Before discussing final semantics let me say something about traditional semantics, also called initial semantics. Here we have in a very broad setting an interpretation function, this is the paradigm of categorical semantics. Can be contrued as the unique morphism going from syntax onto semantics. Now, if we take some kind of view which focuses on syntax, then we can try to construe syntax as an initial object. And view therefore this morphism interpretation going from syntax to its models which in fact are called F-algebras, as an initial function. This is a syntax or oriented view-point, a static view-point which provides composition of characterisations of our constructors.
