Rewrite the not function from the previous chapter in pattern matching style.

let not b =
  match b with
  | true -> false
  | _ -> true
;;

Use pattern matching to write a recursive function which, given a positive integer n, returns the sum of all the integers from 1 to n.

let rec sum_up_to n =
  match n > 0 with
  | true -> n + sum_up_to (n - 1)
  | _ -> 0
;;

Use pattern matching to write a function which, given two numbers x and n, computes x^n.

(* won't work for negative exponents *)
let rec power x n =
  match n with
  | 0 -> 1
  | 1 -> x
  | _ -> x * power x (n - 1)
;;

For each of the previous three questions, comment on whether you think it is easier to read the function with or without pattern matching. How might you expect this to change if the functions were much larger?

I think that, for the most part, it is easier to read with pattern matching. Although for not and sum_up_to, which only have two cases, might be overkill.

What does match 1 + 1 with 2 -> match 2 + 2 with 3 -> 4 | 4 -> 5 evaluate to?

5;;

There is a special pattern x..y to denote continuous ranges of characters, for example 'a'..'z' will match all lowercase letters. Write functions is_lower and is_upper, each of type char → bool, to decide on the case of a given letter.

let is_lower c =
  match c with
  | 'a'..'z' -> true
  | _ -> false
;;

let is_upper c =
  match c with
  | 'A'..'Z' -> true
  | _ -> false
;;