src/Pure/search.ML
author oheimb
Fri Oct 23 20:34:59 1998 +0200 (1998-10-23)
changeset 5754 98744e38ded1
parent 5693 998af7667fa3
child 5956 ab4d13e9e77a
permissions -rw-r--r--
added SOLVE tactical
paulson@1588
     1
(*  Title: 	search
paulson@1588
     2
    ID:         $Id$
paulson@1588
     3
    Author: 	Lawrence C Paulson and Norbert Voelker
paulson@1588
     4
paulson@1588
     5
Search tacticals
paulson@1588
     6
*)
paulson@1588
     7
paulson@2672
     8
infix 1 THEN_MAYBE THEN_MAYBE';
paulson@2672
     9
paulson@1588
    10
signature SEARCH =
paulson@1588
    11
  sig
paulson@2869
    12
  val DEEPEN  	        : int*int -> (int->int->tactic) -> int -> int -> tactic
paulson@2869
    13
paulson@2672
    14
  val THEN_MAYBE	: tactic * tactic -> tactic
paulson@2672
    15
  val THEN_MAYBE'	: ('a -> tactic) * ('a -> tactic) -> ('a -> tactic)
paulson@2672
    16
paulson@1588
    17
  val trace_DEPTH_FIRST	: bool ref
paulson@1588
    18
  val DEPTH_FIRST	: (thm -> bool) -> tactic -> tactic
paulson@1588
    19
  val DEPTH_SOLVE	: tactic -> tactic
paulson@1588
    20
  val DEPTH_SOLVE_1	: tactic -> tactic
paulson@1588
    21
  val ITER_DEEPEN	: (thm->bool) -> (int->tactic) -> tactic
paulson@1588
    22
  val THEN_ITER_DEEPEN	: tactic -> (thm->bool) -> (int->tactic) -> tactic
paulson@1588
    23
paulson@1588
    24
  val has_fewer_prems	: int -> thm -> bool   
paulson@1588
    25
  val IF_UNSOLVED	: tactic -> tactic
oheimb@5754
    26
  val SOLVE		: tactic -> tactic
paulson@1588
    27
  val trace_BEST_FIRST	: bool ref
paulson@1588
    28
  val BEST_FIRST	: (thm -> bool) * (thm -> int) -> tactic -> tactic
paulson@1588
    29
  val THEN_BEST_FIRST	: tactic -> (thm->bool) * (thm->int) -> tactic
paulson@1588
    30
			  -> tactic
paulson@1588
    31
  val trace_ASTAR	: bool ref
paulson@1588
    32
  val ASTAR	        : (thm -> bool) * (int->thm->int) -> tactic -> tactic
paulson@1588
    33
  val THEN_ASTAR	: tactic -> (thm->bool) * (int->thm->int) -> tactic
paulson@1588
    34
			  -> tactic
paulson@1588
    35
  val BREADTH_FIRST	: (thm -> bool) -> tactic -> tactic
wenzelm@5693
    36
  val QUIET_BREADTH_FIRST	: (thm -> bool) -> tactic -> tactic
paulson@1588
    37
  end;
paulson@1588
    38
paulson@1588
    39
structure Search : SEARCH = 
paulson@1588
    40
struct
paulson@1588
    41
paulson@1588
    42
(**** Depth-first search ****)
paulson@1588
    43
paulson@1588
    44
val trace_DEPTH_FIRST = ref false;
paulson@1588
    45
paulson@1588
    46
(*Searches until "satp" reports proof tree as satisfied.
paulson@1588
    47
  Suppresses duplicate solutions to minimize search space.*)
paulson@1588
    48
fun DEPTH_FIRST satp tac = 
paulson@1588
    49
 let val tac = tracify trace_DEPTH_FIRST tac
paulson@1588
    50
     fun depth used [] = None
paulson@1588
    51
       | depth used (q::qs) =
wenzelm@4270
    52
	  case Seq.pull q of
paulson@1588
    53
	      None         => depth used qs
paulson@1588
    54
	    | Some(st,stq) => 
paulson@1588
    55
		if satp st andalso not (gen_mem eq_thm (st, used))
wenzelm@4270
    56
		then Some(st, Seq.make
paulson@1588
    57
			         (fn()=> depth (st::used) (stq::qs)))
paulson@1588
    58
		else depth used (tac st :: stq :: qs)
wenzelm@4270
    59
  in  traced_tac (fn st => depth [] ([Seq.single st]))  end;
paulson@1588
    60
paulson@1588
    61
paulson@1588
    62
paulson@1588
    63
(*Predicate: Does the rule have fewer than n premises?*)
paulson@1588
    64
fun has_fewer_prems n rule = (nprems_of rule < n);
paulson@1588
    65
paulson@1588
    66
(*Apply a tactic if subgoals remain, else do nothing.*)
paulson@1588
    67
val IF_UNSOLVED = COND (has_fewer_prems 1) all_tac;
paulson@1588
    68
oheimb@5754
    69
(*Force a tactic to solve its goal completely, otherwise fail *)
oheimb@5754
    70
fun SOLVE tac = tac THEN COND (has_fewer_prems 1) all_tac no_tac;
oheimb@5754
    71
paulson@2672
    72
(*Execute tac1, but only execute tac2 if there are at least as many subgoals
paulson@2672
    73
  as before.  This ensures that tac2 is only applied to an outcome of tac1.*)
paulson@3538
    74
fun (tac1 THEN_MAYBE tac2) st = 
paulson@3538
    75
    (tac1  THEN  COND (has_fewer_prems (nprems_of st)) all_tac tac2)  st;
paulson@2672
    76
paulson@2672
    77
fun (tac1 THEN_MAYBE' tac2) x = tac1 x THEN_MAYBE tac2 x;
paulson@2672
    78
paulson@1588
    79
(*Tactical to reduce the number of premises by 1.
paulson@1588
    80
  If no subgoals then it must fail! *)
paulson@3538
    81
fun DEPTH_SOLVE_1 tac st = st |>
paulson@1588
    82
    (case nprems_of st of
paulson@1588
    83
	0 => no_tac
paulson@3538
    84
      | n => DEPTH_FIRST (has_fewer_prems n) tac);
paulson@1588
    85
paulson@1588
    86
(*Uses depth-first search to solve ALL subgoals*)
paulson@1588
    87
val DEPTH_SOLVE = DEPTH_FIRST (has_fewer_prems 1);
paulson@1588
    88
paulson@1588
    89
paulson@1588
    90
paulson@2869
    91
(**** Iterative deepening with pruning ****)
paulson@1588
    92
paulson@1588
    93
fun has_vars (Var _) = true
paulson@1588
    94
  | has_vars (Abs (_,_,t)) = has_vars t
paulson@1588
    95
  | has_vars (f$t) = has_vars f orelse has_vars t
paulson@1588
    96
  | has_vars _ = false;
paulson@1588
    97
paulson@1588
    98
(*Counting of primitive inferences is APPROXIMATE, as the step tactic
paulson@1588
    99
  may perform >1 inference*)
paulson@1588
   100
paulson@1588
   101
(*Pruning of rigid ancestor to prevent backtracking*)
paulson@1588
   102
fun prune (new as (k', np':int, rgd', stq), qs) = 
paulson@1588
   103
    let fun prune_aux (qs, []) = new::qs
paulson@1588
   104
          | prune_aux (qs, (k,np,rgd,q)::rqs) =
paulson@1588
   105
	      if np'+1 = np andalso rgd then
paulson@1588
   106
		  (if !trace_DEPTH_FIRST then
paulson@1588
   107
		       writeln ("Pruning " ^ 
paulson@1588
   108
				string_of_int (1+length rqs) ^ " levels")
paulson@1588
   109
		   else ();
paulson@1588
   110
		   (*Use OLD k: zero-cost solution; see Stickel, p 365*)
paulson@1588
   111
		   (k, np', rgd', stq) :: qs)
paulson@1588
   112
	      else prune_aux ((k,np,rgd,q)::qs, rqs)
paulson@1588
   113
        fun take ([], rqs) = ([], rqs)
paulson@1588
   114
	  | take (arg as ((k,np,rgd,stq)::qs, rqs)) = 
paulson@1588
   115
	        if np' < np then take (qs, (k,np,rgd,stq)::rqs)
paulson@1588
   116
		            else arg
paulson@1588
   117
    in  prune_aux (take (qs, []))  end;
paulson@1588
   118
paulson@1588
   119
paulson@1588
   120
(*Depth-first iterative deepening search for a state that satisfies satp
paulson@1588
   121
  tactic tac0 sets up the initial goal queue, while tac1 searches it.
paulson@1588
   122
  The solution sequence is redundant: the cutoff heuristic makes it impossible
paulson@1588
   123
  to suppress solutions arising from earlier searches, as the accumulated cost
paulson@1588
   124
  (k) can be wrong.*)
paulson@1588
   125
fun THEN_ITER_DEEPEN tac0 satp tac1 = traced_tac (fn st => 
paulson@1588
   126
 let val countr = ref 0
paulson@1588
   127
     and tf = tracify trace_DEPTH_FIRST (tac1 1)
paulson@1588
   128
     and qs0 = tac0 st
paulson@1588
   129
     (*bnd = depth bound; inc = estimate of increment required next*)
paulson@1588
   130
     fun depth (bnd,inc) [] = 
paulson@1588
   131
	     (writeln (string_of_int (!countr) ^ 
paulson@1588
   132
		       " inferences so far.  Searching to depth " ^ 
paulson@1588
   133
		       string_of_int bnd);
paulson@1588
   134
	      (*larger increments make it run slower for the hard problems*)
paulson@1588
   135
	      depth (bnd+inc, 10)) [(0, 1, false, qs0)]
paulson@1588
   136
       | depth (bnd,inc) ((k,np,rgd,q)::qs) =
paulson@1588
   137
	  if k>=bnd then depth (bnd,inc) qs
paulson@1588
   138
          else
paulson@1588
   139
	  case (countr := !countr+1;
paulson@1588
   140
		if !trace_DEPTH_FIRST then
paulson@1588
   141
		    writeln (string_of_int np ^ 
paulson@1588
   142
			     implode (map (fn _ => "*") qs))
paulson@1588
   143
		else ();
wenzelm@4270
   144
		Seq.pull q) of
paulson@1588
   145
	     None         => depth (bnd,inc) qs
paulson@1588
   146
	   | Some(st,stq) => 
paulson@1588
   147
	       if satp st	(*solution!*)
wenzelm@4270
   148
	       then Some(st, Seq.make
paulson@1588
   149
			 (fn()=> depth (bnd,inc) ((k,np,rgd,stq)::qs)))
paulson@1588
   150
paulson@1588
   151
	       else 
paulson@1588
   152
               let val np' = nprems_of st
paulson@1588
   153
		     (*rgd' calculation assumes tactic operates on subgoal 1*)
paulson@1588
   154
                   val rgd' = not (has_vars (hd (prems_of st)))
paulson@1588
   155
                   val k' = k+np'-np+1  (*difference in # of subgoals, +1*)
paulson@1588
   156
               in  if k'+np' >= bnd 
paulson@2143
   157
		   then depth (bnd, Int.min(inc, k'+np'+1-bnd)) qs
paulson@1588
   158
		   else if np' < np (*solved a subgoal; prune rigid ancestors*)
paulson@1588
   159
                   then depth (bnd,inc) 
paulson@1588
   160
		         (prune ((k', np', rgd', tf st), (k,np,rgd,stq) :: qs))
paulson@1588
   161
	           else depth (bnd,inc) ((k', np', rgd', tf st) :: 
paulson@1588
   162
					 (k,np,rgd,stq) :: qs)
paulson@1588
   163
	       end
paulson@1588
   164
  in depth (0,5) [] end);
paulson@1588
   165
paulson@1588
   166
val ITER_DEEPEN = THEN_ITER_DEEPEN all_tac;
paulson@1588
   167
paulson@1588
   168
paulson@2869
   169
(*Simple iterative deepening tactical.  It merely "deepens" any search tactic
paulson@2869
   170
  using increment "inc" up to limit "lim". *)
paulson@2869
   171
fun DEEPEN (inc,lim) tacf m i = 
paulson@3538
   172
  let fun dpn m st = st |> (if has_fewer_prems i st then no_tac
paulson@3538
   173
			    else if m>lim then 
paulson@3538
   174
				(writeln "Giving up..."; no_tac)
paulson@3538
   175
				 else (writeln ("Depth = " ^ string_of_int m);
paulson@3538
   176
				       tacf m i  ORELSE  dpn (m+inc)))
paulson@2869
   177
  in  dpn m  end;
paulson@2869
   178
paulson@1588
   179
(*** Best-first search ***)
paulson@1588
   180
paulson@1588
   181
val trace_BEST_FIRST = ref false;
paulson@1588
   182
paulson@1588
   183
(*Insertion into priority queue of states *)
paulson@1588
   184
fun insert (nth: int*thm, []) = [nth]
paulson@1588
   185
  | insert ((m,th), (n,th')::nths) = 
paulson@1588
   186
      if  n<m then (n,th') :: insert ((m,th), nths)
paulson@1588
   187
      else if  n=m andalso eq_thm(th,th')
paulson@1588
   188
              then (n,th')::nths
paulson@1588
   189
              else (m,th)::(n,th')::nths;
paulson@1588
   190
paulson@1588
   191
(*For creating output sequence*)
paulson@1588
   192
fun some_of_list []     = None
wenzelm@4270
   193
  | some_of_list (x::l) = Some (x, Seq.make (fn () => some_of_list l));
paulson@1588
   194
paulson@1588
   195
paulson@1588
   196
(*Best-first search for a state that satisfies satp (incl initial state)
paulson@1588
   197
  Function sizef estimates size of problem remaining (smaller means better).
paulson@1588
   198
  tactic tac0 sets up the initial priority queue, while tac1 searches it. *)
paulson@1588
   199
fun THEN_BEST_FIRST tac0 (satp, sizef) tac1 = 
paulson@1588
   200
  let val tac = tracify trace_BEST_FIRST tac1
paulson@1588
   201
      fun pairsize th = (sizef th, th);
paulson@1588
   202
      fun bfs (news,nprfs) =
paulson@1588
   203
	   (case  partition satp news  of
paulson@1588
   204
		([],nonsats) => next(foldr insert
paulson@1588
   205
					(map pairsize nonsats, nprfs)) 
paulson@1588
   206
	      | (sats,_)  => some_of_list sats)
paulson@1588
   207
      and next [] = None
paulson@1588
   208
        | next ((n,prf)::nprfs) =
paulson@1588
   209
	    (if !trace_BEST_FIRST 
paulson@1588
   210
	       then writeln("state size = " ^ string_of_int n ^ 
paulson@1588
   211
		         "  queue length =" ^ string_of_int (length nprfs))  
paulson@1588
   212
               else ();
wenzelm@4270
   213
	     bfs (Seq.list_of (tac prf), nprfs))
wenzelm@4270
   214
      fun btac st = bfs (Seq.list_of (tac0 st),  [])
paulson@1588
   215
  in traced_tac btac end;
paulson@1588
   216
paulson@1588
   217
(*Ordinary best-first search, with no initial tactic*)
paulson@1588
   218
val BEST_FIRST = THEN_BEST_FIRST all_tac;
paulson@1588
   219
paulson@1588
   220
(*Breadth-first search to satisfy satpred (including initial state) 
paulson@1588
   221
  SLOW -- SHOULD NOT USE APPEND!*)
wenzelm@5693
   222
fun gen_BREADTH_FIRST message satpred (tac:tactic) = 
wenzelm@4270
   223
  let val tacf = Seq.list_of o tac;
paulson@1588
   224
      fun bfs prfs =
paulson@1588
   225
	 (case  partition satpred prfs  of
paulson@1588
   226
	      ([],[]) => []
paulson@1588
   227
	    | ([],nonsats) => 
wenzelm@5693
   228
		  (message("breadth=" ^ string_of_int(length nonsats) ^ "\n");
paulson@2672
   229
		   bfs (List.concat (map tacf nonsats)))
paulson@1588
   230
	    | (sats,_)  => sats)
wenzelm@4270
   231
  in (fn st => Seq.of_list (bfs [st])) end;
paulson@1588
   232
wenzelm@5693
   233
val BREADTH_FIRST = gen_BREADTH_FIRST prs;
wenzelm@5693
   234
val QUIET_BREADTH_FIRST = gen_BREADTH_FIRST (K ());
wenzelm@5693
   235
paulson@1588
   236
paulson@1588
   237
(*  Author: 	Norbert Voelker, FernUniversitaet Hagen
paulson@1588
   238
    Remarks:    Implementation of A*-like proof procedure by modification
paulson@1588
   239
		of the existing code for BEST_FIRST and best_tac so that the 
paulson@1588
   240
		current level of search is taken into account.
paulson@1588
   241
*)		
paulson@1588
   242
paulson@1588
   243
(*Insertion into priority queue of states, marked with level *)
paulson@1588
   244
fun insert_with_level (lnth: int*int*thm, []) = [lnth]
paulson@1588
   245
  | insert_with_level ((l,m,th), (l',n,th')::nths) = 
paulson@1588
   246
      if  n<m then (l',n,th') :: insert_with_level ((l,m,th), nths)
paulson@1588
   247
      else if  n=m andalso eq_thm(th,th')
paulson@1588
   248
              then (l',n,th')::nths
paulson@1588
   249
              else (l,m,th)::(l',n,th')::nths;
paulson@1588
   250
paulson@1588
   251
(*For creating output sequence*)
paulson@1588
   252
fun some_of_list []     = None
wenzelm@4270
   253
  | some_of_list (x::l) = Some (x, Seq.make (fn () => some_of_list l));
paulson@1588
   254
paulson@1588
   255
val trace_ASTAR = ref false; 
paulson@1588
   256
paulson@1588
   257
fun THEN_ASTAR tac0 (satp, costf) tac1 = 
paulson@1588
   258
  let val tf = tracify trace_ASTAR tac1;   
paulson@1588
   259
      fun bfs (news,nprfs,level) =
paulson@1588
   260
      let fun cost thm = (level, costf level thm, thm)
paulson@1588
   261
      in (case  partition satp news  of
paulson@1588
   262
            ([],nonsats) 
paulson@1588
   263
		 => next (foldr insert_with_level (map cost nonsats, nprfs))
paulson@1588
   264
          | (sats,_)  => some_of_list sats)
paulson@1588
   265
      end and    
paulson@1588
   266
      next []  = None
paulson@1588
   267
        | next ((level,n,prf)::nprfs)  =
paulson@1588
   268
            (if !trace_ASTAR 
paulson@1588
   269
               then writeln("level = " ^ string_of_int level ^
paulson@1588
   270
			 "  cost = " ^ string_of_int n ^ 
paulson@1588
   271
                         "  queue length =" ^ string_of_int (length nprfs))  
paulson@1588
   272
               else ();
wenzelm@4270
   273
             bfs (Seq.list_of (tf prf), nprfs,level+1))
wenzelm@4270
   274
      fun tf st = bfs (Seq.list_of (tac0 st), [], 0)
paulson@1588
   275
  in traced_tac tf end;
paulson@1588
   276
paulson@1588
   277
(*Ordinary ASTAR, with no initial tactic*)
paulson@1588
   278
val ASTAR = THEN_ASTAR all_tac;
paulson@1588
   279
paulson@1588
   280
end;
paulson@1588
   281
paulson@1588
   282
open Search;