Accessing

We can access the components of a namespace by means of the selection operator ".", as with records.

Let us suppose that we keep an amount in euros using the previously defined namespace Euro. Then, we can write a tip function outside Euro that increments a given amount each time it is called.

namespace Euro {

export type t = nat;

export const add = (a: t, b: t) : t => a + b;

export const one: t = 1n;

export const two: t = 2n;

};

type storage = Euro.t;

const tip = (s : storage) : storage =>

Euro.add (s, Euro.one);

In principle, we could change the implementation of Euro, without having to change the storage type or the function tip. For example, if we decide later that we should support manipulating negative values, we could change Euro as follows:

namespace Euro {

export type t = int;

export const add = (a: t, b: t) : t => a + b;

export const one: t = 1;

export const two: t = 2;

};

The code of tip still works, and no change is needed. Abstraction accomplished!

Note that code using the namespace Euro might still break the abstraction if it directly uses the underlying representation of Euro.t. Client code should always try to respect the interface provided by the namespace, and not make assumptions on its current underlying representation. For example, Euro.t is a transparent alias of nat (or int). In order to hide the representation of a type in a namespace, we need to constrain the namesapce with an interface.