TAO in one line

Darius JJ Chuck

2021-07-09

Today I’d like to illustrate the simplicity and the mathematical beauty of TAO.

If we leave certain parts abstract, TAO’s grammar can be defined in one line of ABNF, like so:

TAO = *(open TAO close / 1*symbol)

The abstract portions are in lowercase blue. The meaning of this line is:

A TAO is ZERO OR MORE parts, each of which is EITHER an open followed by a TAO followed by a close OR one or more symbols.

If we define open to be [, close to be ], and symbol to be:

"`" any / (any - "[" - "]" - "`")

Then the grammar will match the same strings as the canonical grammar.

It’s interesting to contrast this definition with an abstract definition of a Dyck language:

S = *(open S close)

As we can see the only difference is that TAO adds the 1*symbol alternative before the closing paren in the definition.

A Dyck language can express any kind of a tree structure. TAO can express any kind of a tree structure with interleaved data. Or better: interleafed, as the data is always carried in the leafs (leaves) of the tree structures.