Generate rectangular parallelepipeds
a) Let mult be a product function and unit be its neutral element. Implement the power_function that uses this product:
let rec power_function mult unit x n = ... ;;
val power_function : ('a -> 'a -> 'a) -> 'a -> 'a -> int -> 'a = <fun>
As exemples power_int and power_real are the n-th power of respectively an int and a real:
let power_int = power_function ( * ) 1;; let power_real = power_function ( *. ) 1.0;;
b) What is the cryptic following function ?
power_function (+) 0;; - : int -> int -> int = <fun>
c) Let interval be the following function:
let interval min max = [[min];[max]];;
Implement mult_interval, a fonction that does an ad-hoc product of two intervals:
let rec mult_interval a b = ... ;; val mult_interval : 'a list list -> 'a list list -> 'a list list = <fun>
The following uses-cases show you what this ad-hoc product mult_interval is supposed to be.
(* create an hyper-cube *) let power_interval = power_function mult_interval [[]];;
(* create the unit cube *) let unit_cube = power_interval (interval 0 1) 3;; val unit_cube : int list list = [[0; 0; 0]; [0; 0; 1]; [0; 1; 0]; [0; 1; 1]; [1; 0; 0]; [1; 0; 1]; [1; 1; 0]; [1; 1; 1]]
(* create a square, origin-centered, size two *) let square_2 = power_interval (interval (-1) 1) 2;; val square_2 : int list list = [[-1; -1]; [-1; 1]; [1; -1]; [1; 1]]
d) Are the following two rectangular parallelepipeds the same one?
power_interval (interval 0 1) 6;; power_interval unit_cube 2;;
e) Are the following two rectangular parallelepipeds the same one?
mult_interval unit_cube square_2;; mult_interval square_2 unit_cube;;
Why?