Lambda the Ultimate

The understanding of state is one of the oldest and newest areas of research. The Event Calculus provides a precise logical semantics of state and situation. There is an interesting survey paper at the bottom of the page with all the details: "Event Calculus in Classical Logic" . Also a previous discussion topic: Dynamic Semantics .

I’m confused about the relation between closures and the implementation of higher-order functions. My understanding is that closures were first used to implement higher-functions in Scheme and that closures play the same role in languages such as Perl and Python. Other functional languages don’t appear to make explicit mention of closures. In my own experience with the language K, I can directly pass and return functions to and from other functions, with no reference to a lexical closure. So I’m tempted to conclude that closures are simply one technique for implementing higher on functions. However I read in CTM:

Higher-order programming is the collection of programming techniques that become available when using procedure values in programs. Procedure values are also known as lexically-scoped closures.

Can anyone give me some insight here, or just a reference for further study?