Question

This is a programming question of Ocaml language

(* 5. Consider the following higher-order function reduce *)

let rec reduce (f:'a -> 'b -> 'b) (u:'b) (xs:'a list) : 'b =
match xs with
| [] -> u
| hd::tl -> f hd (reduce f u tl);;

(* Consider the following functions defined using reduce *)

let sum xs = reduce (fun x y -> x+y) 0 xs
let prod xs = reduce (fun x y -> x*y) 1 xs

(* What do the sum and prod functions do? What does the reduce
function do? Trace the following code to help figure this out.
Show your trace and provide your explanation here:

Answer 1

sum takes an integer list as an input and outputs the sum of the elements

prod takes an integer list as an input and outputs the product of the elements

let rec reduce (f:'a -> 'b -> 'b) (u:'b) (xs:'a list) : 'b -> Input to reduce is a function, initial value of the answer, and a list of integer and it outputs an integer

match xs with -> Then it checks if list is empty or not

| [] -> u -> If list is empty return the initial value which came as input

| hd::tl -> f hd (reduce f u tl);; -> If list is not empty apply the function to first element of the list and the ouput from recursive call to the same function.

Example: sum [1;2;3]

reduce(f,0,[1;2;3]) -> 1 + reduce(f,0,[2;3]) -> 2 + reduce(f,0,[3]) -> 3 + reduce(f,0,[])

reduce(f,0,[]) returns u;

Similar recusive call is made for prod