  Logical relations built on top of an operational semantics are one of the
most successful proof methods in programming language semantics. In recent
years, more and more expressive notions of operationally-based logical
relations have been designed and applied to specific families of languages.
However, a unifying abstract framework for operationally-based logical
relations is still missing. We show how fibrations can provide a uniform
treatment of operational logical relations, using as reference example a
lambda-calculus with generic effects endowed with a novel, abstract operational
semantics defined on a large class of categories. Moreover, this abstract
perspective allows us to give a solid mathematical ground also to differential
logical relations -- a recently introduced notion of higher-order distance
between programs -- both pure and effectful, bringing them back to a common
picture with traditional ones.
