A major overhaul was done to the Burro language, resulting in version 2.0. Whatever Burro 1.0 might have achieved, it wasn't its primary goal. As Alex Smith was kind enough to point out, the set of Burro 1.0 programs don't actually form a group.
Burro 2.0 fixes the design of the language to avoid the problem. It is defined as an executable semantics written in Literate Haskell/Markdown which includes both a proof that Burro 2.0 programs form a group, and a demonstration of how one can map a Turing machine to a Burro program.
Check it out at http://catseye.tc/projects/burro/