(* Title: Pure/net.ML
ID: $Id$
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
type 'a net
exception DELETE and INSERT
val delete: (key list * 'a) * 'b net * ('a * 'b -> bool) -> 'b net
val delete_term: (term * 'a) * 'b net * ('a * 'b -> bool) -> 'b net
val empty: 'a net
val insert: (key list * 'a) * 'a net * ('a*'a -> bool) -> 'a net
val insert_term: (term * 'a) * 'a net * ('a*'a -> bool) -> 'a net
val lookup: 'a net * key list -> 'a list
val match_term: 'a net -> term -> 'a list
val key_of_term: term -> key list
val unify_term: 'a net -> term -> 'a list
val dest: 'a net -> (key list * 'a) list
val merge: 'a net * 'a net * ('a*'a -> bool) -> 'a net
end;
structure Net : NET =
struct
datatype key = CombK | VarK | AtomK of string;
(*Bound variables*)
fun string_of_bound i = "*B*" ^ chr (i div 256) ^ chr (i mod 256);
(*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 (string_of_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, []);
(*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 ((keys,x), net, eq) =
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 net' = if_none (Symtab.lookup (atoms, a)) empty;
val atoms' = Symtab.update ((a, ins1(keys,net')), atoms);
in Net{comb=comb, var=var, atoms=atoms'} end
in ins1 (keys,net) end;
fun insert_term ((t,x), net, eq) = insert((key_of_term t, x), net, eq);
(*** 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 ((keys, x), net, eq) =
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 ((t,x), net, eq) = delete((key_of_term t, x), net, eq);
(*** 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) =
foldr net_skip (Symtab.fold (cons o #2) atoms (var::nets)) (net_skip (comb,[]));
(** 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 => foldr (matching unif t) nets (rands f (comb,[]))
| Const(c,_) => look1 (atoms, c) nets
| Free(c,_) => look1 (atoms, c) nets
| Bound i => look1 (atoms, string_of_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 = List.concat (map (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,[]));
(** dest **)
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) @
List.concat (map (fn (a, net) => map (cons_fst (AtomK a)) (dest net))
(Symtab.dest atoms));
(** merge **)
fun add eq keys_x net = insert (keys_x, net, eq) handle INSERT => net;
fun merge (net1, net2, eq) = fold (add eq) (dest net2) net1;
end;