Encoding Register Machines

We can represent a Register Machine as a list of instructions, where the -th instruction in the list represents

Being careful about stuff, we can encode it into some encoding alphabet.
Then we can use Encoding Alphabets in Binary Words to encode the register machine into binary.
We can do a similar thing with Configuration of a Register Machine

Let these encodings be and .

Lemma

The transformation function

where transforms to is computable.

Lemma

The Computation Sequence function

is computable.