Defunctionalized Interpreters for Call-by-Need Evaluation

Starting from the standard call-by-need reduction for the λ-calculus that is common to Ariola, Felleisen, Maraist, Odersky, and Wadler, we inter-derive a series of hygienic semantic artifacts: a reductionfree stateless abstract machine, a continuation-passing evaluation function, and what appears to be the first heapless natural semantics for call-by-need evaluation. Furthermore we observe that a data structure and a judgment in this natural semantics are in defunctionalized form. The refunctionalized counterpart of this evaluation function is an extended direct semantics in the sense of Cartwright and Felleisen. Overall, the semantic artifacts presented here are simpler than many other such artifacts that have been independently worked out, and which require ingenuity, skill, and independent soundness proofs on a caseby-case basis. They are also simpler to inter-derive because the interderivational tools (e.g., refocusing and defunctionalization) already exist.