src/Pure/net.ML
author wenzelm
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Object logic specific operations.
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(*  Title: 	Pure/net.ML
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    ID:         $Id$
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    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1993  University of Cambridge
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Discrimination nets: a data structure for indexing items
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From the book 
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    E. Charniak, C. K. Riesbeck, D. V. McDermott. 
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    Artificial Intelligence Programming.
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    (Lawrence Erlbaum Associates, 1980).  [Chapter 14]
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match_term no longer treats abstractions as wildcards; instead they match 
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only wildcards in patterns.  Requires operands to be beta-eta-normal.
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*)
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signature NET = 
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  sig
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  type key
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  type 'a net
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  exception DELETE and INSERT
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  val delete: (key list * 'a) * 'a net * ('a*'a -> bool) -> 'a net
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  val delete_term:   (term * 'a) * 'a net * ('a*'a -> bool) -> 'a net
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  val empty: 'a net
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  val insert: (key list * 'a) * 'a net * ('a*'a -> bool) -> 'a net
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  val insert_term:   (term * 'a) * 'a net * ('a*'a -> bool) -> 'a net
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  val lookup: 'a net * key list -> 'a list
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  val match_term: 'a net -> term -> 'a list
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  val key_of_term: term -> key list
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  val unify_term: 'a net -> term -> 'a list
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  val dest: 'a net -> (key list * 'a) list
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  val merge: 'a net * 'a net * ('a*'a -> bool) -> 'a net
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  end;
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structure Net : NET = 
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struct
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datatype key = CombK | VarK | AtomK of string;
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(*Bound variables*)
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fun string_of_bound i = "*B*" ^ chr i;
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(*Keys are preorder lists of symbols -- Combinations, Vars, Atoms.
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  Any term whose head is a Var is regarded entirely as a Var.
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  Abstractions are also regarded as Vars;  this covers eta-conversion
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    and "near" eta-conversions such as %x.?P(?f(x)).
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*)
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fun add_key_of_terms (t, cs) = 
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  let fun rands (f$t, cs) = CombK :: rands (f, add_key_of_terms(t, cs))
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	| rands (Const(c,_), cs) = AtomK c :: cs
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	| rands (Free(c,_),  cs) = AtomK c :: cs
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	| rands (Bound i,  cs)   = AtomK (string_of_bound i) :: cs
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  in case (head_of t) of
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      Var _ => VarK :: cs
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    | Abs _ => VarK :: cs
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    | _     => rands(t,cs)
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  end;
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(*convert a term to a list of keys*)
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fun key_of_term t = add_key_of_terms (t, []);
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(*Trees indexed by key lists: each arc is labelled by a key.
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  Each node contains a list of items, and arcs to children.
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  Keys in the association list (alist) are stored in ascending order.
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  The empty key addresses the entire net.
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  Lookup functions preserve order in items stored at same level.
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*)
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datatype 'a net = Leaf of 'a list
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		| Net of {comb: 'a net, 
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			  var: 'a net,
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			  alist: (string * 'a net) list};
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val empty = Leaf[];
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val emptynet = Net{comb=empty, var=empty, alist=[]};
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(*** Insertion into a discrimination net ***)
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exception INSERT;	(*duplicate item in the net*)
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(*Adds item x to the list at the node addressed by the keys.
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  Creates node if not already present.
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  eq is the equality test for items. 
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  The empty list of keys generates a Leaf node, others a Net node.
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*)
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fun insert ((keys,x), net, eq) =
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  let fun ins1 ([], Leaf xs) = 
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            if gen_mem eq (x,xs) then  raise INSERT  else Leaf(x::xs)
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        | ins1 (keys, Leaf[]) = ins1 (keys, emptynet)   (*expand empty...*)
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        | ins1 (CombK :: keys, Net{comb,var,alist}) =
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	    Net{comb=ins1(keys,comb), var=var, alist=alist}
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	| ins1 (VarK :: keys, Net{comb,var,alist}) =
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	    Net{comb=comb, var=ins1(keys,var), alist=alist}
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	| ins1 (AtomK a :: keys, Net{comb,var,alist}) =
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	    let fun newpair net = (a, ins1(keys,net)) 
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		fun inslist [] = [newpair empty]
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		  | inslist((b: string, netb) :: alist) =
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		      if a=b then newpair netb :: alist
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		      else if a<b then (*absent, ins1ert in alist*)
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			  newpair empty :: (b,netb) :: alist
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		      else (*a>b*) (b,netb) :: inslist alist
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	    in  Net{comb=comb, var=var, alist= inslist alist}  end
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  in  ins1 (keys,net)  end;
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fun insert_term ((t,x), net, eq) = insert((key_of_term t, x), net, eq);
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(*** Deletion from a discrimination net ***)
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exception DELETE;	(*missing item in the net*)
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(*Create a new Net node if it would be nonempty*)
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fun newnet {comb=Leaf[], var=Leaf[], alist=[]} = empty
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  | newnet {comb,var,alist} = Net{comb=comb, var=var, alist=alist};
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(*add new (b,net) pair to the alist provided net is nonempty*)
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fun conspair((b, Leaf[]), alist) = alist
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  | conspair((b, net), alist)    = (b, net) :: alist;
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(*Deletes item x from the list at the node addressed by the keys.
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  Raises DELETE if absent.  Collapses the net if possible.
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  eq is the equality test for items. *)
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fun delete ((keys, x), net, eq) = 
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  let fun del1 ([], Leaf xs) =
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            if gen_mem eq (x,xs) then Leaf (gen_rem eq (xs,x))
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            else raise DELETE
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	| del1 (keys, Leaf[]) = raise DELETE
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	| del1 (CombK :: keys, Net{comb,var,alist}) =
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	    newnet{comb=del1(keys,comb), var=var, alist=alist}
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	| del1 (VarK :: keys, Net{comb,var,alist}) =
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	    newnet{comb=comb, var=del1(keys,var), alist=alist}
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	| del1 (AtomK a :: keys, Net{comb,var,alist}) =
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	    let fun newpair net = (a, del1(keys,net)) 
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		fun dellist [] = raise DELETE
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		  | dellist((b: string, netb) :: alist) =
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		      if a=b then conspair(newpair netb, alist)
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		      else if a<b then (*absent*) raise DELETE
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		      else (*a>b*)  (b,netb) :: dellist alist
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	    in  newnet{comb=comb, var=var, alist= dellist alist}  end
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  in  del1 (keys,net)  end;
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fun delete_term ((t,x), net, eq) = delete((key_of_term t, x), net, eq);
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(*** Retrieval functions for discrimination nets ***)
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exception OASSOC;
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(*Ordered association list lookup*)
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fun oassoc ([], a: string) = raise OASSOC
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  | oassoc ((b,x)::pairs, a) =
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      if b<a then oassoc(pairs,a)
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      else if a=b then x
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      else raise OASSOC;
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(*Return the list of items at the given node, [] if no such node*)
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fun lookup (Leaf(xs), []) = xs
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  | lookup (Leaf _, _::_) = []	(*non-empty keys and empty net*)
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  | lookup (Net{comb,var,alist}, CombK :: keys) = lookup(comb,keys)
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  | lookup (Net{comb,var,alist}, VarK :: keys) = lookup(var,keys)
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  | lookup (Net{comb,var,alist}, AtomK a :: keys) = 
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      lookup(oassoc(alist,a),keys)  handle  OASSOC => [];
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(*Skipping a term in a net.  Recursively skip 2 levels if a combination*)
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fun net_skip (Leaf _, nets) = nets
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  | net_skip (Net{comb,var,alist}, nets) = 
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    foldr net_skip 
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          (net_skip (comb,[]), 
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	   foldr (fn ((_,net), nets) => net::nets) (alist, var::nets));
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(** Matching and Unification**)
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(*conses the linked net, if present, to nets*)
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fun look1 (alist, a) nets =
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       oassoc(alist,a) :: nets  handle  OASSOC => nets;
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(*Return the nodes accessible from the term (cons them before nets) 
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  "unif" signifies retrieval for unification rather than matching.
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  Var in net matches any term.
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  Abs or Var in object: if "unif", regarded as wildcard, 
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                                   else matches only a variable in net.
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*)
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fun matching unif t (net,nets) =
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  let fun rands _ (Leaf _, nets) = nets
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	| rands t (Net{comb,alist,...}, nets) =
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	    case t of 
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		f$t => foldr (matching unif t) (rands f (comb,[]), nets)
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	      | Const(c,_) => look1 (alist, c) nets
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	      | Free(c,_)  => look1 (alist, c) nets
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	      | Bound i    => look1 (alist, string_of_bound i) nets
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	      | _      	   => nets
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  in 
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     case net of
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	 Leaf _ => nets
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       | Net{var,...} =>
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	     let val etat = Pattern.eta_contract_atom t
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	     in case (head_of etat) of
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		 Var _ => if unif then net_skip (net,nets)
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			  else var::nets	   (*only matches Var in net*)
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  (*If "unif" then a var instantiation in the abstraction could allow
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    an eta-reduction, so regard the abstraction as a wildcard.*)
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	       | Abs _ => if unif then net_skip (net,nets)
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			  else var::nets	   (*only a Var can match*)
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	       | _ => rands etat (net, var::nets)  (*var could match also*)
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	     end
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  end;
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fun extract_leaves l = List.concat (map (fn Leaf(xs) => xs) l);
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(*return items whose key could match t, WHICH MUST BE BETA-ETA NORMAL*)
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fun match_term net t = 
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    extract_leaves (matching false t (net,[]));
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(*return items whose key could unify with t*)
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fun unify_term net t = 
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    extract_leaves (matching true t (net,[]));
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(** dest **)
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fun cons_fst x (xs, y) = (x :: xs, y);
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fun dest (Leaf xs) = map (pair []) xs
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  | dest (Net {comb, var, alist}) =
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      map (cons_fst CombK) (dest comb) @
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      map (cons_fst VarK) (dest var) @
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      flat (map (fn (a, net) => map (cons_fst (AtomK a)) (dest net)) alist);
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(** merge **)
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fun add eq (net, keys_x) =
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  insert (keys_x, net, eq) handle INSERT => net;
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fun merge (net1, net2, eq) =
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  foldl (add eq) (net1, dest net2);
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end;