Java Functional Interfaces and Lambda Expressions

Question

Given the following code, can someone please explain why the assertion returns true? Despite having searched around countlessly, I haven't been able to get any appropriate answer for why this might be the case, and what the Java feature(s) cause this behaviour and what restrictions / requirements I would have in similarly creating an interface such as this.
interface X {
  default int foo() {return 1;}
  String bar();
}

public class Exercise{
  public static void main(String[]arg){
    X foo1=()->"hello";
    assert (foo1.bar()).equals("hello");
  }
}

Brian Goetz · Answer

A lambda expression is a concise way to create an instance of a functional interface, which is an interface with one abstract method.  Here, X is a functional interface, with abstract method bar().  You could implement X with:
class XImpl implements X { 
    public String bar() { return "Foo"; }
}

X instance = new XImpl();

or an anonymous class
X anon = new X() { 
    public String bar() { return "foo"; }
};

or a lambda
X lambda = () -> "foo";

Each of these instantiates an implementation of X.  What may be confusing you is the concision of the lambda; because X has only one abstract method, bar, you don't have to say you are implementing bar -- the compiler figures it out.  Since bar() takes no arguments and returns String, the compiler ensures that the shape of the lambda is compatible with the shape of the sole abstract method.
Because an X has a bar() method,
you can call it on each of these instances:
String s1 = instance.bar();
assertEquals(s1, "hello");

String s2 = anon.bar();
assertEquals(s2, "hello");

String s3 = lambda.bar();
assertEquals(s3, "hello");

and you get the same result for each.

Steyrix · Answer

Since method foo() has default implementation, you only need to specify bar() - which you do with X foo1 = ()->"hello".
So, your foo1.bar() returns hello.
UPD: My answer may be unclear, so I should note that 'foo' is not treated as an abstract method by compiler (that lets your interface X satisfy the requirements of declaring functional interface). Brian explains it clearer and more detailed in his answer.

Java Functional Interfaces and Lambda Expressions

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