wenzelm@12319: (*  Title:      Pure/net.ML
wenzelm@12319:     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: 
wenzelm@12319: From the book
wenzelm@12319:     E. Charniak, C. K. Riesbeck, D. V. McDermott.
clasohm@0:     Artificial Intelligence Programming.
clasohm@0:     (Lawrence Erlbaum Associates, 1980).  [Chapter 14]
nipkow@225: 
wenzelm@12319: 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: 
wenzelm@12319: signature NET =
wenzelm@16808: sig
clasohm@0:   type key
wenzelm@16808:   val key_of_term: term -> key list
clasohm@0:   type 'a net
clasohm@0:   val empty: 'a net
wenzelm@16808:   exception INSERT
wenzelm@16808:   val insert: ('a * 'a -> bool) -> key list * 'a -> 'a net -> 'a net
wenzelm@16808:   val insert_term: ('a * 'a -> bool) -> term * 'a -> 'a net -> 'a net
wenzelm@16808:   exception DELETE
wenzelm@16808:   val delete: ('b * 'a -> bool) -> key list * 'b -> 'a net -> 'a net
wenzelm@16808:   val delete_term: ('b * 'a -> bool) -> term * 'b -> 'a net -> 'a net
wenzelm@16808:   val lookup: 'a net -> key list -> 'a list
clasohm@0:   val match_term: 'a net -> term -> 'a list
clasohm@0:   val unify_term: 'a net -> term -> 'a list
wenzelm@16808:   val entries: 'a net -> 'a list
wenzelm@16808:   val subtract: ('b * 'a -> bool) -> 'a net -> 'b net -> 'b list
wenzelm@16808:   val merge: ('a * 'a -> bool) -> 'a net * 'a net -> 'a net
wenzelm@20011:   val content: 'a net -> 'a list
wenzelm@16808: end;
clasohm@0: 
wenzelm@16808: structure Net: NET =
clasohm@0: struct
clasohm@0: 
clasohm@0: datatype key = CombK | VarK | AtomK of string;
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: *)
wenzelm@12319: fun add_key_of_terms (t, cs) =
clasohm@0:   let fun rands (f$t, cs) = CombK :: rands (f, add_key_of_terms(t, cs))
wenzelm@12319:         | rands (Const(c,_), cs) = AtomK c :: cs
wenzelm@12319:         | rands (Free(c,_),  cs) = AtomK c :: cs
wenzelm@20080:         | rands (Bound i,  cs)   = AtomK (Name.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:   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
wenzelm@12319:                 | Net of {comb: 'a net,
wenzelm@12319:                           var: 'a net,
wenzelm@16708:                           atoms: 'a net Symtab.table};
clasohm@0: 
clasohm@0: val empty = Leaf[];
wenzelm@16708: fun is_empty (Leaf []) = true | is_empty _ = false;
wenzelm@16708: val emptynet = Net{comb=empty, var=empty, atoms=Symtab.empty};
clasohm@0: 
clasohm@0: 
clasohm@0: (*** Insertion into a discrimination net ***)
clasohm@0: 
wenzelm@12319: 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.
wenzelm@12319:   eq is the equality test for items.
clasohm@0:   The empty list of keys generates a Leaf node, others a Net node.
clasohm@0: *)
wenzelm@16808: fun insert eq (keys,x) net =
wenzelm@12319:   let fun ins1 ([], Leaf xs) =
wenzelm@16686:             if member eq xs x then  raise INSERT  else Leaf(x::xs)
clasohm@0:         | ins1 (keys, Leaf[]) = ins1 (keys, emptynet)   (*expand empty...*)
wenzelm@16708:         | ins1 (CombK :: keys, Net{comb,var,atoms}) =
wenzelm@16708:             Net{comb=ins1(keys,comb), var=var, atoms=atoms}
wenzelm@16708:         | ins1 (VarK :: keys, Net{comb,var,atoms}) =
wenzelm@16708:             Net{comb=comb, var=ins1(keys,var), atoms=atoms}
wenzelm@16708:         | ins1 (AtomK a :: keys, Net{comb,var,atoms}) =
wenzelm@16708:             let
wenzelm@18939:               val net' = the_default empty (Symtab.lookup atoms a);
wenzelm@17412:               val atoms' = Symtab.update (a, ins1 (keys, net')) atoms;
wenzelm@16708:             in  Net{comb=comb, var=var, atoms=atoms'}  end
clasohm@0:   in  ins1 (keys,net)  end;
clasohm@0: 
wenzelm@16808: fun insert_safe eq entry net = insert eq entry net handle INSERT => net;
wenzelm@16808: fun insert_term eq (t, x) = insert eq (key_of_term t, x);
wenzelm@16808: 
clasohm@0: 
clasohm@0: (*** Deletion from a discrimination net ***)
clasohm@0: 
wenzelm@12319: exception DELETE;       (*missing item in the net*)
clasohm@0: 
clasohm@0: (*Create a new Net node if it would be nonempty*)
wenzelm@16708: fun newnet (args as {comb,var,atoms}) =
wenzelm@16708:   if is_empty comb andalso is_empty var andalso Symtab.is_empty atoms
wenzelm@16708:   then empty else Net args;
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. *)
wenzelm@16808: fun delete eq (keys, x) net =
clasohm@0:   let fun del1 ([], Leaf xs) =
wenzelm@16686:             if member eq xs x then Leaf (remove eq x xs)
clasohm@0:             else raise DELETE
wenzelm@12319:         | del1 (keys, Leaf[]) = raise DELETE
wenzelm@16708:         | del1 (CombK :: keys, Net{comb,var,atoms}) =
wenzelm@16708:             newnet{comb=del1(keys,comb), var=var, atoms=atoms}
wenzelm@16708:         | del1 (VarK :: keys, Net{comb,var,atoms}) =
wenzelm@16708:             newnet{comb=comb, var=del1(keys,var), atoms=atoms}
wenzelm@16708:         | del1 (AtomK a :: keys, Net{comb,var,atoms}) =
wenzelm@16708:             let val atoms' =
wenzelm@17412:               (case Symtab.lookup atoms a of
wenzelm@16708:                 NONE => raise DELETE
wenzelm@16708:               | SOME net' =>
wenzelm@16708:                   (case del1 (keys, net') of
wenzelm@16708:                     Leaf [] => Symtab.delete a atoms
wenzelm@17412:                   | net'' => Symtab.update (a, net'') atoms))
wenzelm@16708:             in  newnet{comb=comb, var=var, atoms=atoms'}  end
clasohm@0:   in  del1 (keys,net)  end;
clasohm@0: 
wenzelm@16808: fun delete_term eq (t, x) = delete eq (key_of_term t, x);
clasohm@0: 
wenzelm@16677: 
clasohm@0: (*** Retrieval functions for discrimination nets ***)
clasohm@0: 
wenzelm@16708: exception ABSENT;
clasohm@0: 
wenzelm@16708: fun the_atom atoms a =
wenzelm@17412:   (case Symtab.lookup atoms a of
wenzelm@16708:     NONE => raise ABSENT
wenzelm@16708:   | SOME net => net);
clasohm@0: 
clasohm@0: (*Return the list of items at the given node, [] if no such node*)
wenzelm@16808: fun lookup (Leaf xs) [] = xs
wenzelm@16808:   | lookup (Leaf _) (_ :: _) = []  (*non-empty keys and empty net*)
wenzelm@16808:   | lookup (Net {comb, var, atoms}) (CombK :: keys) = lookup comb keys
wenzelm@16808:   | lookup (Net {comb, var, atoms}) (VarK :: keys) = lookup var keys
wenzelm@16808:   | lookup (Net {comb, var, atoms}) (AtomK a :: keys) =
wenzelm@16808:       lookup (the_atom atoms a) keys handle ABSENT => [];
clasohm@0: 
clasohm@0: 
clasohm@0: (*Skipping a term in a net.  Recursively skip 2 levels if a combination*)
wenzelm@23178: fun net_skip (Leaf _) nets = nets
wenzelm@23178:   | net_skip (Net{comb,var,atoms}) nets =
wenzelm@23178:       fold_rev net_skip (net_skip comb []) (Symtab.fold (cons o #2) atoms (var::nets));
clasohm@0: 
wenzelm@16808: 
wenzelm@16808: (** Matching and Unification **)
clasohm@0: 
clasohm@0: (*conses the linked net, if present, to nets*)
wenzelm@16708: fun look1 (atoms, a) nets =
wenzelm@16708:   the_atom atoms a :: nets handle ABSENT => nets;
clasohm@0: 
wenzelm@12319: (*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.
wenzelm@12319:   Abs or Var in object: if "unif", regarded as wildcard,
nipkow@225:                                    else matches only a variable in net.
nipkow@225: *)
wenzelm@23178: fun matching unif t net nets =
clasohm@0:   let fun rands _ (Leaf _, nets) = nets
wenzelm@16708:         | rands t (Net{comb,atoms,...}, nets) =
wenzelm@12319:             case t of
wenzelm@23178:                 f$t => fold_rev (matching unif t) (rands f (comb,[])) nets
wenzelm@16708:               | Const(c,_) => look1 (atoms, c) nets
wenzelm@16708:               | Free(c,_)  => look1 (atoms, c) nets
wenzelm@20080:               | Bound i    => look1 (atoms, Name.bound i) nets
wenzelm@12319:               | _          => nets
wenzelm@12319:   in
clasohm@0:      case net of
wenzelm@12319:          Leaf _ => nets
clasohm@0:        | Net{var,...} =>
wenzelm@12319:              case head_of t of
wenzelm@23178:                  Var _ => if unif then net_skip net nets
wenzelm@12319:                           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.*)
wenzelm@23178:                | Abs _ => if unif then net_skip net nets
wenzelm@12319:                           else var::nets           (*only a Var can match*)
wenzelm@12319:                | _ => rands t (net, var::nets)  (*var could match also*)
clasohm@0:   end;
clasohm@0: 
wenzelm@19482: fun extract_leaves l = maps (fn Leaf xs => xs) l;
clasohm@0: 
nipkow@225: (*return items whose key could match t, WHICH MUST BE BETA-ETA NORMAL*)
wenzelm@12319: fun match_term net t =
wenzelm@23178:     extract_leaves (matching false t net []);
clasohm@0: 
clasohm@0: (*return items whose key could unify with t*)
wenzelm@12319: fun unify_term net t =
wenzelm@23178:     extract_leaves (matching true t net []);
clasohm@0: 
wenzelm@3548: 
wenzelm@16808: (** operations on nets **)
wenzelm@16808: 
wenzelm@16808: (*subtraction: collect entries of second net that are NOT present in first net*)
wenzelm@16808: fun subtract eq net1 net2 =
wenzelm@16808:   let
wenzelm@16808:     fun subtr (Net _) (Leaf ys) = append ys
wenzelm@16808:       | subtr (Leaf xs) (Leaf ys) =
wenzelm@16808:           fold_rev (fn y => if member eq xs y then I else cons y) ys
wenzelm@16808:       | subtr (Leaf _) (net as Net _) = subtr emptynet net
wenzelm@16808:       | subtr (Net {comb = comb1, var = var1, atoms = atoms1})
wenzelm@16808:             (Net {comb = comb2, var = var2, atoms = atoms2}) =
wenzelm@16842:           subtr comb1 comb2
wenzelm@16842:           #> subtr var1 var2
wenzelm@16842:           #> Symtab.fold (fn (a, net) =>
wenzelm@18939:             subtr (the_default emptynet (Symtab.lookup atoms1 a)) net) atoms2
wenzelm@16808:   in subtr net1 net2 [] end;
wenzelm@16808: 
wenzelm@16808: fun entries net = subtract (K false) empty net;
wenzelm@16808: 
wenzelm@16808: 
wenzelm@16808: (* merge *)
wenzelm@3548: 
wenzelm@3548: fun cons_fst x (xs, y) = (x :: xs, y);
wenzelm@3548: 
wenzelm@3548: fun dest (Leaf xs) = map (pair []) xs
wenzelm@16708:   | dest (Net {comb, var, atoms}) =
wenzelm@3560:       map (cons_fst CombK) (dest comb) @
wenzelm@3560:       map (cons_fst VarK) (dest var) @
wenzelm@19482:       maps (fn (a, net) => map (cons_fst (AtomK a)) (dest net)) (Symtab.dest atoms);
wenzelm@3548: 
wenzelm@16808: fun merge eq (net1, net2) = fold (insert_safe eq) (dest net2) net1;
wenzelm@3548: 
wenzelm@20011: fun content net = map #2 (dest net);
wenzelm@20011: 
clasohm@0: end;