Logical relations for call-by-value delimited continuations

Logical relations, defined inductively on the structure of types, provide a powerful tool to characterize higher-order functions. They often enable us to prove correctness of a program transformer written with higher-order functions concisely. This paper demonstrates that the technique of logical relations can be used to characterize call-by-value functions as well as delimited continuations. Based on the traditional logical relations for call-by-name functions, logical relations for call-by-value functions are first defined, whose CPS variant is used to prove the correctness of an offline specializer for the call-by-value λ-calculus. They are then modified to cope with delimited continuations and are used to establish the correctness of an offline specializer for the call-by-value λ-calculus with delimited continuation constructs, shift and reset. This is the first correctness proof for such a specializer. Along the development, correctness of the continuation-based and shift/reset-based let-insertion and A-normalization is established.