How to separate out the context-free part of a language from the context-sensitive part?

I read this fantastic post on the comp.theory list:

http://coding.derkeiler.com/Archive/General/comp.theory/2004-03/0189.html

The poster makes the point that most programming languages define a context-free core, and then have additional algorithms which run on the parse tree to filter out constructs that are illegal in the language:

This separates out the context-free part of the language from the context-sensitive part -- which is generally regarded as good practice (a kind of modular "programming" discipline for language design).

Can you provide a "Hello World" example to illustrate this technique? That is, provde a simple context-sensitive language, identify the context-free core, and then sketch out how to parse an input using the context-free core followed by filtering out illegal constructs in the parse tree.

Can you refer me to any articles or books that discuss this technique?

One of the simplest languages that are not context-free is one where the words are of the type aⁿbⁿcⁿ (a, b, and c repeated the same number of times, that is, abc, aabbcc, aaabbbccc, ...).

You can parse it using a grammar for the context-free language {aⁿbⁿc^m}, where the number of c's is not restricted. Once you have the parse tree, you check using a separate algorithm that the number of repetitions of c is equal to the number of repetitions of a and b.