src/Pure/net.ML

+(*  Title: 	net
+    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]
+*)
+
+signature NET = 
+  sig
+  type key
+  type 'a net
+  exception DELETE and INSERT
+  val delete: (key list * 'a) * 'a net * ('a*'a -> bool) -> 'a net
+  val delete_term:   (term * 'a) * 'a net * ('a*'a -> bool) -> 'a 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
+  end;
+
+
+functor NetFun () : NET = 
+struct
+
+datatype key = CombK | VarK | AtomK of string;
+
+(*Only 'loose' bound variables could arise, since Abs nodes are skipped*)
+fun string_of_bound i = "*B*" ^ chr i;
+
+(*Keys are preorder lists of symbols -- constants, Vars, bound vars, ...
+  Any term whose head is a Var is regarded entirely as a Var;
+  abstractions are also regarded as Vars (to cover eta-conversion)
+*)
+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 (_,_,t) => VarK :: cs
+    | _ => rands(t,cs)
+  end;
+
+(*convert a term to a key -- 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.
+  Keys in the association list (alist) are stored in ascending order.
+  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,
+			  alist: (string * 'a net) list};
+
+val empty = Leaf[];
+val emptynet = Net{comb=empty, var=empty, alist=[]};
+
+
+(*** 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 gen_mem eq (x,xs) then  raise INSERT  else Leaf(x::xs)
+        | ins1 (keys, Leaf[]) = ins1 (keys, emptynet)   (*expand empty...*)
+        | ins1 (CombK :: keys, Net{comb,var,alist}) =
+	    Net{comb=ins1(keys,comb), var=var, alist=alist}
+	| ins1 (VarK :: keys, Net{comb,var,alist}) =
+	    Net{comb=comb, var=ins1(keys,var), alist=alist}
+	| ins1 (AtomK a :: keys, Net{comb,var,alist}) =
+	    let fun newpair net = (a, ins1(keys,net)) 
+		fun inslist [] = [newpair empty]
+		  | inslist((b: string, netb) :: alist) =
+		      if a=b then newpair netb :: alist
+		      else if a<b then (*absent, ins1ert in alist*)
+			  newpair empty :: (b,netb) :: alist
+		      else (*a>b*) (b,netb) :: inslist alist
+	    in  Net{comb=comb, var=var, alist= inslist alist}  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 {comb=Leaf[], var=Leaf[], alist=[]} = empty
+  | newnet {comb,var,alist} = Net{comb=comb, var=var, alist=alist};
+
+(*add new (b,net) pair to the alist provided net is nonempty*)
+fun conspair((b, Leaf[]), alist) = alist
+  | conspair((b, net), alist)    = (b, net) :: alist;
+
+(*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 gen_mem eq (x,xs) then Leaf (gen_rem eq (xs,x))
+            else raise DELETE
+	| del1 (keys, Leaf[]) = raise DELETE
+	| del1 (CombK :: keys, Net{comb,var,alist}) =
+	    newnet{comb=del1(keys,comb), var=var, alist=alist}
+	| del1 (VarK :: keys, Net{comb,var,alist}) =
+	    newnet{comb=comb, var=del1(keys,var), alist=alist}
+	| del1 (AtomK a :: keys, Net{comb,var,alist}) =
+	    let fun newpair net = (a, del1(keys,net)) 
+		fun dellist [] = raise DELETE
+		  | dellist((b: string, netb) :: alist) =
+		      if a=b then conspair(newpair netb, alist)
+		      else if a<b then (*absent*) raise DELETE
+		      else (*a>b*)  (b,netb) :: dellist alist
+	    in  newnet{comb=comb, var=var, alist= dellist alist}  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 OASSOC;
+
+(*Ordered association list lookup*)
+fun oassoc ([], a: string) = raise OASSOC
+  | oassoc ((b,x)::pairs, a) =
+      if b<a then oassoc(pairs,a)
+      else if a=b then x
+      else raise OASSOC;
+
+(*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,alist}, CombK :: keys) = lookup(comb,keys)
+  | lookup (Net{comb,var,alist}, VarK :: keys) = lookup(var,keys)
+  | lookup (Net{comb,var,alist}, AtomK a :: keys) = 
+      lookup(oassoc(alist,a),keys)  handle  OASSOC => [];
+
+
+(*Skipping a term in a net.  Recursively skip 2 levels if a combination*)
+fun net_skip (Leaf _, nets) = nets
+  | net_skip (Net{comb,var,alist}, nets) = 
+    foldr net_skip 
+          (net_skip (comb,[]), 
+	   foldr (fn ((_,net), nets) => net::nets) (alist, var::nets));
+
+(** Matching and Unification**)
+
+(*conses the linked net, if present, to nets*)
+fun look1 (alist, a) nets =
+       oassoc(alist,a) :: nets  handle  OASSOC => 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 in object (and Var if "unif") regarded as wildcard.
+  If not "unif", Var in object only matches a variable in net.*)
+fun matching unif t (net,nets) =
+  let fun rands _ (Leaf _, nets) = nets
+	| rands t (Net{comb,alist,...}, nets) =
+	    case t of 
+		(f$t) => foldr (matching unif t) (rands f (comb,[]), nets)
+	      | (Const(c,_)) => look1 (alist, c) nets
+	      | (Free(c,_))  => look1 (alist, c) nets
+	      | (Bound i)    => look1 (alist, string_of_bound i) 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*)
+	     | Abs(_,_,u) => net_skip (net,nets)   (*could match anything*)
+	     | _ => rands t (net, var::nets)	   (*var could match also*)
+  end;
+
+val extract_leaves = flat o map (fn Leaf(xs) => xs);
+
+(*return items whose key could match t*)
+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,[]));
+
+end;