Declaring
Tuples gather a given number of values in a specific order and those
values, called components, can be retrieved by their index
(position). Probably the most common tuple is the pair. For
example, if we were storing coordinates on a two dimensional grid we
might use a pair [x, y] to store the coordinates x and y. There
is a specific order, so [y, x] is not equal to [x, y] in
general. The number of components is part of the type of a tuple, so,
for example, we cannot add an extra component to a pair and obtain a
triple of the same type: [x, y] has always a different type from
[x, y, z], whereas [y, x] might have the same type as [x, y].
Tuple components can be of arbitrary types. A pair is a 2-tuple. If it
contains a first component of type t_1 and a second component of
type t_2, its type is written [t_1, t_2]. If more components:
[t1, t2, ..., t_n]. (We can think of tuple types as products of
types.) Tuple types do not have to be defined before they can be used:
but it is sometimes more informative to define a type. Type
definitions are introduced with the keyword type, like value
definitions are with const. Instead of a value expression as a
right-hand side, we have a type expression: