Plotkin, in his seminal article Call-by-name, call-by-value and the λ-calculus, formalized evaluation strategies and simulations using operational semantics and continuations. In particular, he showed how call-by-name evaluation could be simulated under call-by-value evaluation and vice versa. Since Algol 60, however, call-by-name is both implemented and simulated with thunks rather than with continuations. We recast

We demonstrate the usefulness of higher-order rewriting techniques for specializing programs, i.e., for partial evaluation. More precisely, we demonstrate how casting program specializers as combinatory reduction systems (CRSs) makes it possible to formalize the corresponding program transformations as meta-reductions, i.e., reductions in the internal "substitution calculus." For partial-evaluation problems, this means that instead of having to prove on a case-by-case basis that one's "two-level functions" operate properly, one can concisely formalize them as a combinatory reduction system and obtain as a corollary that static reduction does not go wrong and yields a well-formed residual program.

We formalize a partial evaluator for Eugenio Moggi's computational metalanguage. This formalization gives an evaluation-order independent view of binding-time analysis and program specialization, including a proper treatment of call unfolding, and enables us to express the essence of "control-based binding-time improvements" for let expressions. Specifically,