How to make sense of this context-sensitive production in a textbook? (a typo perhaps?) In Chapter 1 of Kenneth Slonneger and Barry L. Kurtz's Formal Syntax and Semantics of Programming Languages: A Laboratory Based Approach, an example of its production is given to illustrate the nature of context-sensitive grammar (page 3):

&lt;thing&gt; b ::= b &lt;thing&gt;


where &lt;thing&gt; is a non-terminal and b is a terminal. 

I cannot see how this fits the form

$$αAβ → αγβ $$
(where $α$ and $β$ are strings, $A$ is a non-terminal and $γ$ is a non-empty string) for context-sensitive grammar unless the right hand side ends with $b$ as well:

&lt;thing&gt; b ::= b &lt;thing&gt; b


in which case we get $α=ε$, $β=b$ and $γ = b\; \text{&lt;thing&gt;}$.

Perhaps I haven't viewed it in the right angle? (Or is this a typo?)
First, they describe noncontracting grammars, and give an example: the one you are quoting.

Next, they write: equivalently, we can use a different restriction on grammars, and describe the context-sensitive grammars.

Chomsky proved the equivalence in 1963.