This project is to implement a more efficient runtime for all or part of the language. Particularly interesting would be to target the OCaml bytecode, or a mild variation thereof.
For pretty-printing, we currently have a system (the Munger mk.2) that typesets into LaTeX mathematics that has been input directly in (ASCIIfied) conventional notation. One possibility would be to redesign this from the ground up, so one could specify the grammar for ASCII notation, together with the LaTeX it should be rendered into, something like this:
e ::=
() { () }
( COMMALIST(es) ) { ( COMMALIST(es) ) }
\x:T.e { \lambda x : T. e }
col e hm T { [ e ]_{ hm }^{ T } }
and have a lexer, parser, and pretty-printer automatically generated. This would let one write informal ASCII mathematics in perhaps the most lightweight style possible and still produce production-quality typeset output. Choosing an appropriate class of grammars is an interesting question here: if LALR(1) is not rich enough to deal with our informal grammars (or if yacc is too tiresome), we could think of taking advantage of the fact that we rarely want to munge much code at a time, so could use a class of grammars that is less efficiently (but more simply?) parsable. Going further, one might do some lightweight sanity checking of the syntax.
Another possibility is to produce an implementation of some of the other features as an extension to emacs. It would require some understanding of informal proofs, careful user-interface design, and a certain amount of Emacs lisp.
A further option would be to focus on variable binding, substitution, rule instantiation, etc, implementing the Nominal Unification algorithm recently developed by Urban, Pitts and Gabbay, implementing a backtracking search for rule instantiation, and tying that into an editor and/or pretty-printer. See James Cheney's alphaProlog.
Some more detailed discussion of desirable features is available on request. For all of these, most of the system would probably be best written in OCaml or ML.
Alisdair Wren also has ideas along these lines, and may be prepared to supervise a project.