src/Pure/search.ML
author paulson
Fri Feb 21 15:31:47 1997 +0100 (1997-02-21)
changeset 2672 85d7e800d754
parent 2143 093bbe6d333b
child 2869 acee08856cc9
permissions -rw-r--r--
Replaced "flat" by the Basis Library function List.concat
     1 (*  Title: 	search
     2     ID:         $Id$
     3     Author: 	Lawrence C Paulson and Norbert Voelker
     4 
     5 Search tacticals
     6 *)
     7 
     8 infix 1 THEN_MAYBE THEN_MAYBE';
     9 
    10 signature SEARCH =
    11   sig
    12   val THEN_MAYBE	: tactic * tactic -> tactic
    13   val THEN_MAYBE'	: ('a -> tactic) * ('a -> tactic) -> ('a -> tactic)
    14 
    15   val trace_DEPTH_FIRST	: bool ref
    16   val DEPTH_FIRST	: (thm -> bool) -> tactic -> tactic
    17   val DEPTH_SOLVE	: tactic -> tactic
    18   val DEPTH_SOLVE_1	: tactic -> tactic
    19   val ITER_DEEPEN	: (thm->bool) -> (int->tactic) -> tactic
    20   val THEN_ITER_DEEPEN	: tactic -> (thm->bool) -> (int->tactic) -> tactic
    21 
    22   val has_fewer_prems	: int -> thm -> bool   
    23   val IF_UNSOLVED	: tactic -> tactic
    24   val trace_BEST_FIRST	: bool ref
    25   val BEST_FIRST	: (thm -> bool) * (thm -> int) -> tactic -> tactic
    26   val THEN_BEST_FIRST	: tactic -> (thm->bool) * (thm->int) -> tactic
    27 			  -> tactic
    28   val trace_ASTAR	: bool ref
    29   val ASTAR	        : (thm -> bool) * (int->thm->int) -> tactic -> tactic
    30   val THEN_ASTAR	: tactic -> (thm->bool) * (int->thm->int) -> tactic
    31 			  -> tactic
    32   val BREADTH_FIRST	: (thm -> bool) -> tactic -> tactic
    33   end;
    34 
    35 structure Search : SEARCH = 
    36 struct
    37 
    38 (**** Depth-first search ****)
    39 
    40 val trace_DEPTH_FIRST = ref false;
    41 
    42 (*Searches until "satp" reports proof tree as satisfied.
    43   Suppresses duplicate solutions to minimize search space.*)
    44 fun DEPTH_FIRST satp tac = 
    45  let val tac = tracify trace_DEPTH_FIRST tac
    46      fun depth used [] = None
    47        | depth used (q::qs) =
    48 	  case Sequence.pull q of
    49 	      None         => depth used qs
    50 	    | Some(st,stq) => 
    51 		if satp st andalso not (gen_mem eq_thm (st, used))
    52 		then Some(st, Sequence.seqof
    53 			         (fn()=> depth (st::used) (stq::qs)))
    54 		else depth used (tac st :: stq :: qs)
    55   in  traced_tac (fn st => depth [] ([Sequence.single st]))  end;
    56 
    57 
    58 
    59 (*Predicate: Does the rule have fewer than n premises?*)
    60 fun has_fewer_prems n rule = (nprems_of rule < n);
    61 
    62 (*Apply a tactic if subgoals remain, else do nothing.*)
    63 val IF_UNSOLVED = COND (has_fewer_prems 1) all_tac;
    64 
    65 (*Execute tac1, but only execute tac2 if there are at least as many subgoals
    66   as before.  This ensures that tac2 is only applied to an outcome of tac1.*)
    67 fun tac1 THEN_MAYBE tac2 = STATE
    68     (fn st => tac1  THEN  
    69 	 COND (has_fewer_prems (nprems_of st)) all_tac tac2);
    70 
    71 fun (tac1 THEN_MAYBE' tac2) x = tac1 x THEN_MAYBE tac2 x;
    72 
    73 (*Tactical to reduce the number of premises by 1.
    74   If no subgoals then it must fail! *)
    75 fun DEPTH_SOLVE_1 tac = STATE
    76  (fn st => 
    77     (case nprems_of st of
    78 	0 => no_tac
    79       | n => DEPTH_FIRST (has_fewer_prems n) tac));
    80 
    81 (*Uses depth-first search to solve ALL subgoals*)
    82 val DEPTH_SOLVE = DEPTH_FIRST (has_fewer_prems 1);
    83 
    84 
    85 
    86 (**** Iterative deepening ****)
    87 
    88 fun has_vars (Var _) = true
    89   | has_vars (Abs (_,_,t)) = has_vars t
    90   | has_vars (f$t) = has_vars f orelse has_vars t
    91   | has_vars _ = false;
    92 
    93 (*Counting of primitive inferences is APPROXIMATE, as the step tactic
    94   may perform >1 inference*)
    95 
    96 (*Pruning of rigid ancestor to prevent backtracking*)
    97 fun prune (new as (k', np':int, rgd', stq), qs) = 
    98     let fun prune_aux (qs, []) = new::qs
    99           | prune_aux (qs, (k,np,rgd,q)::rqs) =
   100 	      if np'+1 = np andalso rgd then
   101 		  (if !trace_DEPTH_FIRST then
   102 		       writeln ("Pruning " ^ 
   103 				string_of_int (1+length rqs) ^ " levels")
   104 		   else ();
   105 		   (*Use OLD k: zero-cost solution; see Stickel, p 365*)
   106 		   (k, np', rgd', stq) :: qs)
   107 	      else prune_aux ((k,np,rgd,q)::qs, rqs)
   108         fun take ([], rqs) = ([], rqs)
   109 	  | take (arg as ((k,np,rgd,stq)::qs, rqs)) = 
   110 	        if np' < np then take (qs, (k,np,rgd,stq)::rqs)
   111 		            else arg
   112     in  prune_aux (take (qs, []))  end;
   113 
   114 
   115 (*Depth-first iterative deepening search for a state that satisfies satp
   116   tactic tac0 sets up the initial goal queue, while tac1 searches it.
   117   The solution sequence is redundant: the cutoff heuristic makes it impossible
   118   to suppress solutions arising from earlier searches, as the accumulated cost
   119   (k) can be wrong.*)
   120 fun THEN_ITER_DEEPEN tac0 satp tac1 = traced_tac (fn st => 
   121  let val countr = ref 0
   122      and tf = tracify trace_DEPTH_FIRST (tac1 1)
   123      and qs0 = tac0 st
   124      (*bnd = depth bound; inc = estimate of increment required next*)
   125      fun depth (bnd,inc) [] = 
   126 	     (writeln (string_of_int (!countr) ^ 
   127 		       " inferences so far.  Searching to depth " ^ 
   128 		       string_of_int bnd);
   129 	      (*larger increments make it run slower for the hard problems*)
   130 	      depth (bnd+inc, 10)) [(0, 1, false, qs0)]
   131        | depth (bnd,inc) ((k,np,rgd,q)::qs) =
   132 	  if k>=bnd then depth (bnd,inc) qs
   133           else
   134 	  case (countr := !countr+1;
   135 		if !trace_DEPTH_FIRST then
   136 		    writeln (string_of_int np ^ 
   137 			     implode (map (fn _ => "*") qs))
   138 		else ();
   139 		Sequence.pull q) of
   140 	     None         => depth (bnd,inc) qs
   141 	   | Some(st,stq) => 
   142 	       if satp st	(*solution!*)
   143 	       then Some(st, Sequence.seqof
   144 			 (fn()=> depth (bnd,inc) ((k,np,rgd,stq)::qs)))
   145 
   146 	       else 
   147                let val np' = nprems_of st
   148 		     (*rgd' calculation assumes tactic operates on subgoal 1*)
   149                    val rgd' = not (has_vars (hd (prems_of st)))
   150                    val k' = k+np'-np+1  (*difference in # of subgoals, +1*)
   151                in  if k'+np' >= bnd 
   152 		   then depth (bnd, Int.min(inc, k'+np'+1-bnd)) qs
   153 		   else if np' < np (*solved a subgoal; prune rigid ancestors*)
   154                    then depth (bnd,inc) 
   155 		         (prune ((k', np', rgd', tf st), (k,np,rgd,stq) :: qs))
   156 	           else depth (bnd,inc) ((k', np', rgd', tf st) :: 
   157 					 (k,np,rgd,stq) :: qs)
   158 	       end
   159   in depth (0,5) [] end);
   160 
   161 val ITER_DEEPEN = THEN_ITER_DEEPEN all_tac;
   162 
   163 
   164 (*** Best-first search ***)
   165 
   166 val trace_BEST_FIRST = ref false;
   167 
   168 (*Insertion into priority queue of states *)
   169 fun insert (nth: int*thm, []) = [nth]
   170   | insert ((m,th), (n,th')::nths) = 
   171       if  n<m then (n,th') :: insert ((m,th), nths)
   172       else if  n=m andalso eq_thm(th,th')
   173               then (n,th')::nths
   174               else (m,th)::(n,th')::nths;
   175 
   176 (*For creating output sequence*)
   177 fun some_of_list []     = None
   178   | some_of_list (x::l) = Some (x, Sequence.seqof (fn () => some_of_list l));
   179 
   180 
   181 (*Best-first search for a state that satisfies satp (incl initial state)
   182   Function sizef estimates size of problem remaining (smaller means better).
   183   tactic tac0 sets up the initial priority queue, while tac1 searches it. *)
   184 fun THEN_BEST_FIRST tac0 (satp, sizef) tac1 = 
   185   let val tac = tracify trace_BEST_FIRST tac1
   186       fun pairsize th = (sizef th, th);
   187       fun bfs (news,nprfs) =
   188 	   (case  partition satp news  of
   189 		([],nonsats) => next(foldr insert
   190 					(map pairsize nonsats, nprfs)) 
   191 	      | (sats,_)  => some_of_list sats)
   192       and next [] = None
   193         | next ((n,prf)::nprfs) =
   194 	    (if !trace_BEST_FIRST 
   195 	       then writeln("state size = " ^ string_of_int n ^ 
   196 		         "  queue length =" ^ string_of_int (length nprfs))  
   197                else ();
   198 	     bfs (Sequence.list_of_s (tac prf), nprfs))
   199       fun btac st = bfs (Sequence.list_of_s (tac0 st),  [])
   200   in traced_tac btac end;
   201 
   202 (*Ordinary best-first search, with no initial tactic*)
   203 val BEST_FIRST = THEN_BEST_FIRST all_tac;
   204 
   205 (*Breadth-first search to satisfy satpred (including initial state) 
   206   SLOW -- SHOULD NOT USE APPEND!*)
   207 fun BREADTH_FIRST satpred tac = 
   208   let val tacf = Sequence.list_of_s o tac;
   209       fun bfs prfs =
   210 	 (case  partition satpred prfs  of
   211 	      ([],[]) => []
   212 	    | ([],nonsats) => 
   213 		  (prs("breadth=" ^ string_of_int(length nonsats) ^ "\n");
   214 		   bfs (List.concat (map tacf nonsats)))
   215 	    | (sats,_)  => sats)
   216   in (fn st => Sequence.s_of_list (bfs [st])) end;
   217 
   218 
   219 (*  Author: 	Norbert Voelker, FernUniversitaet Hagen
   220     Remarks:    Implementation of A*-like proof procedure by modification
   221 		of the existing code for BEST_FIRST and best_tac so that the 
   222 		current level of search is taken into account.
   223 *)		
   224 
   225 (*Insertion into priority queue of states, marked with level *)
   226 fun insert_with_level (lnth: int*int*thm, []) = [lnth]
   227   | insert_with_level ((l,m,th), (l',n,th')::nths) = 
   228       if  n<m then (l',n,th') :: insert_with_level ((l,m,th), nths)
   229       else if  n=m andalso eq_thm(th,th')
   230               then (l',n,th')::nths
   231               else (l,m,th)::(l',n,th')::nths;
   232 
   233 (*For creating output sequence*)
   234 fun some_of_list []     = None
   235   | some_of_list (x::l) = Some (x, Sequence.seqof (fn () => some_of_list l));
   236 
   237 val trace_ASTAR = ref false; 
   238 
   239 fun THEN_ASTAR tac0 (satp, costf) tac1 = 
   240   let val tf = tracify trace_ASTAR tac1;   
   241       fun bfs (news,nprfs,level) =
   242       let fun cost thm = (level, costf level thm, thm)
   243       in (case  partition satp news  of
   244             ([],nonsats) 
   245 		 => next (foldr insert_with_level (map cost nonsats, nprfs))
   246           | (sats,_)  => some_of_list sats)
   247       end and    
   248       next []  = None
   249         | next ((level,n,prf)::nprfs)  =
   250             (if !trace_ASTAR 
   251                then writeln("level = " ^ string_of_int level ^
   252 			 "  cost = " ^ string_of_int n ^ 
   253                          "  queue length =" ^ string_of_int (length nprfs))  
   254                else ();
   255              bfs (Sequence.list_of_s (tf prf), nprfs,level+1))
   256       fun tf st = bfs (Sequence.list_of_s (tac0 st), [], 0)
   257   in traced_tac tf end;
   258 
   259 (*Ordinary ASTAR, with no initial tactic*)
   260 val ASTAR = THEN_ASTAR all_tac;
   261 
   262 end;
   263 
   264 open Search;