Type systems don't concern themselves with what data you can put into the variable. They concern themselves with what you're allowed to do with that variable. Mathmatically, it makes no sense to take the square root of a string, or call an insert() method on an object that only runs selects, or give a background the color of laptop.

The holy grail is a program that is proven correct just by the fact that you compiled it without errors. Good, strong type systems are a major step in that direction. I'm not sure we'll ever actually reach that point, but it's good to try.

Or unless you have a type "Non-negative number".

Which you can define easily in Perl 6 :):

  my subtype NonNegativeNumber of Num where { not $^a < 0 };

  my NonNegativeNumber $x =  3; # works
  my NonNegativeNumber $y = -3; # dies
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Another example of using subtypes:

  my subtype HTTP::Request::Method of Str where {
    $^method eq any <GET POST HEAD ...>;
  };

  method send_using(HTTP::Request::Method $method) {
    ...;
    # Note: You don't have to manually check for $method
    # not being a valid HTTP method :).
  }
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--Ingo

...for square roots even if you can trust the compiler that you are getting a number, you have to make sure that it is not negative (unless your sqrt function deals with complex numbers).

$a = ["abc",123];
$b = -1;
print sqrt($a);
print sqrt($b);
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