src/HOL/Tools/ATP/reduce_axiomsN.ML
author mengj
Mon Feb 13 14:05:43 2006 +0100 (2006-02-13)
changeset 19035 678ef6658a0e
parent 19009 bb29bf9d3a72
child 19200 1da6b9a1575d
permissions -rw-r--r--
Fixed a bug of type unification.
     1 structure ReduceAxiomsN =
     2 (* Author: Jia Meng, Cambridge University Computer Laboratory
     3    
     4    Two filtering strategies *)
     5 
     6 struct
     7 
     8 val pass_mark = ref 0.5;
     9 val strategy = ref 1;
    10 
    11 fun pol_to_int true = 1
    12   | pol_to_int false = ~1;
    13 
    14 fun part refs [] (s1,s2) = (s1,s2)
    15   | part refs (s::ss) (s1,s2) = if (s mem refs) then (part refs ss (s::s1,s2)) else (part refs ss (s1,s::s2));
    16 
    17 
    18 fun pol_mem _ [] = false
    19   | pol_mem (pol,const) ((p,c)::pcs) = if ((pol = not p) andalso (const = c)) then true else pol_mem (pol,const) pcs;
    20 
    21 
    22 fun part_w_pol refs [] (s1,s2) = (s1,s2)
    23   | part_w_pol refs (s::ss) (s1,s2) = if (pol_mem s refs) then (part_w_pol refs ss (s::s1,s2)) else (part_w_pol refs ss (s1,s::s2));
    24 
    25 
    26 fun add_term_consts_rm ncs (Const(c, _)) cs = if (c mem ncs) then cs else (c ins_string cs)
    27   | add_term_consts_rm ncs (t $ u) cs =
    28       add_term_consts_rm ncs t (add_term_consts_rm ncs u cs)
    29   | add_term_consts_rm ncs (Abs(_,_,t)) cs = add_term_consts_rm ncs t cs
    30   | add_term_consts_rm ncs _ cs = cs;
    31 
    32 fun term_consts_rm ncs t = add_term_consts_rm ncs t [];
    33 
    34 fun consts_of_term term = term_consts_rm ["Trueprop","==>","all","Ex","op &", "op |", "Not", "All", "op -->", "op =", "==", "True", "False"] term;
    35 
    36 
    37 fun add_term_pconsts_rm ncs (Const(c,_)) pol cs = if (c mem ncs) then cs else ((pol,c) ins cs)
    38   | add_term_pconsts_rm ncs (Const("Not",_)$P) pol cs = add_term_pconsts_rm ncs P (not pol) cs
    39   | add_term_pconsts_rm ncs (P$Q) pol cs = 
    40     add_term_pconsts_rm ncs P pol (add_term_pconsts_rm ncs Q pol cs)
    41   | add_term_pconsts_rm ncs (Abs(_,_,t)) pol cs = add_term_pconsts_rm ncs t pol cs
    42   | add_term_pconsts_rm ncs _ _ cs = cs;
    43 
    44 
    45 fun term_pconsts_rm ncs t = add_term_pconsts_rm ncs t true [];
    46 
    47 
    48 fun pconsts_of_term term = term_pconsts_rm ["Trueprop","==>","all","Ex","op &", "op |", "Not", "All", "op -->", "op =", "==", "True", "False"] term;
    49 
    50 fun consts_in_goal goal = consts_of_term goal;
    51 fun get_goal_consts cs = foldl (op union_string) [] (map consts_in_goal cs);
    52 
    53 
    54 fun pconsts_in_goal goal = pconsts_of_term goal;
    55 fun get_goal_pconsts cs = foldl (op union) [] (map pconsts_in_goal cs);
    56 
    57 
    58 (*************************************************************************)
    59 (*            the first relevance filtering strategy                     *)
    60 (*************************************************************************)
    61 
    62 fun find_clause_weight_s_1 (refconsts : string list) consts wa = 
    63     let val (rel,irrel) = part refconsts consts ([],[])
    64     in
    65 	((real (length rel))/(real (length consts))) * wa
    66     end;
    67 
    68 fun find_clause_weight_m_1 [] (_,w) = w 
    69   | find_clause_weight_m_1 ((_,(refconsts,wa))::y) (consts,w) =
    70     let val w' = find_clause_weight_s_1 refconsts consts wa
    71     in
    72 	if (w < w') then find_clause_weight_m_1 y (consts,w')
    73 	else find_clause_weight_m_1 y (consts,w)
    74     end;
    75 
    76 
    77 fun relevant_clauses_ax_g_1 _ []  _ (ax,r) = (ax,r)
    78   | relevant_clauses_ax_g_1 gconsts  ((clsthm,(consts,_))::y) P (ax,r) =
    79     let val weight = find_clause_weight_s_1 gconsts consts 1.0
    80     in
    81 	if  P <= weight then relevant_clauses_ax_g_1 gconsts y P ((clsthm,(consts,weight))::ax,r)
    82 	else relevant_clauses_ax_g_1 gconsts y P (ax,(clsthm,(consts,weight))::r)
    83     end;
    84 
    85 
    86 fun relevant_clauses_ax_1 rel_axs  [] P (addc,tmpc) keep = 
    87     (case addc of [] => rel_axs @ keep
    88 		| _ => case tmpc of [] => addc @ rel_axs @ keep
    89 				  | _ => relevant_clauses_ax_1 addc tmpc P ([],[]) (rel_axs @ keep))
    90   | relevant_clauses_ax_1 rel_axs ((clsthm,(consts,weight))::e_axs) P (addc,tmpc) keep = 
    91     let val weight' = find_clause_weight_m_1 rel_axs (consts,weight) 
    92 	val e_ax' = (clsthm,(consts, weight'))
    93     in
    94 	
    95 	if P <= weight' then relevant_clauses_ax_1 rel_axs e_axs P ((clsthm,(consts,weight'))::addc,tmpc) keep
    96 	else relevant_clauses_ax_1 rel_axs e_axs P (addc,(clsthm,(consts,weight'))::tmpc) keep 
    97     end;
    98 
    99 
   100 fun initialize [] ax_weights = ax_weights
   101   | initialize ((cls,thm)::clss_thms) ax_weights =
   102     let val tm = prop_of thm
   103 	val consts = consts_of_term tm
   104     in
   105 	initialize clss_thms (((cls,thm),(consts,0.0))::ax_weights)
   106     end;
   107 
   108 fun relevance_filter1_aux axioms goals = 
   109     let val pass = !pass_mark
   110 	val axioms_weights = initialize axioms []
   111 	val goals_consts = get_goal_consts goals
   112 	val (rel_clauses,nrel_clauses) = relevant_clauses_ax_g_1 goals_consts axioms_weights pass ([],[]) 
   113     in
   114 	relevant_clauses_ax_1 rel_clauses nrel_clauses pass ([],[]) []
   115     end;
   116 
   117 fun relevance_filter1 axioms goals = map fst (relevance_filter1_aux axioms goals);
   118 
   119 
   120 
   121 
   122 (*************************************************************************)
   123 (*            the second relevance filtering strategy                    *)
   124 (*************************************************************************)
   125 
   126 fun find_clause_weight_s_2 (refpconsts : (bool * string) list) pconsts wa = 
   127     let val (rel,irrel) = part_w_pol refpconsts pconsts ([],[])
   128     in
   129 	((real (length rel))/(real (length pconsts))) * wa
   130     end;
   131 
   132 fun find_clause_weight_m_2 [] (_,w) = w 
   133   | find_clause_weight_m_2 ((_,(refpconsts,wa))::y) (pconsts,w) =
   134     let val w' = find_clause_weight_s_2 refpconsts pconsts wa
   135     in
   136 	if (w < w') then find_clause_weight_m_2 y (pconsts,w')
   137 	else find_clause_weight_m_2 y (pconsts,w)
   138     end;
   139 
   140 
   141 fun relevant_clauses_ax_g_2 _ []  _ (ax,r) = (ax,r)
   142   | relevant_clauses_ax_g_2 gpconsts  ((clsthm,(pconsts,_))::y) P (ax,r) =
   143     let val weight = find_clause_weight_s_2 gpconsts pconsts 1.0
   144     in
   145 	if  P <= weight then relevant_clauses_ax_g_2 gpconsts y P ((clsthm,(pconsts,weight))::ax,r)
   146 	else relevant_clauses_ax_g_2 gpconsts y P (ax,(clsthm,(pconsts,weight))::r)
   147     end;
   148 
   149 
   150 fun relevant_clauses_ax_2 rel_axs  [] P (addc,tmpc) keep = 
   151     (case addc of [] => rel_axs @ keep
   152 		| _ => case tmpc of [] => addc @ rel_axs @ keep
   153 				  | _ => relevant_clauses_ax_2 addc tmpc P ([],[]) (rel_axs @ keep))
   154   | relevant_clauses_ax_2 rel_axs ((clsthm,(pconsts,weight))::e_axs) P (addc,tmpc) keep = 
   155     let val weight' = find_clause_weight_m_2 rel_axs (pconsts,weight) 
   156 	val e_ax' = (clsthm,(pconsts, weight'))
   157     in
   158 	
   159 	if P <= weight' then relevant_clauses_ax_2 rel_axs e_axs P ((clsthm,(pconsts,weight'))::addc,tmpc) keep
   160 	else relevant_clauses_ax_2 rel_axs e_axs P (addc,(clsthm,(pconsts,weight'))::tmpc) keep 
   161     end;
   162 
   163 
   164 fun initialize_w_pol [] ax_weights = ax_weights
   165   | initialize_w_pol ((cls,thm)::clss_thms) ax_weights =
   166     let val tm = prop_of thm
   167 	val consts = pconsts_of_term tm
   168     in
   169 	initialize_w_pol clss_thms (((cls,thm),(consts,0.0))::ax_weights)
   170     end;
   171 
   172 
   173 fun relevance_filter2_aux axioms goals = 
   174     let val pass = !pass_mark
   175 	val axioms_weights = initialize_w_pol axioms []
   176 	val goals_consts = get_goal_pconsts goals
   177 	val (rel_clauses,nrel_clauses) = relevant_clauses_ax_g_2 goals_consts axioms_weights pass ([],[]) 
   178     in
   179 	relevant_clauses_ax_2 rel_clauses nrel_clauses pass ([],[]) []
   180     end;
   181 
   182 fun relevance_filter2 axioms goals = map fst (relevance_filter2_aux axioms goals);
   183 
   184 (******************************************************************)
   185 (*       the third relevance filtering strategy                   *)
   186 (******************************************************************)
   187 
   188 (*** unit clauses ***)
   189 datatype clause_type = Unit_neq | Unit_geq | Other
   190 
   191 val add_unit = ref true;
   192 
   193 
   194 fun literals_of_term args (Const ("Trueprop",_) $ P) = literals_of_term args P
   195   | literals_of_term args (Const ("op |",_) $ P $ Q) = 
   196     literals_of_term (literals_of_term args P) Q
   197   | literals_of_term args P = (P::args);
   198 
   199 
   200 fun is_ground t = if (term_vars t = []) then (term_frees t = []) else false;
   201 
   202 
   203 fun eq_clause_type (P,Q) = 
   204     if ((is_ground P) orelse (is_ground Q)) then Unit_geq else Other;
   205 
   206 fun unit_clause_type (Const ("op =",_) $ P $ Q) = eq_clause_type (P,Q)
   207   | unit_clause_type _ = Unit_neq;
   208 
   209 fun clause_type tm = 
   210     let val lits = literals_of_term [] tm
   211 	val nlits = length lits
   212     in 
   213 	if (nlits > 1) then Other
   214 	else unit_clause_type (hd lits)
   215     end;
   216 
   217 (*** constants with types ***)
   218 
   219 datatype const_typ =  CTVar | CType of string * const_typ list
   220 
   221 fun uni_type (CType (con1,args1)) (CType (con2,args2)) = (con1 = con2) andalso (uni_types args1 args2)
   222   | uni_type (CType (_,_)) CTVar = true
   223   | uni_type CTVar CTVar = true
   224   | uni_type CTVar _ = false
   225 
   226 and 
   227      uni_types [] [] = true
   228       | uni_types (a1::as1) (a2::as2) = (uni_type a1 a2) andalso (uni_types as1 as2);
   229 
   230 
   231 
   232 fun uni_constants (c1,ctp1) (c2,ctp2) = (c1 = c2) andalso (uni_types ctp1 ctp2);
   233 
   234 fun uni_mem _ [] = false
   235   | uni_mem (c,c_typ) ((c1,c_typ1)::ctyps) = (uni_constants (c1,c_typ1) (c,c_typ)) orelse (uni_mem (c,c_typ) ctyps);
   236 
   237 
   238 
   239 fun const_typ_of (Type (c,typs)) = CType (c,map const_typ_of typs) 
   240   | const_typ_of (TFree(_,_)) = CTVar
   241   | const_typ_of (TVar(_,_)) = CTVar
   242 
   243 
   244 fun const_w_typ thy (c,tp) = 
   245     let val tvars = Sign.const_typargs thy (c,tp)
   246     in
   247 	(c,map const_typ_of tvars)
   248     end;
   249 
   250 fun add_term_consts_typs_rm thy ncs (Const(c, tp)) cs = if (c mem ncs) then cs else (const_w_typ thy (c,tp) ins cs)
   251   | add_term_consts_typs_rm thy ncs (t $ u) cs =
   252       add_term_consts_typs_rm thy ncs  t (add_term_consts_typs_rm thy ncs u cs)
   253   | add_term_consts_typs_rm thy ncs (Abs(_,_,t)) cs = add_term_consts_typs_rm thy ncs t cs
   254   | add_term_consts_typs_rm thy ncs _ cs = cs;
   255 
   256 fun term_consts_typs_rm thy ncs t = add_term_consts_typs_rm thy ncs t [];
   257 
   258 fun consts_typs_of_term thy term = term_consts_typs_rm thy ["Trueprop","==>","all","Ex","op &", "op |", "Not", "All", "op -->", "op =", "==", "True", "False"] term;
   259 
   260 
   261 fun consts_typs_in_goal thy goal = consts_typs_of_term thy goal;
   262 
   263 fun get_goal_consts_typs thy cs = foldl (op union) [] (map (consts_typs_in_goal thy) cs)
   264 
   265 
   266 (******** filter clauses ********)
   267 
   268 fun part3 gctyps [] (s1,s2) = (s1,s2)
   269   | part3 gctyps (s::ss) (s1,s2) = if (uni_mem s gctyps) then part3 gctyps ss (s::s1,s2) else part3 gctyps ss (s1,s::s2);
   270 
   271 
   272 fun find_clause_weight_s_3 gctyps consts_typs wa =
   273     let val (rel,irrel) = part3 gctyps consts_typs ([],[])
   274     in
   275 	((real (length rel))/(real (length consts_typs))) * wa
   276     end;
   277 
   278 
   279 fun find_clause_weight_m_3 [] (_,w) = w
   280   | find_clause_weight_m_3 ((_,(_,(refconsts_typs,wa)))::y) (consts_typs,w) =
   281     let val w' = find_clause_weight_s_3 refconsts_typs consts_typs wa
   282     in
   283 	if (w < w') then find_clause_weight_m_3 y (consts_typs,w')
   284 	else find_clause_weight_m_3 y (consts_typs,w)
   285     end;
   286 
   287 
   288 fun relevant_clauses_ax_g_3 _ [] _ (ax,r) = (ax,r)
   289   | relevant_clauses_ax_g_3 gctyps ((cls_typ,(clsthm,(consts_typs,_)))::y) P (ax,r) =
   290     let val weight = find_clause_weight_s_3 gctyps consts_typs 1.0
   291     in
   292 	if P <= weight then relevant_clauses_ax_g_3 gctyps y P ((cls_typ,(clsthm,(consts_typs,weight)))::ax,r)
   293 	else relevant_clauses_ax_g_3 gctyps y P (ax,(cls_typ,(clsthm,(consts_typs,weight)))::r)
   294     end;
   295 
   296 fun relevant_clauses_ax_3 rel_axs [] P (addc,tmpc) keep =
   297     (case addc of [] => (rel_axs @ keep,tmpc)
   298 		| _ => case tmpc of [] => (addc @ rel_axs @ keep,[])
   299 				  | _ => relevant_clauses_ax_3 addc tmpc P ([],[]) (rel_axs @ keep))
   300   | relevant_clauses_ax_3 rel_axs ((cls_typ,(clsthm,(consts_typs,weight)))::e_axs) P (addc,tmpc) keep =
   301     let val weight' = find_clause_weight_m_3 rel_axs (consts_typs,weight)
   302 	val e_ax' = (cls_typ,(clsthm,(consts_typs,weight')))
   303     in
   304 	if P <= weight' then relevant_clauses_ax_3 rel_axs e_axs P (e_ax'::addc,tmpc) keep
   305 	else relevant_clauses_ax_3 rel_axs e_axs P (addc,e_ax'::tmpc) keep
   306     end;
   307 
   308 fun initialize3 thy [] ax_weights = ax_weights
   309   | initialize3 thy ((cls,thm)::clss_thms) ax_weights =
   310     let val tm = prop_of thm
   311 	val cls_type = clause_type tm
   312 	val consts = consts_typs_of_term thy tm
   313     in
   314 	initialize3 thy clss_thms ((cls_type,((cls,thm),(consts,0.0)))::ax_weights)
   315     end;
   316 
   317 fun add_unit_clauses ax [] = ax
   318   | add_unit_clauses ax ((cls_typ,consts_weight)::cs) =
   319     case cls_typ of Unit_neq => add_unit_clauses ((cls_typ,consts_weight)::ax) cs
   320 		  | Unit_geq => add_unit_clauses ((cls_typ,consts_weight)::ax) cs
   321 		  | Other => add_unit_clauses ax cs;
   322 
   323 fun relevance_filter3_aux thy axioms goals = 
   324     let val pass = !pass_mark
   325 	val axioms_weights = initialize3 thy axioms []
   326 	val goals_consts_typs = get_goal_consts_typs thy goals
   327 	val (rel_clauses,nrel_clauses) = relevant_clauses_ax_g_3 goals_consts_typs axioms_weights pass ([],[]) 
   328 	val (ax,r) = relevant_clauses_ax_3 rel_clauses nrel_clauses pass ([],[]) []
   329     in
   330 	if (!add_unit) then add_unit_clauses ax r else ax
   331     end;
   332 
   333 fun relevance_filter3 thy axioms goals = map fst (map snd (relevance_filter3_aux thy axioms goals));
   334     
   335 
   336 
   337 (******************************************************************)
   338 (* Generic functions for relevance filtering                      *)
   339 (******************************************************************)
   340 
   341 exception RELEVANCE_FILTER of string;
   342 
   343 fun relevance_filter thy axioms goals = 
   344     let val cls = (case (!strategy) of 1 => relevance_filter1 axioms goals
   345 				     | 2 => relevance_filter2 axioms goals
   346 				     | 3 => relevance_filter3 thy axioms goals
   347 				     | _ => raise RELEVANCE_FILTER("strategy doesn't exists"))
   348     in
   349 	cls
   350     end;
   351 
   352 
   353 end;