Thread with Lambda expression

If you intend on running a single method only with no arguments you can replace the lambda with a method reference.

For instance:

Thread t = new Thread(() -> {
        foo();
    });

can be more succinctly expressed as

Thread t = new Thread(this::foo);

To start it

t.start();

You have created a functional interface Predicate whose method is declared to throw an InterruptedException, which is a checked exception. However, you call test() in the body of a lambda expression as the parameter to the Thread constructor that takes a Runnable, whose run() method is not declared to throw any checked exceptions. Therefore, because the exception is not caught in the body, a compiler error occurs.

Incidentally, it may be confusing to name your own interface Predicate, because of the built-in functional interface java.util.function.Predicate whose functional method returns a boolean.

Because run() can't throw an Exception, you must catch the exception and handle it. You might log the exception and its stack trace. You might wrap the exception in a RuntimeException. Either way, catching the checked exception will allow the code to compile. Example:

Thread t1 = new Thread(() -> {
    try {
        prod.test();
    } catch (InterruptedException e) {
        // handle: log or throw in a wrapped RuntimeException
        throw new RuntimeException("InterruptedException caught in lambda", e);
    }
});

As @rgettman says, the name Predicate is unhappy... Anyways, you could take advantage of default methods in Java:

interface PredicateButPleaseChangeMyName {

    void test() throws InterruptedException;

    default void tryTest() {
       try {
          this.test();
       } catch (InterruptedException e) {
          // handle e (log or wrap in a RuntimeException)
       }
    }
}

Then, in your main method, simply create the threads by calling the default tryTest() method:

Thread t1 = new Thread(() -> prod.tryTest());
Thread t2 = new Thread(() -> cons.tryTest());