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structure ReduceAxiomsN =


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(* Author: Jia Meng, Cambridge University Computer Laboratory


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Two filtering strategies *)


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struct


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val pass_mark = ref 0.5;


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val strategy = ref 1;


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fun pol_to_int true = 1


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 pol_to_int false = ~1;


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fun part refs [] (s1,s2) = (s1,s2)


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 part refs (s::ss) (s1,s2) = if (s mem refs) then (part refs ss (s::s1,s2)) else (part refs ss (s1,s::s2));


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fun pol_mem _ [] = false


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 pol_mem (pol,const) ((p,c)::pcs) = if ((pol = not p) andalso (const = c)) then true else pol_mem (pol,const) pcs;


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fun part_w_pol refs [] (s1,s2) = (s1,s2)


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 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));


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fun add_term_consts_rm ncs (Const(c, _)) cs = if (c mem ncs) then cs else (c ins_string cs)


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 add_term_consts_rm ncs (t $ u) cs =


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add_term_consts_rm ncs t (add_term_consts_rm ncs u cs)


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 add_term_consts_rm ncs (Abs(_,_,t)) cs = add_term_consts_rm ncs t cs


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 add_term_consts_rm ncs _ cs = cs;


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fun term_consts_rm ncs t = add_term_consts_rm ncs t [];


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fun consts_of_term term = term_consts_rm ["Trueprop","==>","all","Ex","op &", "op ", "Not", "All", "op >", "op =", "==", "True", "False"] term;


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fun add_term_pconsts_rm ncs (Const(c,_)) pol cs = if (c mem ncs) then cs else ((pol,c) ins cs)


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 add_term_pconsts_rm ncs (Const("Not",_)$P) pol cs = add_term_pconsts_rm ncs P (not pol) cs


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 add_term_pconsts_rm ncs (P$Q) pol cs =


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add_term_pconsts_rm ncs P pol (add_term_pconsts_rm ncs Q pol cs)


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 add_term_pconsts_rm ncs (Abs(_,_,t)) pol cs = add_term_pconsts_rm ncs t pol cs


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 add_term_pconsts_rm ncs _ _ cs = cs;


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fun term_pconsts_rm ncs t = add_term_pconsts_rm ncs t true [];


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fun pconsts_of_term term = term_pconsts_rm ["Trueprop","==>","all","Ex","op &", "op ", "Not", "All", "op >", "op =", "==", "True", "False"] term;


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fun consts_in_goal goal = consts_of_term goal;


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fun get_goal_consts cs = foldl (op union_string) [] (map consts_in_goal cs);


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fun pconsts_in_goal goal = pconsts_of_term goal;


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fun get_goal_pconsts cs = foldl (op union) [] (map pconsts_in_goal cs);


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(*************************************************************************)


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(* the first relevance filtering strategy *)


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(*************************************************************************)


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fun find_clause_weight_s_1 (refconsts : string list) consts wa =


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let val (rel,irrel) = part refconsts consts ([],[])


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in


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((real (length rel))/(real (length consts))) * wa


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end;


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fun find_clause_weight_m_1 [] (_,w) = w


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 find_clause_weight_m_1 ((_,(refconsts,wa))::y) (consts,w) =


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let val w' = find_clause_weight_s_1 refconsts consts wa


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in


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if (w < w') then find_clause_weight_m_1 y (consts,w')


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else find_clause_weight_m_1 y (consts,w)


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end;


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fun relevant_clauses_ax_g_1 _ [] _ (ax,r) = (ax,r)


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 relevant_clauses_ax_g_1 gconsts ((clsthm,(consts,_))::y) P (ax,r) =


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let val weight = find_clause_weight_s_1 gconsts consts 1.0


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in


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if P <= weight then relevant_clauses_ax_g_1 gconsts y P ((clsthm,(consts,weight))::ax,r)


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else relevant_clauses_ax_g_1 gconsts y P (ax,(clsthm,(consts,weight))::r)


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end;


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fun relevant_clauses_ax_1 rel_axs [] P (addc,tmpc) keep =


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(case addc of [] => rel_axs @ keep


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 _ => case tmpc of [] => addc @ rel_axs @ keep


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 _ => relevant_clauses_ax_1 addc tmpc P ([],[]) (rel_axs @ keep))


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 relevant_clauses_ax_1 rel_axs ((clsthm,(consts,weight))::e_axs) P (addc,tmpc) keep =


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let val weight' = find_clause_weight_m_1 rel_axs (consts,weight)


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val e_ax' = (clsthm,(consts, weight'))


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in


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if P <= weight' then relevant_clauses_ax_1 rel_axs e_axs P ((clsthm,(consts,weight'))::addc,tmpc) keep


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else relevant_clauses_ax_1 rel_axs e_axs P (addc,(clsthm,(consts,weight'))::tmpc) keep


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end;


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fun initialize [] ax_weights = ax_weights


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 initialize ((cls,thm)::clss_thms) ax_weights =


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let val tm = prop_of thm


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val consts = consts_of_term tm


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in


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initialize clss_thms (((cls,thm),(consts,0.0))::ax_weights)


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end;


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fun relevance_filter1_aux axioms goals =


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let val pass = !pass_mark


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val axioms_weights = initialize axioms []


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val goals_consts = get_goal_consts goals


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val (rel_clauses,nrel_clauses) = relevant_clauses_ax_g_1 goals_consts axioms_weights pass ([],[])


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in


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relevant_clauses_ax_1 rel_clauses nrel_clauses pass ([],[]) []


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end;


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fun relevance_filter1 axioms goals = map fst (relevance_filter1_aux axioms goals);


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(*************************************************************************)


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(* the second relevance filtering strategy *)


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(*************************************************************************)


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fun find_clause_weight_s_2 (refpconsts : (bool * string) list) pconsts wa =


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let val (rel,irrel) = part_w_pol refpconsts pconsts ([],[])


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in


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((real (length rel))/(real (length pconsts))) * wa


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end;


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fun find_clause_weight_m_2 [] (_,w) = w


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 find_clause_weight_m_2 ((_,(refpconsts,wa))::y) (pconsts,w) =


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let val w' = find_clause_weight_s_2 refpconsts pconsts wa


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in


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if (w < w') then find_clause_weight_m_2 y (pconsts,w')


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else find_clause_weight_m_2 y (pconsts,w)


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end;


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fun relevant_clauses_ax_g_2 _ [] _ (ax,r) = (ax,r)


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 relevant_clauses_ax_g_2 gpconsts ((clsthm,(pconsts,_))::y) P (ax,r) =


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let val weight = find_clause_weight_s_2 gpconsts pconsts 1.0


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in


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if P <= weight then relevant_clauses_ax_g_2 gpconsts y P ((clsthm,(pconsts,weight))::ax,r)


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else relevant_clauses_ax_g_2 gpconsts y P (ax,(clsthm,(pconsts,weight))::r)


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end;


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fun relevant_clauses_ax_2 rel_axs [] P (addc,tmpc) keep =


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(case addc of [] => rel_axs @ keep


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 _ => case tmpc of [] => addc @ rel_axs @ keep


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 _ => relevant_clauses_ax_2 addc tmpc P ([],[]) (rel_axs @ keep))


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 relevant_clauses_ax_2 rel_axs ((clsthm,(pconsts,weight))::e_axs) P (addc,tmpc) keep =


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let val weight' = find_clause_weight_m_2 rel_axs (pconsts,weight)


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val e_ax' = (clsthm,(pconsts, weight'))


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in


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if P <= weight' then relevant_clauses_ax_2 rel_axs e_axs P ((clsthm,(pconsts,weight'))::addc,tmpc) keep


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else relevant_clauses_ax_2 rel_axs e_axs P (addc,(clsthm,(pconsts,weight'))::tmpc) keep


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end;


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fun initialize_w_pol [] ax_weights = ax_weights


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 initialize_w_pol ((cls,thm)::clss_thms) ax_weights =


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let val tm = prop_of thm


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val consts = pconsts_of_term tm


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in


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initialize_w_pol clss_thms (((cls,thm),(consts,0.0))::ax_weights)


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end;


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fun relevance_filter2_aux axioms goals =


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let val pass = !pass_mark


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val axioms_weights = initialize_w_pol axioms []


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val goals_consts = get_goal_pconsts goals


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val (rel_clauses,nrel_clauses) = relevant_clauses_ax_g_2 goals_consts axioms_weights pass ([],[])


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in


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relevant_clauses_ax_2 rel_clauses nrel_clauses pass ([],[]) []


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end;


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fun relevance_filter2 axioms goals = map fst (relevance_filter2_aux axioms goals);


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(******************************************************************)


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(* Generic functions for relevance filtering *)


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(******************************************************************)


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exception RELEVANCE_FILTER of string;


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fun relevance_filter axioms goals =


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let val cls = (case (!strategy) of 1 => relevance_filter1 axioms goals


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 2 => relevance_filter2 axioms goals


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 _ => raise RELEVANCE_FILTER("strategy doesn't exists"))


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in


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cls


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end;


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end; 