clasohm@1460: (*  Title: 	net
clasohm@0:     ID:         $Id$
clasohm@1460:     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
clasohm@0:     Copyright   1993  University of Cambridge
clasohm@0: 
clasohm@0: Discrimination nets: a data structure for indexing items
clasohm@0: 
clasohm@0: From the book 
clasohm@0:     E. Charniak, C. K. Riesbeck, D. V. McDermott. 
clasohm@0:     Artificial Intelligence Programming.
clasohm@0:     (Lawrence Erlbaum Associates, 1980).  [Chapter 14]
nipkow@225: 
nipkow@228: match_term no longer treats abstractions as wildcards; instead they match 
nipkow@228: only wildcards in patterns.  Requires operands to be beta-eta-normal.
clasohm@0: *)
clasohm@0: 
clasohm@0: signature NET = 
clasohm@0:   sig
clasohm@0:   type key
clasohm@0:   type 'a net
clasohm@0:   exception DELETE and INSERT
clasohm@0:   val delete: (key list * 'a) * 'a net * ('a*'a -> bool) -> 'a net
clasohm@0:   val delete_term:   (term * 'a) * 'a net * ('a*'a -> bool) -> 'a net
clasohm@0:   val empty: 'a net
clasohm@0:   val insert: (key list * 'a) * 'a net * ('a*'a -> bool) -> 'a net
clasohm@0:   val insert_term:   (term * 'a) * 'a net * ('a*'a -> bool) -> 'a net
clasohm@0:   val lookup: 'a net * key list -> 'a list
clasohm@0:   val match_term: 'a net -> term -> 'a list
clasohm@0:   val key_of_term: term -> key list
clasohm@0:   val unify_term: 'a net -> term -> 'a list
clasohm@0:   end;
clasohm@0: 
clasohm@0: 
paulson@1500: structure Net : NET = 
clasohm@0: struct
clasohm@0: 
clasohm@0: datatype key = CombK | VarK | AtomK of string;
clasohm@0: 
nipkow@225: (*Bound variables*)
clasohm@0: fun string_of_bound i = "*B*" ^ chr i;
clasohm@0: 
nipkow@228: (*Keys are preorder lists of symbols -- Combinations, Vars, Atoms.
nipkow@225:   Any term whose head is a Var is regarded entirely as a Var.
nipkow@228:   Abstractions are also regarded as Vars;  this covers eta-conversion
nipkow@228:     and "near" eta-conversions such as %x.?P(?f(x)).
clasohm@0: *)
clasohm@0: fun add_key_of_terms (t, cs) = 
clasohm@0:   let fun rands (f$t, cs) = CombK :: rands (f, add_key_of_terms(t, cs))
clasohm@1460: 	| rands (Const(c,_), cs) = AtomK c :: cs
clasohm@1460: 	| rands (Free(c,_),  cs) = AtomK c :: cs
clasohm@1460: 	| rands (Bound i,  cs)   = AtomK (string_of_bound i) :: cs
clasohm@0:   in case (head_of t) of
nipkow@225:       Var _ => VarK :: cs
nipkow@228:     | Abs _ => VarK :: cs
nipkow@225:     | _     => rands(t,cs)
clasohm@0:   end;
clasohm@0: 
nipkow@225: (*convert a term to a list of keys*)
clasohm@0: fun key_of_term t = add_key_of_terms (t, []);
clasohm@0: 
clasohm@0: 
clasohm@0: (*Trees indexed by key lists: each arc is labelled by a key.
clasohm@0:   Each node contains a list of items, and arcs to children.
clasohm@0:   Keys in the association list (alist) are stored in ascending order.
clasohm@0:   The empty key addresses the entire net.
clasohm@0:   Lookup functions preserve order in items stored at same level.
clasohm@0: *)
clasohm@0: datatype 'a net = Leaf of 'a list
clasohm@1460: 		| Net of {comb: 'a net, 
clasohm@1460: 			  var: 'a net,
clasohm@1460: 			  alist: (string * 'a net) list};
clasohm@0: 
clasohm@0: val empty = Leaf[];
clasohm@0: val emptynet = Net{comb=empty, var=empty, alist=[]};
clasohm@0: 
clasohm@0: 
clasohm@0: (*** Insertion into a discrimination net ***)
clasohm@0: 
clasohm@1460: exception INSERT;	(*duplicate item in the net*)
clasohm@0: 
clasohm@0: 
clasohm@0: (*Adds item x to the list at the node addressed by the keys.
clasohm@0:   Creates node if not already present.
clasohm@0:   eq is the equality test for items. 
clasohm@0:   The empty list of keys generates a Leaf node, others a Net node.
clasohm@0: *)
clasohm@0: fun insert ((keys,x), net, eq) =
clasohm@0:   let fun ins1 ([], Leaf xs) = 
clasohm@0:             if gen_mem eq (x,xs) then  raise INSERT  else Leaf(x::xs)
clasohm@0:         | ins1 (keys, Leaf[]) = ins1 (keys, emptynet)   (*expand empty...*)
clasohm@0:         | ins1 (CombK :: keys, Net{comb,var,alist}) =
clasohm@1460: 	    Net{comb=ins1(keys,comb), var=var, alist=alist}
clasohm@1460: 	| ins1 (VarK :: keys, Net{comb,var,alist}) =
clasohm@1460: 	    Net{comb=comb, var=ins1(keys,var), alist=alist}
clasohm@1460: 	| ins1 (AtomK a :: keys, Net{comb,var,alist}) =
clasohm@1460: 	    let fun newpair net = (a, ins1(keys,net)) 
clasohm@1460: 		fun inslist [] = [newpair empty]
clasohm@1460: 		  | inslist((b: string, netb) :: alist) =
clasohm@1460: 		      if a=b then newpair netb :: alist
clasohm@1460: 		      else if a<b then (*absent, ins1ert in alist*)
clasohm@1460: 			  newpair empty :: (b,netb) :: alist
clasohm@1460: 		      else (*a>b*) (b,netb) :: inslist alist
clasohm@1460: 	    in  Net{comb=comb, var=var, alist= inslist alist}  end
clasohm@0:   in  ins1 (keys,net)  end;
clasohm@0: 
clasohm@0: fun insert_term ((t,x), net, eq) = insert((key_of_term t, x), net, eq);
clasohm@0: 
clasohm@0: (*** Deletion from a discrimination net ***)
clasohm@0: 
clasohm@1460: exception DELETE;	(*missing item in the net*)
clasohm@0: 
clasohm@0: (*Create a new Net node if it would be nonempty*)
clasohm@0: fun newnet {comb=Leaf[], var=Leaf[], alist=[]} = empty
clasohm@0:   | newnet {comb,var,alist} = Net{comb=comb, var=var, alist=alist};
clasohm@0: 
clasohm@0: (*add new (b,net) pair to the alist provided net is nonempty*)
clasohm@0: fun conspair((b, Leaf[]), alist) = alist
clasohm@0:   | conspair((b, net), alist)    = (b, net) :: alist;
clasohm@0: 
clasohm@0: (*Deletes item x from the list at the node addressed by the keys.
clasohm@0:   Raises DELETE if absent.  Collapses the net if possible.
clasohm@0:   eq is the equality test for items. *)
clasohm@0: fun delete ((keys, x), net, eq) = 
clasohm@0:   let fun del1 ([], Leaf xs) =
clasohm@0:             if gen_mem eq (x,xs) then Leaf (gen_rem eq (xs,x))
clasohm@0:             else raise DELETE
clasohm@1460: 	| del1 (keys, Leaf[]) = raise DELETE
clasohm@1460: 	| del1 (CombK :: keys, Net{comb,var,alist}) =
clasohm@1460: 	    newnet{comb=del1(keys,comb), var=var, alist=alist}
clasohm@1460: 	| del1 (VarK :: keys, Net{comb,var,alist}) =
clasohm@1460: 	    newnet{comb=comb, var=del1(keys,var), alist=alist}
clasohm@1460: 	| del1 (AtomK a :: keys, Net{comb,var,alist}) =
clasohm@1460: 	    let fun newpair net = (a, del1(keys,net)) 
clasohm@1460: 		fun dellist [] = raise DELETE
clasohm@1460: 		  | dellist((b: string, netb) :: alist) =
clasohm@1460: 		      if a=b then conspair(newpair netb, alist)
clasohm@1460: 		      else if a<b then (*absent*) raise DELETE
clasohm@1460: 		      else (*a>b*)  (b,netb) :: dellist alist
clasohm@1460: 	    in  newnet{comb=comb, var=var, alist= dellist alist}  end
clasohm@0:   in  del1 (keys,net)  end;
clasohm@0: 
clasohm@0: fun delete_term ((t,x), net, eq) = delete((key_of_term t, x), net, eq);
clasohm@0: 
clasohm@0: (*** Retrieval functions for discrimination nets ***)
clasohm@0: 
clasohm@0: exception OASSOC;
clasohm@0: 
clasohm@0: (*Ordered association list lookup*)
clasohm@0: fun oassoc ([], a: string) = raise OASSOC
clasohm@0:   | oassoc ((b,x)::pairs, a) =
clasohm@0:       if b<a then oassoc(pairs,a)
clasohm@0:       else if a=b then x
clasohm@0:       else raise OASSOC;
clasohm@0: 
clasohm@0: (*Return the list of items at the given node, [] if no such node*)
clasohm@0: fun lookup (Leaf(xs), []) = xs
clasohm@1460:   | lookup (Leaf _, _::_) = []	(*non-empty keys and empty net*)
clasohm@0:   | lookup (Net{comb,var,alist}, CombK :: keys) = lookup(comb,keys)
clasohm@0:   | lookup (Net{comb,var,alist}, VarK :: keys) = lookup(var,keys)
clasohm@0:   | lookup (Net{comb,var,alist}, AtomK a :: keys) = 
clasohm@0:       lookup(oassoc(alist,a),keys)  handle  OASSOC => [];
clasohm@0: 
clasohm@0: 
clasohm@0: (*Skipping a term in a net.  Recursively skip 2 levels if a combination*)
clasohm@0: fun net_skip (Leaf _, nets) = nets
clasohm@0:   | net_skip (Net{comb,var,alist}, nets) = 
clasohm@0:     foldr net_skip 
clasohm@0:           (net_skip (comb,[]), 
clasohm@1460: 	   foldr (fn ((_,net), nets) => net::nets) (alist, var::nets));
clasohm@0: 
clasohm@0: (** Matching and Unification**)
clasohm@0: 
clasohm@0: (*conses the linked net, if present, to nets*)
clasohm@0: fun look1 (alist, a) nets =
clasohm@0:        oassoc(alist,a) :: nets  handle  OASSOC => nets;
clasohm@0: 
clasohm@0: (*Return the nodes accessible from the term (cons them before nets) 
clasohm@0:   "unif" signifies retrieval for unification rather than matching.
clasohm@0:   Var in net matches any term.
nipkow@225:   Abs or Var in object: if "unif", regarded as wildcard, 
nipkow@225:                                    else matches only a variable in net.
nipkow@225: *)
clasohm@0: fun matching unif t (net,nets) =
clasohm@0:   let fun rands _ (Leaf _, nets) = nets
clasohm@1460: 	| rands t (Net{comb,alist,...}, nets) =
clasohm@1460: 	    case t of 
clasohm@1460: 		f$t => foldr (matching unif t) (rands f (comb,[]), nets)
clasohm@1460: 	      | Const(c,_) => look1 (alist, c) nets
clasohm@1460: 	      | Free(c,_)  => look1 (alist, c) nets
clasohm@1460: 	      | Bound i    => look1 (alist, string_of_bound i) nets
clasohm@1460: 	      | _      	   => nets
clasohm@0:   in 
clasohm@0:      case net of
clasohm@1460: 	 Leaf _ => nets
clasohm@0:        | Net{var,...} =>
paulson@2836: 	     let val etat = Pattern.eta_contract_atom t
paulson@2836: 	     in case (head_of etat) of
paulson@2836: 		 Var _ => if unif then net_skip (net,nets)
paulson@2836: 			  else var::nets	   (*only matches Var in net*)
paulson@2836:   (*If "unif" then a var instantiation in the abstraction could allow
paulson@2836:     an eta-reduction, so regard the abstraction as a wildcard.*)
paulson@2836: 	       | Abs _ => if unif then net_skip (net,nets)
paulson@2836: 			  else var::nets	   (*only a Var can match*)
paulson@2836: 	       | _ => rands etat (net, var::nets)  (*var could match also*)
paulson@2836: 	     end
clasohm@0:   end;
clasohm@0: 
paulson@2672: fun extract_leaves l = List.concat (map (fn Leaf(xs) => xs) l);
clasohm@0: 
nipkow@225: (*return items whose key could match t, WHICH MUST BE BETA-ETA NORMAL*)
clasohm@0: fun match_term net t = 
clasohm@0:     extract_leaves (matching false t (net,[]));
clasohm@0: 
clasohm@0: (*return items whose key could unify with t*)
clasohm@0: fun unify_term net t = 
clasohm@0:     extract_leaves (matching true t (net,[]));
clasohm@0: 
clasohm@0: end;