BBC BASIC was the native programming language on Acorn's BBC Micro. It's a structured BASIC dialect and supports procedures and functions, permitting far nicer code than the line-numbered GOTO and GOSUB code on other contemporary machines. It also has a built-in assembler, for inline assembly.
There is no source available, which is where the problems start to come in. Fortunately, J.G.Harston has developed a utility that permits the platform-agnostic BBC BASIC interpreter to be relocated. However, it assumes that the system has a jump table in RAM from $FF80..$FFFF (this jump table would be used to call platform-specific code); this memory range is not executable on the TI-83+. Execution protection in the $C000..$FFFF range may also cause issues for inline assembly code (which is, naturally, executed from RAM).
The TI-OS does not offer an especially suitable environment for BBC BASIC either; it is mainly menu driven (a command-line driven environment is preferable), does not have a plain text editor and does not use ASCII. To resolve this issues, I've concentrated on developing a suitable environment for BBC BASIC to live in, including a command-line interface and text editor.
Text files are stored as AppVars with a TEXTFILE header, and I've developed a Windows-based notepad clone for editing them (it saves and loads directly to and from .8xv). The following commands are currently supported (see here for a reference from the Windows verion): BYE, COPY, DELETE, DIR, ERASE, EXEC, QUIT, RENAME, TYPE, |.
To enter the editor, EDIT can be used. This presents a full-screen editor a little like the TI-OS program editor, but edits plain text files.
The interface transparently supports AT keyboards (which are rather easier to type on than the TI's keypad). The character resolution is 24 columns in 10 rows (4x6 pixel characters), giving you quite a lot of room to see what you're working on.
I intend on the final program being a 2-page Flash application; one page for BBC BASIC, and one page for the environment and OS interface. This unfortunately makes this a TI-83+ only project.
Even if I don't manage to shoe-horn BBC BASIC onto the TI-83+, the interface code (which uses direct hardware access for everything but opening and editing AppVars) could be useful for other projects.