We construct a universal reversible Turing machine (URTM)
from first principles. We take a strict approach to the semantics of reversible
Turing machines (RTMs), under which they can compute exactly
all injective, computable functions, but not non-injective ones. The natural
notion of universality for RTMs is RTM-universality, where programs
are considered part of both input and output of a URTM.
The machine described here is the first URTM which does not depend
on reversibilizing any existing universal machine. The interpretive
overhead of the URTM is limited to a (program dependent) constant
factor slowdown, with no other complexity-wise cost wrt time and space.
The URTM is also able to function as an inverse interpreter for RTMs
at no asymptotic cost, simply by reversing the string representing the
interpreted machine.