author | wenzelm |
Sun, 30 May 2010 14:14:30 +0200 | |
changeset 37192 | 8cdddd689ea9 |
parent 35012 | c3e3ac3ca091 |
child 38635 | f76ad0771f67 |
permissions | -rw-r--r-- |
6118 | 1 |
(* Title: Pure/General/table.ML |
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Author: Markus Wenzel and Stefan Berghofer, TU Muenchen |
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Generic tables. Efficient purely functional implementation using |
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balanced 2-3 trees. |
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*) |
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||
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signature KEY = |
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sig |
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type key |
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val ord: key * key -> order |
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end; |
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signature TABLE = |
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sig |
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type key |
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type 'a table |
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exception DUP of key |
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exception SAME |
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exception UNDEF of key |
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val empty: 'a table |
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val is_empty: 'a table -> bool |
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val map: ('a -> 'b) -> 'a table -> 'b table |
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val map': (key -> 'a -> 'b) -> 'a table -> 'b table |
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val fold: (key * 'b -> 'a -> 'a) -> 'b table -> 'a -> 'a |
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val fold_rev: (key * 'b -> 'a -> 'a) -> 'b table -> 'a -> 'a |
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val dest: 'a table -> (key * 'a) list |
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val keys: 'a table -> key list |
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val min_key: 'a table -> key option |
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val max_key: 'a table -> key option |
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c3e3ac3ca091
removed unused "boundary" of Table/Graph.get_first;
wenzelm
parents:
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diff
changeset
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val get_first: (key * 'a -> 'b option) -> 'a table -> 'b option |
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val exists: (key * 'a -> bool) -> 'a table -> bool |
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val forall: (key * 'a -> bool) -> 'a table -> bool |
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val lookup: 'a table -> key -> 'a option |
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val defined: 'a table -> key -> bool |
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val update: key * 'a -> 'a table -> 'a table |
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val update_new: key * 'a -> 'a table -> 'a table (*exception DUP*) |
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val default: key * 'a -> 'a table -> 'a table |
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val map_entry: key -> ('a -> 'a) -> 'a table -> 'a table |
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val map_default: key * 'a -> ('a -> 'a) -> 'a table -> 'a table |
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d2d1138e0ddc
replaced exception TableFun/GraphFun.DUPS by TableFun/GraphFun.DUP;
wenzelm
parents:
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diff
changeset
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val make: (key * 'a) list -> 'a table (*exception DUP*) |
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val join: (key -> 'a * 'a -> 'a) (*exception DUP/SAME*) -> |
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replaced exception TableFun/GraphFun.DUPS by TableFun/GraphFun.DUP;
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parents:
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diff
changeset
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'a table * 'a table -> 'a table (*exception DUP*) |
d2d1138e0ddc
replaced exception TableFun/GraphFun.DUPS by TableFun/GraphFun.DUP;
wenzelm
parents:
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diff
changeset
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val merge: ('a * 'a -> bool) -> 'a table * 'a table -> 'a table (*exception DUP*) |
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val delete: key -> 'a table -> 'a table (*exception UNDEF*) |
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val delete_safe: key -> 'a table -> 'a table |
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val member: ('b * 'a -> bool) -> 'a table -> key * 'b -> bool |
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val insert: ('a * 'a -> bool) -> key * 'a -> 'a table -> 'a table (*exception DUP*) |
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val remove: ('b * 'a -> bool) -> key * 'b -> 'a table -> 'a table |
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val lookup_list: 'a list table -> key -> 'a list |
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val cons_list: key * 'a -> 'a list table -> 'a list table |
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val insert_list: ('a * 'a -> bool) -> key * 'a -> 'a list table -> 'a list table |
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val remove_list: ('b * 'a -> bool) -> key * 'b -> 'a list table -> 'a list table |
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val update_list: ('a * 'a -> bool) -> key * 'a -> 'a list table -> 'a list table |
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val make_list: (key * 'a) list -> 'a list table |
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val dest_list: 'a list table -> (key * 'a) list |
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val merge_list: ('a * 'a -> bool) -> 'a list table * 'a list table -> 'a list table |
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end; |
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||
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renamed functor TableFun to Table, and GraphFun to Graph;
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parents:
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functor Table(Key: KEY): TABLE = |
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struct |
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(* datatype table *) |
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type key = Key.key; |
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datatype 'a table = |
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Empty | |
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Branch2 of 'a table * (key * 'a) * 'a table | |
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Branch3 of 'a table * (key * 'a) * 'a table * (key * 'a) * 'a table; |
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exception DUP of key; |
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(* empty *) |
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val empty = Empty; |
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fun is_empty Empty = true |
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| is_empty _ = false; |
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(* map and fold combinators *) |
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fun map_table f = |
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let |
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fun map Empty = Empty |
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| map (Branch2 (left, (k, x), right)) = |
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Branch2 (map left, (k, f k x), map right) |
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| map (Branch3 (left, (k1, x1), mid, (k2, x2), right)) = |
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Branch3 (map left, (k1, f k1 x1), map mid, (k2, f k2 x2), map right); |
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in map end; |
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fun fold_table f = |
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let |
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fun fold Empty x = x |
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| fold (Branch2 (left, p, right)) x = |
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fold right (f p (fold left x)) |
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| fold (Branch3 (left, p1, mid, p2, right)) x = |
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fold right (f p2 (fold mid (f p1 (fold left x)))); |
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in fold end; |
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fun fold_rev_table f = |
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let |
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fun fold Empty x = x |
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| fold (Branch2 (left, p, right)) x = |
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fold left (f p (fold right x)) |
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| fold (Branch3 (left, p1, mid, p2, right)) x = |
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fold left (f p1 (fold mid (f p2 (fold right x)))); |
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in fold end; |
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fun dest tab = fold_rev_table cons tab []; |
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fun keys tab = fold_rev_table (cons o #1) tab []; |
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(* min/max keys *) |
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fun min_key Empty = NONE |
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| min_key (Branch2 (Empty, (k, _), _)) = SOME k |
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| min_key (Branch3 (Empty, (k, _), _, _, _)) = SOME k |
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| min_key (Branch2 (left, _, _)) = min_key left |
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| min_key (Branch3 (left, _, _, _, _)) = min_key left; |
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fun max_key Empty = NONE |
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| max_key (Branch2 (_, (k, _), Empty)) = SOME k |
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| max_key (Branch3 (_, _, _, (k, _), Empty)) = SOME k |
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| max_key (Branch2 (_, _, right)) = max_key right |
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| max_key (Branch3 (_, _, _, _, right)) = max_key right; |
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(* get_first *) |
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||
35012
c3e3ac3ca091
removed unused "boundary" of Table/Graph.get_first;
wenzelm
parents:
33162
diff
changeset
|
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fun get_first f = |
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let |
35012
c3e3ac3ca091
removed unused "boundary" of Table/Graph.get_first;
wenzelm
parents:
33162
diff
changeset
|
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fun get Empty = NONE |
31618
2e4430b84303
improved get_first: check boundary before entering subtrees;
wenzelm
parents:
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diff
changeset
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| get (Branch2 (left, (k, x), right)) = |
35012
c3e3ac3ca091
removed unused "boundary" of Table/Graph.get_first;
wenzelm
parents:
33162
diff
changeset
|
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(case get left of |
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NONE => |
35012
c3e3ac3ca091
removed unused "boundary" of Table/Graph.get_first;
wenzelm
parents:
33162
diff
changeset
|
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(case f (k, x) of |
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NONE => get right |
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| some => some) |
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| some => some) |
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31618
2e4430b84303
improved get_first: check boundary before entering subtrees;
wenzelm
parents:
31616
diff
changeset
|
144 |
| get (Branch3 (left, (k1, x1), mid, (k2, x2), right)) = |
35012
c3e3ac3ca091
removed unused "boundary" of Table/Graph.get_first;
wenzelm
parents:
33162
diff
changeset
|
145 |
(case get left of |
31616 | 146 |
NONE => |
35012
c3e3ac3ca091
removed unused "boundary" of Table/Graph.get_first;
wenzelm
parents:
33162
diff
changeset
|
147 |
(case f (k1, x1) of |
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NONE => |
35012
c3e3ac3ca091
removed unused "boundary" of Table/Graph.get_first;
wenzelm
parents:
33162
diff
changeset
|
149 |
(case get mid of |
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NONE => |
35012
c3e3ac3ca091
removed unused "boundary" of Table/Graph.get_first;
wenzelm
parents:
33162
diff
changeset
|
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(case f (k2, x2) of |
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NONE => get right |
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| some => some) |
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| some => some) |
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| some => some) |
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| some => some); |
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35012
c3e3ac3ca091
removed unused "boundary" of Table/Graph.get_first;
wenzelm
parents:
33162
diff
changeset
|
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in get end; |
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35012
c3e3ac3ca091
removed unused "boundary" of Table/Graph.get_first;
wenzelm
parents:
33162
diff
changeset
|
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fun exists pred = is_some o get_first (fn entry => if pred entry then SOME () else NONE); |
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fun forall pred = not o exists (not o pred); |
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(* lookup *) |
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fun lookup tab key = |
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let |
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fun look Empty = NONE |
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| look (Branch2 (left, (k, x), right)) = |
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(case Key.ord (key, k) of |
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LESS => look left |
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| EQUAL => SOME x |
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| GREATER => look right) |
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| look (Branch3 (left, (k1, x1), mid, (k2, x2), right)) = |
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(case Key.ord (key, k1) of |
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LESS => look left |
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| EQUAL => SOME x1 |
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| GREATER => |
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(case Key.ord (key, k2) of |
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LESS => look mid |
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| EQUAL => SOME x2 |
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| GREATER => look right)); |
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in look tab end; |
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fun defined tab key = |
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let |
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fun def Empty = false |
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| def (Branch2 (left, (k, x), right)) = |
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(case Key.ord (key, k) of |
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LESS => def left |
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| EQUAL => true |
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| GREATER => def right) |
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| def (Branch3 (left, (k1, x1), mid, (k2, x2), right)) = |
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(case Key.ord (key, k1) of |
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LESS => def left |
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| EQUAL => true |
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| GREATER => |
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(case Key.ord (key, k2) of |
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LESS => def mid |
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| EQUAL => true |
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| GREATER => def right)); |
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in def tab end; |
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(* modify *) |
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datatype 'a growth = |
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Stay of 'a table | |
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Sprout of 'a table * (key * 'a) * 'a table; |
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exception SAME; |
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fun modify key f tab = |
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let |
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fun modfy Empty = Sprout (Empty, (key, f NONE), Empty) |
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| modfy (Branch2 (left, p as (k, x), right)) = |
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(case Key.ord (key, k) of |
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LESS => |
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(case modfy left of |
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Stay left' => Stay (Branch2 (left', p, right)) |
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| Sprout (left1, q, left2) => Stay (Branch3 (left1, q, left2, p, right))) |
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| EQUAL => Stay (Branch2 (left, (k, f (SOME x)), right)) |
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| GREATER => |
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(case modfy right of |
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Stay right' => Stay (Branch2 (left, p, right')) |
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| Sprout (right1, q, right2) => |
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Stay (Branch3 (left, p, right1, q, right2)))) |
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| modfy (Branch3 (left, p1 as (k1, x1), mid, p2 as (k2, x2), right)) = |
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(case Key.ord (key, k1) of |
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LESS => |
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(case modfy left of |
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Stay left' => Stay (Branch3 (left', p1, mid, p2, right)) |
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| Sprout (left1, q, left2) => |
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Sprout (Branch2 (left1, q, left2), p1, Branch2 (mid, p2, right))) |
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| EQUAL => Stay (Branch3 (left, (k1, f (SOME x1)), mid, p2, right)) |
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| GREATER => |
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(case Key.ord (key, k2) of |
237 |
LESS => |
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(case modfy mid of |
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Stay mid' => Stay (Branch3 (left, p1, mid', p2, right)) |
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| Sprout (mid1, q, mid2) => |
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Sprout (Branch2 (left, p1, mid1), q, Branch2 (mid2, p2, right))) |
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| EQUAL => Stay (Branch3 (left, p1, mid, (k2, f (SOME x2)), right)) |
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| GREATER => |
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(case modfy right of |
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Stay right' => Stay (Branch3 (left, p1, mid, p2, right')) |
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| Sprout (right1, q, right2) => |
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Sprout (Branch2 (left, p1, mid), p2, Branch2 (right1, q, right2))))); |
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in |
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(case modfy tab of |
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Stay tab' => tab' |
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| Sprout br => Branch2 br) |
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handle SAME => tab |
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end; |
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fun update (key, x) tab = modify key (fn _ => x) tab; |
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fun update_new (key, x) tab = modify key (fn NONE => x | SOME _ => raise DUP key) tab; |
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fun default (key, x) tab = modify key (fn NONE => x | SOME _ => raise SAME) tab; |
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fun map_entry key f = modify key (fn NONE => raise SAME | SOME x => f x); |
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fun map_default (key, x) f = modify key (fn NONE => f x | SOME y => f y); |
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||
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(* delete *) |
264 |
||
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exception UNDEF of key; |
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267 |
local |
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||
269 |
fun compare NONE (k2, _) = LESS |
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| compare (SOME k1) (k2, _) = Key.ord (k1, k2); |
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fun if_eq EQUAL x y = x |
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| if_eq _ x y = y; |
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fun del (SOME k) Empty = raise UNDEF k |
276 |
| del NONE (Branch2 (Empty, p, Empty)) = (p, (true, Empty)) |
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277 |
| del NONE (Branch3 (Empty, p, Empty, q, Empty)) = |
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(p, (false, Branch2 (Empty, q, Empty))) |
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| del k (Branch2 (Empty, p, Empty)) = (case compare k p of |
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EQUAL => (p, (true, Empty)) | _ => raise UNDEF (the k)) |
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| del k (Branch3 (Empty, p, Empty, q, Empty)) = (case compare k p of |
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EQUAL => (p, (false, Branch2 (Empty, q, Empty))) |
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| _ => (case compare k q of |
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EQUAL => (q, (false, Branch2 (Empty, p, Empty))) |
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| _ => raise UNDEF (the k))) |
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| del k (Branch2 (l, p, r)) = (case compare k p of |
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LESS => (case del k l of |
288 |
(p', (false, l')) => (p', (false, Branch2 (l', p, r))) |
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289 |
| (p', (true, l')) => (p', case r of |
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290 |
Branch2 (rl, rp, rr) => |
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291 |
(true, Branch3 (l', p, rl, rp, rr)) |
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292 |
| Branch3 (rl, rp, rm, rq, rr) => (false, Branch2 |
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293 |
(Branch2 (l', p, rl), rp, Branch2 (rm, rq, rr))))) |
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| ord => (case del (if_eq ord NONE k) r of |
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(p', (false, r')) => (p', (false, Branch2 (l, if_eq ord p' p, r'))) |
296 |
| (p', (true, r')) => (p', case l of |
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297 |
Branch2 (ll, lp, lr) => |
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298 |
(true, Branch3 (ll, lp, lr, if_eq ord p' p, r')) |
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299 |
| Branch3 (ll, lp, lm, lq, lr) => (false, Branch2 |
|
300 |
(Branch2 (ll, lp, lm), lq, Branch2 (lr, if_eq ord p' p, r')))))) |
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| del k (Branch3 (l, p, m, q, r)) = (case compare k q of |
302 |
LESS => (case compare k p of |
|
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LESS => (case del k l of |
304 |
(p', (false, l')) => (p', (false, Branch3 (l', p, m, q, r))) |
|
305 |
| (p', (true, l')) => (p', (false, case (m, r) of |
|
306 |
(Branch2 (ml, mp, mr), Branch2 _) => |
|
307 |
Branch2 (Branch3 (l', p, ml, mp, mr), q, r) |
|
308 |
| (Branch3 (ml, mp, mm, mq, mr), _) => |
|
309 |
Branch3 (Branch2 (l', p, ml), mp, Branch2 (mm, mq, mr), q, r) |
|
310 |
| (Branch2 (ml, mp, mr), Branch3 (rl, rp, rm, rq, rr)) => |
|
311 |
Branch3 (Branch2 (l', p, ml), mp, Branch2 (mr, q, rl), rp, |
|
312 |
Branch2 (rm, rq, rr))))) |
|
15531 | 313 |
| ord => (case del (if_eq ord NONE k) m of |
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(p', (false, m')) => |
315 |
(p', (false, Branch3 (l, if_eq ord p' p, m', q, r))) |
|
316 |
| (p', (true, m')) => (p', (false, case (l, r) of |
|
317 |
(Branch2 (ll, lp, lr), Branch2 _) => |
|
318 |
Branch2 (Branch3 (ll, lp, lr, if_eq ord p' p, m'), q, r) |
|
319 |
| (Branch3 (ll, lp, lm, lq, lr), _) => |
|
320 |
Branch3 (Branch2 (ll, lp, lm), lq, |
|
321 |
Branch2 (lr, if_eq ord p' p, m'), q, r) |
|
322 |
| (_, Branch3 (rl, rp, rm, rq, rr)) => |
|
323 |
Branch3 (l, if_eq ord p' p, Branch2 (m', q, rl), rp, |
|
324 |
Branch2 (rm, rq, rr)))))) |
|
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| ord => (case del (if_eq ord NONE k) r of |
15014 | 326 |
(q', (false, r')) => |
327 |
(q', (false, Branch3 (l, p, m, if_eq ord q' q, r'))) |
|
328 |
| (q', (true, r')) => (q', (false, case (l, m) of |
|
329 |
(Branch2 _, Branch2 (ml, mp, mr)) => |
|
330 |
Branch2 (l, p, Branch3 (ml, mp, mr, if_eq ord q' q, r')) |
|
331 |
| (_, Branch3 (ml, mp, mm, mq, mr)) => |
|
332 |
Branch3 (l, p, Branch2 (ml, mp, mm), mq, |
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333 |
Branch2 (mr, if_eq ord q' q, r')) |
|
334 |
| (Branch3 (ll, lp, lm, lq, lr), Branch2 (ml, mp, mr)) => |
|
335 |
Branch3 (Branch2 (ll, lp, lm), lq, Branch2 (lr, p, ml), mp, |
|
336 |
Branch2 (mr, if_eq ord q' q, r')))))); |
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337 |
||
15665 | 338 |
in |
339 |
||
15761 | 340 |
fun delete key tab = snd (snd (del (SOME key) tab)); |
341 |
fun delete_safe key tab = delete key tab handle UNDEF _ => tab; |
|
15014 | 342 |
|
15665 | 343 |
end; |
344 |
||
15014 | 345 |
|
19031 | 346 |
(* membership operations *) |
16466 | 347 |
|
348 |
fun member eq tab (key, x) = |
|
17412 | 349 |
(case lookup tab key of |
16466 | 350 |
NONE => false |
351 |
| SOME y => eq (x, y)); |
|
15761 | 352 |
|
353 |
fun insert eq (key, x) = |
|
354 |
modify key (fn NONE => x | SOME y => if eq (x, y) then raise SAME else raise DUP key); |
|
355 |
||
356 |
fun remove eq (key, x) tab = |
|
17412 | 357 |
(case lookup tab key of |
15761 | 358 |
NONE => tab |
359 |
| SOME y => if eq (x, y) then delete key tab else tab); |
|
360 |
||
361 |
||
19031 | 362 |
(* simultaneous modifications *) |
363 |
||
29004 | 364 |
fun make entries = fold update_new entries empty; |
5015 | 365 |
|
12287 | 366 |
fun join f (table1, table2) = |
23655
d2d1138e0ddc
replaced exception TableFun/GraphFun.DUPS by TableFun/GraphFun.DUP;
wenzelm
parents:
21065
diff
changeset
|
367 |
let fun add (key, y) tab = modify key (fn NONE => y | SOME x => f key (x, y)) tab; |
30283
520872460b7b
TableFun.join/merge: optimize the important special case where the tables coincide -- NOTE: this changes both the operational behaviour and the result for non-standard join/eq notion;
wenzelm
parents:
29606
diff
changeset
|
368 |
in if pointer_eq (table1, table2) then table1 else fold_table add table2 table1 end; |
12287 | 369 |
|
19031 | 370 |
fun merge eq = join (fn key => fn xy => if eq xy then raise SAME else raise DUP key); |
5015 | 371 |
|
372 |
||
19031 | 373 |
(* list tables *) |
15761 | 374 |
|
18946 | 375 |
fun lookup_list tab key = these (lookup tab key); |
25391 | 376 |
|
377 |
fun cons_list (key, x) tab = modify key (fn NONE => [x] | SOME xs => x :: xs) tab; |
|
5015 | 378 |
|
20124 | 379 |
fun insert_list eq (key, x) = |
380 |
modify key (fn NONE => [x] | SOME xs => if Library.member eq xs x then raise SAME else x :: xs); |
|
25391 | 381 |
|
18946 | 382 |
fun remove_list eq (key, x) tab = |
15761 | 383 |
map_entry key (fn xs => (case Library.remove eq x xs of [] => raise UNDEF key | ys => ys)) tab |
384 |
handle UNDEF _ => delete key tab; |
|
5015 | 385 |
|
25391 | 386 |
fun update_list eq (key, x) = |
387 |
modify key (fn NONE => [x] | SOME [] => [x] | SOME (xs as y :: _) => |
|
388 |
if eq (x, y) then raise SAME else Library.update eq x xs); |
|
389 |
||
390 |
fun make_list args = fold_rev cons_list args empty; |
|
19482
9f11af8f7ef9
tuned basic list operators (flat, maps, map_filter);
wenzelm
parents:
19073
diff
changeset
|
391 |
fun dest_list tab = maps (fn (key, xs) => map (pair key) xs) (dest tab); |
19031 | 392 |
fun merge_list eq = join (fn _ => Library.merge eq); |
5015 | 393 |
|
394 |
||
5681 | 395 |
(*final declarations of this structure!*) |
16446 | 396 |
fun map f = map_table (K f); |
397 |
val map' = map_table; |
|
398 |
val fold = fold_table; |
|
28334 | 399 |
val fold_rev = fold_rev_table; |
5015 | 400 |
|
401 |
end; |
|
402 |
||
31971
8c1b845ed105
renamed functor TableFun to Table, and GraphFun to Graph;
wenzelm
parents:
31621
diff
changeset
|
403 |
structure Inttab = Table(type key = int val ord = int_ord); |
8c1b845ed105
renamed functor TableFun to Table, and GraphFun to Graph;
wenzelm
parents:
31621
diff
changeset
|
404 |
structure Symtab = Table(type key = string val ord = fast_string_ord); |
8c1b845ed105
renamed functor TableFun to Table, and GraphFun to Graph;
wenzelm
parents:
31621
diff
changeset
|
405 |
structure Symreltab = Table(type key = string * string |
30647
ef8f46c3158a
added Symreltab (binary relations of symbols) instance of TableFun
haftmann
parents:
30290
diff
changeset
|
406 |
val ord = prod_ord fast_string_ord fast_string_ord); |
ef8f46c3158a
added Symreltab (binary relations of symbols) instance of TableFun
haftmann
parents:
30290
diff
changeset
|
407 |