
    val params = Logic.strip_params Bi	        (*params of subgoal i*)
clasohm@0
   228
    val params = rev(rename_wrt_term Bi params) (*as they are printed*)
clasohm@0
   229
    val paramTs = map #2 params
clasohm@0
   230
    and inc = maxidx+1
clasohm@0
   231
    fun liftvar (Var ((a,j), T)) = Var((a, j+inc), paramTs---> incr_tvar inc T)
clasohm@0
   232
      | liftvar t = raise TERM("Variable expected", [t]);
clasohm@0
   233
    fun liftterm t = list_abs_free (params, 
clasohm@1460
   234
				    Logic.incr_indexes(paramTs,inc) t)
clasohm@0
   235
    (*Lifts instantiation pair over params*)
lcp@230
   236
    fun liftpair (cv,ct) = (cterm_fun liftvar cv, cterm_fun liftterm ct)
clasohm@0
   237
    fun lifttvar((a,i),ctyp) =
clasohm@1460
   238
	let val {T,sign} = rep_ctyp ctyp
clasohm@1460
   239
	in  ((a,i+inc), ctyp_of sign (incr_tvar inc T)) end
paulson@1501
   240
    val rts = types_sorts rule and (types,sorts) = types_sorts st
clasohm@0
   241
    fun types'(a,~1) = (case assoc(params,a) of None => types(a,~1) | sm => sm)
clasohm@0
   242
      | types'(ixn) = types ixn;
nipkow@949
   243
    val used = add_term_tvarnames
paulson@1501
   244
                  (#prop(rep_thm st) $ #prop(rep_thm rule),[])
nipkow@949
   245
    val (Tinsts,insts) = read_insts sign rts (types',sorts) used sinsts
clasohm@0
   246
in instantiate (map lifttvar Tinsts, map liftpair insts)
paulson@1501
   247
               (lift_rule (st,i) rule)
clasohm@0
   248
end;
clasohm@0
   249
nipkow@1966
   250
(*Like lift_inst_rule but takes cterms, not strings.
nipkow@1966
   251
  The cterms must be functions of the parameters of the subgoal,
nipkow@1966
   252
  i.e. they are assumed to be lifted already!
nipkow@1966
   253
  Also: types of Vars must be fully instantiated already *)
nipkow@1975
   254
fun term_lift_inst_rule (st, i, Tinsts, insts, rule) =
nipkow@1966
   255
let val {maxidx,sign,...} = rep_thm st
nipkow@1966
   256
    val (_, _, Bi, _) = dest_state(st,i)
nipkow@1966
   257
    val params = Logic.strip_params Bi          (*params of subgoal i*)
nipkow@1966
   258
    val paramTs = map #2 params
nipkow@1966
   259
    and inc = maxidx+1
nipkow@1975
   260
    fun liftvar ((a,j), T) = Var((a, j+inc), paramTs---> incr_tvar inc T)
nipkow@1975
   261
    (*lift only Var, not term, which must be lifted already*)
nipkow@1975
   262
    fun liftpair (v,t) = (cterm_of sign (liftvar v), cterm_of sign t)
nipkow@1975
   263
    fun liftTpair((a,i),T) = ((a,i+inc), ctyp_of sign (incr_tvar inc T))
nipkow@1975
   264
in instantiate (map liftTpair Tinsts, map liftpair insts)
nipkow@1966
   265
               (lift_rule (st,i) rule)
nipkow@1966
   266
end;
clasohm@0
   267
clasohm@0
   268
(*** Resolve after lifting and instantation; may refer to parameters of the
clasohm@0
   269
     subgoal.  Fails if "i" is out of range.  ***)
clasohm@0
   270
clasohm@0
   271
(*compose version: arguments are as for bicompose.*)
paulson@3538
   272
fun compose_inst_tac sinsts (bires_flg, rule, nsubgoal) i st = st |>
paulson@3538
   273
  (compose_tac (bires_flg, lift_inst_rule (st, i, sinsts, rule), nsubgoal) i
paulson@3538
   274
   handle TERM (msg,_)   => (writeln msg;  no_tac)
paulson@3538
   275
	| THM  (msg,_,_) => (writeln msg;  no_tac));
clasohm@0
   276
lcp@761
   277
(*"Resolve" version.  Note: res_inst_tac cannot behave sensibly if the
lcp@761
   278
  terms that are substituted contain (term or type) unknowns from the
lcp@761
   279
  goal, because it is unable to instantiate goal unknowns at the same time.
lcp@761
   280
paulson@2029
   281
  The type checker is instructed not to freeze flexible type vars that
nipkow@952
   282
  were introduced during type inference and still remain in the term at the
nipkow@952
   283
  end.  This increases flexibility but can introduce schematic type vars in
nipkow@952
   284
  goals.
lcp@761
   285
*)
clasohm@0
   286
fun res_inst_tac sinsts rule i =
clasohm@0
   287
    compose_inst_tac sinsts (false, rule, nprems_of rule) i;
clasohm@0
   288
paulson@1501
   289
(*eresolve elimination version*)
clasohm@0
   290
fun eres_inst_tac sinsts rule i =
clasohm@0
   291
    compose_inst_tac sinsts (true, rule, nprems_of rule) i;
clasohm@0
   292
lcp@270
   293
(*For forw_inst_tac and dres_inst_tac.  Preserve Var indexes of rl;
lcp@270
   294
  increment revcut_rl instead.*)
clasohm@0
   295
fun make_elim_preserve rl = 
lcp@270
   296
  let val {maxidx,...} = rep_thm rl
clasohm@922
   297
      fun cvar ixn = cterm_of Sign.proto_pure (Var(ixn,propT));
lcp@270
   298
      val revcut_rl' = 
clasohm@1460
   299
	  instantiate ([],  [(cvar("V",0), cvar("V",maxidx+1)),
clasohm@1460
   300
			     (cvar("W",0), cvar("W",maxidx+1))]) revcut_rl
clasohm@0
   301
      val arg = (false, rl, nprems_of rl)
clasohm@0
   302
      val [th] = Sequence.list_of_s (bicompose false arg 1 revcut_rl')
clasohm@0
   303
  in  th  end
clasohm@0
   304
  handle Bind => raise THM("make_elim_preserve", 1, [rl]);
clasohm@0
   305
lcp@270
   306
(*instantiate and cut -- for a FACT, anyway...*)
lcp@270
   307
fun cut_inst_tac sinsts rule = res_inst_tac sinsts (make_elim_preserve rule);
clasohm@0
   308
lcp@270
   309
(*forward tactic applies a RULE to an assumption without deleting it*)
lcp@270
   310
fun forw_inst_tac sinsts rule = cut_inst_tac sinsts rule THEN' assume_tac;
lcp@270
   311
lcp@270
   312
(*dresolve tactic applies a RULE to replace an assumption*)
clasohm@0
   313
fun dres_inst_tac sinsts rule = eres_inst_tac sinsts (make_elim_preserve rule);
clasohm@0
   314
paulson@1951
   315
(*Deletion of an assumption*)
paulson@1951
   316
fun thin_tac s = eres_inst_tac [("V",s)] thin_rl;
paulson@1951
   317
lcp@270
   318
(*** Applications of cut_rl ***)
clasohm@0
   319
clasohm@0
   320
(*Used by metacut_tac*)
clasohm@0
   321
fun bires_cut_tac arg i =
clasohm@1460
   322
    resolve_tac [cut_rl] i  THEN  biresolve_tac arg (i+1) ;
clasohm@0
   323
clasohm@0
   324
(*The conclusion of the rule gets assumed in subgoal i,
clasohm@0
   325
  while subgoal i+1,... are the premises of the rule.*)
clasohm@0
   326
fun metacut_tac rule = bires_cut_tac [(false,rule)];
clasohm@0
   327
clasohm@0
   328
(*Recognizes theorems that are not rules, but simple propositions*)
clasohm@0
   329
fun is_fact rl =
clasohm@0
   330
    case prems_of rl of
clasohm@1460
   331
	[] => true  |  _::_ => false;
clasohm@0
   332
clasohm@0
   333
(*"Cut" all facts from theorem list into the goal as assumptions. *)
clasohm@0
   334
fun cut_facts_tac ths i =
clasohm@0
   335
    EVERY (map (fn th => metacut_tac th i) (filter is_fact ths));
clasohm@0
   336
clasohm@0
   337
(*Introduce the given proposition as a lemma and subgoal*)
clasohm@0
   338
fun subgoal_tac sprop = res_inst_tac [("psi", sprop)] cut_rl;
clasohm@0
   339
lcp@439
   340
(*Introduce a list of lemmas and subgoals*)
lcp@439
   341
fun subgoals_tac sprops = EVERY' (map subgoal_tac sprops);
lcp@439
   342
clasohm@0
   343
clasohm@0
   344
(**** Indexing and filtering of theorems ****)
clasohm@0
   345
clasohm@0
   346
(*Returns the list of potentially resolvable theorems for the goal "prem",
clasohm@1460
   347
	using the predicate  could(subgoal,concl).
clasohm@0
   348
  Resulting list is no longer than "limit"*)
clasohm@0
   349
fun filter_thms could (limit, prem, ths) =
clasohm@0
   350
  let val pb = Logic.strip_assums_concl prem;   (*delete assumptions*)
clasohm@0
   351
      fun filtr (limit, []) = []
clasohm@1460
   352
	| filtr (limit, th::ths) =
clasohm@1460
   353
	    if limit=0 then  []
clasohm@1460
   354
	    else if could(pb, concl_of th)  then th :: filtr(limit-1, ths)
clasohm@1460
   355
	    else filtr(limit,ths)
clasohm@0
   356
  in  filtr(limit,ths)  end;
clasohm@0
   357
clasohm@0
   358
clasohm@0
   359
(*** biresolution and resolution using nets ***)
clasohm@0
   360
clasohm@0
   361
(** To preserve the order of the rules, tag them with increasing integers **)
clasohm@0
   362
clasohm@0
   363
(*insert tags*)
clasohm@0
   364
fun taglist k [] = []
clasohm@0
   365
  | taglist k (x::xs) = (k,x) :: taglist (k+1) xs;
clasohm@0
   366
clasohm@0
   367
(*remove tags and suppress duplicates -- list is assumed sorted!*)
clasohm@0
   368
fun untaglist [] = []
clasohm@0
   369
  | untaglist [(k:int,x)] = [x]
clasohm@0
   370
  | untaglist ((k,x) :: (rest as (k',x')::_)) =
clasohm@0
   371
      if k=k' then untaglist rest
clasohm@0
   372
      else    x :: untaglist rest;
clasohm@0
   373
clasohm@0
   374
(*return list elements in original order*)
paulson@2228
   375
fun orderlist kbrls = untaglist (sort (fn(x,y)=> #1 x < #1 y) kbrls); 
clasohm@0
   376
clasohm@0
   377
(*insert one tagged brl into the pair of nets*)
lcp@1077
   378
fun insert_tagged_brl (kbrl as (k,(eres,th)), (inet,enet)) =
clasohm@0
   379
    if eres then 
clasohm@1460
   380
	case prems_of th of
clasohm@1460
   381
	    prem::_ => (inet, Net.insert_term ((prem,kbrl), enet, K false))
clasohm@1460
   382
	  | [] => error"insert_tagged_brl: elimination rule with no premises"
clasohm@0
   383
    else (Net.insert_term ((concl_of th, kbrl), inet, K false), enet);
clasohm@0
   384
clasohm@0
   385
(*build a pair of nets for biresolution*)
lcp@670
   386
fun build_netpair netpair brls = 
lcp@1077
   387
    foldr insert_tagged_brl (taglist 1 brls, netpair);
clasohm@0
   388
paulson@1801
   389
(*delete one kbrl from the pair of nets;
paulson@1801
   390
  we don't know the value of k, so we use 0 and ignore it in the comparison*)
paulson@1801
   391
local
paulson@1801
   392
  fun eq_kbrl ((k,(eres,th)), (k',(eres',th'))) = eq_thm (th,th')
paulson@1801
   393
in
paulson@1801
   394
fun delete_tagged_brl (brl as (eres,th), (inet,enet)) =
paulson@1801
   395
    if eres then 
paulson@1801
   396
	case prems_of th of
paulson@1801
   397
	    prem::_ => (inet, Net.delete_term ((prem, (0,brl)), enet, eq_kbrl))
paulson@2814
   398
	  | []      => (inet,enet)     (*no major premise: ignore*)
paulson@1801
   399
    else (Net.delete_term ((concl_of th, (0,brl)), inet, eq_kbrl), enet);
paulson@1801
   400
end;
paulson@1801
   401
paulson@1801
   402
clasohm@0
   403
(*biresolution using a pair of nets rather than rules*)
clasohm@0
   404
fun biresolution_from_nets_tac match (inet,enet) =
clasohm@0
   405
  SUBGOAL
clasohm@0
   406
    (fn (prem,i) =>
clasohm@0
   407
      let val hyps = Logic.strip_assums_hyp prem
clasohm@0
   408
          and concl = Logic.strip_assums_concl prem 
clasohm@0
   409
          val kbrls = Net.unify_term inet concl @
paulson@2672
   410
                      List.concat (map (Net.unify_term enet) hyps)
clasohm@0
   411
      in PRIMSEQ (biresolution match (orderlist kbrls) i) end);
clasohm@0
   412
clasohm@0
   413
(*versions taking pre-built nets*)
clasohm@0
   414
val biresolve_from_nets_tac = biresolution_from_nets_tac false;
clasohm@0
   415
val bimatch_from_nets_tac = biresolution_from_nets_tac true;
clasohm@0
   416
clasohm@0
   417
(*fast versions using nets internally*)
lcp@670
   418
val net_biresolve_tac =
lcp@670
   419
    biresolve_from_nets_tac o build_netpair(Net.empty,Net.empty);
lcp@670
   420
lcp@670
   421
val net_bimatch_tac =
lcp@670
   422
    bimatch_from_nets_tac o build_netpair(Net.empty,Net.empty);
clasohm@0
   423
clasohm@0
   424
(*** Simpler version for resolve_tac -- only one net, and no hyps ***)
clasohm@0
   425
clasohm@0
   426
(*insert one tagged rl into the net*)
clasohm@0
   427
fun insert_krl (krl as (k,th), net) =
clasohm@0
   428
    Net.insert_term ((concl_of th, krl), net, K false);
clasohm@0
   429
clasohm@0
   430
(*build a net of rules for resolution*)
clasohm@0
   431
fun build_net rls = 
clasohm@0
   432
    foldr insert_krl (taglist 1 rls, Net.empty);
clasohm@0
   433
clasohm@0
   434
(*resolution using a net rather than rules; pred supports filt_resolve_tac*)
clasohm@0
   435
fun filt_resolution_from_net_tac match pred net =
clasohm@0
   436
  SUBGOAL
clasohm@0
   437
    (fn (prem,i) =>
clasohm@0
   438
      let val krls = Net.unify_term net (Logic.strip_assums_concl prem)
clasohm@0
   439
      in 
clasohm@1460
   440
	 if pred krls  
clasohm@0
   441
         then PRIMSEQ
clasohm@1460
   442
		(biresolution match (map (pair false) (orderlist krls)) i)
clasohm@0
   443
         else no_tac
clasohm@0
   444
      end);
clasohm@0
   445
clasohm@0
   446
(*Resolve the subgoal using the rules (making a net) unless too flexible,
clasohm@0
   447
   which means more than maxr rules are unifiable.      *)
clasohm@0
   448
fun filt_resolve_tac rules maxr = 
clasohm@0
   449
    let fun pred krls = length krls <= maxr
clasohm@0
   450
    in  filt_resolution_from_net_tac false pred (build_net rules)  end;
clasohm@0
   451
clasohm@0
   452
(*versions taking pre-built nets*)
clasohm@0
   453
val resolve_from_net_tac = filt_resolution_from_net_tac false (K true);
clasohm@0
   454
val match_from_net_tac = filt_resolution_from_net_tac true (K true);
clasohm@0
   455
clasohm@0
   456
(*fast versions using nets internally*)
clasohm@0
   457
val net_resolve_tac = resolve_from_net_tac o build_net;
clasohm@0
   458
val net_match_tac = match_from_net_tac o build_net;
clasohm@0
   459
clasohm@0
   460
clasohm@0
   461
(*** For Natural Deduction using (bires_flg, rule) pairs ***)
clasohm@0
   462
clasohm@0
   463
(*The number of new subgoals produced by the brule*)
lcp@1077
   464
fun subgoals_of_brl (true,rule)  = nprems_of rule - 1
lcp@1077
   465
  | subgoals_of_brl (false,rule) = nprems_of rule;
clasohm@0
   466
clasohm@0
   467
(*Less-than test: for sorting to minimize number of new subgoals*)
clasohm@0
   468
fun lessb (brl1,brl2) = subgoals_of_brl brl1 < subgoals_of_brl brl2;
clasohm@0
   469
clasohm@0
   470
clasohm@0
   471
(*** Meta-Rewriting Tactics ***)
clasohm@0
   472
clasohm@0
   473
fun result1 tacf mss thm =
wenzelm@3554
   474
  apsome fst (Sequence.pull (tacf mss thm));
clasohm@0
   475
paulson@2145
   476
(*Rewrite subgoal i only.  SELECT_GOAL avoids inefficiencies in goals_conv.*)
paulson@2145
   477
fun asm_rewrite_goal_tac mode prover_tac mss =
paulson@2145
   478
      SELECT_GOAL 
paulson@2145
   479
        (PRIMITIVE
paulson@2145
   480
	   (rewrite_goal_rule mode (result1 prover_tac) mss 1));
clasohm@0
   481
lcp@69
   482
(*Rewrite throughout proof state. *)
lcp@69
   483
fun rewrite_tac defs = PRIMITIVE(rewrite_rule defs);
clasohm@0
   484
clasohm@0
   485
(*Rewrite subgoals only, not main goal. *)
lcp@69
   486
fun rewrite_goals_tac defs = PRIMITIVE (rewrite_goals_rule defs);
clasohm@0
   487
clasohm@1460
   488
fun rewtac def = rewrite_goals_tac [def];
clasohm@0
   489
clasohm@0
   490
paulson@1501
   491
(*** for folding definitions, handling critical pairs ***)
lcp@69
   492
lcp@69
   493
(*The depth of nesting in a term*)
lcp@69
   494
fun term_depth (Abs(a,T,t)) = 1 + term_depth t
paulson@2145
   495
  | term_depth (f$t) = 1 + Int.max(term_depth f, term_depth t)
lcp@69
   496
  | term_depth _ = 0;
lcp@69
   497
lcp@69
   498
val lhs_of_thm = #1 o Logic.dest_equals o #prop o rep_thm;
lcp@69
   499
lcp@69
   500
(*folding should handle critical pairs!  E.g. K == Inl(0),  S == Inr(Inl(0))
lcp@69
   501
  Returns longest lhs first to avoid folding its subexpressions.*)
lcp@69
   502
fun sort_lhs_depths defs =
lcp@69
   503
  let val keylist = make_keylist (term_depth o lhs_of_thm) defs
lcp@69
   504
      val keys = distinct (sort op> (map #2 keylist))
lcp@69
   505
  in  map (keyfilter keylist) keys  end;
lcp@69
   506
lcp@69
   507
fun fold_tac defs = EVERY 
lcp@69
   508
    (map rewrite_tac (sort_lhs_depths (map symmetric defs)));
lcp@69
   509
lcp@69
   510
fun fold_goals_tac defs = EVERY 
lcp@69
   511
    (map rewrite_goals_tac (sort_lhs_depths (map symmetric defs)));
lcp@69
   512
lcp@69
   513
lcp@69
   514
(*** Renaming of parameters in a subgoal
lcp@69
   515
     Names may contain letters, digits or primes and must be
lcp@69
   516
     separated by blanks ***)
clasohm@0
   517
clasohm@0
   518
(*Calling this will generate the warning "Same as previous level" since
clasohm@0
   519
  it affects nothing but the names of bound variables!*)
clasohm@0
   520
fun rename_tac str i = 
clasohm@0
   521
  let val cs = explode str 
clasohm@0
   522
  in  
clasohm@0
   523
  if !Logic.auto_rename 
clasohm@0
   524
  then (writeln"Note: setting Logic.auto_rename := false"; 
clasohm@1460
   525
	Logic.auto_rename := false)
clasohm@0
   526
  else ();
clasohm@0
   527
  case #2 (take_prefix (is_letdig orf is_blank) cs) of
clasohm@0
   528
      [] => PRIMITIVE (rename_params_rule (scanwords is_letdig cs, i))
clasohm@0
   529
    | c::_ => error ("Illegal character: " ^ c)
clasohm@0
   530
  end;
clasohm@0
   531
paulson@1501
   532
(*Rename recent parameters using names generated from a and the suffixes,
paulson@1501
   533
  provided the string a, which represents a term, is an identifier. *)
clasohm@0
   534
fun rename_last_tac a sufs i = 
clasohm@0
   535
  let val names = map (curry op^ a) sufs
clasohm@0
   536
  in  if Syntax.is_identifier a
clasohm@0
   537
      then PRIMITIVE (rename_params_rule (names,i))
clasohm@0
   538
      else all_tac
clasohm@0
   539
  end;
clasohm@0
   540
paulson@2043
   541
(*Prunes all redundant parameters from the proof state by rewriting.
paulson@2043
   542
  DOES NOT rewrite main goal, where quantification over an unused bound
paulson@2043
   543
    variable is sometimes done to avoid the need for cut_facts_tac.*)
paulson@2043
   544
val prune_params_tac = rewrite_goals_tac [triv_forall_equality];
clasohm@0
   545
paulson@1501
   546
(*rotate_tac n i: rotate the assumptions of subgoal i by n positions, from
paulson@1501
   547
  right to left if n is positive, and from left to right if n is negative.*)
paulson@2672
   548
fun rotate_tac 0 i = all_tac
paulson@2672
   549
  | rotate_tac k i = PRIMITIVE (rotate_rule k i);
nipkow@1209
   550
clasohm@0
   551
end;
paulson@1501
   552
paulson@1501
   553
open Tactic;