(* Title: Pure/net.ML
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1993 University of Cambridge
Discrimination nets: a data structure for indexing items
From the book
E. Charniak, C. K. Riesbeck, D. V. McDermott.
Artificial Intelligence Programming.
(Lawrence Erlbaum Associates, 1980). [Chapter 14]
match_term no longer treats abstractions as wildcards; instead they match
only wildcards in patterns. Requires operands to be beta-eta-normal.
*)
signature NET =
sig
type key
val key_of_term: term -> key list
val encode_type: typ -> term
type 'a net
val empty: 'a net
val is_empty: 'a net -> bool
exception INSERT
val insert: ('a * 'a -> bool) -> key list * 'a -> 'a net -> 'a net
val insert_term: ('a * 'a -> bool) -> term * 'a -> 'a net -> 'a net
val insert_safe: ('a * 'a -> bool) -> key list * 'a -> 'a net -> 'a net
val insert_term_safe: ('a * 'a -> bool) -> term * 'a -> 'a net -> 'a net
exception DELETE
val delete: ('b * 'a -> bool) -> key list * 'b -> 'a net -> 'a net
val delete_term: ('b * 'a -> bool) -> term * 'b -> 'a net -> 'a net
val delete_safe: ('b * 'a -> bool) -> key list * 'b -> 'a net -> 'a net
val delete_term_safe: ('b * 'a -> bool) -> term * 'b -> 'a net -> 'a net
val lookup: 'a net -> key list -> 'a list
val match_term: 'a net -> term -> 'a list
val unify_term: 'a net -> term -> 'a list
val entries: 'a net -> 'a list
val subtract: ('b * 'a -> bool) -> 'a net -> 'b net -> 'b list
val merge: ('a * 'a -> bool) -> 'a net * 'a net -> 'a net
val content: 'a net -> 'a list
end;
structure Net: NET =
struct
datatype key = CombK | VarK | AtomK of string;
(*Keys are preorder lists of symbols -- Combinations, Vars, Atoms.
Any term whose head is a Var is regarded entirely as a Var.
Abstractions are also regarded as Vars; this covers eta-conversion
and "near" eta-conversions such as %x.?P(?f(x)).
*)
fun add_key_of_terms (t, cs) =
let fun rands (f$t, cs) = CombK :: rands (f, add_key_of_terms(t, cs))
| rands (Const(c,_), cs) = AtomK c :: cs
| rands (Free(c,_), cs) = AtomK c :: cs
| rands (Bound i, cs) = AtomK (Name.bound i) :: cs
in case head_of t of
Var _ => VarK :: cs
| Abs _ => VarK :: cs
| _ => rands(t,cs)
end;
(*convert a term to a list of keys*)
fun key_of_term t = add_key_of_terms (t, []);
(*encode_type -- for indexing purposes*)
fun encode_type (Type (c, Ts)) = Term.list_comb (Const (c, dummyT), map encode_type Ts)
| encode_type (TFree (a, _)) = Free (a, dummyT)
| encode_type (TVar (a, _)) = Var (a, dummyT);
(*Trees indexed by key lists: each arc is labelled by a key.
Each node contains a list of items, and arcs to children.
The empty key addresses the entire net.
Lookup functions preserve order in items stored at same level.
*)
datatype 'a net = Leaf of 'a list
| Net of {comb: 'a net,
var: 'a net,
atoms: 'a net Symtab.table};
val empty = Leaf[];
fun is_empty (Leaf []) = true | is_empty _ = false;
val emptynet = Net{comb=empty, var=empty, atoms=Symtab.empty};
(*** Insertion into a discrimination net ***)
exception INSERT; (*duplicate item in the net*)
(*Adds item x to the list at the node addressed by the keys.
Creates node if not already present.
eq is the equality test for items.
The empty list of keys generates a Leaf node, others a Net node.
*)
fun insert eq (keys,x) net =
let fun ins1 ([], Leaf xs) =
if member eq xs x then raise INSERT else Leaf(x::xs)
| ins1 (keys, Leaf[]) = ins1 (keys, emptynet) (*expand empty...*)
| ins1 (CombK :: keys, Net{comb,var,atoms}) =
Net{comb=ins1(keys,comb), var=var, atoms=atoms}
| ins1 (VarK :: keys, Net{comb,var,atoms}) =
Net{comb=comb, var=ins1(keys,var), atoms=atoms}
| ins1 (AtomK a :: keys, Net{comb,var,atoms}) =
let val atoms' = Symtab.map_default (a, empty) (fn net' => ins1 (keys, net')) atoms;
in Net{comb=comb, var=var, atoms=atoms'} end
in ins1 (keys,net) end;
fun insert_term eq (t, x) = insert eq (key_of_term t, x);
fun insert_safe eq entry net = insert eq entry net handle INSERT => net;
fun insert_term_safe eq entry net = insert_term eq entry net handle INSERT => net;
(*** Deletion from a discrimination net ***)
exception DELETE; (*missing item in the net*)
(*Create a new Net node if it would be nonempty*)
fun newnet (args as {comb,var,atoms}) =
if is_empty comb andalso is_empty var andalso Symtab.is_empty atoms
then empty else Net args;
(*Deletes item x from the list at the node addressed by the keys.
Raises DELETE if absent. Collapses the net if possible.
eq is the equality test for items. *)
fun delete eq (keys, x) net =
let fun del1 ([], Leaf xs) =
if member eq xs x then Leaf (remove eq x xs)
else raise DELETE
| del1 (keys, Leaf[]) = raise DELETE
| del1 (CombK :: keys, Net{comb,var,atoms}) =
newnet{comb=del1(keys,comb), var=var, atoms=atoms}
| del1 (VarK :: keys, Net{comb,var,atoms}) =
newnet{comb=comb, var=del1(keys,var), atoms=atoms}
| del1 (AtomK a :: keys, Net{comb,var,atoms}) =
let val atoms' =
(case Symtab.lookup atoms a of
NONE => raise DELETE
| SOME net' =>
(case del1 (keys, net') of
Leaf [] => Symtab.delete a atoms
| net'' => Symtab.update (a, net'') atoms))
in newnet{comb=comb, var=var, atoms=atoms'} end
in del1 (keys,net) end;
fun delete_term eq (t, x) = delete eq (key_of_term t, x);
fun delete_safe eq entry net = delete eq entry net handle DELETE => net;
fun delete_term_safe eq entry net = delete_term eq entry net handle DELETE => net;
(*** Retrieval functions for discrimination nets ***)
exception ABSENT;
fun the_atom atoms a =
(case Symtab.lookup atoms a of
NONE => raise ABSENT
| SOME net => net);
(*Return the list of items at the given node, [] if no such node*)
fun lookup (Leaf xs) [] = xs
| lookup (Leaf _) (_ :: _) = [] (*non-empty keys and empty net*)
| lookup (Net {comb, var, atoms}) (CombK :: keys) = lookup comb keys
| lookup (Net {comb, var, atoms}) (VarK :: keys) = lookup var keys
| lookup (Net {comb, var, atoms}) (AtomK a :: keys) =
lookup (the_atom atoms a) keys handle ABSENT => [];
(*Skipping a term in a net. Recursively skip 2 levels if a combination*)
fun net_skip (Leaf _) nets = nets
| net_skip (Net{comb,var,atoms}) nets =
fold_rev net_skip (net_skip comb []) (Symtab.fold (cons o #2) atoms (var::nets));
(** Matching and Unification **)
(*conses the linked net, if present, to nets*)
fun look1 (atoms, a) nets =
the_atom atoms a :: nets handle ABSENT => nets;
(*Return the nodes accessible from the term (cons them before nets)
"unif" signifies retrieval for unification rather than matching.
Var in net matches any term.
Abs or Var in object: if "unif", regarded as wildcard,
else matches only a variable in net.
*)
fun matching unif t net nets =
let fun rands _ (Leaf _, nets) = nets
| rands t (Net{comb,atoms,...}, nets) =
case t of
f$t => fold_rev (matching unif t) (rands f (comb,[])) nets
| Const(c,_) => look1 (atoms, c) nets
| Free(c,_) => look1 (atoms, c) nets
| Bound i => look1 (atoms, Name.bound i) nets
| _ => nets
in
case net of
Leaf _ => nets
| Net{var,...} =>
case head_of t of
Var _ => if unif then net_skip net nets
else var::nets (*only matches Var in net*)
(*If "unif" then a var instantiation in the abstraction could allow
an eta-reduction, so regard the abstraction as a wildcard.*)
| Abs _ => if unif then net_skip net nets
else var::nets (*only a Var can match*)
| _ => rands t (net, var::nets) (*var could match also*)
end;
fun extract_leaves l = maps (fn Leaf xs => xs) l;
(*return items whose key could match t, WHICH MUST BE BETA-ETA NORMAL*)
fun match_term net t =
extract_leaves (matching false t net []);
(*return items whose key could unify with t*)
fun unify_term net t =
extract_leaves (matching true t net []);
(** operations on nets **)
(*subtraction: collect entries of second net that are NOT present in first net*)
fun subtract eq net1 net2 =
let
fun subtr (Net _) (Leaf ys) = append ys
| subtr (Leaf xs) (Leaf ys) =
fold_rev (fn y => if member eq xs y then I else cons y) ys
| subtr (Leaf _) (net as Net _) = subtr emptynet net
| subtr (Net {comb = comb1, var = var1, atoms = atoms1})
(Net {comb = comb2, var = var2, atoms = atoms2}) =
subtr comb1 comb2
#> subtr var1 var2
#> Symtab.fold (fn (a, net) =>
subtr (the_default emptynet (Symtab.lookup atoms1 a)) net) atoms2
in subtr net1 net2 [] end;
fun entries net = subtract (K false) empty net;
(* merge *)
fun cons_fst x (xs, y) = (x :: xs, y);
fun dest (Leaf xs) = map (pair []) xs
| dest (Net {comb, var, atoms}) =
map (cons_fst CombK) (dest comb) @
map (cons_fst VarK) (dest var) @
maps (fn (a, net) => map (cons_fst (AtomK a)) (dest net)) (Symtab.dest atoms);
fun merge eq (net1, net2) =
fold (insert_safe eq) (dest net2) net1; (* FIXME non-canonical merge order!?! *)
fun content net = map #2 (dest net);
end;