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(* Title: Pure/General/balanced_tree.ML
Author: Lawrence C Paulson and Makarius
Balanced binary trees.
*)
signature BALANCED_TREE =
sig
val make: ('a * 'a -> 'a) -> 'a list -> 'a
val dest: ('a -> 'a * 'a) -> int -> 'a -> 'a list
val access: {left: 'a -> 'a, right: 'a -> 'a, init: 'a} -> int -> int -> 'a
val accesses: {left: 'a -> 'a, right: 'a -> 'a, init: 'a} -> int -> 'a list
end;
structure Balanced_Tree: BALANCED_TREE =
struct
fun make _ [] = raise List.Empty
| make _ [x] = x
| make f xs =
let
val m = length xs div 2;
val (ps, qs) = chop m xs;
in f (make f ps, make f qs) end;
fun dest f n x =
if n <= 0 then raise List.Empty
else if n = 1 then [x]
else
let
val m = n div 2;
val (left, right) = f x;
in dest f m left @ dest f (n - m) right end;
(*construct something of the form f(...g(...(x)...)) for balanced access*)
fun access {left = f, right = g, init = x} len i =
let
fun acc 1 _ = x
| acc n i =
let val m = n div 2 in
if i <= m then f (acc m i)
else g (acc (n - m) (i - m))
end;
in if 1 <= i andalso i <= len then acc len i else raise Subscript end;
(*construct ALL such accesses; could try harder to share recursive calls!*)
fun accesses {left = f, right = g, init = x} len =
let
fun acc 1 = [x]
| acc n =
let
val m = n div 2;
val accs_left = acc m;
val accs_right =
if n - m = m then accs_left
else acc (n - m);
in map f accs_left @ map g accs_right end;
in if 1 <= len then acc len else raise Subscript end;
end;
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