I have this confusion related to context sensitive grammar. I was referring to this article http://en.wikipedia.org/wiki/Context-sensitive_grammar. And it has given an example of production rules for a context sensitive grammer like
$\begin{align} S&\to aSBC\\ S&\to aBC\\ CB&\to HB\\ HB&\to HC\\ HC&\to BC\\ aB&\to ab\\ bB&\to bb\\ bC&\to bc\\ cC&\to cc \end{align}$
I am a bit confused about how the rule $S \to aSBC$ fits the definition of a context sensitive grammar. I mean there is no context here.
Normally for context sensitive grammar we have rules like
$\alpha A\beta \to \alpha \omega\beta\quad\text{ where $\omega$ is not null}$
But in this example $S\to aSBC$ what are $\alpha$ and $\beta$. Are they null? If they are null and I have this rule $AB\to CD$, then it is also valid, since I am taking the $\alpha$ and $\beta$ as null well so it is a perfectly valid rule for context sensitive. In fact I can have any rule if I go this way, there is no restriction? It just doesn't need to be contracting and then everything is a context sensitive grammar?