§ Reversible computation as groups on programs
If we consider a language like
where every program is reversible, we can then get a group structure on
programs with the identity program not computing anything at all, the inverse
performing the reverse operation.
Alternatively, one can use the trick from quantum mechanics of using anciliary
qubits to build reversible classical gates.
The question is, do either of these approaches allow for better-than-STOKE
exploration of the program space? Ie, can we somehow exploit the
discrete group structure (in the case of Janus) or the Lie group structure
of the unitary group (as in the QM case) to find programs in far quicker ways?