Accept Infinity as an Integer argument

Question

I have the following function, albeit contrived:

Foo[x_Integer] :=
  Module[{i},
   i = 1;
   While[i <= x && i <= 10, i++];
   i - 1
   ];

I am looking for the following

Foo[1] = 1
.
.
.
Foo[10] = 10
Foo[11] = 10
Foo[Infinity] = 10

However Foo[Infinity] returns Foo[\[Infinity]] and not 10 .

Is there an something that I can do, short of: Foo[Infinity] = 10; to get Foo[Infinity] to return 10 ? The problem is i <= 10 is static in my contrived example, but will be dynamic in practice.

Answer 1

You can do this by using Alternatives to have the pattern accept either an integer or Infinity as an argument, like so:

Pillsy`Foo[x : (_Integer | Infinity)] :=
 Module[{limit = Min[x, 10], i = 1},
  While[i <= limit, ++i];
  i - 1]

It helps that Mathematica functions like Min and Max usually do the right thing with Infinity as an argument.