By Hickey J.
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Additional info for Introduction to the Objective Caml programming language
Arrays can be created with the [ |e1 ; . . ; en | ] syntax, which creates an array of length n initialized with the values computed from the expressions e1 , . . , en . (i) construction. Array indices start from 0. Arrays are bounds-checked. (i) <- e assignment statement. (2) <- 9;; : unit = () a;; : int array = [|1; 3; 9; 7|] The Array library module defines additional functions on arrays. create function, which requires a length and initializer argument. length function returns the number of elements in the array.
30 CHAPTER 4. BASIC PATTERN MATCHING 0 val is_one : int -> bool =
This can be done in two parts. First find the location where the node is to be inserted. If possible, add the new node with a Red label because this would preserve invariant 3. This may, however, violate invariant 2 because the new Red node may have a Red parent. If this happens, the balance function migrates the Red label upward in the tree. # let balance = function Black, Node (Red, Node (Red, a, x, b), y, c), z, d -> Node (Red, Node (Black, a, x, b), y, Node (Black, c, | Black, Node (Red, a, x, Node (Red, b, y, c)), z, d -> Node (Red, Node (Black, a, x, b), y, Node (Black, c, | Black, a, x, Node (Red, Node (Red, b, y, c), z, d) -> Node (Red, Node (Black, a, x, b), y, Node (Black, c, | Black, a, x, Node (Red, b, y, Node (Red, c, z, d)) -> Node (Red, Node (Black, a, x, b), y, Node (Black, c, | a, b, c, d -> Node (a, b, c, d) let insert x s = let rec ins = function Leaf -> Node (Red, Leaf, x, Leaf) | Node (color, a, y, b) as s -> if x < y then balance (color, ins a, y, b) else if x > y then balance (color, a, y, ins b) else s in match ins s with (* guaranteed to be non-empty *) Node (_, a, y, b) -> Node (Black, a, y, b) | Leaf -> raise (Invalid_argument "insert");; z, d)) z, d)) z, d)) z, d)) 44 CHAPTER 6.