structure ReduceAxiomsN =

(* Author: Jia Meng, Cambridge University Computer Laboratory

   Two filtering strategies *)

struct

val pass_mark = ref 0.5;

val strategy = ref 1;

fun pol_to_int true = 1

  | pol_to_int false = ~1;

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

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

fun pol_mem _ [] = false

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

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

  | 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));

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

  | add_term_consts_rm ncs (t $ u) cs =

      add_term_consts_rm ncs t (add_term_consts_rm ncs u cs)

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

  | add_term_consts_rm ncs _ cs = cs;

fun term_consts_rm ncs t = add_term_consts_rm ncs t [];

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

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

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

  | add_term_pconsts_rm ncs (P$Q) pol cs = 

    add_term_pconsts_rm ncs P pol (add_term_pconsts_rm ncs Q pol cs)

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

  | add_term_pconsts_rm ncs _ _ cs = cs;

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

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

fun consts_in_goal goal = consts_of_term goal;

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

fun pconsts_in_goal goal = pconsts_of_term goal;

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

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

(*            the first relevance filtering strategy                     *)

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

fun find_clause_weight_s_1 (refconsts : string list) consts wa = 

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

    in

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

    end;

fun find_clause_weight_m_1 [] (_,w) = w 

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

    let val w' = find_clause_weight_s_1 refconsts consts wa

    in

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

	else find_clause_weight_m_1 y (consts,w)

    end;

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

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

    let val weight = find_clause_weight_s_1 gconsts consts 1.0

    in

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

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

    end;

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

    (case addc of [] => rel_axs @ keep

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

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

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

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

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

    in

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

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

    end;

fun initialize [] ax_weights = ax_weights

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

    let val tm = prop_of thm

	val consts = consts_of_term tm

    in

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

    end;

fun relevance_filter1_aux axioms goals = 

    let val pass = !pass_mark

	val axioms_weights = initialize axioms []

	val goals_consts = get_goal_consts goals

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

    in

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

    end;

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

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

(*            the second relevance filtering strategy                    *)

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

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

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

    in

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

    end;

fun find_clause_weight_m_2 [] (_,w) = w 

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

    let val w' = find_clause_weight_s_2 refpconsts pconsts wa

    in

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

	else find_clause_weight_m_2 y (pconsts,w)

    end;

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

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

    let val weight = find_clause_weight_s_2 gpconsts pconsts 1.0

    in

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

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

    end;

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

    (case addc of [] => rel_axs @ keep

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

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

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

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

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

    in

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

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

    end;

fun initialize_w_pol [] ax_weights = ax_weights

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

    let val tm = prop_of thm

	val consts = pconsts_of_term tm

    in

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

    end;

fun relevance_filter2_aux axioms goals = 

    let val pass = !pass_mark

	val axioms_weights = initialize_w_pol axioms []

	val goals_consts = get_goal_pconsts goals

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

    in

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

    end;

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

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

(* Generic functions for relevance filtering                      *)

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

exception RELEVANCE_FILTER of string;

fun relevance_filter axioms goals = 

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

				     | 2 => relevance_filter2 axioms goals

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

    in

	cls

    end;

end;