Sound Specialization in the Presence of Computational Effects

Moggi's computational lambda calculus c is a well-established model of computation. We deene a two-level version c of the computational lambda calculus and demonstrate that it is an inevitable description for sound specialization. We implement the calculus in terms of a standard two-level lambda calculus via a continuation-passing style transformation. This transformation is sound and complete with respect to c; it forms a reeection in the two-level lambda calculus of c. As a practical ramiication of this work we show that several published specialization algorithms are unsound and develop a sound specializer similar to continuation-based specializers.