Relational Parametricity and Control
  We study the equational theory of Parigot's second-order &lambda;&mu;-calculus in connection with a call-by-name continuation-passing style (CPS) translation into a fragment of the second-order &lambda;-calculus. It is observed that the relational parametricity on the target calculus induces a natural notion of equivalence on the &lambda;&mu;-terms. On the other hand, the unconstrained relational parametricity on the &lambda;&mu;-calculus turns out to be inconsistent with this CPS semantics. Following these facts, we propose to formulate the relational parametricity on the &lambda;&mu;-calculus in a constrained way, which might be called ``focal parametricity''. 
Masahito Hasegawa