I don't understand the purpose of this? We already have variable binding lists; what is this mechanism for? Can you give a description and some examples of use?

The binding dictionary is similar to substitution dictionary for Expr variables. We could use a single dictionary but it would need to be global (or pass it around as an additional argument) for functions like reset-trail to work. We also need a separate unify function which can handle list of variables. I made the dictionary an attribute, and unify a method of the class instead.
Usage example:
env = APPEND_container()
env.add_var(x, True)
This would make env[x] return True.
Most of the other methods like new_variable() and reset_trail() would only be used internally. Their usage can be found in the tests.