(* Title: Pure/General/table.ML
Author: Markus Wenzel and Stefan Berghofer, TU Muenchen
Generic tables. Efficient purely functional implementation using
balanced 2-3 trees.
*)
signature KEY =
sig
type key
val ord: key ord
end;
signature TABLE =
sig
structure Key: KEY
type key
type 'a table
exception DUP of key
exception SAME
exception UNDEF of key
val size: 'a table -> int
val empty: 'a table
val build: ('a table -> 'a table) -> 'a table
val is_empty: 'a table -> bool
val map: (key -> 'a -> 'b) -> 'a table -> 'b table
val fold: (key * 'b -> 'a -> 'a) -> 'b table -> 'a -> 'a
val fold_rev: (key * 'b -> 'a -> 'a) -> 'b table -> 'a -> 'a
val dest: 'a table -> (key * 'a) list
val keys: 'a table -> key list
val min: 'a table -> (key * 'a) option
val max: 'a table -> (key * 'a) option
val exists: (key * 'a -> bool) -> 'a table -> bool
val forall: (key * 'a -> bool) -> 'a table -> bool
val get_first: (key * 'a -> 'b option) -> 'a table -> 'b option
val lookup_key: 'a table -> key -> (key * 'a) option
val lookup: 'a table -> key -> 'a option
val defined: 'a table -> key -> bool
val update: key * 'a -> 'a table -> 'a table
val update_new: key * 'a -> 'a table -> 'a table (*exception DUP*)
val default: key * 'a -> 'a table -> 'a table
val map_entry: key -> ('a -> 'a) (*exception SAME*) -> 'a table -> 'a table
val map_default: key * 'a -> ('a -> 'a) -> 'a table -> 'a table
val make: (key * 'a) list -> 'a table (*exception DUP*)
val join: (key -> 'a * 'a -> 'a) (*exception SAME*) ->
'a table * 'a table -> 'a table (*exception DUP*)
val merge: ('a * 'a -> bool) -> 'a table * 'a table -> 'a table (*exception DUP*)
val delete: key -> 'a table -> 'a table (*exception UNDEF*)
val delete_safe: key -> 'a table -> 'a table
val member: ('b * 'a -> bool) -> 'a table -> key * 'b -> bool
val insert: ('a * 'a -> bool) -> key * 'a -> 'a table -> 'a table (*exception DUP*)
val remove: ('b * 'a -> bool) -> key * 'b -> 'a table -> 'a table
val lookup_list: 'a list table -> key -> 'a list
val cons_list: key * 'a -> 'a list table -> 'a list table
val insert_list: ('a * 'a -> bool) -> key * 'a -> 'a list table -> 'a list table
val remove_list: ('b * 'a -> bool) -> key * 'b -> 'a list table -> 'a list table
val update_list: ('a * 'a -> bool) -> key * 'a -> 'a list table -> 'a list table
val make_list: (key * 'a) list -> 'a list table
val dest_list: 'a list table -> (key * 'a) list
val merge_list: ('a * 'a -> bool) -> 'a list table * 'a list table -> 'a list table
type set = unit table
val insert_set: key -> set -> set
val remove_set: key -> set -> set
val make_set: key list -> set
end;
functor Table(Key: KEY): TABLE =
struct
(* keys *)
structure Key = Key;
type key = Key.key;
exception DUP of key;
(* datatype *)
datatype 'a table =
Empty |
Leaf1 of key * 'a |
Leaf2 of (key * 'a) * (key * 'a) |
Leaf3 of (key * 'a) * (key * 'a) * (key * 'a) |
Branch2 of 'a table * (key * 'a) * 'a table |
Branch3 of 'a table * (key * 'a) * 'a table * (key * 'a) * 'a table;
(*literal copy from set.ML*)
fun make2 (Empty, e, Empty) = Leaf1 e
| make2 (Branch2 (Empty, e1, Empty), e2, right) = make2 (Leaf1 e1, e2, right)
| make2 (left, e1, Branch2 (Empty, e2, Empty)) = make2 (left, e1, Leaf1 e2)
| make2 (Branch3 (Empty, e1, Empty, e2, Empty), e3, right) = make2 (Leaf2 (e1, e2), e3, right)
| make2 (left, e1, Branch3 (Empty, e2, Empty, e3, Empty)) = make2 (left, e1, Leaf2 (e2, e3))
| make2 (Leaf1 e1, e2, Empty) = Leaf2 (e1, e2)
| make2 (Empty, e1, Leaf1 e2) = Leaf2 (e1, e2)
| make2 (Leaf1 e1, e2, Leaf1 e3) = Leaf3 (e1, e2, e3)
| make2 (Leaf2 (e1, e2), e3, Empty) = Leaf3 (e1, e2, e3)
| make2 (Empty, e1, Leaf2 (e2, e3)) = Leaf3 (e1, e2, e3)
| make2 arg = Branch2 arg;
(*literal copy from set.ML*)
fun make3 (Empty, e1, Empty, e2, Empty) = Leaf2 (e1, e2)
| make3 (Branch2 (Empty, e1, Empty), e2, mid, e3, right) = make3 (Leaf1 e1, e2, mid, e3, right)
| make3 (left, e1, Branch2 (Empty, e2, Empty), e3, right) = make3 (left, e1, Leaf1 e2, e3, right)
| make3 (left, e1, mid, e2, Branch2 (Empty, e3, Empty)) = make3 (left, e1, mid, e2, Leaf1 e3)
| make3 (Leaf1 e1, e2, Empty, e3, Empty) = Leaf3 (e1, e2, e3)
| make3 (Empty, e1, Leaf1 e2, e3, Empty) = Leaf3 (e1, e2, e3)
| make3 (Empty, e1, Empty, e2, Leaf1 e3) = Leaf3 (e1, e2, e3)
| make3 arg = Branch3 arg;
(*literal copy from set.ML*)
fun unmake (Leaf1 e) = Branch2 (Empty, e, Empty)
| unmake (Leaf2 (e1, e2)) = Branch3 (Empty, e1, Empty, e2, Empty)
| unmake (Leaf3 (e1, e2, e3)) =
Branch2 (Branch2 (Empty, e1, Empty), e2, Branch2 (Empty, e3, Empty))
| unmake arg = arg;
(* size *)
local
(*literal copy from set.ML*)
fun count Empty n = n
| count (Leaf1 _) n = n + 1
| count (Leaf2 _) n = n + 2
| count (Leaf3 _) n = n + 3
| count (Branch2 (left, _, right)) n = count right (count left (n + 1))
| count (Branch3 (left, _, mid, _, right)) n = count right (count mid (count left (n + 2)));
in
fun size tab = Integer.build (count tab);
end;
(* empty *)
val empty = Empty;
fun build (f: 'a table -> 'a table) = f empty;
fun is_empty Empty = true
| is_empty _ = false;
(* map and fold combinators *)
fun map_table f =
let
fun map Empty = Empty
| map (Leaf1 (k, x)) = Leaf1 (k, f k x)
| map (Leaf2 ((k1, x1), (k2, x2))) = Leaf2 ((k1, f k1 x1), (k2, f k2 x2))
| map (Leaf3 ((k1, x1), (k2, x2), (k3, x3))) =
Leaf3 ((k1, f k1 x1), (k2, f k2 x2), (k3, f k3 x3))
| map (Branch2 (left, (k, x), right)) =
Branch2 (map left, (k, f k x), map right)
| map (Branch3 (left, (k1, x1), mid, (k2, x2), right)) =
Branch3 (map left, (k1, f k1 x1), map mid, (k2, f k2 x2), map right);
in map end;
fun fold_table f =
let
fun fold Empty x = x
| fold (Leaf1 e) x = f e x
| fold (Leaf2 (e1, e2)) x = f e2 (f e1 x)
| fold (Leaf3 (e1, e2, e3)) x = f e3 (f e2 (f e1 x))
| fold (Branch2 (left, e, right)) x =
fold right (f e (fold left x))
| fold (Branch3 (left, e1, mid, e2, right)) x =
fold right (f e2 (fold mid (f e1 (fold left x))));
in fold end;
fun fold_rev_table f =
let
fun fold_rev Empty x = x
| fold_rev (Leaf1 e) x = f e x
| fold_rev (Leaf2 (e1, e2)) x = f e1 (f e2 x)
| fold_rev (Leaf3 (e1, e2, e3)) x = f e1 (f e2 (f e3 x))
| fold_rev (Branch2 (left, e, right)) x =
fold_rev left (f e (fold_rev right x))
| fold_rev (Branch3 (left, e1, mid, e2, right)) x =
fold_rev left (f e1 (fold_rev mid (f e2 (fold_rev right x))));
in fold_rev end;
fun dest tab = Library.build (fold_rev_table cons tab);
fun keys tab = Library.build (fold_rev_table (cons o #1) tab);
(* min/max entries *)
fun min Empty = NONE
| min (Leaf1 e) = SOME e
| min (Leaf2 (e, _)) = SOME e
| min (Leaf3 (e, _, _)) = SOME e
| min (Branch2 (Empty, e, _)) = SOME e
| min (Branch3 (Empty, e, _, _, _)) = SOME e
| min (Branch2 (left, _, _)) = min left
| min (Branch3 (left, _, _, _, _)) = min left;
fun max Empty = NONE
| max (Leaf1 e) = SOME e
| max (Leaf2 (_, e)) = SOME e
| max (Leaf3 (_, _, e)) = SOME e
| max (Branch2 (_, e, Empty)) = SOME e
| max (Branch3 (_, _, _, e, Empty)) = SOME e
| max (Branch2 (_, _, right)) = max right
| max (Branch3 (_, _, _, _, right)) = max right;
(* exists and forall *)
fun exists pred =
let
fun ex Empty = false
| ex (Leaf1 e) = pred e
| ex (Leaf2 (e1, e2)) = pred e1 orelse pred e2
| ex (Leaf3 (e1, e2, e3)) = pred e1 orelse pred e2 orelse pred e3
| ex (Branch2 (left, e, right)) =
ex left orelse pred e orelse ex right
| ex (Branch3 (left, e1, mid, e2, right)) =
ex left orelse pred e1 orelse ex mid orelse pred e2 orelse ex right;
in ex end;
fun forall pred = not o exists (not o pred);
(* get_first *)
fun get_first f =
let
fun get Empty = NONE
| get (Leaf1 e) = f e
| get (Leaf2 (e1, e2)) =
(case f e1 of
NONE => f e2
| some => some)
| get (Leaf3 (e1, e2, e3)) =
(case f e1 of
NONE =>
(case f e2 of
NONE => f e3
| some => some)
| some => some)
| get (Branch2 (left, e, right)) =
(case get left of
NONE =>
(case f e of
NONE => get right
| some => some)
| some => some)
| get (Branch3 (left, e1, mid, e2, right)) =
(case get left of
NONE =>
(case f e1 of
NONE =>
(case get mid of
NONE =>
(case f e2 of
NONE => get right
| some => some)
| some => some)
| some => some)
| some => some);
in get end;
(* lookup *)
fun lookup tab key =
let
fun key_ord k = Key.ord (key, k);
val key_eq = is_equal o key_ord;
fun look Empty = NONE
| look (Leaf1 (k, x)) =
if key_eq k then SOME x else NONE
| look (Leaf2 ((k1, x1), (k2, x2))) =
(case key_ord k1 of
LESS => NONE
| EQUAL => SOME x1
| GREATER => if key_eq k2 then SOME x2 else NONE)
| look (Leaf3 ((k1, x1), (k2, x2), (k3, x3))) =
(case key_ord k2 of
LESS => if key_eq k1 then SOME x1 else NONE
| EQUAL => SOME x2
| GREATER => if key_eq k3 then SOME x3 else NONE)
| look (Branch2 (left, (k, x), right)) =
(case key_ord k of
LESS => look left
| EQUAL => SOME x
| GREATER => look right)
| look (Branch3 (left, (k1, x1), mid, (k2, x2), right)) =
(case key_ord k1 of
LESS => look left
| EQUAL => SOME x1
| GREATER =>
(case key_ord k2 of
LESS => look mid
| EQUAL => SOME x2
| GREATER => look right));
in look tab end;
fun lookup_key tab key =
let
fun key_ord k = Key.ord (key, k);
val key_eq = is_equal o key_ord;
fun look Empty = NONE
| look (Leaf1 (k, x)) =
if key_eq k then SOME (k, x) else NONE
| look (Leaf2 ((k1, x1), (k2, x2))) =
(case key_ord k1 of
LESS => NONE
| EQUAL => SOME (k1, x1)
| GREATER => if key_eq k2 then SOME (k2, x2) else NONE)
| look (Leaf3 ((k1, x1), (k2, x2), (k3, x3))) =
(case key_ord k2 of
LESS => if key_eq k1 then SOME (k1, x1) else NONE
| EQUAL => SOME (k2, x2)
| GREATER => if key_eq k3 then SOME (k3, x3) else NONE)
| look (Branch2 (left, (k, x), right)) =
(case key_ord k of
LESS => look left
| EQUAL => SOME (k, x)
| GREATER => look right)
| look (Branch3 (left, (k1, x1), mid, (k2, x2), right)) =
(case key_ord k1 of
LESS => look left
| EQUAL => SOME (k1, x1)
| GREATER =>
(case key_ord k2 of
LESS => look mid
| EQUAL => SOME (k2, x2)
| GREATER => look right));
in look tab end;
fun defined tab key =
let
fun key_ord k = Key.ord (key, k);
val key_eq = is_equal o key_ord;
fun def Empty = false
| def (Leaf1 (k, _)) = key_eq k
| def (Leaf2 ((k1, _), (k2, _))) =
(case key_ord k1 of
LESS => false
| EQUAL => true
| GREATER => key_eq k2)
| def (Leaf3 ((k1, _), (k2, _), (k3, _))) =
(case key_ord k2 of
LESS => key_eq k1
| EQUAL => true
| GREATER => key_eq k3)
| def (Branch2 (left, (k, _), right)) =
(case key_ord k of
LESS => def left
| EQUAL => true
| GREATER => def right)
| def (Branch3 (left, (k1, _), mid, (k2, _), right)) =
(case key_ord k1 of
LESS => def left
| EQUAL => true
| GREATER =>
(case key_ord k2 of
LESS => def mid
| EQUAL => true
| GREATER => def right));
in def tab end;
(* modify *)
datatype 'a growth =
Stay of 'a table |
Sprout of 'a table * (key * 'a) * 'a table;
exception SAME;
fun modify key f tab =
let
fun key_ord k = Key.ord (key, k);
fun modfy Empty = Sprout (Empty, (key, f NONE), Empty)
| modfy (t as Leaf1 _) = modfy (unmake t)
| modfy (t as Leaf2 _) = modfy (unmake t)
| modfy (t as Leaf3 _) = modfy (unmake t)
| modfy (Branch2 (left, p as (k, x), right)) =
(case key_ord k of
LESS =>
(case modfy left of
Stay left' => Stay (make2 (left', p, right))
| Sprout (left1, q, left2) => Stay (make3 (left1, q, left2, p, right)))
| EQUAL => Stay (make2 (left, (k, f (SOME x)), right))
| GREATER =>
(case modfy right of
Stay right' => Stay (make2 (left, p, right'))
| Sprout (right1, q, right2) =>
Stay (make3 (left, p, right1, q, right2))))
| modfy (Branch3 (left, p1 as (k1, x1), mid, p2 as (k2, x2), right)) =
(case key_ord k1 of
LESS =>
(case modfy left of
Stay left' => Stay (make3 (left', p1, mid, p2, right))
| Sprout (left1, q, left2) =>
Sprout (make2 (left1, q, left2), p1, make2 (mid, p2, right)))
| EQUAL => Stay (make3 (left, (k1, f (SOME x1)), mid, p2, right))
| GREATER =>
(case key_ord k2 of
LESS =>
(case modfy mid of
Stay mid' => Stay (make3 (left, p1, mid', p2, right))
| Sprout (mid1, q, mid2) =>
Sprout (make2 (left, p1, mid1), q, make2 (mid2, p2, right)))
| EQUAL => Stay (make3 (left, p1, mid, (k2, f (SOME x2)), right))
| GREATER =>
(case modfy right of
Stay right' => Stay (make3 (left, p1, mid, p2, right'))
| Sprout (right1, q, right2) =>
Sprout (make2 (left, p1, mid), p2, make2 (right1, q, right2)))));
in
(case modfy tab of
Stay tab' => tab'
| Sprout br => make2 br)
handle SAME => tab
end;
fun update (key, x) tab = modify key (fn _ => x) tab;
fun update_new (key, x) tab = modify key (fn NONE => x | SOME _ => raise DUP key) tab;
fun default (key, x) tab = modify key (fn NONE => x | SOME _ => raise SAME) tab;
fun map_entry key f = modify key (fn NONE => raise SAME | SOME x => f x);
fun map_default (key, x) f = modify key (fn NONE => f x | SOME y => f y);
(* delete *)
exception UNDEF of key;
local
fun compare NONE _ = LESS
| compare (SOME k1) (k2, _) = Key.ord (k1, k2);
fun if_equal ord x y = if is_equal ord then x else y;
(*literal copy from set.ML*)
fun del (SOME k) Empty = raise UNDEF k
| del NONE Empty = raise Match
| del NONE (Leaf1 p) = (p, (true, Empty))
| del NONE (Leaf2 (p, q)) = (p, (false, Leaf1 q))
| del k (Leaf1 p) =
(case compare k p of
EQUAL => (p, (true, Empty))
| _ => raise UNDEF (the k))
| del k (Leaf2 (p, q)) =
(case compare k p of
EQUAL => (p, (false, Leaf1 q))
| _ =>
(case compare k q of
EQUAL => (q, (false, Leaf1 p))
| _ => raise UNDEF (the k)))
| del k (Leaf3 (p, q, r)) = del k (Branch2 (Leaf1 p, q, Leaf1 r))
| del k (Branch2 (l, p, r)) =
(case compare k p of
LESS =>
(case del k l of
(p', (false, l')) => (p', (false, make2 (l', p, r)))
| (p', (true, l')) => (p', case unmake r of
Branch2 (rl, rp, rr) =>
(true, make3 (l', p, rl, rp, rr))
| Branch3 (rl, rp, rm, rq, rr) => (false, make2
(make2 (l', p, rl), rp, make2 (rm, rq, rr)))))
| ord =>
(case del (if_equal ord NONE k) r of
(p', (false, r')) => (p', (false, make2 (l, if_equal ord p' p, r')))
| (p', (true, r')) => (p', case unmake l of
Branch2 (ll, lp, lr) =>
(true, make3 (ll, lp, lr, if_equal ord p' p, r'))
| Branch3 (ll, lp, lm, lq, lr) => (false, make2
(make2 (ll, lp, lm), lq, make2 (lr, if_equal ord p' p, r'))))))
| del k (Branch3 (l, p, m, q, r)) =
(case compare k q of
LESS =>
(case compare k p of
LESS =>
(case del k l of
(p', (false, l')) => (p', (false, make3 (l', p, m, q, r)))
| (p', (true, l')) => (p', (false, case (unmake m, unmake r) of
(Branch2 (ml, mp, mr), Branch2 _) =>
make2 (make3 (l', p, ml, mp, mr), q, r)
| (Branch3 (ml, mp, mm, mq, mr), _) =>
make3 (make2 (l', p, ml), mp, make2 (mm, mq, mr), q, r)
| (Branch2 (ml, mp, mr), Branch3 (rl, rp, rm, rq, rr)) =>
make3 (make2 (l', p, ml), mp, make2 (mr, q, rl), rp,
make2 (rm, rq, rr)))))
| ord =>
(case del (if_equal ord NONE k) m of
(p', (false, m')) =>
(p', (false, make3 (l, if_equal ord p' p, m', q, r)))
| (p', (true, m')) => (p', (false, case (unmake l, unmake r) of
(Branch2 (ll, lp, lr), Branch2 _) =>
make2 (make3 (ll, lp, lr, if_equal ord p' p, m'), q, r)
| (Branch3 (ll, lp, lm, lq, lr), _) =>
make3 (make2 (ll, lp, lm), lq,
make2 (lr, if_equal ord p' p, m'), q, r)
| (_, Branch3 (rl, rp, rm, rq, rr)) =>
make3 (l, if_equal ord p' p, make2 (m', q, rl), rp,
make2 (rm, rq, rr))))))
| ord =>
(case del (if_equal ord NONE k) r of
(q', (false, r')) =>
(q', (false, make3 (l, p, m, if_equal ord q' q, r')))
| (q', (true, r')) => (q', (false, case (unmake l, unmake m) of
(Branch2 _, Branch2 (ml, mp, mr)) =>
make2 (l, p, make3 (ml, mp, mr, if_equal ord q' q, r'))
| (_, Branch3 (ml, mp, mm, mq, mr)) =>
make3 (l, p, make2 (ml, mp, mm), mq,
make2 (mr, if_equal ord q' q, r'))
| (Branch3 (ll, lp, lm, lq, lr), Branch2 (ml, mp, mr)) =>
make3 (make2 (ll, lp, lm), lq, make2 (lr, p, ml), mp,
make2 (mr, if_equal ord q' q, r'))))));
in
fun delete key tab = snd (snd (del (SOME key) tab));
fun delete_safe key tab = if defined tab key then delete key tab else tab;
end;
(* membership operations *)
fun member eq tab (key, x) =
(case lookup tab key of
NONE => false
| SOME y => eq (x, y));
fun insert eq (key, x) =
modify key (fn NONE => x | SOME y => if eq (x, y) then raise SAME else raise DUP key);
fun remove eq (key, x) tab =
(case lookup tab key of
NONE => tab
| SOME y => if eq (x, y) then delete key tab else tab);
(* simultaneous modifications *)
fun make entries = build (fold update_new entries);
fun join f (tab1, tab2) =
let
fun add (key, y) tab = modify key (fn NONE => y | SOME x => f key (x, y)) tab;
in
if pointer_eq (tab1, tab2) then tab1
else if is_empty tab1 then tab2
else fold_table add tab2 tab1
end;
fun merge eq = join (fn key => fn xy => if eq xy then raise SAME else raise DUP key);
(* list tables *)
fun lookup_list tab key = these (lookup tab key);
fun cons_list (key, x) tab = modify key (fn NONE => [x] | SOME xs => x :: xs) tab;
fun insert_list eq (key, x) =
modify key (fn NONE => [x] | SOME xs => if Library.member eq xs x then raise SAME else x :: xs);
fun remove_list eq (key, x) tab =
map_entry key (fn xs => (case Library.remove eq x xs of [] => raise UNDEF key | ys => ys)) tab
handle UNDEF _ => delete key tab;
fun update_list eq (key, x) =
modify key (fn NONE => [x] | SOME [] => [x] | SOME (xs as y :: _) =>
if eq (x, y) then raise SAME else Library.update eq x xs);
fun make_list args = build (fold_rev cons_list args);
fun dest_list tab = maps (fn (key, xs) => map (pair key) xs) (dest tab);
fun merge_list eq = join (fn _ => Library.merge eq);
(* set operations *)
type set = unit table;
fun insert_set x = default (x, ());
fun remove_set x : set -> set = delete_safe x;
fun make_set xs = build (fold insert_set xs);
(* ML pretty-printing *)
val _ =
ML_system_pp (fn depth => fn pretty => fn tab =>
ML_Pretty.to_polyml
(ML_Pretty.enum "," "{" "}"
(ML_Pretty.pair
(ML_Pretty.from_polyml o ML_system_pretty)
(ML_Pretty.from_polyml o pretty))
(dest tab, depth)));
(*final declarations of this structure!*)
val map = map_table;
val fold = fold_table;
val fold_rev = fold_rev_table;
end;
structure Inttab = Table(type key = int val ord = int_ord);
structure Symtab = Table(type key = string val ord = fast_string_ord);
structure Symreltab = Table(type key = string * string
val ord = prod_ord fast_string_ord fast_string_ord);