I learned this either from the mailing list or from reading the library source. Here search means to locate the file from the CLASSPATH, and run means to bring the definitions made in the file into existence as well as executing all the top level statements in the file. This is done before anything else defined in the importing file is executed. And this is done only once.

Here the example I used to explore this feature:

// foo/Foo.fx
import java.lang.System;

var o = Baz {str: "Hello"};
System.out.println(o);

System.out.println("About to import bar.Bar");
import bar.Bar;
System.out.println("Done to import bar.Bar");

System.out.println("About to import bar.Bar again");
import bar.Bar;
System.out.println("Done to import bar.Bar again");

// bar/Bar.fx
import java.lang.System;

class Baz {
  attribute str: String*;
}

System.out.println("From bar.Bar");

[weiqi@gao] $export CLASSPATH=.
[weiqi@gao] $javafx.sh foo.Foo
compile thread: Thread[AWT-EventQueue-0,6,main]
compile 0.018
From bar.Bar
Baz {str: ['Hello']}
About to import bar.Bar
Done to import bar.Bar
About to import bar.Bar again
Done to import bar.Bar again
init: 0.064