model n of integer type

Question

I am working on a module which involves a set of natural numbers. As a result I need to model some n of type integer. How can I go about it?

Eg. sum of i for continuously increasing sequence of i starting at 1 = n(n+1)/2

How can I model n here?

Answer 1

The requirements are that we should be able to use n as an integer. I think I figured it out.

type element_i = N of nativeint | CNN of nativeint * nativeint
(* element_i can be an integer or a*n+b represented as (a,b))

let to_string_i e = 
  match e with 
  | N z   -> "%d" z 
  | CNN c -> " (%d xn + %d) " (fst c) (snd c)

let plus_i a b =
  match (a, b) with 
  | (N a1, N b1)   -> N (a1 + b1)
  | (N a1, CNN b1) -> CNN (fst b1, (snd b1) + a1)
  | (CNN a1, N b1) -> CNN (fst a1, (snd a1) + b1)

let times_i a b = 
  match (a, b) with 
  | (N a1, N b1)  -> N (a1 * b1)
  | (N a1,CNN b1) -> CNN ((fst b1) * a1, (snd b1) * a1)
  | (CNN a1,N b1) -> CNN ((fst a1) * b1, (snd a1) * b1)