This is a very interesting comparison between how the architects of Java and Scala each implemented optional values.
First, what is a functor? From Categories for the Working Mathematician (Mac Lane):
A functor is a morphism of categories. In detail, for categories C and B a functor T:C->B with domain C and codomain B consists of two suitably related functions: The object function T, which assigns to each object c of C an object TC of B and the arrow function (also written T) which assigns to each arrow f:c->c' of C and Tf: Tc->Tc' of B, in such a way that
T(1c) = 1Tc, T(g o f) = Tg o TfThis takes several readings to sink in. So don't bother. Let's look at some code.
Actually, the first rule is the identity law that says if you map over something with the output being the same as the input you get what you started with. That's too trivial to spend any more time on.
The second can be written in Scala as:
val x: Option = ...
x.map(f compose g) } == x.map(g).map(f) // true
Optional x = ...
x.map(f).map(g).equals( x.map(g.compose(f)) ) // true... Sometimes. See below.
"If I map a function across a List, I should get back a List of the same size as I started with, and with all the elements in the corresponding order. This means I can guarantee some things, like for instance if I reverse the order of the list and then map the function, I will get the same result as mapping the function and then reversing the list. I can refactor without fear." (from Wesely-Smith's post)
How Scala and Java differ
The two radically diverge on their treatment of nulls. Firstly, in Java, if you did this:
Optional ofNull = Optional.of(null);
Whereas, in Scala you could do this:
val optionWithNull = Option(null)
which would actually be a None. Or, you could do this:
val someWithNull = Some(null)
which is very different. It really is Something that contains a reference to a null.
In this way, Java is less expressive. If, say we wanted to get a value (mapped in an Option) from a Map, Scala could distinguish between the value not being there (None) and it being there but it being null (Some(null)). An equivalent in Java:
System.out.println(map.size()); // 3