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src/Pure/net.ML

author | wenzelm |

Sat, 21 Jan 2006 23:02:14 +0100 | |

changeset 18728 | 6790126ab5f6 |

parent 17412 | e26cb20ef0cc |

child 18939 | 18e2a2676d80 |

permissions | -rw-r--r-- |

simplified type attribute;

(* 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 val key_of_term: term -> key list type 'a net val empty: 'a net exception INSERT val insert: ('a * 'a -> bool) -> key list * 'a -> 'a net -> 'a net val insert_term: ('a * 'a -> bool) -> term * 'a -> 'a net -> 'a net exception DELETE val delete: ('b * 'a -> bool) -> key list * 'b -> 'a net -> 'a net val delete_term: ('b * 'a -> bool) -> term * 'b -> 'a net -> 'a net val lookup: 'a net -> key list -> 'a list val match_term: 'a net -> term -> 'a list val unify_term: 'a net -> term -> 'a list val entries: 'a net -> 'a list val subtract: ('b * 'a -> bool) -> 'a net -> 'b net -> 'b list val merge: ('a * 'a -> bool) -> 'a net * 'a net -> 'a net end; structure Net: NET = struct datatype key = CombK | VarK | AtomK of string; (*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 (Term.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 eq (keys,x) net = 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_safe eq entry net = insert eq entry net handle INSERT => net; fun insert_term eq (t, x) = insert eq (key_of_term t, x); (*** 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 eq (keys, x) net = 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 eq (t, x) = delete eq (key_of_term t, x); (*** 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, Term.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,[])); (** operations on nets **) (*subtraction: collect entries of second net that are NOT present in first net*) fun subtract eq net1 net2 = let fun subtr (Net _) (Leaf ys) = append ys | subtr (Leaf xs) (Leaf ys) = fold_rev (fn y => if member eq xs y then I else cons y) ys | subtr (Leaf _) (net as Net _) = subtr emptynet net | subtr (Net {comb = comb1, var = var1, atoms = atoms1}) (Net {comb = comb2, var = var2, atoms = atoms2}) = subtr comb1 comb2 #> subtr var1 var2 #> Symtab.fold (fn (a, net) => subtr (if_none (Symtab.lookup atoms1 a) emptynet) net) atoms2 in subtr net1 net2 [] end; fun entries net = subtract (K false) empty net; (* merge *) 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)); fun merge eq (net1, net2) = fold (insert_safe eq) (dest net2) net1; end;