(* Authors: Jia Meng, NICTA and Lawrence C Paulson, Cambridge University Computer Laboratory

   ID: $Id$

   Filtering strategies *)

structure ReduceAxiomsN =

struct

val pass_mark = ref 0.6;

val reduction_factor = ref 1.0;

(*Whether all "simple" unit clauses should be included*)

val add_unit = ref false;

val unit_pass_mark = ref 0.0;

(*Including equality in this list might be expected to stop rules like subset_antisym from

  being chosen, but for some reason filtering works better with them listed.*)

val standard_consts =

  ["Trueprop","==>","all","Ex","op &","op |","Not","All","op -->",

   "op =","==","True","False"];

(*** unit clauses ***)

datatype clause_kind = Unit_neq | Unit_geq | Other

fun literals_of_term args (Const ("Trueprop",_) $ P) = literals_of_term args P

  | literals_of_term args (Const ("op |",_) $ P $ Q) = 

    literals_of_term (literals_of_term args P) Q

  | literals_of_term args P = P::args;

fun is_ground t = (term_vars t = []) andalso (term_frees t = []);

fun eq_clause_type (P,Q) = 

    if ((is_ground P) orelse (is_ground Q)) then Unit_geq else Other;

fun unit_clause_type (Const ("op =",_) $ P $ Q) = eq_clause_type (P,Q)

  | unit_clause_type _ = Unit_neq;

fun clause_kind tm = 

    case literals_of_term [] tm of

        [lit] => unit_clause_type lit

      | _ => Other;

(*** constants with types ***)

(*An abstraction of Isabelle types*)

datatype const_typ =  CTVar | CType of string * const_typ list

fun uni_type (CType(con1,args1)) (CType(con2,args2)) = con1=con2 andalso uni_types args1 args2

  | uni_type (CType _) CTVar = true

  | uni_type CTVar CTVar = true

  | uni_type CTVar _ = false

and uni_types [] [] = true

  | uni_types (a1::as1) (a2::as2) = uni_type a1 a2 andalso uni_types as1 as2;

fun uni_constants (c1,ctp1) (c2,ctp2) = (c1=c2) andalso uni_types ctp1 ctp2;

fun uni_mem _ [] = false

  | uni_mem (c,c_typ) ((c1,c_typ1)::ctyps) =

      uni_constants (c1,c_typ1) (c,c_typ) orelse uni_mem (c,c_typ) ctyps;

fun const_typ_of (Type (c,typs)) = CType (c, map const_typ_of typs) 

  | const_typ_of (TFree _) = CTVar

  | const_typ_of (TVar _) = CTVar

fun const_with_typ thy (c,typ) = 

    let val tvars = Sign.const_typargs thy (c,typ)

    in (c, map const_typ_of tvars) end

    handle TYPE _ => (c,[]);   (*Variable (locale constant): monomorphic*)   

(*Free variables are counted, as well as constants, to handle locales*)

fun add_term_consts_typs_rm thy (Const(c, typ)) cs =

      if (c mem standard_consts) then cs 

      else const_with_typ thy (c,typ) ins cs

  | add_term_consts_typs_rm thy (Free(c, typ)) cs =

      const_with_typ thy (c,typ) ins cs

  | add_term_consts_typs_rm thy (t $ u) cs =

      add_term_consts_typs_rm thy t (add_term_consts_typs_rm thy u cs)

  | add_term_consts_typs_rm thy (Abs(_,_,t)) cs = add_term_consts_typs_rm thy t cs

  | add_term_consts_typs_rm thy _ cs = cs;

fun consts_typs_of_term thy t = add_term_consts_typs_rm thy t [];

fun get_goal_consts_typs thy cs = foldl (op union) [] (map (consts_typs_of_term thy) cs)

(**** Constant / Type Frequencies ****)

local

fun cons_nr CTVar = 0

  | cons_nr (CType _) = 1;

in

fun const_typ_ord TU =

  case TU of

    (CType (a, Ts), CType (b, Us)) =>

      (case fast_string_ord(a,b) of EQUAL => dict_ord const_typ_ord (Ts,Us) | ord => ord)

  | (T, U) => int_ord (cons_nr T, cons_nr U);

end;

structure CTtab = TableFun(type key = const_typ list val ord = dict_ord const_typ_ord);

fun count_axiom_consts thy ((t,_), tab) = 

  let fun count_const (a, T, tab) =

	let val (c, cts) = const_with_typ thy (a,T)

	    val cttab = Option.getOpt (Symtab.lookup tab c, CTtab.empty)

	    val n = Option.getOpt (CTtab.lookup cttab cts, 0)

	in 

	    Symtab.update (c, CTtab.update (cts, n+1) cttab) tab

	end

      fun count_term_consts (Const(a,T), tab) = count_const(a,T,tab)

	| count_term_consts (Free(a,T), tab) = count_const(a,T,tab)

	| count_term_consts (t $ u, tab) =

	    count_term_consts (t, count_term_consts (u, tab))

	| count_term_consts (Abs(_,_,t), tab) = count_term_consts (t, tab)

	| count_term_consts (_, tab) = tab

  in  count_term_consts (t, tab)  end;

(******** filter clauses ********)

(*The default ignores the constant-count and gives the old Strategy 3*)

val weight_fn = ref (fn x : real => 1.0);

fun const_weight ctab (c, cts) =

  let val pairs = CTtab.dest (Option.valOf (Symtab.lookup ctab c))

      fun add ((cts',m), n) = if uni_types cts cts' then m+n else n

  in  List.foldl add 0 pairs  end;

fun add_ct_weight ctab ((c,T), w) =

  w + !weight_fn (real (const_weight ctab (c,T)));

fun consts_typs_weight ctab =

    List.foldl (add_ct_weight ctab) 0.0;

(*Relevant constants are weighted according to frequency, 

  but irrelevant constants are simply counted. Otherwise, Skolem functions,

  which are rare, would harm a clause's chances of being picked.*)

fun clause_weight ctab gctyps consts_typs =

    let val rel = filter (fn s => uni_mem s gctyps) consts_typs

        val rel_weight = consts_typs_weight ctab rel

    in

	rel_weight / (rel_weight + real (length consts_typs - length rel))

    end;

fun relevant_clauses ctab rel_axs [] (addc,tmpc) keep =

      if null addc orelse null tmpc 

      then (addc @ rel_axs @ keep, tmpc)   (*termination!*)

      else relevant_clauses ctab addc tmpc ([],[]) (rel_axs @ keep)

  | relevant_clauses ctab rel_axs ((clstm,(consts_typs,w))::e_axs) (addc,tmpc) keep =

      let fun clause_weight_ax (_,(refconsts_typs,wa)) =

              wa * clause_weight ctab refconsts_typs consts_typs;

          val weight' = List.foldl Real.max w (map clause_weight_ax rel_axs)

	  val e_ax' = (clstm, (consts_typs,weight'))

      in

	if !pass_mark <= weight' 

	then relevant_clauses ctab rel_axs e_axs (e_ax'::addc, tmpc) keep

	else relevant_clauses ctab rel_axs e_axs (addc, e_ax'::tmpc) keep

      end;

fun pair_consts_typs_axiom thy (tm,name) =

    ((tm,name), (consts_typs_of_term thy tm));

(*Unit clauses other than non-trivial equations can be included subject to

  a separate (presumably lower) mark. *)

fun good_unit_clause ((t,_), (_,w)) = 

     !unit_pass_mark <= w andalso

     (case clause_kind t of

	  Unit_neq => true

	| Unit_geq => true

	| Other => false);

fun axiom_ord ((_,(_,w1)), (_,(_,w2))) = Real.compare (w2,w1);

fun showconst (c,cttab) = 

      List.app (fn n => Output.debug (Int.toString n ^ " occurrences of " ^ c))

	        (map #2 (CTtab.dest cttab))

fun show_cname (name,k) = name ^ "__" ^ Int.toString k;

fun showax ((_,cname), (_,w)) = 

    Output.debug ("Axiom " ^ show_cname cname ^ " has weight " ^ Real.toString w)

exception ConstFree;

fun dest_ConstFree (Const aT) = aT

  | dest_ConstFree (Free aT) = aT

  | dest_ConstFree _ = raise ConstFree;

(*Look for definitions of the form f ?x1 ... ?xn = t, but not reversed.*)

fun defines thy (tm,(name,n)) gctypes =

  let fun defs hs =

        let val (rator,args) = strip_comb hs

            val ct = const_with_typ thy (dest_ConstFree rator)

        in  forall is_Var args andalso uni_mem ct gctypes  end

        handle ConstFree => false

  in    

    case tm of Const ("Trueprop",_) $ (Const("op =",_) $ lhs $ _) => 

          defs lhs andalso

          (Output.debug ("Definition found: " ^ name ^ "_" ^ Int.toString n); true)

      | _ => false

  end

fun relevance_filter_aux thy axioms goals = 

  let val const_tab = List.foldl (count_axiom_consts thy) Symtab.empty axioms

      val goals_consts_typs = get_goal_consts_typs thy goals

      fun relevant [] (rels,nonrels) = (rels,nonrels)

	| relevant ((clstm,consts_typs)::axs) (rels,nonrels) =

	    let val weight = clause_weight const_tab goals_consts_typs consts_typs

		val ccc = (clstm, (consts_typs,weight))

	    in

	      if !pass_mark <= weight orelse defines thy clstm goals_consts_typs

	      then relevant axs (ccc::rels, nonrels)

	      else relevant axs (rels, ccc::nonrels)

	    end

      val (rel_clauses,nrel_clauses) =

	  relevant (map (pair_consts_typs_axiom thy) axioms) ([],[]) 

      val (rels,nonrels) = relevant_clauses const_tab rel_clauses nrel_clauses ([],[]) []

      val max_filtered = floor (!reduction_factor * real (length rels))

      val rels' = Library.take(max_filtered, Library.sort axiom_ord rels)

  in

      if !Output.show_debug_msgs then

	   (List.app showconst (Symtab.dest const_tab);

	    List.app showax rels)

      else ();

      if !add_unit then (filter good_unit_clause nonrels) @ rels'

      else rels'

  end;

fun relevance_filter thy axioms goals =

  map #1 (relevance_filter_aux thy axioms goals);

end;