(* 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;