  Relational type systems have been designed for several applications including
information flow, differential privacy, and cost analysis. In order to achieve
the best results, these systems often use relational refinements and relational
effects to maximally exploit the similarity in the structure of the two
programs being compared. Relational type systems are appealing for relational
properties because they deliver simpler and more precise verification than what
could be derived from typing the two programs separately. However, relational
type systems do not yet achieve the practical appeal of their non-relational
counterpart, in part because of the lack of a general foundations for
implementing them.
  In this paper, we take a step in this direction by developing bidirectional
relational type checking for systems with relational refinements and effects.
Our approach achieves the benefits of bidirectional type checking, in a
relational setting. In particular, it significantly reduces the need for typing
annotations through the combination of type checking and type inference. In
order to highlight the foundational nature of our approach, we develop
bidirectional versions of several relational type systems which incrementally
combine many different components needed for expressive relational analysis.
