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+ 2.1 Arrays

Now we have some background in sums and products, we can move on to arrays. Consider:

  var a1 : int * int * int = 1,2,3;

Here a is a tuple with the components which are all integers. Its very boring to write this out so we will allow a more compact notation:

  var a2 : int ^ 3 = 1,2,3;

The {^} operator is being used to mean exponentiation, or raising to a power. It makes sense, and follows mathematical tradition, where real spaces is denoted {R^3} (only with the 3 printed as a superscript!).

But wait, you say! We know that

  3 = 1 + 1 + 1

by definition. So it seems we have not merely allowed you to write {int^3} but it follows from the usual index laws:

T^n * T^m = T^(n+m)