EDIT: The demo comes before TML is written under TML. I made a mistake initially. Demo is the next main step

I had to ask Ohad

Yes, the Earley Parser is a very important component to the TML, but it will be applied on the next layer (TML written in TML).

There are a lot of reasons why TML has to be rewritten in TML (rather than just in C++).  Firstly, the entire idea of Tau revolves heavily around self definition. Tau is about defining its own rules using its own rules, which is how we'll get to a protocol that can amend itself in subsequent blocks according to the real time consensus of its users in the current block.

Additionally, implementing the TML using BDDs gives it a unique feature: it enables the TML defined under itself to carry significant performance increases over the original. This means it no longer makes any sense to implement the parser over the original C++ TML as one would rather implement it over the faster version and the Parser itself is not necessary for self definition. 

Similarly, the demo will come once TML is defined under itself. <- wrong, it's coming before that

BDDs are one of the best things to have happened to the project since the discovery of Partial Fixed Points (only known decidable, self defining logic that supports negation). It is truly very well suited to our needs and offers extraordinary advantages over alternatives. 

Finally, Ohad doesn't anticipate this next step (TML over TML) to be as difficult as the previous one and it shouldn't take anywhere near as long.