Sound Specialization in the Presence of Computational Effects

Moggi's computational lambda calculus λc is a well-established model of computation. We define a two-level version λc 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 λc; it forms a reflection in the two-level lambda calculus of λc. As a practical ramification of this work we show that several published specialization algorithms are unsound and develop a sound specializer similar to continuation-based specializers.

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