Modules 2
=========

1. Can we add a function to multiple modules at the same time?

   Arithmetic intervals: Range of integers 3, 4, 5, 6, 7
                         Closed interval of real numbers: all numbers between 3.2 and 4.8
                         All words in the dictionary between "compiler" and "language": "compressor", "docket",
                           "floatation", ..., "compressors"

   - An interval is defined by two endpoints
   - We want to be able to answer the question: Is an element e contained in some interval intvl?
     contains : intvl -> t -> bool
   - Essential requirement: We need to be able to compare.

   module type Comparable =
     sig
       type t
       val compare : t -> t -> int
       (* compare x y < 0 iff x < y *)
       (* compare x y = 0 iff x = y *)
       (* compare x y > 0 iff x > y *)
     end

   module IntComparable : Comparable = ...
   module FloatComparable : Comparable = ...
   module StringComparable : Comparable = ...

   We want to be able to talk about "type t intvl" for any type t which is comparable.

   type int_intvl = Range of int * int
   let int_intvl_contains = ...

   type float_intvl = Range of float * float
   let float_intvl_contains = ...

   module Make_Interval (Endpoint : Comparable) =
     struct
       let (<=) x y = (Endpoint.compare x y <= 0)
       type intvl = Empty | Range of Endpoint.t * Endpoint.t
       let contains intvl x =
         match intvl with
         | Empty -> false
         | Range(lo, hi) -> lo <= x && x <= hi
     end

    module type Comparable =
     sig
       type t
       val compare : 'a -> 'a -> int
       (* compare x y < 0 iff x < y *)
       (* compare x y = 0 iff x = y *)
       (* compare x y > 0 iff x > y *)
     end;;

    module IntComparable : Comparable =
      struct
        type t = int
        let string_to_t s = Int.from_string s
        let compare x y = x - y
      end

    let x : IntComparable.t = 3

    module Make_Interval (Endpoint : Comparable) =
     struct
       let (<=) x y = (Endpoint.compare x y <= 0)
       type intvl = Empty | Range of Endpoint.t * Endpoint.t
       let contains intvl x =
         match intvl with
         | Empty -> false
         | Range(lo, hi) -> lo <= x && x <= hi
     end